Many Worlds
Mark Palenik
mechanics (beyond the introductory stuff, i.e. simple solutions to the
schrodinger equation, the uncertainty principle, etc.), but to fulfill my
advanced composition requirements, I'm taking a class "The Philosophy of
Physics", which isn't really a course for physics majors, although there is
no reason for physics majors *not* to take it.
One of subjects discussed in the class was the various interpretations of
quantum mechanics and quantum measurement. The "many worlds" picture was
presented as, more or less, the only "reasonable" viewpoint by the
proffessor, and he stated that most cosmologists, and cosmology oriented
physics departments regard this as the correct interpretation.
Is this really the case? Do most physicists regard "collapse" as an
unrealistic, difficult to explain idea, or is it a reasonable assumption to
make that some physical proccess does, in fact, cause wave function collapse
(or decoherence, but in any event, a "single world" outcome)?
He also stated that the point at which quantum states can be separated into
different worlds is related to their distance apart in Hilbert space, and
that it seems that if the Hilbert space has a finite size, "worlds" should
be able to recombine, although we never really see that on a large scale.
It seems to me that if this interpretation is correct, that worlds could
"recombine" (and he has suggested that there is some experimental evidence
for this on a small scale), but is Hilbert space really something that we
would expect to run out of? Is it actually assumed to occupy a finite size?
I don't know much about QM, but I have heard the term Hilbert space before,
and it always seemed to me that it was a mathematical representation, and
not necessarrily a finite volume for things to occuppy. And even if the
Hilbert space is infinite, or expanding, wouldn't the coordinates within it
still be calculated the same way, as in, if two "worlds" occupy the same
point in Hilbert space, they should do so no matter how large the space is?
Finally, I had, in the past, believed that Stephen Hawking's "wave function
of the universe" concept was a little bit different from the older "many
worlds" ideas. However, my proffessor has refferred to them both as the
same thing. Is this true?
Arnold Neumaier
> I'm an undergraduated physics major, who so far hasn't had any real quantum
> mechanics (beyond the introductory stuff, i.e. simple solutions to the
> schrodinger equation, the uncertainty principle, etc.), but to fulfill my
> advanced composition requirements, I'm taking a class "The Philosophy of
> Physics", which isn't really a course for physics majors, although there is
> no reason for physics majors *not* to take it.
>
> One of subjects discussed in the class was the various interpretations of
> quantum mechanics and quantum measurement. The "many worlds" picture was
> presented as, more or less, the only "reasonable" viewpoint by the
> proffessor, and he stated that most cosmologists, and cosmology oriented
> physics departments regard this as the correct interpretation.
see http://www.mat.univie.ac.at/~neum/manyworlds.txt
> Is this really the case? Do most physicists regard "collapse" as an
> unrealistic, difficult to explain idea, or is it a reasonable assumption to
> make that some physical proccess does, in fact, cause wave function collapse
> (or decoherence, but in any event, a "single world" outcome)?
No. Most believe that collapse is explained by decoherence, but in which
interpretation the latter should be seen is as controversial as ever.
Arnold Neumaier
Arkadiusz Jadczyk
<markp...@wideopenwest.com> wrote:
>Is this really the case? Do most physicists regard "collapse" as an
>unrealistic, difficult to explain idea, or is it a reasonable assumption to
>make that some physical proccess does, in fact, cause wave function collapse
>(or decoherence, but in any event, a "single world" outcome)?
You see, even if it is true that "most physicists regard "collapse" as
an unrealistic, difficult to explain idea" - that does not necessarily
mean that collapse IS unrealistic or difficult to explain. History of
physics teaches us that progress in physics is not achieved by
majority voting. All really new ideas were considered, at the beginning,
and by narrow minded majority, as "unrealistic" and difficult to
explain.
John Bell, commenting upon GRW spontaneous collapse model wrote:
"He (Schroedinger) might have seen in it a hint of something good to
come. He would have liked, I think, that the theory is completely
determined by the equations, which do not have to be talked away from
time to time. He would have liked the complete absence of particles from
the theory, and yet the emergence of "particle tracks", and more
generally of the 'particularity of the world', on the macroscopic level.
He might not have liked the GRW jumps, but he would have disliked them
less than the old quantum jumps of his time. [...]
For myself, I see the GRW model as a very nice illustration of how
quantum mechanics, to become rational, requires only a change which is
very small (on some measures!)."
Note that John Bell felt it necessary to add the comment: "on some
measures". So, he knew that there are physicists who are ready to accept
the collapse with an ease, as a simple and rational step forward, and
there are others (with different "measures") who are not.
ark
--
Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm
--
Phillip Helbig---remove CLOTHES to reply
<Arnold....@univie.ac.at> writes:
> > One of subjects discussed in the class was the various interpretations of
> > quantum mechanics and quantum measurement. The "many worlds" picture was
> > presented as, more or less, the only "reasonable" viewpoint by the
> > proffessor, and he stated that most cosmologists, and cosmology oriented
> > physics departments regard this as the correct interpretation.
> No. Most believe that collapse is explained by decoherence, but in which
> interpretation the latter should be seen is as controversial as ever.
I don't spend much time thinking about the validity of different
interpretations of QM, but I have to admit that my "gut feeling" was
that none were satisfactory, though all had their pros and cons. After
reading David Deutsch's THE FABRIC OF REALITY, however, my feeling is
that the MW interpretation looks a bit more "believable", if that's the
right word. On the whole, I like the book, though it has a few weak
points. Bryce de Witt wrote a review (I believe it can be found on
Deutsch's website) which I think sums up the many good and few bad
points of the book well:
http://naturalscience.com/ns/books/book02.html
r...@maths.tcd.ie
>Mark Palenik wrote:
>> Is this really the case? Do most physicists regard "collapse" as an
>> unrealistic, difficult to explain idea, or is it a reasonable assumption to
>> make that some physical proccess does, in fact, cause wave function collapse
>> (or decoherence, but in any event, a "single world" outcome)?
>No. Most believe that collapse is explained by decoherence, but in which
>interpretation the latter should be seen is as controversial as ever.
I should add that, though most physicists may believe this; it is
not correct. Decoherence explains why the off-diagonal elements of
the density matrix become zero; for collapse, all but one of
the diagonal elements become zero too, so decoherence isn't
enough for collapse. That is, decoherence gives you many worlds
which don't interact, but no "single world" outcome.
If anyone advocates decoherence as the solution to the measurement
problem, they are perhaps unwittingly advocating a many worlds
interpretation. On the other hand, most physicists do not explicitly
advocate many worlds; it's not exactly a mainstream viewpoint.
R.
Robert Calvert
<r...@maths.tcd.ie> wrote in message
news:c66rp8$hbo$1...@lanczos.maths.tcd.ie...
my opinion.
I've often wondered if decoherence is really just an illusion that's created
by the fact that our minds can't see (at least, so far as we know) into any
of the adjacent universes. In the real universe (or what we would call the
multiverse), light probably is made up of waves and no particles. But since
the universe that we can perceive is constantly being disconnected from the
rest of the multiverse, wave functions are constantly appearing to collapse
and light appears to us as particles. This undoubtedly explains why
everything that light does before it manifest itself as a particle manifest
itself as a wave prior to that time and, in fact, prior to the time that we
can detect it.
Robert
Martin Hogbin
> I'm an undergraduated physics major, who so far hasn't had any real quantum
> mechanics (beyond the introductory stuff, i.e. simple solutions to the
> schrodinger equation, the uncertainty principle, etc.), but to fulfill my
> advanced composition requirements, I'm taking a class "The Philosophy of
> Physics", which isn't really a course for physics majors, although there is
> no reason for physics majors *not* to take it.
>
> One of subjects discussed in the class was the various interpretations of
> quantum mechanics and quantum measurement. The "many worlds" picture was
> presented as, more or less, the only "reasonable" viewpoint by the
> proffessor, and he stated that most cosmologists, and cosmology oriented
> physics departments regard this as the correct interpretation.
>
> Is this really the case?
Not as far as I know. There have been several surveys
of physicists asking their preferred interpretations of QM,
including, I believe, a rather biased one in which the
'many-worlds' view was preferred. I think other surveys
have shown that most physicists actually prefer the 'shut-
up-and-calculate' approach.
Personally, I prefer the Copenhagen interpretation. In
my opinion the many-worlds interpretation could be ruled
out by Ockham's blunt instrument.
> Do most physicists regard "collapse" as an
> unrealistic, difficult to explain idea, or is it a reasonable assumption to
> make that some physical proccess does, in fact, cause wave function collapse
I am not sure if the wave function collapse was ever
meant to be taken as literally as that.
Martin Hogbin
Mark Palenik
news:4084DC58...@univie.ac.at...
> Mark Palenik wrote:
<snip>
>
> see http://www.mat.univie.ac.at/~neum/manyworlds.txt
>
>
> > Is this really the case? Do most physicists regard "collapse" as an
> > unrealistic, difficult to explain idea, or is it a reasonable assumption
to
> > make that some physical proccess does, in fact, cause wave function
collapse
> > (or decoherence, but in any event, a "single world" outcome)?
>
> No. Most believe that collapse is explained by decoherence, but in which
> interpretation the latter should be seen is as controversial as ever.
>
Thanks for the reference. I'm assuming the above "No" was in regards to the
assumption that some physical process causes collapse/decherence, especially
after starting to read the link.
Since I sent the message, I had done a few searches on line for "many
worlds", or "collapse", "decoherence", etc., and the links I found seemed to
be highly in favor of many worlds (I couldn't find any that weren't, really,
with the exception of one that I already had). The link you sent addressed
a few things that I had been wondering about, but assummed that my
incomplete knowledge of the subject was what was leading me to those
questions. I had been wondering at what point "nearly" orthogonal
components are "nearly" orthogonal enough to never significantly interfere
and constitute "measurement". It seems there is no clear cut answer.
Also, in class, being that it isn't a very scientifically demanding class,
it sounded as if the entire universe would be split at once, but from the
reading I had done online, it sounded like the splitting was, as you put it
"a subjective process", which would only effect directly interacting
objects. It sounds like some of the confusion I had on that issue may not
be due solely to my current lack of knowledge.
Anyway, although perhaps I shouldn't be, I am happy to hear that the many
worlds theory is not the complete, and perfect, sole possible explanation
that it was made out to be (actually the professor did admit a few problems,
but on the whole made it sound much more reasonable than any other
interpretation). I've always thought, though, that if one particular theory
is indistinguishable from another, and has few significant impacts, we can
afford not to think about it too much until most of the important stuff has
been resolved.
Arnold Neumaier
> Arnold Neumaier <Arnold....@univie.ac.at> writes:
>
>
>>Mark Palenik wrote:
>
>
>>>Is this really the case? Do most physicists regard "collapse" as an
>>>unrealistic, difficult to explain idea, or is it a reasonable assumption to
>>>make that some physical proccess does, in fact, cause wave function collapse
>>>(or decoherence, but in any event, a "single world" outcome)?
>
>
>>No. Most believe that collapse is explained by decoherence, but in which
>>interpretation the latter should be seen is as controversial as ever.
>
>
> I should add that, though most physicists may believe this; it is
> not correct. Decoherence explains why the off-diagonal elements of
> the density matrix become zero; for collapse, all but one of
> the diagonal elements become zero too, so decoherence isn't
> enough for collapse. That is, decoherence gives you many worlds
> which don't interact, but no "single world" outcome.
>
> If anyone advocates decoherence as the solution to the measurement
> problem, they are perhaps unwittingly advocating a many worlds
> interpretation.
This is not necessary. It is sufficient if
they advocate the statistical interpretation of quantum mechanics,
which asserts that QM is never about a single system but only about
large ensembles of equally prepared systems. For these, one does
not need an explanation why a single event actually happens, since
on average, one indeed gets the full diagonal density matrix.
So the missing bit from decoherence to collapse is needed only if one
wants to have a QM of single systems.
Arnold Neumaier
slyboy
> of quantum mechanics and quantum measurement. The "many worlds"
> picture was presented as, more or less, the only "reasonable"
> viewpoint by the proffessor, and he stated that most cosmologists,
> and cosmology oriented physics departments regard this as the correct
> interpretation.
>
emphasis on his own opinion for an introductory course in the subject.
Many worlds is by no means universally accepted, although it is quite
popular in the cosmology, quantum gravity and quantum computing
communities. Even in these areas, there are quite a few physicists who
do not adhere to many worlds theories.
> He also stated that the point at which quantum states can be separated
> intodifferent worlds is related to their distance apart in Hilbert
> space, and that it seems that if the Hilbert space has a finite size,
> "worlds" should be able to recombine, although we never really see
> that on a large scale. It seems to me that if this interpretation is
> correct, that worlds could
> "recombine" (and he has suggested that there is some experimental
> evidence
> for this on a small scale), but is Hilbert space really something
> that we
> would expect to run out of? Is it actually assumed to occupy a finite
> size?
> I don't know much about QM, but I have heard the term Hilbert space
> before,
> and it always seemed to me that it was a mathematical representation,
> and
> not necessarrily a finite volume for things to occuppy. And even if
> the
> Hilbert space is infinite, or expanding, wouldn't the coordinates
> within it
> still be calculated the same way, as in, if two "worlds" occupy the
> same
> point in Hilbert space, they should do so no matter how large the
> space is?
>
I'm not quite sure what this 'distance apart in Hilbert Space' is all
about, but I presume he was trying to explain 'decoherence'
(http://plato.stanford.edu/entries/qm-decoherence/).
For more info on the foundations of quantum mechanics see
http://plato.stanford.edu/entries/qm/ and related entries. It is not
completely comprehensive, but it will give you some more of the
background beyond many worlds.
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r...@maths.tcd.ie
Arnold Neumaier <Arnold....@univie.ac.at> writes:
True; I should amend my statement above to: If anyone advocates
decoherence as the solution to the measurement problem *and*
believes that the wavefunction is a complete description of
the system, then they are perhaps unwittingly advocating a
many worlds interpretation. I should also add that most physicists
do indeed believe that the wavefunction is a complete description
of the system.
R.
Martin Hogbin
"Robert Calvert" <Herc...@pcstarnet.com> wrote in message news:108hbnf...@corp.supernews.com...
> >
> I'm a little surprised by this. The evidence for the MWI is overwhelming in
> my opinion.
Evidence? What evidence?
Martin Hogbin
Arnold Neumaier
> Since I sent the message, I had done a few searches on line for "many
> worlds", or "collapse", "decoherence", etc., and the links I found seemed to
> be highly in favor of many worlds (I couldn't find any that weren't, really,
> with the exception of one that I already had).
quant-ph/0303047 might be interesting,
and the book
J. Bub,
Interpreting the Quantum World
Cambridge University Press, 1997.
> Also, in class, being that it isn't a very scientifically demanding class,
> it sounded as if the entire universe would be split at once, but from the
> reading I had done online, it sounded like the splitting was, as you put it
> "a subjective process", which would only effect directly interacting
> objects.
The splitting is a very ill-defined process, since no one can give
any indication of at which times and into how many branches the
splitting should occur. It is related to the vagueness of what actually
constitutes a measurement.
> Anyway, although perhaps I shouldn't be, I am happy to hear that the many
> worlds theory is not the complete, and perfect, sole possible explanation
> that it was made out to be (actually the professor did admit a few problems,
> but on the whole made it sound much more reasonable than any other
> interpretation).
Among the traditional interpretations, the Statistical Interpretation
discussed by Ballentine in Rev. Mod. Phys. 42, 358-381 (1970) is the
least demanding (asssumes less than the Copenhagen interpretation
and the Many Worlds interpretation) and the most consistent one.
It explains almost everything, and only has the disatvantage that
it explicitly excludes the applicability of QM to single systems
or very small ensembles (such as the few solar neutrinos or top quarks
actually detected so far).
For large ensembles, there seems to be no disagreement about the
interpretation. Modern experiments appear to need, however, a QM
of individual sytems, and that's where controversy and confusion
prevails. I find none of the existing interpretations convincing,
and wrote up in Int. J. Mod. Phys. B 17 (2003), 2937-2980
= quant-ph/0303047 my own constructive view of the matter.
Arnold Neumaier
Streamking
I was reading some of John Gribbin's book Schödinger's Kittens in the
plane last night (am not finished because I started thinking) but as
far as I know it's just an interpretation, just like the Copenhagen
interpretation.
It's a theory created by people that refuse to accept the need of
consiousness to collapse the wave function, although I've never
understand that argument and think that it's a wrong interpretation of
the Copenhagen interpretation. The endless loop of observers in
superposition until there is a consious observer is absurd and must be
wrong.
I always thought of the many-worlds interpretation as a splitting of
the universe (at the moment of quantum measurement, i.e. wave
collaps) into an infinite number of 'parallel' universes that do not
interact, but what I've understand you can also see it as an infinite
amount of parallel universes that do not split (and by definition not
interact) but are there as a tree of all possibilities (outcomes of
the measurements)
But all of this sounds also absurd for the following reason:
If this is really true then at this moment (although I've no idea how
this is defined, which observer etc.)
there must be an infinite amount of identical parallel universes like
our universe.
If observer 1 now sets up a quantum device that produces two random
numbers 0 or 1 (for example a random generator triggered by a decaying
particle) and it passes all random tests it's extremely unlikely that
observer 2 will only measures number 0 forever, he or she will think
that there is something wrong
and probably reject quantum mechanics. Of course even with real random
there is a chance this will happen, but if you now set up this
experiment you will see it will not happen, or you are the one that
will from now 'split' into the universe that will forever give the
results, 0, 0, 0,... If we in our universe calculate this chance (and
EVERYONE in all other equivalent parallel universes) we are almost
sure it will not happen, but by the assumption of an inlimited amount
of parallel universes it WILL HAPPEN for you now. Since good
randomness (what is random, the decimals of PI behave like that
although they are far from random) is a quantum property I think that
it's better think of parallel universes where the measurements will
always pass the random tests. But this means that only a subset of the
tree structure will fulfill, but that doesn't sound natural and
therefor it's better to reject the whole idea of parallel universes to
solve the wave collaps. Of course this is no proof, can it be proved ?
Edwin Havik
Charles Francis
>True; I should amend my statement above to: If anyone advocates
>decoherence as the solution to the measurement problem *and* believes
>that the wavefunction is a complete description of the system, then
>they are perhaps unwittingly advocating a many worlds interpretation. I
>should also add that most physicists do indeed believe that the
>wavefunction is a complete description of the system.
I doubt that, since in the mainstream interpretations like Copenhagen
and Dirac-Von Neumann, to which most physicists adhere, are based on the
idea that you cannot have a complete description of the system.
Regards
--
Charles Francis
Robert Calvert
news:c66p8j$1jk$1...@sparta.btinternet.com...
How does it do this? I suppose the same thing was said about Special
Relativity back in the days when Einstein first conjured up this infuriating
and seemingly contradictory theory. But, as we all know, Special Relativity
has been put to every test imaginable since those early days and, as most
physicists would probably attest to today, Einstein really was right after
all. Sometimes truth really is stranger than fiction.
Personally, I don't see how the Many Worlds interpretation violates Ockham's
razor. What causes the interior of the earth to remain hot? One credible
explanation is that radioactive decay keeps the earth's interior hot.
Another not-so-credible explanation is that the Devil is constantly stoking
his fires down there so he can keep all the lost souls in eternal torment.
It's not hard to see which one of these explanations violates Ockham's razor
since the former relies on a reasonable cause and effect relationship that's
based on well known and thoroughly proven laws of physics and the latter is
based on a very unproven superstition that doesn't depend on any known law
of physics. If anything, I would say that the Copenhagen interpretation
violates Ockham's razor more than the Many Worlds interpretation. After all,
the only thing the Copenhagen interpretation does is say that such and such
is the way it is because - well - it just is. It's sort of like Newton's
gravity. Even though Newton was able to predict the future positions of
planets and moons using his concept of gravity, he never did figure out what
gravity actually is. It wasn't until General Relativity came along that
anybody could say anything other than "it just is".
Obviously, I liken the Copenhagen interpretation to Newton's gravity and the
Many Worlds interpretation to General Relativity (i.e. the former is a
coping strategy that came before anybody understood what it was and the
latter is a more tangible explanation that came later).
Robert
Here's an explanation Ockham's razor:
http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node10.html
scerir
> Many worlds is by no means universally accepted, although it is quite
> popular in the cosmology, quantum gravity and quantum computing
> communities. Even in these areas, there are quite a few physicists who
> do not adhere to many worlds theories.
There is an interesting power-point exposition, by Cramer, on
a recent experiment by Afshar (at Harvard). According to Cramer
the experiment has shown the MWI to be wrong, and the orthodox
interpretation to be wrong also. (Of course the Transactional
Interpretation is safe, but I do not understand how the advanced
and the retarded wave always meet themselves at the right points!)
http://faculty.washington.edu/jcramer/PowerPoint/43
S.S. Afshar is giving a lecture about that April, 27.
http://faculty.physics.tamu.edu/belyanin/amoseminars.html
Afshar's result is not completely new, imo. I mean that Zurek and Wootters,
in their famous *gedanken* experiment (1979), already got something like
it: an interference pattern, while the "welcher weg" was known up to 99%.
Explanation of Afshar's experiment, in terms of Cramer's advanced and
retarded fields, has something to do with a paper by Wim Rietdijk (1980)
on the necessity of a backward causation, to explain the momentum
distribution of particles in the two-slit set-up, given the fact that
"smart" screens capable of recording both the "welcher weg" and the
interference pattern, are possible (as shown by Zurek and Wootters).
s.
r...@maths.tcd.ie
Charles Francis <cha...@clef.demon.co.uk> writes:
No; the mainstream interpretations, including the ones you mention,
are based on the idea that the wavefunction is the complete
description of the system and that the things which Einstein called
"elements of physical reality", such as the position of a particle
before it is measured, do not exist. The interpretations in which
the wavefunction is not a complete description are called "hidden
variable interpretations", such as Bohm's, which is a counterexample
to the incorrect and ubiquitous claim that you can't have a more
complete description than the state vector. Most physicists do
not advocate hidden variable interpretations.
The many worlds interpretation is an attempt to reconcile the
assertion that the wavefunction is a complete description with
the idea that the wavefunction is a description of the system
itself rather than a description of our knowledge about the
system.
R.
Robert Calvert
"Martin Hogbin" <goatN...@hogbin.org> wrote in message
news:c66p8j$1jk$1...@sparta.btinternet.com...
<snip>
Robert
Here's an description of Ockham's razor:
http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node10.html
Arkadiusz Jadczyk
There is also this possibility that both Copenhagen and MWI respect
Ockham's razor, and yet both are defective.
Take for instance this question:
what mechanism decides about the timing of branchings? How often they
happen and exactly when and why? Similar question is never answered
in the CI.
But:
a) experimentalists measure these times (as for instance 27 Apr 2004
18:41:41 +0000 (UTC), when the above message has been written)
b) Bohmian mechanics, GRW and EEQT propose mechanisms for generating
these events and comparing their timings with reality.
Somehow majority of physicists seem to tend to not hear about this
though ...
scerir
> There is an interesting power-point exposition, by Cramer, on
> a recent experiment by Afshar (at Harvard).
> http://faculty.washington.edu/jcramer/PowerPoint/43
That link does not work now, this one is better!
http://faculty.washington.edu/jcramer/PowerPoint/Boskone_0402.ppt
s.
Arnold Neumaier
> No; the mainstream interpretations, including the ones you mention,
> are based on the idea that the wavefunction is the complete
> description of the system and that the things which Einstein called
> "elements of physical reality", such as the position of a particle
> before it is measured, do not exist. The interpretations in which
> the wavefunction is not a complete description are called "hidden
> variable interpretations", such as Bohm's, which is a counterexample
> to the incorrect and ubiquitous claim that you can't have a more
> complete description than the state vector. Most physicists do
> not advocate hidden variable interpretations.
But there is also the Statistical Interpretation of Ballentine which
asserts that the wave function is a complete description of an ensemble
of QM systems only. This is the least demanding one and is probably the
minimal consensus among physicists. And it is quite likely that,
beyond that, most physicists don't have a very pronounced stand on the
matter.
Arnold Neumaier
r...@maths.tcd.ie
Arnold Neumaier <Arnold....@univie.ac.at> writes:
>r...@maths.tcd.ie wrote:
>> No; the mainstream interpretations, including the ones you mention,
>> are based on the idea that the wavefunction is the complete
>> description of the system and that the things which Einstein called
>> "elements of physical reality", such as the position of a particle
>> before it is measured, do not exist. The interpretations in which
>> the wavefunction is not a complete description are called "hidden
>> variable interpretations", such as Bohm's, which is a counterexample
>> to the incorrect and ubiquitous claim that you can't have a more
>> complete description than the state vector. Most physicists do
>> not advocate hidden variable interpretations.
>But there is also the Statistical Interpretation of Ballentine which
>asserts that the wave function is a complete description of an ensemble
>of QM systems only. This is the least demanding one and is probably the
>minimal consensus among physicists.
Indeed, most physicists would probably agree that this is a very
reasonable interpretation and might claim that it is their own after
they've been told about it. However, the interpretation is equivalent
to saying "There are hidden variables, which distinguish the individual
system from the ensemble," and most physicists, having advocated the
interpretation a moment before, would wriggle and writhe and try
to deny this equivalence, although it is true. The reason for this
wriggling is a received (i.e. taught) aversion to the idea of hidden
variables. Ballentine's interpretation seems to go far enough to
say that there is something that distinguishes one system from
another in an ensemble, where the ensemble is represented by a
wavefunction, but stops short of calling the distinguishing
characteristic a hidden variable, which is exactly what it is.
In his excellent paper [1], Ballentine says, on the subject:
The Statistical Interpretation, which regards quantum states
as being descriptive of ensembles of similarly prepared systems,
is completely open with respect to hidden variables. It does
not demand them, but it makes the search for them entirely
reasonable. On the other hand, the Copenhagen Interpretation,
which regards a state vector as an exhaustive description of
an individual system, is antipathetic to the idea of hidden
variables, since a more complete description than that
provided by a state vector would contradict that interpretation.
He is correct about Copenhagen's antipathy to hidden variables, but
he probably felt a pang of dishonesty as he wrote that his interpretation
is open with respect to hidden variables. If different measurement
results are due to one system being different from another in a way
that is not captured by the wavefunction, then that's a hidden
variable (advocates of Copenhagen and hidden variables might be
surprised to find themselves agreeing on this fact). The hidden
variable is the answer to the question: "Which member of the ensemble
is this system?" Omitting any discussion of this fact will make the
interpretation palatable to those who won't notice it themselves,
and to those who will notice it and think that surely this subtlety
has been addressed somewhere.
That's a recipe for a popular interpretation.
>And it is quite likely that,
>beyond that, most physicists don't have a very pronounced stand on the
>matter.
There is a widespread consensus in the physics community that people
who think about interpretations of quantum mechanics are fools wasting
their time.
R.
1. Ballentine, Rev. Mod. Phys. 42, 4, Oct 1970 p358
Charles Francis
>
>
>Arnold Neumaier <Arnold....@univie.ac.at> writes:
>
>>r...@maths.tcd.ie wrote:
>
>>> No; the mainstream interpretations, including the ones you mention,
>>> are based on the idea that the wavefunction is the complete
>>> description of the system and that the things which Einstein called
>>> "elements of physical reality", such as the position of a particle
>>> before it is measured, do not exist. The interpretations in which
>>> the wavefunction is not a complete description are called "hidden
>>> variable interpretations", such as Bohm's, which is a counterexample
>>> to the incorrect and ubiquitous claim that you can't have a more
>>> complete description than the state vector. Most physicists do
>>> not advocate hidden variable interpretations.
>
>>But there is also the Statistical Interpretation of Ballentine which
>>asserts that the wave function is a complete description of an ensemble
>>of QM systems only. This is the least demanding one and is probably the
>>minimal consensus among physicists.
Only if it is a description of an ensemble it would be a classical
probability function. There must be more to it than that.
>
>Indeed, most physicists would probably agree that this is a very
>reasonable interpretation and might claim that it is their own after
>they've been told about it. However, the interpretation is equivalent
>to saying "There are hidden variables, which distinguish the individual
>system from the ensemble,"
No it is not. There is nothing to say that elements of such an ensemble
are describable by hidden variables. In any case probabilities do apply
to relationships between in and out states. The wave amplitude is just a
conjugate root. But that is not what is meant by a hidden variable.
>and most physicists, having advocated the
>interpretation a moment before, would wriggle and writhe and try
>to deny this equivalence, although it is true. The reason for this
>wriggling is a received (i.e. taught) aversion to the idea of hidden
>variables.
Actually it is because hidden variables, in the conventional sense, do
not explain the laws of quantum probability.
>Ballentine's interpretation seems to go far enough to
>say that there is something that distinguishes one system from
>another in an ensemble, where the ensemble is represented by a
>wavefunction, but stops short of calling the distinguishing
>characteristic a hidden variable, which is exactly what it is.
You really need to think harder. Just because you cannot see something
it does not follow that it does not exist.
>In his excellent paper [1], Ballentine says, on the subject:
>
> The Statistical Interpretation, which regards quantum states
> as being descriptive of ensembles of similarly prepared systems,
> is completely open with respect to hidden variables. It does
> not demand them, but it makes the search for them entirely
> reasonable. On the other hand, the Copenhagen Interpretation,
> which regards a state vector as an exhaustive description of
> an individual system,
That may be true of certain versions of the Copenhagen interpretation. I
would say certain misinterpretations of it.
> is antipathetic to the idea of hidden
> variables, since a more complete description than that
> provided by a state vector would contradict that interpretation.
>
>He is correct about Copenhagen's antipathy to hidden variables, but
>he probably felt a pang of dishonesty as he wrote that his interpretation
>is open with respect to hidden variables.
Don't you feel a pang of dishonesty making statements like that?
>If different measurement
>results are due to one system being different from another in a way
>that is not captured by the wavefunction, then that's a hidden
>variable (advocates of Copenhagen and hidden variables might be
>surprised to find themselves agreeing on this fact).
?????
>The hidden
>variable is the answer to the question: "Which member of the ensemble
>is this system?"
That may apply perfectly to the probabilistic results of measurements,
which are physical. But it does not work for the wave function.
Regards
--
Charles Francis
Charles Francis
>
>
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
>>In message <c6jcf4$1e6g$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>>True; I should amend my statement above to: If anyone advocates
>>>decoherence as the solution to the measurement problem *and* believes
>>>that the wavefunction is a complete description of the system, then
>>>they are perhaps unwittingly advocating a many worlds interpretation. I
>>>should also add that most physicists do indeed believe that the
>>>wavefunction is a complete description of the system.
>
>>I doubt that, since in the mainstream interpretations like Copenhagen
>>and Dirac-Von Neumann, to which most physicists adhere, are based on the
>>idea that you cannot have a complete description of the system.
>
>No; the mainstream interpretations, including the ones you mention,
>are based on the idea that the wavefunction is the complete
That is clearly wrong. E.g. Heisenberg in physics and Philosophy p15
states "This probability function represents a mixture of two things,
partly a fact and partly our knowledge of a fact"
> The interpretations in which
>the wavefunction is not a complete description are called "hidden
>variable interpretations",
No, that is silly. Hidden variables means that what is not known about
the state can be described in terms of hidden variables. We know that
that is not true. Just because what is not known is not describable in
terms of hidden variables it does not follow that everything is known.
>The many worlds interpretation is an attempt to reconcile the
>assertion that the wavefunction is a complete description with
>the idea that the wavefunction is a description of the system
>itself rather than a description of our knowledge about the
>system.
Then it is an attempt to reconcile ideas which are wrong. The
wavefunction clearly describes only our knowledge of the system, and
there is no scientific way to claim more than that.
--
Charles Francis
Arnold Neumaier
>>asserts that the wave function is a complete description of an ensemble
>>of QM systems only. This is the least demanding one and is probably the
>>minimal consensus among physicists.
>
> Indeed, most physicists would probably agree that this is a very
> reasonable interpretation and might claim that it is their own after
> they've been told about it. However, the interpretation is equivalent
> to saying "There are hidden variables, which distinguish the individual
> system from the ensemble," and most physicists, having advocated the
> interpretation a moment before, would wriggle and writhe and try
> to deny this equivalence, although it is true.
It is not equivalent. It just admits ignorance about what happens
for an individual system. Not the best solution but, after all, we
are all ignorant about most things, and it is better to admit
ignorance than to claim a knowledge which is absent or inconsistent.
> Ballentine's interpretation seems to go far enough to
> say that there is something that distinguishes one system from
> another in an ensemble, where the ensemble is represented by a
> wavefunction, but stops short of calling the distinguishing
> characteristic a hidden variable, which is exactly what it is.
No. Distinguishing variables are, for example, the position and time
of the experiment. It doesn't help to have this to improve the
predictions. What we calculate is always a highly idealized situation.
Arnold Neumaier
r...@maths.tcd.ie
> In message <c6p792$18h$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>Indeed, most physicists would probably agree that this is a very
>>reasonable interpretation and might claim that it is their own after
>>they've been told about it. However, the interpretation is equivalent
>>to saying "There are hidden variables, which distinguish the individual
>>system from the ensemble,"
>No it is not. There is nothing to say that elements of such an ensemble
>are describable by hidden variables. In any case probabilities do apply
>to relationships between in and out states. The wave amplitude is just a
>conjugate root. But that is not what is meant by a hidden variable.
It's not clear to me what you are trying to say. It has been proven
that such ensembles can be described with hidden variables, so I
don't understand why you would suggest that they can't be. Probability
applies to all areas of physics in which exact predictions can't be
made, including classical mechanics; it is no surprise to anybody
that it also applies to relationships between in and out states, and
I don't understand what point you are making when you explicitly
say so. I don't understand the sense in which you use the expression
"conjugate root". I don't know what the "that" is which is supposedly
not meant by a hidden variable.
>>and most physicists, having advocated the
>>interpretation a moment before, would wriggle and writhe and try
>>to deny this equivalence, although it is true. The reason for this
>>wriggling is a received (i.e. taught) aversion to the idea of hidden
>>variables.
>Actually it is because hidden variables, in the conventional sense, do
>not explain the laws of quantum probability.
I don't know what you mean by the "conventional sense" of hidden
variables, but there are indeed hidden variable theories which,
as you say, explain the laws of quantum probability. That is not
to say that I advocate them, but I acknowledge their existence.
>>Ballentine's interpretation seems to go far enough to
>>say that there is something that distinguishes one system from
>>another in an ensemble, where the ensemble is represented by a
>>wavefunction, but stops short of calling the distinguishing
>>characteristic a hidden variable, which is exactly what it is.
>You really need to think harder. Just because you cannot see something
>it does not follow that it does not exist.
Please, explain it to me. Please also explain why Ballentine didn't
address this point.
>>In his excellent paper [1], Ballentine says, on the subject:
>>
>> The Statistical Interpretation, which regards quantum states
>> as being descriptive of ensembles of similarly prepared systems,
>> is completely open with respect to hidden variables. It does
>> not demand them, but it makes the search for them entirely
>> reasonable. On the other hand, the Copenhagen Interpretation,
>> which regards a state vector as an exhaustive description of
>> an individual system,
>That may be true of certain versions of the Copenhagen interpretation. I
>would say certain misinterpretations of it.
It seems everybody has their own interpretation of Copenhagen.
>> is antipathetic to the idea of hidden
>> variables, since a more complete description than that
>> provided by a state vector would contradict that interpretation.
>>
>>He is correct about Copenhagen's antipathy to hidden variables, but
>>he probably felt a pang of dishonesty as he wrote that his interpretation
>>is open with respect to hidden variables.
>Don't you feel a pang of dishonesty making statements like that?
No; I actually believe that he wasn't fooled by his own argument.
Let me present the case again. The situation that requires
explanation is that two systems described by the same quantum
state yield different results when a particular measurement is
performed, and evidently the wavefunction only allows us to
predict probabilities of results, and not individual results
themselves. What could possibly be going on?
Ballentine's answer is that the reason the wavefunction doesn't
have enough information to predict the result is because the
wavefunction is a symbolic representation, not of an individual
system, but of an ensemble of similarly prepared systems. Thus,
we are told, it is not surprising at all that two systems
described by the same wavefunction yield different meaurement
results - the similarity between the two systems only extends
as far as they are representable by wavefunctions. Now, let
us introduce the hidden variable which says which element of the
ensemble a given system is. This is clearly hidden, since it
isn't represented anywhere in the wavefunction, and it is clearly
a variable, since it varies from one system to another.
Now there are two possibilities; one is that specifying the
value of this variable is sufficient, along with the
wavefunction, to "uniquely determine the result of any
measurement on a system", as Ballentine says in his definition
of a hidden variable. If that is the case then Ballentine's
interpretation is just a hidden variable interpretation.
If it is not the case, then we would have to say that the
property of not yielding unique well defined measurement
results remains even in the case when the specification
of the system is complete (because, you see, to identify
both the ensemble and the element within it is to completely
specify which system it is). Ballentine's interpretation, "The
measurement results aren't unique because we haven't specified
an individual system, only an ensemble," would need to be
changed to "Even if it weren't an ensemble, and even if we did
specify an individual system, the results would still be
probabilistic." That is, the "it's an ensemble" approach would have
absolutely no explanatory power at all, because the issue
requiring explanation would remain even when it wasn't an ensemble.
>>If different measurement
>>results are due to one system being different from another in a way
>>that is not captured by the wavefunction, then that's a hidden
>>variable (advocates of Copenhagen and hidden variables might be
>>surprised to find themselves agreeing on this fact).
>?????
My apologies for being unclear; I meant that they might be surprised
to find themselves agreeing with each other about something for a change.
>>The hidden
>>variable is the answer to the question: "Which member of the ensemble
>>is this system?"
>That may apply perfectly to the probabilistic results of measurements,
>which are physical. But it does not work for the wave function.
I don't understand what you mean by the expression "work for the
wave function." As I mentioned, there are schemes, Bohm's theory
for example, in which it works perfectly well; the values of the
auxilliary variables are both an answer to the question "Which
member of the emsemble is it?" and they are exactly what must be
specified in order to uniquely determine the result of any measurement.
R.
r...@maths.tcd.ie
>In message <c6mecs$2a5q$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>
>>No; the mainstream interpretations, including the ones you mention,
>>are based on the idea that the wavefunction is the complete
>That is clearly wrong. E.g. Heisenberg in physics and Philosophy p15
>states "This probability function represents a mixture of two things,
>partly a fact and partly our knowledge of a fact"
Yes; Heisenberg was a positivist. For him, an unobserved event was
a non-event. It's ironic that the wavefunction isn't observable.
>> The interpretations in which
>>the wavefunction is not a complete description are called "hidden
>>variable interpretations",
>No, that is silly. Hidden variables means that what is not known about
>the state can be described in terms of hidden variables.
Can you clarify that sentence? I don't understand what you are
trying to say.
>We know that that is not true.
We know that there are consistent hidden variable interpretations.
>Just because what is not known is not describable in
>terms of hidden variables it does not follow that everything is known.
I never claimed that what is not known is not describable in terms
of hidden variables - it was you who claimed that, as though you
had seen a proof somewhere. Counterexamples exist. Remember, I'm
not saying that there are hidden variables, only that Ballentine's
interpretation is equivalent to the statement that there are.
>>The many worlds interpretation is an attempt to reconcile the
>>assertion that the wavefunction is a complete description with
>>the idea that the wavefunction is a description of the system
>>itself rather than a description of our knowledge about the
>>system.
>Then it is an attempt to reconcile ideas which are wrong. The
>wavefunction clearly describes only our knowledge of the system, and
>there is no scientific way to claim more than that.
The wavefunction, together with its evolution, tells us about
something more than merely our knowledge. A spread-out
wavefunction can exhibit interference if it is incident on
a screen with two slits. Mere ignorance of a particle's position
cannot do the same.
R.
Italo Vecchi
Thanks for the link, Serafino, you always come up with interesting stuff.
Slide 44:"Copenhagen-influenced expectation: The measurement-type forces
particle-like behavior, so there should be no interference, and no minima."
I am not sure what is the meaning of this sentence.
Anyways the insertion of the wires obviously modifies the experimental setting,
tranforming it from a pure position measurement to a hybrid one (see below).
Slide 46:"Transactional-influenced expectation: The initial offer waves pass
through both slits on their way to possible absorbers. At the wires, the offer
waves cancel in first order, so that no transactions can form and no photons
can be intercepted by the wires."
I think anyone agrees on that , offer or not. That the photon propagates as a
wave won't surprise anyone, copenhagite or many-worldist.
By the way, the inserted wires diffract the photon, but the experimental
setting in slides 46 and previous is DIFFERENT from that in Slide 47 where the
results are described!
Notice the mirrors.
Bah. Any Cramer-Afshar advocate out there?
IV
----------------
"Call nothing true until it has been officially denied"
Mike Stone
Italo Vecchi
> By the way, the inserted wires diffract the photon, but the experimental
> setting in slides 46 and previous is DIFFERENT from that in Slide 47 where the
> results are described!
> Notice the mirrors.
>
Here are some additional comments on slide 47. Mind the mirrors.
Case 1. No Grid -> No loss
Position measurement
Case 2 Grid + 1 Slit -> 6% Loss
This is a hybrid measurement where some information is extracted at
the grid. Mirrors (see Slide 47) are needed to catch the photons
diffracted by the grid.
Case 3 Grid + 2 slits -> Negligible loss
Position measurement again. No mirrors are needed since the grid
doesn't induce significant absorption and diffraction and the wave
behaviour of the photon is unaffected. No information is extracted at
the grid.
Long live Copenhagen.
IV
------------------------------
"Now you see it, now you don't"
Charles Francis
In message <c6u4dq$1fp9$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>
>I never claimed that what is not known is not describable in terms
>of hidden variables - it was you who claimed that, as though you
>had seen a proof somewhere. Counterexamples exist. Remember, I'm
>not saying that there are hidden variables, only that Ballentine's
>interpretation is equivalent to the statement that there are.
>
lightlike polarisation as one. I just don't think it reasonable to say
that the laws of quantum mechanics can be interpreted as dud to hidden
variables. And nor do I think Bohmian mechanics reasonable.
>>>The many worlds interpretation is an attempt to reconcile the
>>>assertion that the wavefunction is a complete description with
>>>the idea that the wavefunction is a description of the system
>>>itself rather than a description of our knowledge about the
>>>system.
>
>>Then it is an attempt to reconcile ideas which are wrong. The
>>wavefunction clearly describes only our knowledge of the system, and
>>there is no scientific way to claim more than that.
>
>The wavefunction, together with its evolution, tells us about
>something more than merely our knowledge. A spread-out
>wavefunction can exhibit interference if it is incident on
>a screen with two slits. Mere ignorance of a particle's position
>cannot do the same.
If position only exists as a relative concept, then perhaps it can.
Certainly something like that would have to happen.
Regards
--
Charles Francis
r...@maths.tcd.ie
>r...@maths.tcd.ie wrote:
>> Arnold Neumaier <Arnold....@univie.ac.at> writes:
>>
>>>But there is also the Statistical Interpretation of Ballentine ...
>>
>> ... the interpretation is equivalent
>> to saying "There are hidden variables, which distinguish the individual
>> system from the ensemble," and most physicists, having advocated the
>> interpretation a moment before, would wriggle and writhe and try
>> to deny this equivalence, although it is true.
>It is not equivalent. It just admits ignorance about what happens
>for an individual system. Not the best solution but, after all, we
>are all ignorant about most things, and it is better to admit
>ignorance than to claim a knowledge which is absent or inconsistent.
The interpretation makes a stronger statement than a humble admission
of ignorance. The stronger statement is that the probabilistic
nature of quantum mechanics is *solely* due to the fact that the
quantum state refers to an ensemble. If it says anything weaker
than that then it says nothing at all (see my reply to Charles
Francis). That means that, in order for the interpretation to
say anything nontrivial, it must take the view that the predictions
would not be probabilistic were the wavefunction a complete
description of the individual system. If you assert that individual
systems can exhibit inherently probabilistic behaviour, there's
no point in trying to explain probablistic behaviour by pointing
to ensembles.
>> Ballentine's interpretation seems to go far enough to
>> say that there is something that distinguishes one system from
>> another in an ensemble, where the ensemble is represented by a
>> wavefunction, but stops short of calling the distinguishing
>> characteristic a hidden variable, which is exactly what it is.
>No. Distinguishing variables are, for example, the position and time
>of the experiment. It doesn't help to have this to improve the
>predictions. What we calculate is always a highly idealized situation.
Indeed; the representation in terms of wavefunctions abstracts away
from all such supposedly contingent variables. Here you are giving
an example of a distinguishing characteristic in an attempt to
support your position that there need not be any.
R.
Charles Francis
In message <c6thrl$1b0b$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
writes
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
>> In message <c6p792$18h$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>
>>>Indeed, most physicists would probably agree that this is a very
>>>reasonable interpretation and might claim that it is their own after
>>>they've been told about it. However, the interpretation is equivalent
>>>to saying "There are hidden variables, which distinguish the individual
>>>system from the ensemble,"
>
>>No it is not. There is nothing to say that elements of such an ensemble
>>are describable by hidden variables. In any case probabilities do apply
>>to relationships between in and out states. The wave amplitude is just a
>>conjugate root. But that is not what is meant by a hidden variable.
>
>It's not clear to me what you are trying to say. It has been proven
>that such ensembles can be described with hidden variables, so I
>don't understand why you would suggest that they can't be.
I don't agree.
>Probability
>applies to all areas of physics in which exact predictions can't be
>made, including classical mechanics; it is no surprise to anybody
>that it also applies to relationships between in and out states, and
>I don't understand what point you are making when you explicitly
>say so. I don't understand the sense in which you use the expression
>"conjugate root".
Simply that P(f|x) = <x|f><f|x>
> I don't know what the "that" is which is supposedly
>not meant by a hidden variable.
x
>
>>>and most physicists, having advocated the
>>>interpretation a moment before, would wriggle and writhe and try
>>>to deny this equivalence, although it is true. The reason for this
>>>wriggling is a received (i.e. taught) aversion to the idea of hidden
>>>variables.
>
>>Actually it is because hidden variables, in the conventional sense, do
>>not explain the laws of quantum probability.
>
>I don't know what you mean by the "conventional sense" of hidden
>variables, but there are indeed hidden variable theories which,
>as you say, explain the laws of quantum probability.
I assume you are talking about Bohmian mechanics. But it does not
explain quantum probability. It builds it in as an assumed process for
which there is no mechanism and which requires the instantaneous
propagation of non-local effects. That is not an explanation for
anything, or even a sensible interpretation.
>That is not
>to say that I advocate them, but I acknowledge their existence.
I acknowledge the existence of numerous attempts at interpretation, but
I do not call them actual interpretations.
>
>Please, explain it to me. Please also explain why Ballentine didn't
>address this point.
Unfortunately I do not have access to Ballentine's paper. I merely
remark that you assume that the unknowns in a quantum system are
describable by variables, and that that is not necessarily the case.
>>That may be true of certain versions of the Copenhagen interpretation. I
>>would say certain misinterpretations of it.
>
>It seems everybody has their own interpretation of Copenhagen.
This is always a problem in discussing Copenhagen. It is symptomatic of
physical theories which are widely followed but in fact do not make
sense. For example Lavoisier remarked that there were as many theories
of phlogiston as there were chemists.
>Let me present the case again. The situation that requires
>explanation is that two systems described by the same quantum
>state yield different results when a particular measurement is
>performed, and evidently the wavefunction only allows us to
>predict probabilities of results, and not individual results
>themselves. What could possibly be going on?
>
>Ballentine's answer is that the reason the wavefunction doesn't
>have enough information to predict the result is because the
>wavefunction is a symbolic representation, not of an individual
>system, but of an ensemble of similarly prepared systems. Thus,
>we are told, it is not surprising at all that two systems
>described by the same wavefunction yield different meaurement
>results - the similarity between the two systems only extends
>as far as they are representable by wavefunctions. Now, let
>us introduce the hidden variable which says which element of the
>ensemble a given system is. This is clearly hidden, since it
>isn't represented anywhere in the wavefunction, and it is clearly
>a variable, since it varies from one system to another.
But if you do that you would get classical probability, not quantum
probability.
>Now there are two possibilities; one is that specifying the
>value of this variable is sufficient, along with the
>wavefunction, to "uniquely determine the result of any
>measurement on a system", as Ballentine says in his definition
>of a hidden variable. If that is the case then Ballentine's
>interpretation is just a hidden variable interpretation.
That may be. But it is also not qm.
>
>If it is not the case, then we would have to say that the
>property of not yielding unique well defined measurement
>results remains even in the case when the specification
>of the system is complete (because, you see, to identify
>both the ensemble and the element within it is to completely
>specify which system it is). Ballentine's interpretation, "The
>measurement results aren't unique because we haven't specified
>an individual system, only an ensemble," would need to be
>changed to "Even if it weren't an ensemble, and even if we did
>specify an individual system, the results would still be
>probabilistic." That is, the "it's an ensemble" approach would have
>absolutely no explanatory power at all, because the issue
>requiring explanation would remain even when it wasn't an ensemble.
>
>>>If different measurement
>>>results are due to one system being different from another in a way
>>>that is not captured by the wavefunction, then that's a hidden
>>>variable (advocates of Copenhagen and hidden variables might be
>>>surprised to find themselves agreeing on this fact).
>
>>?????
>
>My apologies for being unclear; I meant that they might be surprised
>to find themselves agreeing with each other about something for a change.
I meant that I could not see advocates of Copenhagen agreeing that this
was caused by a hidden variable. Although Bohmian mechanics is cited as
counter example to Von Neumann's proof of no hidden variables, it does
it only by invoking most preposterous mechanisms. You appear to think
that the proof is wrong using a more ordinary form of hidden variable.
It is not.
Regards
--
Charles Francis
Martin Hogbin
"Robert Calvert" <Herc...@pcstarnet.com> wrote in message news:108teq4...@corp.supernews.com...
> "Martin Hogbin" <goatN...@hogbin.org> wrote in message
> > In my opinion the many-worlds interpretation
> > could be ruled out by Ockham's blunt instrument.
>
> How does it do this?
> I suppose the same thing was said about Special
> Relativity back in the days when Einstein first conjured up this infuriating
> and seemingly contradictory theory.
There is no parallel between interpretations of QM
and different theories of space and time.
All the interpretations of QM are interpretations
of the same theory. That is to say the same maths
and the same experimental predictions.
Relativity makes different predictions from Newtonian
physics and uses different maths.
> Personally, I don't see how the Many Worlds interpretation violates Ockham's
> razor.
In my opinion the many-worlds interpretation is a
prime candidate for the chop by Ockham's razor.
> Here's an description of Ockham's razor:
> http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node10.html
It is hard to see how a theory can have more
needless entities that an infinite number of universes
(although I believe there is a QM interpretation
which does). The Copenhagen interpretation, on
the other hand has essentially nothing other than that
which is measured. By applying Ockham's razor
we should prefer this until there is a good reason to
believe otherwise.
Martin Hogbin
Aaron Denney
> I meant that I could not see advocates of Copenhagen agreeing that this
> was caused by a hidden variable. Although Bohmian mechanics is cited as
> counter example to Von Neumann's proof of no hidden variables, it does
> it only by invoking most preposterous mechanisms. You appear to think
> that the proof is wrong using a more ordinary form of hidden variable.
> It is not.
Two points:
First I thought that only _local_ hidden-variables were ruled out;
non-local should be fine.
Second, I thought that Bohmian particles did not influence the evolution
of the quantum pilot-wave, so would not be hidden-variables in the usual
sense.
--
Aaron Denney
-><-
scerir
'Any Cramer-Afshar advocate out there?'
Well, I'm still trying to understand why J.Cramer says
that Afshar experiment proves the "orthodox" interpretation
to be wrong. ("Orthodox" is better than "Copenhagen", imo,
see Don Howard, "Who Invented the Copenhagen Interpretation?
A Study in Mythology", http://www.nd.edu/~dhoward1/ , section
"papers and manuscripts").
It seems, to me, that J.Cramer says that "orthodox"
interpretation is wrong in two different ways.
-1. About 6% of photons must be absorbed by those wires
(and they are not).
-2. Complementarity principle says that interference
pattern and a perfect information about the "welcher weg"
(or, in von Weizsaecker's terms: superposition of amplitudes
and localization) cannot coexist (and here there is an
*indirect* evidence of interference pattern - at the wires -
and information about the "welcher weg" - at the screen).
Actually J.Cramer also wrote:
"Yes, in my opinion, the Afshar Experiment falsifies
both the Copenhagen Interpretation and the Many-Worlds
Interpretation by demonstrating in a two-pinhole setup
the presence of complete wave interference in an unambiguous
"which way" measurement. My Transactional Interpretation
has no problem in explaining what Afshar observes.
The offer waves through the two pinholes cancel on
his wires, so no source-wire transactions can form.
Therefore, the insertion of the wires constitutes an
"interaction-free" measurement, all photons from the source
end up at one of the two pinhole images, and it is an
unambiguous "which-way" measurement. The Bohr's
Complemantarity Principle, the CI, and the MWI have all
lead us to believe that there should be no wave interference
effects in an unambiguous "which-way" measurement.
The Afshar Experiment demonstrates that this is inconsistent
with data and with the quantum formalism.
I don't think the agreement with the Afshar result depends
on the time symmetry of the TI. It's more that the TI
transactions closely follow what goes on in a QM calculation
(e.g. an overlap integral), and the quantum formalism is
consistent with Afshar. The MWI and CI get in trouble by
making pronouncements about when you will and will not get
interference that turn out to be inconsistent with the QM
formalism."
But why 6% of photons must be absorbed, by those wires,
according to Cramer's interpretation of "orthodox"
interpretation? I'm inclined to believe that his
reasoning may be this one. We have a perfect (?) information,
at the screen, about the "welcher weg" the particle
took. Thus we know the path the particle (photon) took,
from the specific slit to the specific point on the screen.
Also take in account that there is a principle of conservation
of momentum. Thus, it must happen that a certain number
(say 6%) of particles (photons) must be absorbed by those wires.
[I don't know whether this interpretation of Cramer's
interpretation of the "orthodox" interpretation is correct,
or not. But this reasoning, imo, does not sound perfectly,
because of that insertion of those wires, between the two-slit
and the screen. According to Renninger and Dicke even "negative"
measurements seem to cause a "collapse". According to
Elitzur, Vaidman, Aharonov even "interaction free"
measurements have consequences.]
Why, according to Cramer's interpretation, Bohr's complementarity
principle is violated, by Afshar experiment? Because here we
have both a manifestation of interference (at the wires)
and a perfect information of "welcher weg" (at the screen).
[We know that, after the Greenberger & Yasin relation
P^2 + V^2 = 1, where P is the probability for the photon
taking one of the two possible paths, and V the visibility
of the fringes, and many related experiments, like
http://arxiv.org/abs/quant-ph/9908072
http://arxiv.org/abs/quant-ph/0311179
http://arxiv.org/abs/quant-ph/0201026
http://arxiv.org/abs/quant-ph/0404013
show that there is a "smooth" transition between the wave-like
and the particle-like nature, depending on the information about
the "welcher weg". See also Wootters and Zurek,
"Complementarity in the double-slit experiment: Quantum
nonseparability and a quantitative statement of Bohr's principle",
PR, D-19, 1979, p.473-484). Thus the coexistence of some
"interference" and some "localization" is a well-know fact,
something usual. But here, in Afshar exp., it seems that a 100%
localization (at the screen) coexists with a (virtual) 100%
interference pattern (at the wires). Maybe the complementarity
principle does not work "at a distance" :-)]
Btw, it seems interesting to point out that if we "erase"
the information about the "welcher weg", according to
"orthodox" (interpretation of) QM, we restore the interference
pattern (at the screen also). Thus if we set a quantum "eraser"
between those wires and the screen, we destroy any information
about the "welcher weg", and no photon can be absorbed,
any more, by those wires. ... A sort of backward causality :-)
Cari saluti,
s.
r...@maths.tcd.ie
> In message <c6thrl$1b0b$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
>writes
>>
>>It's not clear to me what you are trying to say. It has been proven
>>that such ensembles can be described with hidden variables, so I
>>don't understand why you would suggest that they can't be.
>I don't agree.
From what you say later, it seems that you dislike Bohmian
mechanics. That's fine with me; I'm not a Bohmian.
>>>Actually it is because hidden variables, in the conventional sense, do
>>>not explain the laws of quantum probability.
>>
>>I don't know what you mean by the "conventional sense" of hidden
>>variables, but there are indeed hidden variable theories which,
>>as you say, explain the laws of quantum probability.
>I assume you are talking about Bohmian mechanics. But it does not
>explain quantum probability. It builds it in as an assumed process for
>which there is no mechanism
The probability distribution in Bohmian mechanics can be seen to
be natural because it's equivariant; if |psi|^2 is the distribution
at one time, it will be the distribution at all future times. I
believe (though I haven't seen a proof and would be interested
in seeing one if anyone can point me to one) that in any dynamical
system with an equivariant distribution on its states, that same
distribution is the best prior.
>and which requires the instantaneous
>propagation of non-local effects. That is not an explanation for
>anything, or even a sensible interpretation.
Well, what Bell's theorem showed was the non-locality of quantum
mechanics itself. It's not entirely fair to complain abot Bohmian
mechanics being non-local when experiments have shown that non-locality
is a fact of life. Wavefunction collapse is non-local and so is
the splitting of the universe into many worlds, but, of course,
everybody will jump in here and claim that their personal interpretation
or variant of Copenhagen or Everett isn't non-local. Inevitably,
such "interpretations" merely amount to having a "way of thinking
abuot it" which is equivalent to "never admit that it is non-local."
It's the experiments which indicate non-locality; having a local
interpretation of the qm formalism isn't a virtue.
>>Please, explain it to me. Please also explain why Ballentine didn't
>>address this point.
>Unfortunately I do not have access to Ballentine's paper. I merely
>remark that you assume that the unknowns in a quantum system are
>describable by variables, and that that is not necessarily the case.
That's not quite my position, but it is close to it. What I am
claiming is that if there is an ensemble, and a system which is
one of the elements of the ensemble, then which element it is
is a variable. Also, when you claim that in a quantum system
it is not necessarily true that the unknowns can be described
by variables, all you are really saying is that you dislike
hidden variables. The hidden variable interpretations aren't
inconsistent.
>>Ballentine's answer is that the reason the wavefunction doesn't
>>have enough information to predict the result is because the
>>wavefunction is a symbolic representation, not of an individual
>>system, but of an ensemble of similarly prepared systems. Thus,
>>we are told, it is not surprising at all that two systems
>>described by the same wavefunction yield different meaurement
>>results - the similarity between the two systems only extends
>>as far as they are representable by wavefunctions. Now, let
>>us introduce the hidden variable which says which element of the
>>ensemble a given system is. This is clearly hidden, since it
>>isn't represented anywhere in the wavefunction, and it is clearly
>>a variable, since it varies from one system to another.
>But if you do that you would get classical probability, not quantum
>probability.
Can you explain the difference between classical and quantum
probability to me? Would it have something to do with "quantum
probability" having a little label attached which says "No
hidden variables" and classical probability having a label
which says "Hidden variables"?
>>Now there are two possibilities; one is that specifying the
>>value of this variable is sufficient, along with the
>>wavefunction, to "uniquely determine the result of any
>>measurement on a system", as Ballentine says in his definition
>>of a hidden variable. If that is the case then Ballentine's
>>interpretation is just a hidden variable interpretation.
>That may be. But it is also not qm.
If it gives the same predictions as qm in all circumstances
where those predictions are correct, then not being qm is
hardly a bad point, unless you are saying that you like qm
and don't like things which aren't qm, in which case it
is merely your personal taste.
>>>>If different measurement
>>>>results are due to one system being different from another in a way
>>>>that is not captured by the wavefunction, then that's a hidden
>>>>variable (advocates of Copenhagen and hidden variables might be
>>>>surprised to find themselves agreeing on this fact).
>>
>>>?????
>>
>>My apologies for being unclear; I meant that they might be surprised
>>to find themselves agreeing with each other about something for a change.
>I meant that I could not see advocates of Copenhagen agreeing that this
>was caused by a hidden variable.
No no; I meant that they would agree that if there is something
extra and unknown, apart from the wavefunction, determining
the outcomes of experiments, then it's a hidden variable, and
they would both agree on that but Copenhagen people would
dislike it while hidden variables people might like it.
>Although Bohmian mechanics is cited as
>counter example to Von Neumann's proof of no hidden variables, it does
>it only by invoking most preposterous mechanisms. You appear to think
>that the proof is wrong using a more ordinary form of hidden variable.
>It is not.
Actually, I think Bell gives an explicit example of a much more
simple hidden variable which provides a counterexample to Von
Neumann's proof in Speakable and Unspeakable. I'll dig it out
and post it when I have the chance.
R.
Charles Francis
In message <c762c5$8qd$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>I assume you are talking about Bohmian mechanics. But it does not
>>explain quantum probability. It builds it in as an assumed process for
>>which there is no mechanism
>
>The probability distribution in Bohmian mechanics can be seen to
>be natural because it's equivariant; if |psi|^2 is the distribution
>at one time, it will be the distribution at all future times. I
>believe (though I haven't seen a proof and would be interested
>in seeing one if anyone can point me to one) that in any dynamical
>system with an equivariant distribution on its states, that same
>distribution is the best prior.
>
>>and which requires the instantaneous
>>propagation of non-local effects. That is not an explanation for
>>anything, or even a sensible interpretation.
>
>Well, what Bell's theorem showed was the non-locality of quantum
>mechanics itself.
It doesn't show anything so strong. It only shows that the definition of
locality as used by Bell is faulty. Indeed this definition is replaced
by a commutator condition in qed. However if one takes an orthodox view,
that it is not meaningful to talk of measured quantities between
measurements, it is natural to recognise that it is not possible to talk
of position, or of space-time between measurements, in other words to
adopt the relationist idea that position only exists as a relationship
between matter and matter.
>Wavefunction collapse is non-local
One may as well say that the collapse of a classical probability
distribution when a result becomes known is non local. Probability is
only a mathematical function, and likewise the wave function is just the
sqrt of probability multiplied by a physically meaningless complex
phase.
>
>
>>Unfortunately I do not have access to Ballentine's paper. I merely
>>remark that you assume that the unknowns in a quantum system are
>>describable by variables, and that that is not necessarily the case.
>
>That's not quite my position, but it is close to it. What I am
>claiming is that if there is an ensemble, and a system which is
>one of the elements of the ensemble, then which element it is
>is a variable.
Ok
> Also, when you claim that in a quantum system
>it is not necessarily true that the unknowns can be described
>by variables, all you are really saying is that you dislike
>hidden variables.
All I am really saying is that what you describe above is not what I
understand by hidden variables. Certainly it is possible to write down,
for any observable K with eigenvalues k_i, a classical probability
function
P(k_i | f) = | < k_i | f > |^2
and say that this classical probability distribution runs over the set
of projection operators |k_i><k_i|, so that the projection operators are
the random variable. Or even that the index i is the random variable.
But this is trivial When Von Neumann did the original no-go theorem for
hidden variables I don't think that is what he meant at all, and if it
had occurred to him he would have found a form of words to exclude it.
He was talking about systems having hidden parameters controlling the
outcome of experiments. That is a different thing.
>>>Ballentine's answer is that the reason the wavefunction doesn't
>>>have enough information to predict the result is because the
>>>wavefunction is a symbolic representation, not of an individual
>>>system, but of an ensemble of similarly prepared systems. Thus,
>>>we are told, it is not surprising at all that two systems
>>>described by the same wavefunction yield different meaurement
>>>results - the similarity between the two systems only extends
>>>as far as they are representable by wavefunctions. Now, let
>>>us introduce the hidden variable which says which element of the
>>>ensemble a given system is. This is clearly hidden, since it
>>>isn't represented anywhere in the wavefunction, and it is clearly
>>>a variable, since it varies from one system to another.
>
>>But if you do that you would get classical probability, not quantum
>>probability.
>
>Can you explain the difference between classical and quantum
>probability to me? Would it have something to do with "quantum
>probability" having a little label attached which says "No
>hidden variables" and classical probability having a label
>which says "Hidden variables"?
We have
P(k_i | f) = | < k_i | f > |^2
where P is a classical probability distribution. What we have to explain
is that |f> obeys a Schroedinger equation, and that when combining
probabilities we do not have classical probability laws.
>>>Now there are two possibilities; one is that specifying the
>>>value of this variable is sufficient, along with the
>>>wavefunction, to "uniquely determine the result of any
>>>measurement on a system", as Ballentine says in his definition
>>>of a hidden variable. If that is the case then Ballentine's
>>>interpretation is just a hidden variable interpretation.
>
>>That may be. But it is also not qm.
>
>If it gives the same predictions as qm in all circumstances
>where those predictions are correct, then not being qm is
>hardly a bad point, unless you are saying that you like qm
>and don't like things which aren't qm, in which case it
>is merely your personal taste.
No, I am saying that for such an interpretation to be qm the reasons for
quantum superposition must be clearly demonstrated. When looking at such
claims I have generally find that superposition is assumed, not
demonstrated.
Regards
--
Charles Francis
r...@maths.tcd.ie
Aaron Denney <wno...@ofb.net> writes:
>On 2004-05-03, Charles Francis <cha...@clef.demon.co.uk> wrote:
>> I meant that I could not see advocates of Copenhagen agreeing that this
>> was caused by a hidden variable. Although Bohmian mechanics is cited as
>> counter example to Von Neumann's proof of no hidden variables, it does
>> it only by invoking most preposterous mechanisms. You appear to think
>> that the proof is wrong using a more ordinary form of hidden variable.
>> It is not.
>Two points:
>First I thought that only _local_ hidden-variables were ruled out;
>non-local should be fine.
Actually, nothing at all was ruled out because the proof was incorrect.
Here's a short sketch of the proof and Bell's counterexample, which
will hopefully explain why I "appear to think that the proof is wrong
using a more ordinary form of hidden variable."
We consider a spin-1/2 particle, for which the observables are
2x2 Hermitian matrices of the form a+b.sigma, where a is a real number,
b a real 3-dimensional vector and sigma represents a vector
of Pauli matrices. The possible results of observing such an
observable are a plus or minus |b|.
A "dispersion free state", which can be considered to be specified
by a quantum state psi (a spinor) and an extra hidden variable,
lambda, has a unique answer determined only by a, b, psi, and lambda.
Von Neumann's proof starts from the assumption that: "Any real
linear combination of any two Hermitian operators represents an
observable, and the same linear combination of expectation values
is the expectation value of the combination." This is required by
Von Neumann to be true of the dispersion free states. Thus, the
expectation value E(a,b,psi,lambda) of the dispersion free state
must be linear in a and b. However, a dispersion free state has,
for an expectation value, one of the eigenvalues a+|b| or a-|b|,
neither of which are linear functions of b. Hence any dispersion
free state must fail to satisfy Von Neumann's assumption and is
therefore impossible.
Bell's counterexample is simple: the hidden variable, lambda, is
a real number between -1/2 and 1/2. Psi and lambda together identify
the dispersion free state. By a change of coordinates,
psi=(1,0)^T, where ^T means transpose. Let b_x, b_y and b_z be
the components of b in this coordinate system. Then measurement
of a+b.sigma on the state specified by psi and lambda reults with
certainty in the eigenvalue
a+|b|sign(lambda|b|+|b_z|/2)sign(X)
where X= b_z if b_z!=0
b_x if b_z=0 and b_x!=0
b_y if b_z=b_x=0
and sign(x)=1 if x>=0 and 0 if x<0
Uniformly integrating over lambda gives the expectation value of psi,
which is a+b_z. This is mostly taken from the first paper in Bell's
Speakable and Unspeakable in Quantum Mechanics; note that the hidden
variables, and the way it determines the outcome, is as simple as
one could hope for.
What went wrong with Von Neumann's proof? Bell teaches us that
he was incorrect to require that expectation values should add
for dispersion free states. That is, Von Neumann would say that
if the thing to be measured is (sigma_x + sigma_y)/sqrt(2), and the
results of measuring sigma_x and sigma_y are both 1, then we should
get (1+1)/sqrt(2)=sqrt(2), but obviously when we measure we will get
either 1 or -1 and never sqrt(2). Bell's counterexample doesn't
behave like this and neither should it - one can't simultaneously
measure (sigma_x + sigma_y)/sqrt(2), sigma_x and sigma_y, because
they require different experiments. We might measure sigma_x of
one dispersion free state, but then when we try to measure sigma_y,
we will be making the measurement on a *different* dispersion free
state, although the quantum state will be the same; after all, we
can only prepare quantum states and can't control the hidden
variables. That is, in order to agree with the predictions of quantum
mechanics, only the ensemble (the quantum state) must satisfy Von
Neumann's assumption, and not the dispersion free state itself.
>Second, I thought that Bohmian particles did not influence the evolution
>of the quantum pilot-wave, so would not be hidden-variables in the usual
>sense.
Indeed; in Bohm's interpretation, the particle positions are the visible
variables and the wavefunction is the hidden variable. Note that it
is not the addition of the particle positions which makes the theory
nonlocal; the particle positions are local and it is the wavefunction,
which is also present in all the other interpretations of quantum
mechanics, which is nonlocal. The particle positions merely make the
nonlocality more manifest by taking their cues from the nonlocal
wavefunction which controls their motion.
R.
Italo Vecchi
>
> It seems, to me, that J.Cramer says that "orthodox"
> interpretation is wrong in two different ways.
>
> -1. About 6% of photons must be absorbed by those wires
> (and they are not).
Of course they are not, in the 2-slits case of Afshar's experiment the
wires, if they are positioned appropriately, do not change anything.
They are placed where there is no wave. You may as well put them in
your pocket,
> -2. Complementarity principle says that interference
> pattern and a perfect information about the "welcher weg"
> (or, in von Weizsaecker's terms: superposition of amplitudes
> and localization) cannot coexist (and here there is an
> *indirect* evidence of interference pattern - at the wires -
> and information about the "welcher weg" - at the screen).
The "welcher Weg" talk is based on a misunderstanding. it's obvious
that the photon does not have a position before being measured.
Whatever you measure afterwards, the photon goes through both slits.
In Copenhagen photons, as anything else including cats, evolve as
waves (or as ripples on waves) described by a Schroedinger equation
until they are measured/perceived. It's measurement (as I believe,
non-unitary perception) that quantises the photon into a "particle" (
the whole talk of "particles" is unnecessary and actually misleading).
Afshar's experiment indeed illustrates vividly that talk of "welcher
Weg" is meaningless. As you point out this had been demonstrated
previously also by Elitzur-Vaidman beautiful but improperly named
"interaction-free" measurements. In Afshar's 2-Slits case there is no
measurement at the wires, since the amplitude of the photon there is
zero, whereas it's fractional but not null at Elitzur-Vaidman's bomb.
Cordialmente,
IV
Eric Dennis
> Charles Francis <cha...@clef.demon.co.uk> writes:
> >Although Bohmian mechanics is cited as
> >counter example to Von Neumann's proof of no hidden variables, it does
> >it only by invoking most preposterous mechanisms. You appear to think
> >that the proof is wrong using a more ordinary form of hidden variable.
> >It is not.
>
> Actually, I think Bell gives an explicit example of a much more
> simple hidden variable which provides a counterexample to Von
> Neumann's proof in Speakable and Unspeakable. I'll dig it out
> and post it when I have the chance.
>
> R.
It seems like Charles regards Bohm's theory as preposterous because it
is non-local. What needs to be spelled out, which Rof has alluded to
before, is that Bell's inequality has nothing to do especially with
hidden variables or quantum mechanics or any other fancy thing. Bell's
inequality is a simple critereon that any local theory must satisfy --
where "local" is defined in a very plain way: nothing over here can
affect the state of something over there faster than light -- by
virtue of its locality.
r...@maths.tcd.ie
>In message <c762c5$8qd$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>Well, what Bell's theorem showed was the non-locality of quantum
>>mechanics itself.
>It doesn't show anything so strong. It only shows that the definition of
>locality as used by Bell is faulty.
Remember what I said about everybody having their own personal
interpretation which gives them a "way of thinking about it" which
amounts to "never admit that it's nonlocal"? Changing the
definition of locality is certainly a good way of achieving
this.
>Indeed this definition is replaced by a commutator condition in qed.
Indeed it is.
Bell's "faulty" idea of locality with which he derived his inequalities
was the following. There are two measurement angles, say phi_1 and phi_2,
which are controlled by distant experimenters. Each gets a measurement
result, say r_1 and r_2 respectively. Locality (according to Bell)
means that the result r_2 does not depend on the angle of the distant
measuring device, phi_1. What was proven was that the predictions
of quantum mechanics do not satisfy this criterion. The vanishing
of spacelike commutators is not strong enough to guarantee no
action at a distance, but it is stong enough to prevent paradoxes.
>However if one takes an orthodox view,
>that it is not meaningful to talk of measured quantities between
>measurements, it is natural to recognise that it is not possible to talk
>of position, or of space-time between measurements, in other words to
>adopt the relationist idea that position only exists as a relationship
>between matter and matter.
That sounds like a "way of thinking about it." Generally, when
people start advocating ways of thinking about it which consist
of dictums like "never talk about such-and-such a thing", then
I tend to lose interest until they provide an alternative thing
to talk about and show how to use it to calculate things which
could not have been calculated in the old scheme.
>>Wavefunction collapse is non-local
>One may as well say that the collapse of a classical probability
>distribution when a result becomes known is non local.
When somebody updates his or her internal representation of
the world to take into account the reception of new information,
that is a local act and is what happens when a probability
distribution collapses. Einstein, Bohr, Born and others at the
relevant time debated whether the wavefunction collapse was
the same phenomenon or not. It's not so obvious, because
the wavefunction is not just a probability distribution; it
encodes other information as well, for example, for a
free particle, psi(x)=exp(ikx) encodes the speed of
the particle. The debate ended before Bell's inequalities
were published, which showed that if the predictions of
quantum mechanics were correct, then wavefunction collapse
cannot be interpreted as merely the updating of an internal
representation, since it affects the results of distant
measurements.
>Probability is
>only a mathematical function, and likewise the wave function is just the
>sqrt of probability multiplied by a physically meaningless complex
>phase.
The phase isn't meaningless; it determines what kinds of
interference will occur. For example, in a two-slit diffraction
experiment, putting a phase-shifter over one of the slits (say
a piece of glass if you're using light) will alter the interference
pattern observed by shifting the positions of the fringes.
Also, I'm not sure what point you're making by belittling
probability distributions and wavefunctions.
>> Also, when you claim that in a quantum system
>>it is not necessarily true that the unknowns can be described
>>by variables, all you are really saying is that you dislike
>>hidden variables.
>All I am really saying is that what you describe above is not what I
>understand by hidden variables. Certainly it is possible to write down,
>for any observable K with eigenvalues k_i, a classical probability
>function
> P(k_i | f) = | < k_i | f > |^2
>and say that this classical probability distribution runs over the set
>of projection operators |k_i><k_i|, so that the projection operators are
>the random variable. Or even that the index i is the random variable.
>But this is trivial When Von Neumann did the original no-go theorem for
>hidden variables I don't think that is what he meant at all, and if it
>had occurred to him he would have found a form of words to exclude it.
>He was talking about systems having hidden parameters controlling the
>outcome of experiments. That is a different thing.
That is exactly what I am talking about; see my more recent post
for a description of why Von Neumann's proof is incorrect and how the
type of hidden variables you did have in mind can actually be
assigned.
>>>But if you do that you would get classical probability, not quantum
>>>probability.
>>
>>Can you explain the difference between classical and quantum
>>probability to me? Would it have something to do with "quantum
>>probability" having a little label attached which says "No
>>hidden variables" and classical probability having a label
>>which says "Hidden variables"?
>We have
> P(k_i | f) = | < k_i | f > |^2
>where P is a classical probability distribution.
Ok...
>What we have to explain
>is that |f> obeys a Schroedinger equation,
Why should the time evolution of |f> have anything to
do with the introduction of a new, hitherto unheard of
type of probability distinct from the probability that
we knew before?
>and that when combining
>probabilities we do not have classical probability laws.
When combining probabilities we have all the usual laws of
probability. Perhaps what you are thinking of is the idea
that measurement destroys interference. The orthodox
interpretation serves us well here: if K is measured while the
representation of the quantum system is |f>, then the
probability that the result of the measurement is k_i is
P(k_i|f). P(k_i|f) should *not* be thought of as the
probability that the value of K is k_i in the absence
of measurement. It is only by making this mistake that
one might find that "we do not have classical probability
laws."
Regards,
R.
Italo Vecchi
>
> It seems, to me, that J.Cramer says that "orthodox"
> interpretation is wrong in two different ways.
>
> -1. About 6% of photons must be absorbed by those wires
> (and they are not).
Of course they are not. In the 2-slits case of Afshar's experiment the
wires, if they are positioned appropriately, do not change anything.
They are placed where there is no wave. You may as well put them in
your pocket,
> -2. Complementarity principle says that interference
> pattern and a perfect information about the "welcher weg"
> (or, in von Weizsaecker's terms: superposition of amplitudes
> and localization) cannot coexist (and here there is an
> *indirect* evidence of interference pattern - at the wires -
> and information about the "welcher weg" - at the screen).
The "welcher Weg" talk is based on a misunderstanding. It's obvious
that the photon does not have a position before being measured.
Whatever you measure afterwards, the photon goes through both slits.
In Copenhagen photons, as anything else including cats, evolve as
waves (or as ripples on waves) described by a Schroedinger equation
until they are measured/perceived. It's measurement (as I believe,
non-unitary perception) that quantises the photon into a "particle" (
the whole talk of "particles" is unnecessary and actually misleading).
Afshar's experiment indeed illustrates vividly that talk of "welcher
Weg" is meaningless. As you point out this had been demonstrated
previously also by Elitzur-Vaidman beautiful but improperly named
"interaction-free" measurements. In Afshar's 2-Slits case however
there is no measurement at the wires, since the amplitude of the
photon there is negligible, whereas it's fractional (1/2 actually) but
scerir
"Italo Vecchi"
> Whatever you measure afterwards, the photon goes through both slits.
> In Copenhagen photons, as anything else including cats, evolve as
> waves (or as ripples on waves) described by a Schroedinger equation
> until they are measured/perceived. It's measurement (as I believe,
> non-unitary perception) that quantises the photon into a "particle"
As Lawrence Bragg said "Everything in the future is a wave, everything
in the past is a particle". Sometimes it seem to me that Afshar's
experiment would like to reverse that statement !
Now I remember that P. Bush, in (circa) 1995, developed (Found.Phys.?)
a theory of unsharp measurements and invented a very strange double
Mach-Zehnder interferometer to show both an interference pattern
(in the lower part of the set-up) and a "welcher weg" information
(in the upper part). Mah.
Regards,
s.
Charles Francis
In message <c7e53j$2msn$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
I think it is a bit more than that. Relationism existed prior to quantum
mechanics, and was adopted by some of the greatest mathematical minds in
Europe before Newtonian absolute space became ingrained. The fact is
that the fundamental precept of relationism, that you cannot say where
something is unless you can say where it is in relation to other matter,
remains empirically true. The trick, and it is clearly a subtle trick,
is to show how this fundamental precept leads to quantum laws.
>Generally, when
>people start advocating ways of thinking about it which consist
>of dictums like "never talk about such-and-such a thing", then
>I tend to lose interest until they provide an alternative thing
>to talk about and show how to use it to calculate things which
>could not have been calculated in the old scheme.
That's a tall order for a post. I shall send you a paper.
>>>Wavefunction collapse is non-local
>
>>One may as well say that the collapse of a classical probability
>>distribution when a result becomes known is non local.
>
>When somebody updates his or her internal representation of
>the world to take into account the reception of new information,
>that is a local act and is what happens when a probability
>distribution collapses. Einstein, Bohr, Born and others at the
>relevant time debated whether the wavefunction collapse was
>the same phenomenon or not. It's not so obvious, because
>the wavefunction is not just a probability distribution; it
>encodes other information as well, for example, for a
>free particle, psi(x)=exp(ikx) encodes the speed of
>the particle. The debate ended before Bell's inequalities
>were published, which showed that if the predictions of
>quantum mechanics were correct, then wavefunction collapse
>cannot be interpreted as merely the updating of an internal
>representation, since it affects the results of distant
>measurements.
That assumes a prior concept of distance, which I do not accept. We have
the fact that to measure a distance there has to be a transfer of
information. If there is no such transfer then distance has no empirical
meaning. Note, that this is a purely logical statement, which might have
been made by Descartes or Leibniz without any prior training in the
orthodox interpretation of qm.
>>Probability is
>>only a mathematical function, and likewise the wave function is just the
>>sqrt of probability multiplied by a physically meaningless complex
>>phase.
>
>The phase isn't meaningless; it determines what kinds of
>interference will occur. For example, in a two-slit diffraction
>experiment, putting a phase-shifter over one of the slits (say
>a piece of glass if you're using light) will alter the interference
>pattern observed by shifting the positions of the fringes.
Sure. Phase differences have meaning. Absolute phase does not.
>Also, I'm not sure what point you're making by belittling
>probability distributions and wavefunctions.
I don't think I am belittling probability distributions and wave
functions. Probability distributions are what we have. Wave functions
are a legitimate means of calculation from them. They become more
legitimate if one can provide an explanation for the Schrodinger
equation, instead of being forced to accept it as an assumption.
>That is exactly what I am talking about; see my more recent post
>for a description of why Von Neumann's proof is incorrect and how the
>type of hidden variables you did have in mind can actually be
>assigned.
Ok. Clearly I have a flaky memory at times. D'Espagnat describes much as
you say, and follows by commenting
"Bell, however, has shown that all of the hidden variable theories (such
as Bohm's) which, statistically, reproduce exactly the predictions of
quantum mechanics.... have a general property in common. This property
is that for some experiments it necessarily happens that the readings on
a measurement apparatus M1, located at a certain place, depend on the
settings of another apparatus, M2, located at another, possibly very
distant, place and not connected in any apparent way with the first one.
The readings on M1 can accordingly be modified, for given values of the
hidden variables simply by hanging the positions of some pieces of
equipment in M2.
I think I do find this sort of non-locality unacceptable. Of course this
is rather different from the form of non-locality which I advocate,
which is that something does not have location in the absence of
physical communication/contact with other matter, so that for example it
is impossible to talk of the separation of the particles in EPR until
they are measured. Note that this form of "non-locality" is local in the
sense that contact is necessary for the transmission of physical
effects. More precisely by 'contact' I mean emission/absorption of
photons (or intermediate boson)
>>What we have to explain
>>is that |f> obeys a Schroedinger equation,
>
>Why should the time evolution of |f> have anything to
>do with the introduction of a new, hitherto unheard of
>type of probability distinct from the probability that
>we knew before?
I don't think it does. | < k_i | f > |^2 is a probability just like it
was before, and it is phase independent, whatever the time evolution.
>>and that when combining
>>probabilities we do not have classical probability laws.
>
>When combining probabilities we have all the usual laws of
>probability. Perhaps what you are thinking of is the idea
>that measurement destroys interference. The orthodox
>interpretation serves us well here: if K is measured while the
>representation of the quantum system is |f>, then the
>probability that the result of the measurement is k_i is
>P(k_i|f). P(k_i|f) should *not* be thought of as the
>probability that the value of K is k_i in the absence
>of measurement. It is only by making this mistake that
>one might find that "we do not have classical probability
>laws."
Yes. That is precisely what I mean.
Regards
--
Charles Francis
Mark Palenik
vec...@weirdtech.com (Italo Vecchi) wrote in message news:<61789046.04050...@posting.google.com>...
Well, I had to remove some white things that were blocking the images
in one of the power point slides, but I found two additional pictures,
that were covered up, which show that the wires *are* in fact
affecting the measurement. Why precisely this effect wouldn't occurr
with anything other than the transactional interpretation, I don't
know. I agree that that is probably a bad assumption.
I also found it rather ironic that in earlier slides, he specifically
said that different interpretations should not produce different
experimental outcomes, that only different formulisms should do so,
and while admitting that his model is only an interpretation, claiming
that it has produced a different experimental prediction.
slyboy
> who think about interpretations of quantum mechanics are fools
> wasting their time.
That may be true, but it is a consensus that is almost certainly wrong
and also one that is slowly beginning to break down. Studies of
quantum foundations have lead us to the idea of quantum
computing/information. Technology developed to test Bell inequalities
and to generate coherent superpositions of large numbers of particles
have found a multitude of different applications.
Perhaps those who justify their arguments about quantum mechanics based
on lengthy philisophical diatribes have not contributed much to this,
but none of this would have happened if the quantum debate was not
still ongoing.
Ultimately, we are going to have to deal with the problems with quantum
mechanics if we want to go beyond the contemporary understanding of
physics. In particluar, I think it is likely that we have to deal with
them if we are ever to meake sense of quantum gravity.
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Charles Francis
Dennis <ede...@princeton.edu> writes
Surely the essence of EPR is that the distance between over here and
over there is not a definable quantity until such time as their
positions have been measured. In such a case we cannot talk about over
there until such time as something has already affected the state.
Regards
--
Charles Francis
Eric Dennis
Charles Francis <cha...@clef.demon.co.uk> wrote
That is a peculair way to constrew EPR's position. Their position is
that things exist, and therefore are talk-about-able ("speakable" as
Bell would say), whether or not they have been measured. But this
whole sideline about whether or not "distance" is a relational concept
is beside the point. Unless you are trying to cast doubt on
propositions like "city A is so-many miles from city B", there's no
real issue here. We know that we measure one photon at city A. We know
that we measure another at city B. We know when we measured them. We
know from repeating the experiment a bunch of times and looking at the
statistics of the measurement results that our choice of dial setting
at A has a reproducible, faster-than-light effect on the measurement
outcome at B (or vice versa).
And if you are trying to cast doubt on propositions like "city A is
so-many miles from city B", then there's no point in getting wrapped
up in intricacies like Bell's inequality.
r...@maths.tcd.ie
>In message <ef463682.04050...@posting.google.com>, Eric
>Dennis <ede...@princeton.edu> writes
>>
>>It seems like Charles regards Bohm's theory as preposterous because it
>>is non-local. What needs to be spelled out, which Rof has alluded to
>>before, is that Bell's inequality has nothing to do especially with
>>hidden variables or quantum mechanics or any other fancy thing. Bell's
>>inequality is a simple critereon that any local theory must satisfy --
>>where "local" is defined in a very plain way: nothing over here can
>>affect the state of something over there faster than light -- by
>>virtue of its locality.
>>
>Surely the essence of EPR is that the distance between over here and
>over there is not a definable quantity until such time as their
>positions have been measured. In such a case we cannot talk about over
>there until such time as something has already affected the state.
Experiments have been performed demonstrating violations of Bell's
inequalities over distances of over four kilometres in Malvern and
over ten kilometres in Geneva, according to Aspect's review in the
March 1999 edition of Nature. So what we have is a polarizer, which
had a very definite position with respect to the buildings and people
of Geneva, and when the setting of that polarizer was changed, by
somebody or some machine standing beside it, the results of measurements
in a very well-defined place 10 kilometres away were affected more
quickly than a light signal could have gotten there from the original
polarizer.
Perhaps what you are saying is that the photons involved were
neither here nor there, or that their polarizations weren't
localised quantities, but it's very clear that we don't have
to worry about the geometry of Geneva becoming somehow ill-defined.
That is, we know very well what we mean by over here and over there,
but we may not know, and it may not be well-defined, which photon
is heading towards which well-defined place.
The upshot is that even if we do imagine some breakdown of
the property of location from the point of view of the
photons, we still have macroscopic objects with well-defined positions
affecting the behaviour of distant macroscopic objects with
well-defined positions.
Once we open the door to the idea of nonlocal interactions, the
difficulty is no longer in finding some mechanism by which a
particular object can affect a distant one, but in reconciling the
fact that this happens with special relativity. That is, once we
admit that the settings of my local device really are affecting the
results of distant experiments, we then have to confront the seemingly
contradictory fact that in somebody's frame of reference, the distant
results were obtained before I even adjusted the settings. All of these
facts have to be faced by big creatures like us who always have well
defined positions with respect to each other.
This is a real problem, to which no generally satisfactory answers
have been given. The orthodox approach is to pretend there's no
problem. Aspect quotes Feynman at the end of the article:
"It has not yet become obvious to me that there is no real
problem ... I have entertained myself always by squeezing the
difficulty of quantum mechanics into a smaller and smaller place,
so as to get more and more worried about this particular item. It
seems almost ridiculous that you can squeeze it to a numerical
question that one thing is bigger than another. But there you
are - it is bigger." Here he is referring to the bound on Bell's
inequalities being breached. Aspect ends by saying "Yes, it is
bigger by 30 standard deviations."
R.
Charles Francis
Dennis <ede...@princeton.edu> writes
>
>Charles Francis <cha...@clef.demon.co.uk> wrote
>> In message <ef463682.04050...@posting.google.com>, Eric
>> Dennis <ede...@princeton.edu> writes
>> >It seems like Charles regards Bohm's theory as preposterous because it
>> >is non-local. What needs to be spelled out, which Rof has alluded to
>> >before, is that Bell's inequality has nothing to do especially with
>> >hidden variables or quantum mechanics or any other fancy thing. Bell's
>> >inequality is a simple critereon that any local theory must satisfy --
>> >where "local" is defined in a very plain way: nothing over here can
>> >affect the state of something over there faster than light -- by
>> >virtue of its locality.
>> >
>>
>> Surely the essence of EPR is that the distance between over here and
>> over there is not a definable quantity until such time as their
>> positions have been measured. In such a case we cannot talk about over
>> there until such time as something has already affected the state.
>
I wasn't so much thinking of EPR's position, but how Dirac or Von
Neumann might have responded to it.
>Their position is
>that things exist, and therefore are talk-about-able ("speakable" as
>Bell would say), whether or not they have been measured. But this
>whole sideline about whether or not "distance" is a relational concept
>is beside the point. Unless you are trying to cast doubt on
>propositions like "city A is so-many miles from city B", there's no
>real issue here.
That is precisely the type of proposition on which qm casts doubt. Not
for cities, which may be said to be continuously measured, but certainly
for elementary particles.
>We know that we measure one photon at city A. We know
>that we measure another at city B. We know when we measured them.
It is tricky enough to talk of this kind of thing. Important to take
care over tenses.
> We
>know from repeating the experiment a bunch of times and looking at the
>statistics of the measurement results that our choice of dial setting
>at A has a reproducible, faster-than-light effect on the measurement
>outcome at B (or vice versa).
Not exactly. The measurement result at B does not, on its own, tell us
anything about dial settings at A.
>
>And if you are trying to cast doubt on propositions like "city A is
>so-many miles from city B", then there's no point in getting wrapped
>up in intricacies like Bell's inequality.
One casts doubt on propositions like "the photon is at city A"
--
Charles Francis
George Buyanovsky
> There is no parallel between interpretations of QM
> and different theories of space and time.
>
> All the interpretations of QM are interpretations
> of the same theory. That is to say the same maths
> and the same experimental predictions.
>
> Relativity makes different predictions from Newtonian
> physics and uses different maths.
Correct, formally those parallels are not adequate. However it is not
quite correct that MWI idea has no constructive power. Quantum
computing or Feynman path integral can be considered (or interpreted)
as a constructive implication of MWI. The sensibility is not essential
for formalism but it is very helpful for human brain to comprehend
formalism to establish associative relations to see the integral
picture of nature.
George
Eric Dennis
Charles Francis <cha...@lluestfarmpoultry.co.uk> wrote
> In message <ef463682.04051...@posting.google.com>, Eric
> Dennis <ede...@princeton.edu> writes
> >Their position is
> >that things exist, and therefore are talk-about-able ("speakable" as
> >Bell would say), whether or not they have been measured. But this
> >whole sideline about whether or not "distance" is a relational concept
> >is beside the point. Unless you are trying to cast doubt on
> >propositions like "city A is so-many miles from city B", there's no
> >real issue here.
>
> That is precisely the type of proposition on which qm casts doubt. Not
> for cities, which may be said to be continuously measured, but certainly
> for elementary particles.
>
> >We know that we measure one photon at city A. We know
> >that we measure another at city B. We know when we measured them.
>
> It is tricky enough to talk of this kind of thing. Important to take
> care over tenses.
>
> > We
> >know from repeating the experiment a bunch of times and looking at the
> >statistics of the measurement results that our choice of dial setting
> >at A has a reproducible, faster-than-light effect on the measurement
> >outcome at B (or vice versa).
>
> Not exactly. The measurement result at B does not, on its own, tell us
> anything about dial settings at A.
Suppose there's a random bit stream being generated in LA and
transmitted to me in NY. Suppose I send a signal to LA which has the
effect of flipping all the subsequent bits. The new bits I receive
tell me nothing about whether or not my signal worked. They looked
random to me before, and they look random now. But when I go over to
LA and look at a record of the generated bit stream, comparing it to
my record of what I received in NY, it's clear my signal worked.
When you deny that Bell experiments prove a faster-than-light A-to-B
effect because we can't tell anything from the A-side results/settings
alone, all you are doing is denying that my signal from NY really
affected the bits in LA because I couldn't verify it in NY at the
time.
> >And if you are trying to cast doubt on propositions like "city A is
> >so-many miles from city B", then there's no point in getting wrapped
> >up in intricacies like Bell's inequality.
>
> One casts doubt on propositions like "the photon is at city A"
As rof was pointing out, who cares about the "photon"? The point of
Bell's experiment is precisely that we don't need to have any
microscopic theory, quantum or otherwise, in order to determine that
something (some normal sized clunky object) over here is affecting
some other such thing over there faster-than-light. To then claim that
through some nuanced conceptual understanding relativistic locality
can accomodate such effects, is really just to junk the entire concept
of relativistic locality.
Daryl McCullough
>>> It seems like Charles regards Bohm's theory as preposterous because it
>>> is non-local. What needs to be spelled out, which Rof has alluded to
>>> before, is that Bell's inequality has nothing to do especially with
>>> hidden variables or quantum mechanics or any other fancy thing. Bell's
>>> inequality is a simple critereon that any local theory must satisfy --
>>> where "local" is defined in a very plain way: nothing over here can
>>> affect the state of something over there faster than light -- by
>>> virtue of its locality.
I don't agree with that characterization. Quantum mechanics violates
Bell's theorem, but it doesn't involve effects propagating faster
than light.
I think that it is important to distinguish two different aspects
of a classical (nonquantum) theory such as General Relativity, both
of which are related to locality (or maybe the word should be
"causality"): (1) Local states, and (2) Local causes.
Local cause means that effects don't propagate faster than light.
What I mean by "local states" is this: You partition the universe into
a countable number of regions of finite size. Then the state
of the universe is determined by giving the state in each partition,
together with how the partitions are connected. Any classical theory
has this property: There is no nonlocal state information; if you know
what's happening in each region of spacetime, then you know all there
is to know about the universe.
Quantum mechanics violates the "local states" rule. The state of
the universe cannot be determined by knowing the states in every
region, because of correlations. Whether QM violates the "local
causes" rule depends on which interpretation of quantum mechanics
you are using.
Bell's theorem basically shows that the predictions of QM cannot
be reproduced by any physical theory with local states and local
causes. (There's actually an additional assumption, pointed out
by Pitowsky and Gudder---which is that Bell assumed that the local
states were well-behaved, mathematically. If you allow for weird
enough local states that involve nonmeasurable sets, you can actually
reproduce the predictions of QM.)
--
Daryl McCullough
Ithaca, NY
Charles Francis
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
>>>
>
>>Surely the essence of EPR is that the distance between over here and
>>over there is not a definable quantity until such time as their
>>positions have been measured. In such a case we cannot talk about over
>>there until such time as something has already affected the state.
>
>Experiments have been performed demonstrating violations of Bell's
>inequalities over distances of over four kilometres in Malvern and
>over ten kilometres in Geneva, according to Aspect's review in the
>March 1999 edition of Nature. So what we have is a polarizer, which
>had a very definite position with respect to the buildings and people
>of Geneva, and when the setting of that polarizer was changed, by
>somebody or some machine standing beside it, the results of measurements
>in a very well-defined place 10 kilometres away were affected more
>quickly than a light signal could have gotten there from the original
>polarizer.
>
>Perhaps what you are saying is that the photons involved were
>neither here nor there, or that their polarizations weren't
>localised quantities, but it's very clear that we don't have
>to worry about the geometry of Geneva becoming somehow ill-defined.
>That is, we know very well what we mean by over here and over there,
>but we may not know, and it may not be well-defined, which photon
>is heading towards which well-defined place.
Yes.
>The upshot is that even if we do imagine some breakdown of
>the property of location from the point of view of the
>photons, we still have macroscopic objects with well-defined positions
>affecting the behaviour of distant macroscopic objects with
>well-defined positions.
Yes, but it is only a correlation and there is a causal connection
because the photons come from the same source.
>Once we open the door to the idea of nonlocal interactions, the
>difficulty is no longer in finding some mechanism by which a
>particular object can affect a distant one, but in reconciling the
>fact that this happens with special relativity. That is, once we
>admit that the settings of my local device really are affecting the
>results of distant experiments, we then have to confront the seemingly
>contradictory fact that in somebody's frame of reference, the distant
>results were obtained before I even adjusted the settings.
Yes. I think the principle problem here is that it is very difficult to
think about. As you know I have a relationist interpretation of quantum
mechanics according to which background space does not exist. I think
what happens is this. What we perceive as a space is actually the net
result of many relationships which exist in matter as a result of the
interactions of particles. For a period of time the photons do not
interact with other matter, and so they do not exist in a positional
relationship with other matter. When they do come to interact they
acquire position relative to the respective apparatus. But at the same
time the photons themselves participate in the creation of space, and
have an influence on the apparatus at the same time.
I do not think the property of spin pertains only to the photon, but to
the relationship between the photon and other matter, for example the
matter of the measurement apparatus. So I think all we are doing here is
establishing that the causal connection between the photons has an
influence on the structure of space at A and B.
> All of these
>facts have to be faced by big creatures like us who always have well
>defined positions with respect to each other.
Its not so clear that we have well defined positions when outside the
light cone. In this case we have to use causal connection from the past
to define position, precisely the sort of causal connection as exists
between the photons.
Regards
--
Charles Francis
r...@maths.tcd.ie
>Eric Dennis says...
>>>> It seems like Charles regards Bohm's theory as preposterous because it
>>>> is non-local. What needs to be spelled out, which Rof has alluded to
>>>> before, is that Bell's inequality has nothing to do especially with
>>>> hidden variables or quantum mechanics or any other fancy thing. Bell's
>>>> inequality is a simple critereon that any local theory must satisfy --
>>>> where "local" is defined in a very plain way: nothing over here can
>>>> affect the state of something over there faster than light -- by
>>>> virtue of its locality.
>I don't agree with that characterization. Quantum mechanics violates
>Bell's theorem, but it doesn't involve effects propagating faster
>than light.
This is a widespread misconception. What is actually the case is that
any theory which violates Bell's inequalities is nonlocal, and
quantum mechanics is not exempt. Whether the effects propagate
or not is debatable and perhaps experimentally addressable (we
could imagine trying to shield the effect).
>I think that it is important to distinguish two different aspects
>of a classical (nonquantum) theory such as General Relativity, both
>of which are related to locality (or maybe the word should be
>"causality"): (1) Local states, and (2) Local causes.
>Local cause means that effects don't propagate faster than light.
>What I mean by "local states" is this: You partition the universe into
>a countable number of regions of finite size. Then the state
>of the universe is determined by giving the state in each partition,
>together with how the partitions are connected. Any classical theory
>has this property: There is no nonlocal state information; if you know
>what's happening in each region of spacetime, then you know all there
>is to know about the universe.
There is a "state of knowledge" versus "state of the system" subtlety
here. If we talk about states of knowledge, then there can be entangled
states in classical systems. For example, I might know that my pen
is in one of my two pockets, but not know which pocket. This is
nonlocal information because finding out what's in one pocket would
tell me something about what's in the other.
>Quantum mechanics violates the "local states" rule. The state of
>the universe cannot be determined by knowing the states in every
>region, because of correlations.
This is tied in to the question of to what extent the wavefunction
represents knowledge. The knowledge that "my pen is in one of
two pockets" is not local information, and cannot be
expressed in the form P_1 AND P_2 AND P_3 AND ... where each P_i
is a statement of the form "The state of affairs in such and such
a region is so and so." Instead, it looks more like P_1 XOR P_2.
So, "nonlocal states" arise even without quantum mechanics,
provided they are considered states of knowledge. The difference
between this classical nonlocality of information and quantum
nonlocality of the wavefunction is that with quantum nonlocality,
the results of local experiments depend on the settings of
distant measuring devices.
>Whether QM violates the "local
>causes" rule depends on which interpretation of quantum mechanics
>you are using.
As I said before, everybody who likes to push their own interpretation
of quantum mechanics pretends that they have an interpretation in
which everything is local, but having a local interpretation is not
a virtue because nonlocality is an experimental fact of life. That
is, it has been demonstrated in experiments that the setting of
one instrument can affect the results obtained on a distant one,
during the time when the instruments are spacelike separated.
>Bell's theorem basically shows that the predictions of QM cannot
>be reproduced by any physical theory with local states and local
>causes.
As Eric clarified, the inequalities and their derivation make no
reference to quantum mechanics. They are a set of conditions that
any local theory must satisfy, where "local" refers to the experimental
predictions of the theory (in such and such an experiment you will
get such and such a result) and not to the mathematical formalism,
which is where ideas like "nonlocal states" reside.
The correct order to apprehend the situation with regard to Bell's
inequalities is the following. First, we read Bell's theorem
and learn that if any theory satisfies the condition of locality
(meaning that the results of a measurement do not depend on
the settings of distant measuring devices), then the predictions
of that theory must satisfy certain inequalities. Then, having
finished reading Bell's theorem, we turn our attention to quantum
mechanics and ask if the predictions therein satisfy those
inequalities. They do not. Then we draw from that whatever conclusions
seem reasonable.
Instead of following this procedure, people usually hear a
different and incorrect story: That Bell's theorem says that
no local hidden variables theory can reproduce the predictions
of quantum mechanics. That's not the theorem; it's a corollary.
Quoting it as though it were the theorem makes people misunderstand
the situation, because they begin to think that quantum mechanics
has some special status making it exempt from the reasoning in
Bell's theorem.
In fact, it is conceivable that somebody could understand Bell's
inequalities and do the experiment and confirm that they are violated
and understand the significance of this fact perfectly
without ever knowing anything about quantum mechanics (although
it's unlikely that it would occur to the individual what experiment
should be performed).
>(There's actually an additional assumption, pointed out
>by Pitowsky and Gudder---which is that Bell assumed that the local
>states were well-behaved, mathematically. If you allow for weird
>enough local states that involve nonmeasurable sets, you can actually
>reproduce the predictions of QM.)
It's not a property of local states that are involved, but a deformation
of probability theory. To give an example of how far from normalcy
you have to get, just after the part in "Quantum Probability"
where he explains how his generalised probability lets "reality,
hidden variables, and the predictions of quantum mechanics live in
harmony together," his theorem 5.7 shows how to construct one
of his extended generalised probability spaces in which A and B
are events, the probability of A is 1/2, the probability of B
is 1/2, and the probability of A AND B is 1.
R.
Alan Forrester
r...@maths.tcd.ie wrote in message news:<c8dtu3$1ajv$1...@lanczos.maths.tcd.ie>...
> >>>> It seems like Charles regards Bohm's theory as preposterous because it
> >>>> is non-local. What needs to be spelled out, which Rof has alluded to
> >>>> before, is that Bell's inequality has nothing to do especially with
> >>>> hidden variables or quantum mechanics or any other fancy thing. Bell's
> >>>> inequality is a simple critereon that any local theory must satisfy --
> >>>> where "local" is defined in a very plain way: nothing over here can
> >>>> affect the state of something over there faster than light -- by
> >>>> virtue of its locality.
>
> >I don't agree with that characterization. Quantum mechanics violates
> >Bell's theorem, but it doesn't involve effects propagating faster
> >than light.
>
> This is a widespread misconception. What is actually the case is that
> any theory which violates Bell's inequalities is nonlocal, and
> quantum mechanics is not exempt. Whether the effects propagate
> or not is debatable and perhaps experimentally addressable (we
> could imagine trying to shield the effect).
No, that's not true, as can be seen by actually looking closely at
what Bell's Theorem says.
http://xxx.lanl.gov/abs/quant-ph/9906007
Bell's Theorem states that if measurement outcomes are described by
local stochastic processes that select a single outcome represented by
a c-number from some set of c-numbers then the results can only
exhibit the correlations given by Bell's formula. However, in quantum
mechanics the outcomes of experiments are not described by c-numbers,
but instead by Hermitian operators. The difference between these two
can be seen by making the fairly obvious observation that operators
don't necessarily commute while c-numbers do.
What do these Hermitian operators represent? Well, they can't describe
a single classical universe since such a universe can always be
dexcribed in terms of c-numbers. Instead they represent a richer
structure which contains many copies of the universe we live in, which
sometimes interact. This structure is called the multiverse (of
course, this is the Many Worlds Interpretation of Quantum Mechanics).
We can observe interactions between these other universes in single
particle interference experiments and EPR experiments but usually it
is rather difficult because of decoherence.
See
http://www.qubit.org/people/david/index.php?path=Parallel%20Universes
and
http://www.quiprocone.org/Protected/DD_lectures.htm
Now how does the MWI account for the EPR correlations? Well, if it's
an experiment on electron spin say each of the entangled electrons are
present in two versions - a spin-up version and a spin-down version.
The electrons interact with the measuring devices and afterwards there
are two non-interacting versions of each measuring device - a spin-up
version and a spin-down version. The two versions of the first
measuring device send a message to the other version of the measuring
device and when the second measuring device receives them there is a
brief interaction that sorts the outcomes so that they pair up in the
appropriate way.
http://xxx.lanl.gov/abs/quant-ph/0003146
So the MWI explains EPR without non-locality. As far as I can tell,
none of the other interpretations allow such an explanation.
I should comment briefly on the statistical interpretation, which
purports to only describe ensembles of physical systems. This doesn't
make much sense. Either it is simply another hidden variables theory
or it denies that there is any such thing as a factual description of
any quantum system in which case it is anti-realistic and since there
is a tenable realistic interpretation - the MWI- it is at an enormous
disadvantage. Finally, the MWI is not susceptible to Occam's Razor,
which actually applies to assumptions about the world and how we ought
to adopt the smallest set os assumptions that explains the facts. The
MWI adoptys fewer and less problematic assumptions than any other
interpretation, just the standard formalism without the collapse
postulate.
Alan Forrester
r...@maths.tcd.ie
>In message <c7ujqf$209s$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>The upshot is that even if we do imagine some breakdown of
>>the property of location from the point of view of the
>>photons, we still have macroscopic objects with well-defined positions
>>affecting the behaviour of distant macroscopic objects with
>>well-defined positions.
>Yes, but it is only a correlation and there is a causal connection
>because the photons come from the same source.
I'm not sure what is achieved by denigrating correlations; if I ignore
correlations between fire and pain because I consider correlations
mere trifling things of no real significance, then I would probably
have had a pain-filled life. Correlations seem to me to be among the
most widely accepted and most persuasive evidence anybody could
require in support of a hypothesis. Also, the fact that the photons
come from the same source can explain why the results of the
distant measurements are related, but it isn't sufficient to explain
why the deliberate choice of one experimenter can affect the distant
result.
>>.. once we
>>admit that the settings of my local device really are affecting the
>>results of distant experiments, we then have to confront the seemingly
>>contradictory fact that in somebody's frame of reference, the distant
>>results were obtained before I even adjusted the settings.
>Yes. I think the principle problem here is that it is very difficult to
>think about. As you know I have a relationist interpretation of quantum
>mechanics according to which background space does not exist.
Which leads the way to the wonderful question of what does, in fact,
exist, but, being fearful of drifting off into philosophy, we must
abandon this line of questioning and pretend we already know the
answers, lest somebody point their finger at us and call us
metaphysicists.
>I think
>what happens is this. What we perceive as a space is actually the net
>result of many relationships which exist in matter as a result of the
>interactions of particles. For a period of time the photons do not
>interact with other matter, and so they do not exist in a positional
>relationship with other matter. When they do come to interact they
>acquire position relative to the respective apparatus. But at the same
>time the photons themselves participate in the creation of space, and
>have an influence on the apparatus at the same time.
To make matters more confusing, accelerating observers will
detect particles even in a vacuum, making the very existence
of the particles which reportedly generate space dependent upon the
motion of the observer; that is, motion through space.
>I do not think the property of spin pertains only to the photon, but to
>the relationship between the photon and other matter, for example the
>matter of the measurement apparatus. So I think all we are doing here is
>establishing that the causal connection between the photons has an
>influence on the structure of space at A and B.
I don't know that it does. Clearly a teleporter would effectively
change the structure of space, in the sense that the distance from
here to Mars would be "small" if I could get there from here in a few
milliseconds, and I consider something nearby if I can get there quickly.
A teleporter can be built in principle if we have faster than light
signalling, so a variant of quantum nonlocality which really did
allow faster than light signalling, even only on a subatomic scale,
might provide a mechanism for changing spatial geometry - that is,
many nonlocal effects on a small scale would look like curvature
from far away, but with quantum nonlocality as it is, there's only
one half of an information teleporter. There's influence but not
control, so what gets transmitted are consequences but not information.
>> All of these
>>facts have to be faced by big creatures like us who always have well
>>defined positions with respect to each other.
>Its not so clear that we have well defined positions when outside the
>light cone. In this case we have to use causal connection from the past
>to define position, precisely the sort of causal connection as exists
>between the photons.
We can piece together where something was a posteriori, by
asking somebody who was standing at the place where we weren't.
If an experiment spans, for example, the width of a city, then
the inhabitants of the city, equipped with clocks and rulers
as they are, can share their results and cumulatively assure
us that the geometry of the city remained intact even over
short timescales when distant parts of the experiment were
spacelike separated.
R.
Eric Dennis
> I don't agree with that characterization. Quantum mechanics violates
> Bell's theorem, but it doesn't involve effects propagating faster
> than light.
I can't say it better than Bell. Take a look at "The Theory of Local
Beables" in Bell's compilation, "Speakable and Unspeakable in Quantum
Mechanics". The derivation of the inequality makes no reference to qm,
to "hidden variables", or to any other microscopic account of whatever
kind of apparatus using whatever kind of projectiles you choose. The
only physical assumption made in the derivation is locality. I don't
see how qm is uniquely able to escape the consequences of this
argument.
Daryl McCullough
>>What I mean by "local states" is this: You partition the universe into
>>a countable number of regions of finite size. Then the state
>>of the universe is determined by giving the state in each partition,
>>together with how the partitions are connected. Any classical theory
>>has this property: There is no nonlocal state information; if you know
>>what's happening in each region of spacetime, then you know all there
>>is to know about the universe.
>
>There is a "state of knowledge" versus "state of the system" subtlety
>here. If we talk about states of knowledge, then there can be entangled
>states in classical systems. For example, I might know that my pen
>is in one of my two pockets, but not know which pocket. This is
>nonlocal information because finding out what's in one pocket would
>tell me something about what's in the other.
Yes, I agree. But in classical physics, nonlocal states of knowledge
can be interpreted as imperfect information about an underlying local
*physical* state. Such an interpretation of quantum mechanics is not
possible (according to Bell's theorem).
>As I said before, everybody who likes to push their own interpretation
>of quantum mechanics pretends that they have an interpretation in
>which everything is local, but having a local interpretation is not
>a virtue because nonlocality is an experimental fact of life. That
>is, it has been demonstrated in experiments that the setting of
>one instrument can affect the results obtained on a distant one,
>during the time when the instruments are spacelike separated.
Well, I'm disputing that. There is no demonstration that the setting
of one instrument can affect the results obtained on a distant one.
That is an *interpretation* of the experimental results.
>>Bell's theorem basically shows that the predictions of QM cannot
>>be reproduced by any physical theory with local states and local
>>causes.
>
>As Eric clarified, the inequalities and their derivation make no
>reference to quantum mechanics.
I didn't mean to say otherwise. Bell's theorem proves an inequality
that should hold for any physical theory with local states and local
causes. The predictions of quantum mechanics violate that inequality.
Therefore, the predictions of QM cannot be reproduced by any physical
theory with local states and local causes.
>They are a set of conditions that
>any local theory must satisfy, where "local" refers to the experimental
>predictions of the theory (in such and such an experiment you will
>get such and such a result) and not to the mathematical formalism,
>which is where ideas like "nonlocal states" reside.
I disagree. The notion of "local" in Bell's theorem necessarily
involves the notion of local states.
Charles Francis
There is a fundamental difference because in the case of
bell there is a causal connection in the past. Nothing has to travel
faster than light.
>
>When you deny that Bell experiments prove a faster-than-light A-to-B
>effect because we can't tell anything from the A-side results/settings
>alone, all you are doing is denying that my signal from NY really
>affected the bits in LA because I couldn't verify it in NY at the
>time.
I do deny that the proposition makes sense until such time as you can
verify it. I think this is due to the manner in which the structure of
space-time is created, that distances really are an expression of lapsed
proper time for two way information transfer.
>
>> >And if you are trying to cast doubt on propositions like "city A is
>> >so-many miles from city B", then there's no point in getting wrapped
>> >up in intricacies like Bell's inequality.
>>
>> One casts doubt on propositions like "the photon is at city A"
>
>As rof was pointing out, who cares about the "photon"? The point of
>Bell's experiment is precisely that we don't need to have any
>microscopic theory, quantum or otherwise, in order to determine that
>something (some normal sized clunky object) over here is affecting
>some other such thing over there faster-than-light. To then claim that
>through some nuanced conceptual understanding relativistic locality
>can accomodate such effects, is really just to junk the entire concept
>of relativistic locality.
--
Charles Francis
r...@maths.tcd.ie
>r...@maths.tcd.ie wrote in message news:<c8dtu3$1ajv$1...@lanczos.maths.tcd.ie>...
>> >I don't agree with that characterization. Quantum mechanics violates
>> >Bell's theorem, but it doesn't involve effects propagating faster
>> >than light.
>>
>> This is a widespread misconception. What is actually the case is that
>> any theory which violates Bell's inequalities is nonlocal, and
>> quantum mechanics is not exempt. Whether the effects propagate
>> or not is debatable and perhaps experimentally addressable (we
>> could imagine trying to shield the effect).
>No, that's not true, as can be seen by actually looking closely at
>what Bell's Theorem says.
>http://xxx.lanl.gov/abs/quant-ph/9906007
This appears to be an illustration of what David Deutsch says,
rather than what Bell says. Perhaps a better place to find out
about Bell's inequalities would be to read Speakable and Unspeakable
in Quantum Mechanics, which is a collection of very clearly written
and very sensible papers by Bell.
>Bell's Theorem states that if measurement outcomes are described by
>local stochastic processes that select a single outcome represented by
>a c-number from some set of c-numbers then the results can only
>exhibit the correlations given by Bell's formula. However, in quantum
>mechanics the outcomes of experiments are not described by c-numbers,
>but instead by Hermitian operators.
This seems like gibberish to me. Clearly you are trying to push
the many worlds interpretation; remember that in the one real world
which you inhabit, measurement results *are* "c-numbers." Try it;
take some numerical measurement results published by experimentalists
and see if they commute, using your pocket calculator.
The Hermitian operators live in the mathematical representation of
the world; they are not the real world itself. This mistake, in
various forms, is very commonly made by otherwise intelligent people,
and not just in physics. There's a group of people who call their
field "general semantics" who use the expression "the map is not
the territory" to try to help people avoid making this exact mistake.
Alfred Korzybski coined the expression "mental hygiene" and used
it to refer to a system he developed to try to prevent the "unsanity"
that comes from an accumulation of such mental problems.
The many worlds interpretation is a meme which has spread very
effectively throughout the physics community, and which infected
me as well in the past. Indeed, it has become mainstream within
the quantum computation community, and probably a large chunk of
the readership of s.p.r. ascribe to it. However, it is fundamentally
based upon the (incorrect) idea that the real word is actually
the same thing as the mathematical representation used. It
also has romantic overtones which give the true believer a
license to daydream about parallel worlds and has just enough of
a touch of metaphysics to let the believers feel that they have
found some deep truth about the world. It's enormously attractive
to those physicists who think about conceptual issues just a little
bit more than the average physicist, so the people who advocate
many worlds can often appear more competent than the conservative
majority.
>What do these Hermitian operators represent? Well, they can't describe
>a single classical universe since such a universe can always be
>dexcribed in terms of c-numbers. Instead they represent a richer
>structure which contains many copies of the universe we live in, which
>sometimes interact.
And probability distributions represent not a single outcome but
a distribution of outcomes, so when I toss a coin, the universe
splits into two universes, one for each result. After all, the
probability distibution and the real world are the same thing,
aren't they?
>This structure is called the multiverse (of
>course, this is the Many Worlds Interpretation of Quantum Mechanics).
>We can observe interactions between these other universes in single
>particle interference experiments and EPR experiments but usually it
>is rather difficult because of decoherence.
>See
>http://www.qubit.org/people/david/index.php?path=Parallel%20Universes
>and
>http://www.quiprocone.org/Protected/DD_lectures.htm
The supposition is that the mathematical representation of the
world given by quantum mechanics is so perfect that any
information missing from the model must also be missing from
the real world. What is missing from the formalism of quantum
mechanics is the fact that experiments have definite outcomes,
rather than distributions of outcomes. We then imagine a distribution
of outcomes with a corresponding distribution of observers and
notice that none of the observers in the distribution can see
outside of their own world. This is compatible with our observation
of a single world, so the fact that I see a single outcome can't
be taken as evidence that there is only a single universe. After that,
we admit to ourselves that it is *possible* that there are
many worlds.
Now, we should realise that, although this is possible, it has
nothing to do with quantum mechanics. We were always free to
imagine other universes with slightly different configurations of
matter from ours. It was always true that the observers in those
universes would only see a single universe, as we do. Quantum
mechanics has just given people an excuse to indulge in these
fantasies and a community of back-patters to reassure them
that it's sensible.
However, it doesn't hold up to scrutiny. Consider, for example,
the role of the observable operators in the many worlds interpretation.
Where do they come from? They are inherited from the Copenhagen
interpretation, where, for each observable operator, there was
a corresponding experiment, consisting of a configuration of matter
(a laboratory and experimental apparatus) which was *outside* of
the quantum mechanical system being investigated and represented
by a Hilbert space.
Now if we decide to have a universal wavefunction, there is no
longer a big laboratory encompassing the system; no set of experiments
and so no corresponding observables. Oh dear; many worlds begins
to look rather structureless because it asserts that the only "real"
thing is the wavefunction, but that's just a vector in an abstract
space. We want the observables back so we turn to the decoherence
people and implore them to give us some justification for using
the Copenhagen observables. They claim that they can do that, by
giving a formula to show which observables will decohere and which
won't, using just the things which really exist, namely the
wavefunction and the Hamiltonian.
Unfortunately, it works too well. We have to plug observables into
the formula to check if they decohere, so what we find ourselves
doing is plugging in the observables which were inherited from
Copenhagen, and giving them the thumbs up when they decohere. However,
those observables are not the only ones which will be compatible
with the Hamiltonian that you used in the decoherence formula; in
fact, there will, in general, be an infinite number of sets of
very different looking operators which decohere, and nothing to
select out a preferred set.
It should have been clear in advance that this was going to happen,
because if you assert that all the information in the universe
is encoded in the Hamiltonian and the wavefunction, then any
two systems with the same Hamiltonian spectrum are going to
be isomorphic, and many physically distinguishable systems
have the same Hamiltonian spectrum.
>Now how does the MWI account for the EPR correlations? Well, if it's
>an experiment on electron spin say each of the entangled electrons are
>present in two versions - a spin-up version and a spin-down version.
>The electrons interact with the measuring devices and afterwards there
>are two non-interacting versions of each measuring device - a spin-up
>version and a spin-down version. The two versions of the first
>measuring device send a message to the other version of the measuring
>device and when the second measuring device receives them there is a
>brief interaction that sorts the outcomes so that they pair up in the
>appropriate way.
>http://xxx.lanl.gov/abs/quant-ph/0003146
>So the MWI explains EPR without non-locality. As far as I can tell,
>none of the other interpretations allow such an explanation.
Yet another insistence that some interpretation or other is great
because it allows us to keep supposing that the world is local. Never
mind that experiments have confirmed that the single world we live
in is nonlocal. I could also, by asserting that "what's real" is
configuration space, rather than the three-dimensional space we
observe, find a "local" interpretation of quantum mechanics, but
I wouldn't expect anybody to take me seriously, and I don't take
many-worlders seriously when they say that it's ok that our
world is nonlocal, because what's truly important is that the
"multiverse" is local. Faced with an unpleasant real world which
doesn't conform to the "no action at a distance" prejudice, they
opt instead for the mathemagical multiverse which does conform,
if only in an algebraic kind of way.
>Finally, the MWI is not susceptible to Occam's Razor,
>which actually applies to assumptions about the world and how we ought
>to adopt the smallest set os assumptions that explains the facts.
Unfortunately, it does require one to confuse the world itself with
the quantum mechanical formalism.
>The
>MWI adoptys fewer and less problematic assumptions than any other
>interpretation, just the standard formalism without the collapse
>postulate.
Or the observables.
R.
Eric Dennis
> > any theory which violates Bell's inequalities is nonlocal, and
> > quantum mechanics is not exempt. Whether the effects propagate
> > or not is debatable and perhaps experimentally addressable (we
> > could imagine trying to shield the effect).
>
> No, that's not true, as can be seen by actually looking closely at
> what Bell's Theorem says.
>
> http://xxx.lanl.gov/abs/quant-ph/9906007
>
This is a paper by David Deutsch. Here are some old remarks I made
about it.
Deutsch basically just uses a Heisenberg representation
(operators evolve, states stay constant) to describe a set of n
qubits.
Each qubit gets its own set of Heisenberg Operators (HOs) which evolve
any
time a gate acts on that qubit. Since, the HOs for a given qubit are
unaffected by any gate which does not act on that qubit, there appears
to
be some notion of locality. However, each HO itself grows in size
(each HO
is a 2^n x 2^n matrix) as the _total_ number of qubits grows. It is
not
clear at all that the HOs are themselves local objects, other than in
the
superficial sense of simply being assigned to individual qubits.
In Deutsch's analysis of the EPR experiment, he does not contemplate
the
two crucial events--which are the acts of _measuring_ the two spins
once
they arrive at their respective detectors. Instead he maintains a
coherent
superposition, and physically carries them back together. This is
simply not the situation relevant to Bell's argument that QM
predictions are non-local. Only when they are measured separately (in
a space-like separated
fashion), and the measurement results are compared, is the
non-locality
manifest. Obviously if those measurements aren't made in the first
place,
there's nothing to talk about.
> Bell's Theorem states that if measurement outcomes are described by
> local stochastic processes that select a single outcome represented by
> a c-number from some set of c-numbers then the results can only
> exhibit the correlations given by Bell's formula. However, in quantum
> mechanics the outcomes of experiments are not described by c-numbers,
> but instead by Hermitian operators. The difference between these two
> can be seen by making the fairly obvious observation that operators
> don't necessarily commute while c-numbers do.
The outcomes of experiments are indeed described by c-numbers (in fact
real numbers) in qm and in reality. Have you ever seen a lock-in that
displays Pauli matrices? Bell's theorem doesn't pay any attention to
the theoretical structure that gives to the real numbers. Any
theoretical structure will do, so long as it is local, then it
satisfies the inequality. See Bell's "The Theory of Local Beables".
> Now how does the MWI account for the EPR correlations? Well, if it's
> an experiment on electron spin say each of the entangled electrons are
> present in two versions - a spin-up version and a spin-down version.
> The electrons interact with the measuring devices and afterwards there
> are two non-interacting versions of each measuring device - a spin-up
> version and a spin-down version. The two versions of the first
> measuring device send a message to the other version of the measuring
> device and when the second measuring device receives them there is a
> brief interaction that sorts the outcomes so that they pair up in the
> appropriate way.
Can you be more specific? What message? Sent when? How fast? Are you
talking about a message that tells the other device when/how to
bifurcate?
Charles Francis
writes
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
>>In message <c7ujqf$209s$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>
>>>The upshot is that even if we do imagine some breakdown of
>>>the property of location from the point of view of the
>>>photons, we still have macroscopic objects with well-defined positions
>>>affecting the behaviour of distant macroscopic objects with
>>>well-defined positions.
>
>>because the photons come from the same source.
>
>I'm not sure what is achieved by denigrating correlations;
I'm not denigrating them. I suggest that this is a correlation, not a
magical ftl effect.
>. Also, the fact that the photons
>come from the same source can explain why the results of the
>distant measurements are related, but it isn't sufficient to explain
>why the deliberate choice of one experimenter can affect the distant
>result.
No. I think this is the hardest of the quantum paradoxes to explain. In
fact I think we need to combine qed with gtr, and then we will be able
to produce a mathematical explanation, showing precisely what the
relationship of spin is to the structure of space-time. I doubt it will
ever be conceptually easy.
>>>.. once we
>>>admit that the settings of my local device really are affecting the
>>>results of distant experiments, we then have to confront the seemingly
>>>contradictory fact that in somebody's frame of reference, the distant
>>>results were obtained before I even adjusted the settings.
>
>>Yes. I think the principle problem here is that it is very difficult to
>>think about. As you know I have a relationist interpretation of quantum
>>mechanics according to which background space does not exist.
>
>Which leads the way to the wonderful question of what does, in fact,
>exist, but, being fearful of drifting off into philosophy, we must
>abandon this line of questioning and pretend we already know the
>answers, lest somebody point their finger at us and call us
>metaphysicists.
No, we must merely learn to be precise and scientific about the
question. The non-existence of background space is a very different
question from the question of existence at all. And rather than drift
off into philosophy we must formalise and mathematise it, make it a
useful tool in studying the universe, rather than the source of endless
waffle it tends to become.
>>I think
>>what happens is this. What we perceive as a space is actually the net
>>result of many relationships which exist in matter as a result of the
>>interactions of particles. For a period of time the photons do not
>>interact with other matter, and so they do not exist in a positional
>>relationship with other matter. When they do come to interact they
>>acquire position relative to the respective apparatus. But at the same
>>time the photons themselves participate in the creation of space, and
>>have an influence on the apparatus at the same time.
>
>To make matters more confusing, accelerating observers will
>detect particles even in a vacuum, making the very existence
>of the particles which reportedly generate space dependent upon the
>motion of the observer; that is, motion through space.
I don't think that is really a problem. Energy is being supplied to
cause the acceleration. It is bound to have an affect.
>
>>I do not think the property of spin pertains only to the photon, but to
>>the relationship between the photon and other matter, for example the
>>matter of the measurement apparatus. So I think all we are doing here is
>>establishing that the causal connection between the photons has an
>>influence on the structure of space at A and B.
>
>I don't know that it does. Clearly a teleporter would effectively
>change the structure of space, in the sense that the distance from
>here to Mars would be "small" if I could get there from here in a few
>milliseconds
That sounds like a a reductio ad absurdum argument that no such thing
can exist.
>, and I consider something nearby if I can get there quickly.
>A teleporter can be built in principle if we have faster than light
>signalling,
But if the structure of space is dependent on the speed of signalling,
as special relativity suggests, then that is reductio ad absurdum too.
>
>>> All of these
>>>facts have to be faced by big creatures like us who always have well
>>>defined positions with respect to each other.
>
>>Its not so clear that we have well defined positions when outside the
>>light cone. In this case we have to use causal connection from the past
>>to define position, precisely the sort of causal connection as exists
>>between the photons.
>
>We can piece together where something was a posteriori, by
>asking somebody who was standing at the place where we weren't.
>If an experiment spans, for example, the width of a city, then
>the inhabitants of the city, equipped with clocks and rulers
>as they are, can share their results and cumulatively assure
>us that the geometry of the city remained intact even over
>short timescales when distant parts of the experiment were
>spacelike separated.
The results can only be shared after the event, so the structure only
gains existence after the event. At which point it again only becomes
possible to establish a correlation between the experiments, not a
causal ftl effect.
--
Charles Francis
Daryl McCullough
>I can't say it better than Bell. Take a look at "The Theory of Local
>Beables" in Bell's compilation, "Speakable and Unspeakable in Quantum
>Mechanics".
I did, just last night.
>The derivation of the inequality makes no reference to qm,
>to "hidden variables", or to any other microscopic account of whatever
>kind of apparatus using whatever kind of projectiles you choose. The
>only physical assumption made in the derivation is locality. I don't
>see how qm is uniquely able to escape the consequences of this
>argument.
I disagree. I think that Bell's notion of "locality" assumes the
existence of local hidden variables. I believe that his reasoning
basically amounts to the following:
Setup:
Assume that we have detectors D1 and D2 that are spatially
distant. Assume that each detector has a continuous range
of possible settings. Assume that detection is binary: the
result is either +1 or -1. Assume that the settings are
chosen independently, and that a subsequent detection attempt
is made, and that the timing is such that it is impossible
for a light signal to pass from one detector to the other.
For each detection event, let A = result at detector D1,
and B = result at detector D2. Perform the experiment
many times, and compute <AB>(s1,s2) = the product of A
and B, averaged over all experiments for which the setting
of D1 is s1 and the setting of D2 is s2.
Bell's locality assumption:
<AB>(s1,s2) = sum over alpha of P(alpha) F1(alpha,s1) F2(alpha,s2)
where
alpha = some unknown parameter
P(alpha) = some unknown probability distribution
F1(alpha,s1), F2(alpha,s2) = unknown functions
It seems to me that alpha is the hidden variable,
and that assuming that the correlation has this form amounts to
what I was calling the assumption of "local states".
r...@maths.tcd.ie
>r...@maths.tcd.ie says...
>>>What I mean by "local states" is this: You partition the universe into
>>>a countable number of regions of finite size. Then the state
>>>of the universe is determined by giving the state in each partition,
>>>together with how the partitions are connected. Any classical theory
>>>has this property: There is no nonlocal state information; if you know
>>>what's happening in each region of spacetime, then you know all there
>>>is to know about the universe.
>>
>>There is a "state of knowledge" versus "state of the system" subtlety
>>here. If we talk about states of knowledge, then there can be entangled
>>states in classical systems. For example, I might know that my pen
>>is in one of my two pockets, but not know which pocket. This is
>>nonlocal information because finding out what's in one pocket would
>>tell me something about what's in the other.
>Yes, I agree. But in classical physics, nonlocal states of knowledge
>can be interpreted as imperfect information about an underlying local
>*physical* state. Such an interpretation of quantum mechanics is not
>possible (according to Bell's theorem).
I can see this can only be settled with a rendition of the theorem,
which I provide below.
>>They are a set of conditions that
>>any local theory must satisfy, where "local" refers to the experimental
>>predictions of the theory (in such and such an experiment you will
>>get such and such a result) and not to the mathematical formalism,
>>which is where ideas like "nonlocal states" reside.
>I disagree. The notion of "local" in Bell's theorem necessarily
>involves the notion of local states.
Ok, so here's the version of the theorem which I find the easiest
to fit inside my head all at once (if anybody knows a simpler
one I'd be pleased to hear about it):
There are two experimenters separated by a distance so large that
a light signal cannot reach one experimenter from the other during
the time in which they are performing measurements. One could
imagine that each can see the other on a television screen, and
are broadcasting while they experiment, so that each experimenter
performs his measurements, makes his notes, and then watches the
television to see the other experimenter doing the same procedure,
knowing that the television signals which he is now watching were
travelling towards him across the vastness of space while he was
doing his experiment a few moments before.
Each experimenter recieves N particles and performs one of
three experiments, A, B or C, on each particle. Each of
the experiments gives either +1 or -1 as an answer. The
experimenter decides for himself which experiment he will
perform on which particle, and deliberately doesn't decide
which to do until just before the particle arrives.
We have fairly good reasons to believe that, if the two
experimenters perform the same experiment (A, B or C), they will
get opposite results (one will get +1 and the other will get -1).
The reasons are both theoretical (conservation laws) and
experimental (whenever it has been tried it has in fact turned
out to be true, and it has been tried millions of times).
The condition of locality which is used here is the condition
that, whatever the results of a given experiment depends upon,
it does not depend upon the choice made by the distant experimenter
about which experiment (A, B, or C) he will perform. That is,
locality means that neither experimenter should find that the results
which he gets have been affected by the choices of the other
experimenter, which he sees on the television a few minutes after
he does the experiment.
We say that an experimental result, X, "depended upon" a choice
from the set {A, B, C} by an experimenter if it can be shown (or
statistically inferred) that, had the experimenter made a different
choice, X would have had a different value. In such a circumstance
we can draw up a table like this:
choice | A B C
|---------
value of X | +1 -1 -1
or at least we could do so if we knew what the various results
would have been in the various circumstances.
When we say that X did not depend on a choice, it means that X would
have had the same value that it actually did regardless of what
choice was made, and we can draw a table that looks like:
choice | A B C
|---------
value of X | +1 +1 +1
where it has been assumed that the result was +1. Drawing
such a table isn't very interesting or worthwhile, but it
is important to realise that the statement that a
result doesn't depend on a choice means that such a table
can be drawn up and is accurate.
Now, back to the experimenters. If experimenter 1 is to declare
that one of his results depended on his own choice of which
experiment to do, but did not depend on the experimenter 2's
choice of which to do, then that means that he can draw
up a table that looks like:
choice of experimenter 1 | A B C
---------------------------|---------
choice A| +1 -1 -1
of B| +1 -1 -1
experimenter 2 C| +1 -1 -1
or at least he could if he knew what the other results would have
been had he made the other choices. Since the choice of experimenter
2 doesn't affect the result, the table can be considered to be
specified by any one of its rows.
Now we add in the bit about the experimenters getting opposite
results when they choose the same experiment, and we realise that
if we suppose that the result of an experimenter depends on
his own choice of what experiment to do, but doesn't depend on the
choice of the other experimenter, then we can draw a pair of tables
like:
1's choice| A B C 2's choice| A B C
|--------- |---------
result | +1 -1 -1 result | -1 +1 +1
or at least we could etc. At least, the statements above about
what depends on what are equivalent to the statement that such
tables can be drawn up.
Then we can categorize the N particles according to the
results that would be obtained upon a measurement of
each of A, B and C, by experimenter 1, knowing that that
fixes the result that experimenter 2 would get. For an
individual particle, each experimenter can, having watched
the other experimenter on the television, partially
reconstruct the tables for each particle. That is, suppose
experimenter 1 performed experiment A and got +1 and
experimenter 2 performed experiment B and got +1. Then
the tables can be reconstructed thus far:
1's choice| A B C 2's choice| A B C
|--------- |---------
result | +1 -1 ? result | -1 +1 ?
That is, experimenter 1 can say to himself: "Well he
did experiment B and got +1, so if I had done experiment
B I would have gotten -1." For him to be wrong on this
point, it would have to be the case that, had he
done experiment B instead of A, he would have gotten
+1 (obviously). That would mean that, had he done experiment B,
experimenter 2 would have to have gotten -1, because the two
experimenters have to get opposite results when they do the same
experiment.
So, either experimenter 1 is correct in drawing
up his table (the table on the left), *or* the result of
experimenter 2 depended on the choice of experimenter 1.
Similarly, experimenter 2 has the same justification
for drawing up the table on the right.
So the two experimenters draw up partially reconstructed
tables for each pair of particles. Now, we don't know
what was in column C in the tables above, but what we
do know is that it was +1 in one table and -1 in the
other. That is, the full table for experimenter 1 was
either:
1's choice| A B C
|---------
result | +1 -1 +1
or
1's choice| A B C
|---------
result | +1 -1 -1
There were N pairs of particles altogether. We can call the number
of pairs for which the first table above was correct N_3, and draw
a table which assigns similar symbols to the numbers of pairs of
particles with each table:
1's choice| A B C 2's choice| A B C
|--------- |---------
N_1 | +1 +1 +1 | -1 -1 -1
N_2 | +1 +1 -1 | -1 -1 +1
N_3 | +1 -1 +1 | -1 +1 -1
N_4 | +1 -1 -1 | -1 +1 +1
N_5 | -1 +1 +1 | +1 -1 -1
N_6 | -1 +1 -1 | +1 -1 +1
N_7 | -1 -1 +1 | +1 +1 -1
N_8 | -1 -1 -1 | +1 +1 +1
where N_1 + ... + N_8 = N
The example given above, where experimenter 1 performed experiment
A and got +1 for a result, and experimenter 2 performed experiment B
and got +1 as a result, would be a contribution to either N_3 or N_4 (we
don't know which because we don't know what result would have been
obtained upon a measurement of C, though we know it would have been
either +1 or -1).
Bell's inequality is: N_3+N_4 <= N1+N3 + N4+N7
which is trivial because all of these are non negative integers,
denoting as they do numbers of particles involved in the
experiments.
The numbers N_3 + N_4 and so on, cannot be measured directly,
since each experimenter can only make one measurement on the
particles which arrive, but they can be estimated in the following
way. Take the number of particles for which the
situation above arose (A +1, B +1), and divide it by the fraction
of experiments for which experiments A and B were performed by
experimenters 1 and 2 respectively. If the choice of which
experiment to do does not affect which table is associated with
that particle, then this will provide a fair sampling - that
is, if the pair of experiments (A,B) was done one nineth of the
time, and 500 of those pairs of experiments yielded +1 for
both, then we infer that, had the pair (A,B) been done all
of the time, there would have been about 9*500 incidents, and
so N_3 + N_4 is about 9*500.
We can make estimates of N1+N3 in a similar way by counting
how often experimenter 1 performs experiment A and gets +1
while experimenter 2 performs C and gets -1. Something similar
works for N4+N7.
Notice that this inference can only systematically fail (as
opposed to failing because of a statistical fluctuation) if
the choice of experimenter B affects the appropriate table
for experimenter A, since the choice of experimenter A is
already taken into account in his table. That is, it can
only fail if experimenter B's choice affects the result
of experimenter A, or vice versa.
For the sake of completeness, I'll add that some people
have historically objected to the use of "counterfactuals",
claiming that this argument makes too much use of "What
would have happened if such and such an experimenter had chosen
something else." In each case, where such "facts" were used in the
proof, there was a good reason. For example, it was supposed that,
had C been performed, either +1 or -1 would have been obtained.
This statement was made because the experiment C has been done many
times before and either +1 or -1 have been obtained in each case.
Such inferences are the stuff of science. That is, this objection,
while self-consistent, is rather too powerful since it rejects
the kind of reasoning used in science all the time. For example,
a person who refuses to accept arguments involving counterfactuals
would not accept as evidence of faster than light signalling an
experiment in which the message "This is a faster than light signal"
was sent at one event and received at a distant destination, because
they would have to object that it is not known, or reasonable to
discuss, what would have been received if a different message had
been sent, and so could not accept the conclusion that the contents
of the sent message "caused" the contents of the received message.
Also notice that during the entire proof of the inequalities, the
things referred to were the experimenters, their choices and
experimental results, they tables they draw up and so on. No
mention is made of any theoretical framework or even of any
theory making the predictions. Essentially, the theorem is not
about theories at all, but says that if certain experimental
results are obtained, namely counts of +1's and -1's which
violate the inequalities, then the choices of one experimenter
affect the results of a distant one.
>There is no demonstration that the setting
>of one instrument can affect the results obtained on a distant one.
>That is an *interpretation* of the experimental results.
I think this is where I say that this appears to be incorrect,
unless you're talking about a loophole.
The experiments were done to look for a evidence that the
setting of one device can affect the results obtained on
a distant one, and the evidence was certainly found. I'll
mention quantum mechanics for the first time in this post
to point out that the role it had was to suggest what the
experiments A, B and C should be.
R.
CobaltFjord
Q12 Is many-worlds a local theory?
The simplest way to see that the many-worlds metatheory is a local theory is to
note that it requires that the wavefunction obey some relativistic wave
equation, the exact form of which is currently unknown, but which is presumed
to be locally Lorentz invariant at all times and everywhere. This is equivalent
to imposing the requirement that locality is enforced at all times and
everywhere. Ergo many-worlds is a local theory.
Another way of seeing this is examine how macrostates evolve. Macrostates
descriptions of objects evolve in a local fashion. Worlds split as the
macrostate description divides inside the light cone of the triggering event.
Thus the splitting is a local process, transmitted causally at light or
sub-light speeds. (See "Does the EPR experiment prohibit locality?" and "When
do worlds split?")
Q32
Does the EPR experiment prohibit locality?
What about Bell's Inequality?
The EPR experiment is widely regarded as the definitive gedanken experiment for
demonstrating that quantum mechanics is non-local (requires faster-than-light
communication) or incomplete. We shall see that it implies neither.
The EPR experiment was devised, in 1935, by Einstein, Podolsky and Rosen to
demonstrate that quantum mechanics was incomplete [E]. Bell, in 1964,
demonstrated that any hidden variables theory, to replicate the predictions of
QM, must be non-local [B]. QM predicts strong correlations between separated
systems, stronger than any local hidden variables theory can offer. Bell
encoded this statistical prediction in the form of some famous inequalities
that apply to any type of EPR experiment. Eberhard, in the late 1970s, extended
Bell's inequalities to cover any local theory, with or without hidden
variables. Thus the EPR experiment plays a central role in sorting and testing
variants of QM. All the experiments attempting to test EPR/Bell's inequality to
date (including Aspect's in the 1980s [As]) are in line with the predictions of
standard QM - hidden variables are ruled out. Here is the paradox of the EPR
experiment. It seems to imply that any physical theory must involve
faster-than-light "things" going on to maintain these "spooky"
action-at-a-distance correlations and yet still be compatible with relativity,
which seems to forbid FTL.
Let's examine the EPR experiment in more detail.
So what did EPR propose? The original proposal was formulated in terms of
correlations between the positions and momenta of two once-coupled particles.
Here I shall describe it in terms of the spin (a type of angular momentum
intrinsic to the particle) of two electrons. [In this treatment I shall ignore
the fact that electrons always form antisymmetric combinations. This does not
alter the results but does simplify the maths.] Two initially coupled
electrons, with opposed spins that sum to zero, move apart from each other
across a distance of perhaps many light years, before being separately
detected, say, by me on Earth and you on Alpha Centauri with our respective
measuring apparatuses. The EPR paradox results from noting that if we choose
the same (parallel) spin axes to measure along then we will observe the two
electrons' spins to be anti-parallel (i.e. when we communicate we find that the
spin on our electrons are correlated and opposed). However if we choose
measurement spin axes that are perpendicular to each other then there is no
correlation between electron spins. Last minute alterations in a detector's
alignment can create or destroy correlations across great distances. This
implies, according to some theorists, that faster-than-light influences
maintain correlations between separated systems in some circumstances and not
others.
Now let's see how many-worlds escapes from this dilemma.
The initial state of the wavefunction of you, me and the electrons and the rest
of the universe may be written:
|psi> = |me> |electrons> |you> |rest of universe>
on in on
Earth deep Alpha
space Centauri
or more compactly, ignoring the rest of the universe, as:
|psi> = |me, electrons, you>
And
|me> represents me on Earth with my detection apparatus.
|electrons> = (|+,-> - |-,+>)/sqrt(2)
represents a pair electrons, with the first electron travelling
towards Earth and the second electron travelling towards Alpha
Centauri.
|+> represents an electron with spin in the +z direction
|-> represents an electron with spin in the -z direction
It is an empirically established fact, which we just have to accept, that we
can relate spin states in one direction to spin states in other directions like
so (where "i" is the sqrt(-1)):
|left> = (|+> - |->)/sqrt(2) (electron with spin in -x direction)
|right> = (|+> + |->)/sqrt(2) (electron with spin in +x direction)
|up> = (|+> + |->i)/sqrt(2) (electron with spin in +y direction)
|down> = (|+> - |->i)/sqrt(2) (electron with spin in -y direction)
and inverting:
|+> = (|right> + |left>)/sqrt(2) = (|up> + |down>)/sqrt(2)
|-> = (|right> - |left>)/sqrt(2) = (|down> - |up>)i/sqrt(2)
(In fancy jargon we say that the spin operators in different directions form
non-commuting observables. I shall eschew such obfuscations.)
Working through the algebra we find that for pairs of electrons:
|+,-> - |-,+> = |left,right> - |right,left>
= |up,down>i - |down,up>
I shall assume that we are capable of either measuring spin in the x or y
direction, which are both perpendicular the line of flight of the electrons.
After having measured the state of the electron my state is described as one of
either:
|me[l]> represents me + apparatus + records having measured
and recorded the x-axis spin as "left"
|me[r]> ditto with the x-axis spin as "right"
|me[u]> ditto with the y-axis spin as "up"
|me[d]> ditto with the y-axis spin as "down"
Similarly for |you> on Alpha Centauri. Notice that it is irrelevant how we have
measured the electron's spin. The details of the measurement process are
irrelevant. (See "What is a measurement?" if you're not convinced.) To model
the process it is sufficient to assume that there is a way, which we have
further assumed does not disturb the electron. (The latter assumption may be
relaxed without altering the results.)
To establish familiarity with the notation let's take the state of the initial
wavefunction as:
|psi>_1 = |me,left,up,you>
/ \
/ \
first electron in left second electron in up state
state heading towards heading towards you on
me on Earth Alpha Centauri
After the electrons arrive at their detectors, I measure the spin along the
x-axis and you along the y-axis. The wavefunction evolves into |psi>_2:
local
|psi>_1 ============> |psi>_2 = |me[l],left,up,you[u]>
observation
which represents me having recorded my electron on Earth with spin left and you
having recorded your electron on Alpha Centauri with spin up. The index in []s
indicates the value of the record. This may be held in the observer's memory,
notebooks or elsewhere in the local environment (not necessarily in a readable
form). If we communicate our readings to each other the wavefunctions evolves
into |psi>_3:
remote
|psi>_2 ============> |psi>_3 = |me[l,u],left,up,you[u,l]>
communication
where the second index in []s represents the remote reading communicated to the
other observer and being recorded locally. Notice that the results both agree
with each other, in the sense that my record of your result agrees with your
record of your result. And vice versa. Our records are consistent.
That's the notation established. Now let's see what happens in the more general
case where, again,:
|electrons> = (|+,-> - |-,+>)/sqrt(2).
First we'll consider the case where you and I have previously arranged to
measure the our respective electron spins along the same x-axis.
Initially the wavefunction of the system of electrons and two experimenters is:
|psi>_1
= |me,electrons,you>
= |me>(|left,right> - |right,left>)|you> /sqrt(2)
= |me,left,right,you> /sqrt(2)
- |me,right,left,you> /sqrt(2)
Neither you or I are yet unambiguously split.
Suppose I perform my measurement first (in some time frame). We get
|psi>_2
= (|me[l],left,right> - |me[r],right,left>)|you> /sqrt(2)
= |me[l],left,right,you> /sqrt(2)
- |me[r],right,left,you> /sqrt(2)
My measurement has split me, although you, having made no measurement, remain
unsplit. In the full expansion the terms that correspond to you are identical.
After the we each have performed our measurements we get:
|psi>_3
= |me[l],left,right,you[r]> /sqrt(2)
- |me[r],right,left,you[l]> /sqrt(2)
The observers (you and me) have been split (on Earth and Alpha Centauri) into
relative states (or local worlds) which correlate with the state of the
electron. If we now communicate over interstellar modem (this will take a few
years since you and I are separated by light years, but no matter). We get:
|psi>_4
= |me[l,r],left,right,you[r,l]> /sqrt(2)
- |me[r,l],right,left,you[l,r]> /sqrt(2)
The world corresponding to the 2nd term in the above expansion, for example,
contains me having seen my electron with spin right and knowing that you have
seen your electron with spin left. So we jointly agree, in both worlds, that
spin has been conserved.
Now suppose that we had prearranged to measure the spins along different axes.
Suppose I measure the x-direction spin and you the y-direction spin. Things get
a bit more complex. To analyse what happens we need to decompose the two
electrons along their respective spin axes.
|psi>_1 =
|me,electrons,you>
= |me>(|+,-> - |-,+>)|you>/sqrt(2)
= |me> (
(|right>+|left>)i(|down>-|up>)
- (|right>-|left>)(|down>+|up>)
) |you> /2*sqrt(2)
= |me> (
|right>(|down>-|up>)i
+ |left> (|down>-|up>)i
- |right>(|down>+|up>)
+ |left> (|down>+|up>)
) |you> /2*sqrt(2)
= |me> (
|right,down> (i-1) - |right,up> (1+i)
+ |left,up> (1-i) + |left,down> (1+i)
) |you> /2*sqrt(2)
= (
+ |me,right,down,you> (i-1)
- |me,right,up,you> (i+1)
+ |me,left,up,you> (1-i)
+ |me,left,down,you> (1+i)
) /2*sqrt(2)
So after you and I make our local observations we get:
|psi>_2 =
(
+ |me[r],right,down,you[d]> (i-1)
- |me[r],right,up,you[u]> (i+1)
+ |me[l],left,up,you[u]> (1-i)
+ |me[l],left,down,you[d]> (1+i)
) /2*sqrt(2)
Each term realises a possible outcome of the joint measurements. The
interesting thing is that whilst we can decompose it into four terms there are
only two states for each observer. Looking at myself, for instance, we can
rewrite this in terms of states relative to *my* records/memories.
|psi>_2 =
(
|me[r],right> ( |down,you[d]> (i-1) - |up,you[u]> (i+1) )
+ |me[l],left> ( |up,you[u]> (1-i) + |down,you[d]> (1+i) )
) /2*sqrt(2)
And we see that there are only two copies of me. Equally we can rewrite the
expression in terms of states relative to your records/memory.
|psi>_2 =
(
( |me[l],left> (1-i) - |me[r],right> (i+1) ) |up,you[u]>
+ ( |me[r],right> (i-1) + |me[l],left> (1+i) ) |down,you[d]>
) /2*sqrt(2)
And see that there are only two copies of you. We have each been split into two
copies, each perceiving a different outcome for our electron's spin, but we
have not been split by the measurement of the remote electron's spin.
After you and I communicate our readings to each other, more than four years
later, we get:
|psi>_3 =
(
+ |me[r,d],right,down,you[d,r]> (i-1)
- |me[r,u],right,up,you[u,r]> (i+1)
+ |me[l,u],left,up,you[u,l]> (1-i)
+ |me[l,d],left,down,you[d,l]> (1+i)
) /2*sqrt(2)
The decomposition into four worlds is forced and unambiguous after
communication with the remote system. Until the two observers communicated
their results to each other they were each unsplit by each others'
measurements, although their own local measurements had split themselves. The
splitting is a local process that is causally transmitted from system to system
at light or sub-light speeds. (This is a point that Everett stressed about
Einstein's remark about the observations of a mouse, in the Copenhagen
interpretation, collapsing the wavefunction of the universe. Everett observed
that it is the mouse that's split by its observation of the rest of the
universe. The rest of the universe is unaffected and unsplit.)
When all communication is complete the worlds have finally decomposed or
decohered from each other. Each world contains a consistent set of observers,
records and electrons, in perfect agreement with the predictions of standard
QM. Further observations of the electrons will agree with the earlier ones and
so each observer, in each world, can henceforth regard the electron's
wavefunction as having collapsed to match the historically recorded, locally
observed values. This justifies our operational adoption of the collapse of the
wavefunction upon measurement, without having to strain our credibility by
believing that it actually happens.
To recap. Many-worlds is local and deterministic. Local measurements split
local systems (including observers) in a subjectively random fashion; distant
systems are only split when the causally transmitted effects of the local
interactions reach them. We have not assumed any non-local FTL effects, yet we
have reproduced the standard predictions of QM.
So where did Bell and Eberhard go wrong? They thought that all theories that
reproduced the standard predictions must be non-local. It has been pointed out
by both Albert [A] and Cramer [C] (who both support different interpretations
of QM) that Bell and Eberhard had implicity assumed that every possible
measurement - even if not performed - would have yielded a single definite
result. This assumption is called contra-factual definiteness or CFD [S]. What
Bell and Eberhard really proved was that every quantum theory must either
violate locality or CFD. Many-worlds with its multiplicity of results in
different worlds violates CFD, of course, and thus can be local.
Thus many-worlds is the only local quantum theory in accord with the standard
predictions of QM and, so far, with experiment.
[A] David Z Albert, Bohm's Alternative to Quantum Mechanics Scientific American
(May 1994)
[As] Alain Aspect, J Dalibard, G Roger Experimental test of Bell's inequalities
using time-varying analyzers Physical Review Letters Vol 49 #25 1804 (1982).
[C] John G Cramer The transactional interpretation of quantum mechanics Reviews
of Modern Physics Vol 58 #3 647-687 (1986)
[B] John S Bell: On the Einstein Podolsky Rosen paradox Physics 1 #3 195-200
(1964).
[E] Albert Einstein, Boris Podolsky, Nathan Rosen: Can quantum-mechanical
description of physical reality be considered complete? Physical Review Vol 41
777-780 (15 May 1935).
[S] Henry P Stapp S-matrix interpretation of quantum-theory Physical Review D
Vol 3 #6 1303 (1971)
r...@maths.tcd.ie
Charles Francis <cha...@lluestfarmpoultry.co.uk> writes:
> In message <c8ei6q$1kj4$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
>writes
>>Charles Francis <cha...@clef.demon.co.uk> writes:
>>
>>>In message <c7ujqf$209s$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>
>>>>The upshot is that even if we do imagine some breakdown of
>>>>the property of location from the point of view of the
>>>>photons, we still have macroscopic objects with well-defined positions
>>>>affecting the behaviour of distant macroscopic objects with
>>>>well-defined positions.
>>
>>>Yes, but it is only a correlation and there is a causal connection
>>>because the photons come from the same source.
>>
>>I'm not sure what is achieved by denigrating correlations;
>I'm not denigrating them. I suggest that this is a correlation, not a
>magical ftl effect.
The use of the words "only" and "magical" in the two sentences above
seem, to me at least, to be designed to communicate a certain
attitude rather than any particularly useful information. "Only a
correlation" suggests to me that you mean that correlations should
be disregarded for some unspecified reason. If "magical ftl effet"
were replaced by "instance of one experimenter's choices affecting
the results of an experiment so far away that a light signal
could not travel from the first experimenter to the distant
experiment in time to communicate the effect" in your above
sentence, then the suggestion would become incorrect, because
that is precisely what is indicated. However, that kind of
phenomenon is pretty much what most people would consider a faster
than light effect (at least I would, although I am not necessarily
convinced that there is actually anything travelling across physical
space to communicate the effect). The crucial word would appear
to be "magical", then, and I would certainly agree that I don't
think there is any magic involved. The expression "magical
ftl effect", however, seems designed to encourage the reader
to scoff at the notion that there could be a faster than light
effect at all, without giving any reason for the disparagement.
>>. Also, the fact that the photons
>>come from the same source can explain why the results of the
>>distant measurements are related, but it isn't sufficient to explain
>>why the deliberate choice of one experimenter can affect the distant
>>result.
>No. I think this is the hardest of the quantum paradoxes to explain. In
>fact I think we need to combine qed with gtr, and then we will be able
>to produce a mathematical explanation, showing precisely what the
>relationship of spin is to the structure of space-time. I doubt it will
>ever be conceptually easy.
The many worlds people seem to have convinced themselves that they
have an easy way to understand it, although I believe that that
has more to do with psychology than with physics.
>>>As you know I have a relationist interpretation of quantum
>>>mechanics according to which background space does not exist.
>>
>>Which leads the way to the wonderful question of what does, in fact,
>>exist, but, being fearful of drifting off into philosophy, we must
>>abandon this line of questioning and pretend we already know the
>>answers, lest somebody point their finger at us and call us
>>metaphysicists.
>No, we must merely learn to be precise and scientific about the
>question. The non-existence of background space is a very different
>question from the question of existence at all. And rather than drift
>off into philosophy we must formalise and mathematise it, make it a
>useful tool in studying the universe, rather than the source of endless
>waffle it tends to become.
The question of what "really" does exist, and metaphysical musings,
are relevant when we come, for the first time, to write down some
symbols from which we intend to develop a theoretical framework.
The first symbols written down must refer to something that we
have some conceptual idea of, so that we have an idea of what kind
of algebra they will satisfy.
If we think there are objects, which have positions in space which
can be specified with real numbers, then we write down x^i_o, where
o is a symbol indexing the objects, x^i is the ith coordinate,
and we know about the algebra of real numbers. The assertion that
there are, in fact, objects in space with positions representable
by numbers is a metaphysical statement, so unless somebody can
produce a proof of the assertion, anybody is free to disagree with
it without making a logical mistake. In cases of such disagreement,
the common practice among physicists is to accuse each other of
being metaphysicists, which is considered so dreadful an insult
that it tends to end the debate.
>>>I do not think the property of spin pertains only to the photon, but to
>>>the relationship between the photon and other matter, for example the
>>>matter of the measurement apparatus. So I think all we are doing here is
>>>establishing that the causal connection between the photons has an
>>>influence on the structure of space at A and B.
>>
>>I don't know that it does. Clearly a teleporter would effectively
>>change the structure of space, in the sense that the distance from
>>here to Mars would be "small" if I could get there from here in a few
>>milliseconds
>That sounds like a a reductio ad absurdum argument that no such thing
>can exist.
That wasn't exactly what I had intended; if we have a manifold
like Minkowsi space with a set of fields described by differential
equations, then a teleporter can be considered to be something
which forces the values of the fields in one region to be
equal to the values of the corresponding fields in another
region. This is equivalent to using a manifold with a different
topology, where those two regions are glued together. The set of
solutions to the differential equations on the new manifold will
be smaller than the original set of solutions, but it won't necessarily
be empty.
>>>Its not so clear that we have well defined positions when outside the
>>>light cone. In this case we have to use causal connection from the past
>>>to define position, precisely the sort of causal connection as exists
>>>between the photons.
>>
>>We can piece together where something was a posteriori, by
>>asking somebody who was standing at the place where we weren't.
>>If an experiment spans, for example, the width of a city, then
>>the inhabitants of the city, equipped with clocks and rulers
>>as they are, can share their results and cumulatively assure
>>us that the geometry of the city remained intact even over
>>short timescales when distant parts of the experiment were
>>spacelike separated.
>The results can only be shared after the event, so the structure only
>gains existence after the event.
It seems to me that it is entirely a matter of my own preference
whether I consider events outside my past light cone to exist or
not. An alien species living on a distant world might be surprised
to learn that their structure only gained existence after I
first heard about them; they might even disagree with me.
>At which point it again only becomes
>possible to establish a correlation between the experiments, not a
>causal ftl effect.
It still remains true that, had I made different choices, the
distant experimenter would have gotten different results. It
seems to me that denying the existence of this or that until
this time or that time is merely so much mental contortion to
avoid the inevitable.
R.
r...@maths.tcd.ie
>Eric Dennis says...
>>The derivation of the inequality makes no reference to qm,
>>to "hidden variables", or to any other microscopic account of whatever
>>kind of apparatus using whatever kind of projectiles you choose. The
>>only physical assumption made in the derivation is locality. I don't
>>see how qm is uniquely able to escape the consequences of this
>>argument.
>I disagree. I think that Bell's notion of "locality" assumes the
>existence of local hidden variables.
>Bell's locality assumption:
> <AB>(s1,s2) = sum over alpha of P(alpha) F1(alpha,s1) F2(alpha,s2)
>where
> alpha = some unknown parameter
> P(alpha) = some unknown probability distribution
> F1(alpha,s1), F2(alpha,s2) = unknown functions
>It seems to me that alpha is the hidden variable,
>and that assuming that the correlation has this form amounts to
>what I was calling the assumption of "local states".
This is one of the reasons why I prefer the form of the proof
that I posted, which doesn't have any reference to any
extra parameters or any theoretical structure at all. I believe
it was Eberhard who first formulated the proof that way.
R.
Mark Palenik
like MWI says, in essence, that observers aren't split until they make a
measurement, or interact with something that has made a measurement, keeping
the theory local.
In other words, it seems to me that in order to make MWI a local
interpretation, if I measure the state of an electron that was in a
superposition of spin up and spin down, you wouldn't be split into two
states until you interacted with me (or the electron).
It seems to me that this should have some odd experimental implications.
I'll try to outline one below - let me know if any of my assumptions are
wrong.
Take a radioactive particle and a Geiger counter (like in Schrodinger's cat,
I suppose), and wait for the half life of the particle to pass. The Geiger
counter should then split into two "worlds", detected, and not detected.
Have another device rigged at this time, to somehow put an electron into a
spin up state if the geiger counter detects anything, and spin down if it
doesn't (or two other states that wouldn't be different enough to decohere
into different worlds).
It seems to me that if there is a simple enough mechanism for doing this,
since the spin up and spin down states aren't very different, it should be
possible to put the electron into a superposition of spin up and spin down
( (|up> + |down>)/sqrt(2) ).
If this is in fact possible, it seems to me that there must be some way to
determine this experimentally, although I haven't had enough physics yet to
really know what implications this would have.
In any event, it seems "wrong" to me that this should be possible. Any
thoughts?
scerir
> Many-worlds with its multiplicity of results in
> different worlds violates CFD, of course,
> and thus can be local.
It suggest to change the term "world" (set?)
ot the term "local" (multi-local?). Because
it sounds strange, to me, a many-worlds-locality.
s.
Daryl McCullough
>Each experimenter recieves N particles and performs one of
>three experiments, A, B or C, on each particle. Each of
>the experiments gives either +1 or -1 as an answer. The
>experimenter decides for himself which experiment he will
>perform on which particle, and deliberately doesn't decide
>which to do until just before the particle arrives
[stuff deleted]
>We say that an experimental result, X, "depended upon" a choice
>from the set {A, B, C} by an experimenter if it can be shown (or
>statistically inferred) that, had the experimenter made a different
>choice, X would have had a different value.
[analysis deleted]
I don't have any problem with your analysis---I was thinking
of posting almost exactly the same thing. However, I disagree
with your interpretation. My interpretation of your analysis
is that there is no local hidden variables theory that can
reproduce the predicted correlations.
You seem to think that it is more general than that---that
your analysis makes no assumptions about hidden variables.
But it seems to me that the concept of "the result that
would have been measured, had the experimenters chosen a
different setting" *is* a way of talking about hidden
variables. Assuming that couterfactual questions have
definite (if unknown) answers amounts to the same thing
as assuming a local hidden variable theory.
That is, your counterfactual assumption amounts to the same
thing as assuming that each of the N particles has some unknown
parameter lambda, and that there are three unknown functions
P_A(lambda)
P_B(lambda)
P_C(lambda)
where P_X(lambda) gives the probability of outcome +1 given that
the particle has parameter lambda, and that the experimenter
chooses setting X (X = A,B or C).
Alex Green
> > news:4084DC58...@univie.ac.at...
<snip>
> > No. Most believe that collapse is explained by decoherence, but in which
> > interpretation the latter should be seen is as controversial as ever.
> >
Tegmark and Wheeler have published a straw poll in:
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0101/0101077.pdf
It seems that the many worlds interpretation is most popular amongst
quantum physicists who have a view.
The decoherence theories generally predict many separate worlds rather
than a continuum (search for work by Zeh and by Zurech).
Alex Green
Alex Green
> by the fact that our minds can't see (at least, so far as we know) into any
> of the adjacent universes. In the real universe (or what we would call the
> multiverse), light probably is made up of waves and no particles. But since
> the universe that we can perceive is constantly being disconnected from the
> rest of the multiverse, wave functions are constantly appearing to collapse
> and light appears to us as particles. This undoubtedly explains why
> everything that light does before it manifest itself as a particle manifest
> itself as a wave prior to that time and, in fact, prior to the time that we
> can detect it.
>
Zeh, one of the leading lights in modern decoherence theory may be
agreeing with you. See Zeh's excellent Chapter 2 of D. Giulini, E.
Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh:
Decoherence and the Appearance of a Classical World in Quantum Theory,
2nd edn. (Springer-Verlag, 2003).:
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9506/9506020.pdf
"(3) Any observer (assumed to be local for empirical and dynamical
reasons)
who attempts to observe a subsystem of the nonlocal superposition must
become part of this entanglement. Those of his component states which
are
then related only by nonlocal phase relations describe different
observations.
So we may axiomatically identify these individual component states of
the
observer with states of consciousness (novel psycho-physical
parallelism).
(4) Because of this dynamical autonomy of decohered world components
(“branches”), there is no reason to deny the existence of
“the other” components
which result from the Schr矣dinger equation (“many minds
interpretation”
– Sect. 2.3)."
My own interest in this comes from the problem of why the conscious
observer is a Classical Observer. See:
http://www.users.globalnet.co.uk/~lka/conz.htm
Alex Green
Arnold Neumaier
Alex Green wrote:
>>>"Arnold Neumaier" <Arnold....@univie.ac.at> wrote in message
>>>news:4084DC58...@univie.ac.at...
>
>>>No. Most believe that collapse is explained by decoherence, but in which
>>>interpretation the latter should be seen is as controversial as ever.
>
> Tegmark and Wheeler have published a straw poll in:
> http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0101/0101077.pdf
> It seems that the many worlds interpretation is most popular amongst
> quantum physicists who have a view.
This is not a precise summary. The poll was among attendance of a quantum
computation conference, which provides a very biased smaple of physicists.
Even within this biased sample, the majority (50/90) gave to the
question,
''Which interpretation of quantum mechanics is closest to your own?''
the answer ''None of the above/undecided''. The alternatives were
(a) Copenhagen or consistent histories
(including postulate of explicit collapse): 4
(b) Modified dynamics
(Schrodinger equation modified to give explicit collapse): 4
(c) Many worlds/consistent histories
(no collapse): 30
(d) Bohm
(an ontological interpretation where an auxiliary "pilot wave" allows
particles to have well-defined positions and velocities): 2
Thus the majority of those interested in quantum computations rather
seems to think that no agreement is in reach, and that it is safest
to remain uncommitted.
Arnold Neumaier
Charles Francis
In message <c8r11b$1r8l$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
writes
>
>
>Charles Francis <cha...@lluestfarmpoultry.co.uk> writes:
>
>> In message <c8ei6q$1kj4$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
>>writes
>>>Charles Francis <cha...@clef.demon.co.uk> writes:
>>>
>>>>In message <c7ujqf$209s$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>>
>>>>>The upshot is that even if we do imagine some breakdown of
>>>>>the property of location from the point of view of the
>>>>>photons, we still have macroscopic objects with well-defined positions
>>>>>affecting the behaviour of distant macroscopic objects with
>>>>>well-defined positions.
>>>
>>>>Yes, but it is only a correlation and there is a causal connection
>>>>because the photons come from the same source.
>>>
>>>I'm not sure what is achieved by denigrating correlations;
>
>>I'm not denigrating them. I suggest that this is a correlation, not a
>>magical ftl effect.
>
>The use of the words "only" and "magical" in the two sentences above
>seem, to me at least, to be designed to communicate a certain
>attitude rather than any particularly useful information.
I don't know that, when chatting on a ng , I choose my words carefully
enough to describe them as designed
> "Only a
>correlation" suggests to me that you mean that correlations should
>be disregarded for some unspecified reason.
Quite the opposite. This may be a difference in idiom, but I simply mean
that it does not imply that we need lose either fundamental physical
laws or fundamental principles. If we don't want to modify causality,
all it shows is that we should reject Bell's idea of locality. But that
is fine because I prefer Descartes idea of locality anyway. It doesn't
make me reject locality, merely a particular statement of locality.
>If "magical ftl effet"
>were replaced by "instance of one experimenter's choices affecting
>the results of an experiment so far away that a light signal
>could not travel from the first experimenter to the distant
>experiment in time to communicate the effect" in your above
>sentence, then the suggestion would become incorrect, because
>that is precisely what is indicated. However, that kind of
>phenomenon is pretty much what most people would consider a faster
>than light effect (at least I would, although I am not necessarily
>convinced that there is actually anything travelling across physical
>space to communicate the effect). The crucial word would appear
>to be "magical", then, and I would certainly agree that I don't
>think there is any magic involved. The expression "magical
>ftl effect", however, seems designed to encourage the reader
>to scoff at the notion that there could be a faster than light
>effect at all, without giving any reason for the disparagement.
I am happy enough with ftl in the context of field theory. There is a
non-zero amplitude for particle creation at one point and annihilation
at a point outside the light cone. However my position is that distance
cannot be defined without first establishing simultaneity, and that this
depends on the maximum speed of information transfer. Clearly one cannot
transfer information faster than the maximum speed of information, and I
suppose I do scoff at that.
>>No. I think this is the hardest of the quantum paradoxes to explain. In
>>fact I think we need to combine qed with gtr, and then we will be able
>>to produce a mathematical explanation, showing precisely what the
>>relationship of spin is to the structure of space-time. I doubt it will
>>ever be conceptually easy.
>
>The many worlds people seem to have convinced themselves that they
>have an easy way to understand it, although I believe that that
>has more to do with psychology than with physics.
Yes
>
>>>>As you know I have a relationist interpretation of quantum
>>>>mechanics according to which background space does not exist.
>>>
>>>Which leads the way to the wonderful question of what does, in fact,
>>>exist, but, being fearful of drifting off into philosophy, we must
>>>abandon this line of questioning and pretend we already know the
>>>answers, lest somebody point their finger at us and call us
>>>metaphysicists.
>
>>No, we must merely learn to be precise and scientific about the
>>question. The non-existence of background space is a very different
>>question from the question of existence at all. And rather than drift
>>off into philosophy we must formalise and mathematise it, make it a
>>useful tool in studying the universe, rather than the source of endless
>>waffle it tends to become.
>
>The question of what "really" does exist, and metaphysical musings,
>are relevant when we come, for the first time, to write down some
>symbols from which we intend to develop a theoretical framework.
>The first symbols written down must refer to something that we
>have some conceptual idea of, so that we have an idea of what kind
>of algebra they will satisfy.
I think the first thing is to study how we go about measuring things. We
have to have a conceptual idea of measurement or we cannot go any
further, and, rather than base our ideas on a speculative metaphysical
notion of what we think reality should be like, we can actually analyse
precisely what we do in measurement. The method of measurement defines
the physical quantity, so we can write down symbols corresponding
precisely to that and without relying on induction.
>
>If we think there are objects, which have positions in space which
>can be specified with real numbers, then we write down x^i_o, where
>o is a symbol indexing the objects, x^i is the ith coordinate,
>and we know about the algebra of real numbers. The assertion that
>there are, in fact, objects in space with positions representable
>by numbers is a metaphysical statement, so unless somebody can
>produce a proof of the assertion, anybody is free to disagree with
>it without making a logical mistake.
Yes. But this is not true if we base our physical theory on measurement,
rather than on metaphysics. All we should really assert is that we find
a number if we carry out a measurement, not that the number has an
existence beyond that.
>In cases of such disagreement,
>the common practice among physicists is to accuse each other of
>being metaphysicists, which is considered so dreadful an insult
>that it tends to end the debate.
Fortunately I spent a lot of my formative years as a physicist in
isolation, having come from mathematics.
>>>>I do not think the property of spin pertains only to the photon, but to
>>>>the relationship between the photon and other matter, for example the
>>>>matter of the measurement apparatus. So I think all we are doing here is
>>>>establishing that the causal connection between the photons has an
>>>>influence on the structure of space at A and B.
>>>
>>>I don't know that it does. Clearly a teleporter would effectively
>>>change the structure of space, in the sense that the distance from
>>>here to Mars would be "small" if I could get there from here in a few
>>>milliseconds
>
>>That sounds like a a reductio ad absurdum argument that no such thing
>>can exist.
>
>That wasn't exactly what I had intended; if we have a manifold
>like Minkowsi space with a set of fields described by differential
>equations, then a teleporter can be considered to be something
>which forces the values of the fields in one region to be
>equal to the values of the corresponding fields in another
>region. This is equivalent to using a manifold with a different
>topology, where those two regions are glued together. The set of
>solutions to the differential equations on the new manifold will
>be smaller than the original set of solutions, but it won't necessarily
>be empty.
Don't say that. I might accuse you of being a metaphysician! :-) If we
construct the manifold from the numbers referring to measurements, real
or imagined, none of this works, because the metric on the manifold
depends on the speed of information transfer.
>>>>Its not so clear that we have well defined positions when outside the
>>>>light cone. In this case we have to use causal connection from the past
>>>>to define position, precisely the sort of causal connection as exists
>>>>between the photons.
>>>
>>>We can piece together where something was a posteriori, by
>>>asking somebody who was standing at the place where we weren't.
>>>If an experiment spans, for example, the width of a city, then
>>>the inhabitants of the city, equipped with clocks and rulers
>>>as they are, can share their results and cumulatively assure
>>>us that the geometry of the city remained intact even over
>>>short timescales when distant parts of the experiment were
>>>spacelike separated.
>
>>The results can only be shared after the event, so the structure only
>>gains existence after the event.
>
>It seems to me that it is entirely a matter of my own preference
>whether I consider events outside my past light cone to exist or
>not. An alien species living on a distant world might be surprised
>to learn that their structure only gained existence after I
>first heard about them; they might even disagree with me.
But then it is also a matter of my preference that I believe you exist,
or that the world did not come into existence last Tuesday, complete
with all memories. I think that as a scientists we accept that a
universe exists and that we study it. I am not referring to whether
matter exists outside the light cone, but whether the mathematical
structure I call space-time exists. I expect an alien species, or indeed
you, or Wigner's friend to disagree about that, because I hold that we
each have our own mathematical structures which we call space-time.
Sure, we can get yours and mine to correspond pretty closely, or we can
agree to use the same one based on the same clock and measurements. But
if space-time is just a mathematical structure formed from laws
abstracted from measurement, there is no issue that different
space-times arise by basing measurement on different clocks.
>
>>At which point it again only becomes
>>possible to establish a correlation between the experiments, not a
>>causal ftl effect.
>
>It still remains true that, had I made different choices, the
>distant experimenter would have gotten different results. It
>seems to me that denying the existence of this or that until
>this time or that time is merely so much mental contortion to
>avoid the inevitable.
I have that problem too. What we want is a mechanism. But as I have
intimated I think a mechanism depends on the successful integration of
qed with gtr. So we are going to have to live with it for a little
while.
Regards
--
Charles Francis
eb...@lfa221051.richmond.edu
Alex Green <drale...@yahoo.co.uk> wrote:
>Tegmark and Wheeler have published a straw poll in:
>http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0101/0101077.pdf
>It seems that the many worlds interpretation is most popular amongst
>quantum physicists who have a view.
The results of this poll are interesting, but it's important to note
that it was taken at a quantum computation conference. I wonder
whether a poll of, say, atomic physicists would yield similar results.
-Ted
--
[E-mail me at na...@domain.edu, as opposed to na...@machine.domain.edu.]
r...@maths.tcd.ie
>Assuming that couterfactual questions have
>definite (if unknown) answers amounts to the same thing
>as assuming a local hidden variable theory.
Why local?
R.
r...@maths.tcd.ie
>r...@maths.tcd.ie says...
>>We say that an experimental result, X, "depended upon" a choice
>>from the set {A, B, C} by an experimenter if it can be shown (or
>>statistically inferred) that, had the experimenter made a different
>>choice, X would have had a different value.
>[analysis deleted]
>I don't have any problem with your analysis---I was thinking
>of posting almost exactly the same thing. However, I disagree
>with your interpretation. My interpretation of your analysis
>is that there is no local hidden variables theory that can
>reproduce the predicted correlations.
>You seem to think that it is more general than that---that
>your analysis makes no assumptions about hidden variables.
>But it seems to me that the concept of "the result that
>would have been measured, had the experimenters chosen a
>different setting" *is* a way of talking about hidden
>variables. Assuming that couterfactual questions have
>definite (if unknown) answers amounts to the same thing
>as assuming a local hidden variable theory.
Three responses:
1. As I said in the previous post, if you reject counterfactuals
like this then you would never accept any evidence, even a successful
communication of a very long and complicated message, of a faster
than light effect. In fact, you would never accept any experimental
result as any evidence of a causal relationship, because any statement
of the form "this depended on that" is a statement about counterfactuals,
for example, "The acceleration of the object depended on the force
applied to it, and different forces would have produced different
accelerations." If you reject counterfactuals and regard "what the
object would have done had a different force been applied" as a
despicable hidden variable, then you would never accept F=ma.
2. The statement that the world is local is a statement
which necessarily involves counterfactuals, since it asserts
that my results would have been the same had distant experimenters
made choices other than those they did. If you reject counterfactuals,
then you reject locality (here I mean locality in the real world,
not the my-equation-has-Lorentz-symmetry kind of locality which is
much trumpeted by those who think that the formalism of quantum
mechanics, rather than an experimental result, is in question).
About half of the counterfactual statements I used in the proof
were nothing more than assertions of locality.
3. If we regard the hypothetical experiment as being in the future,
rather than in the past, then we instead have statements like:
i. "My result will not depend on the distant experimenter's choices."
ii. "If we choose to do the same experiments, then we will get the same
results."
iii. "If I do experiment A, I will get a definite result which will be
either +1 or -1. The same applies for B and C."
These statements are not counterfactuals, but are the kinds of statements
that might come from the predictions of a theory of physics (indeed, ii.
and iii. are predictions of quantum mechanics and i. is not). Am I supposed
to imagine that they are all false? Or that they are true before time T and
then, as the results of the experiments arrive, they flip from true to false?
Or is it that iii. is only true for one of {A, B, C}, namely the one
which I will actually choose to do? That would mean that ii. is false
unless we actually do choose the same experiments. It would also
mean that I have no free will, because I would be constrained to
perform the experiment with the definite outcome. And what could i.
mean in such a case? It would have to mean something like "It is
not defined what would happen if I chose to do an experiment other
than X, but, in that non-defined eventuality, the distant experimenter
would get the same result as he does in the single well-defined
case." But I am repeating myself - this is just response 2 again.
What I sometimes find amazing is that, when it comes to quantum
mechanics, otherwise competent physicists can abandon the
very principle upon which all of physics is built - the principle
that we can generalise from many individual observations like
"I did X; I saw Y" to statements of the form "If I do X, then I
will see Y", or, equivalently, "If I had done X, I would have seen Y."
Outside of quantum mechanics, they appear to have no difficulty
using and applying this rule and even in understanding how fundamental
it is to science. This is why I drew attention to F=ma in response 1
above. Quantum mechanics doesn't seem to be just another field of
physics to many physicists, but a mode of thinking in which, for
specific situations, (for example, Bell's inequalities), rejections
of the normal scientific procedures are invoked, as though arguments in
quantum mechanics have some kind of badge or licence which grants
them immunity from the standards we apply to arguments in other
fields of science.
But perhaps it isn't so amazing. Imagine an experiment in which
a child is told, throughout its life, that a specific black
object is white, and is provided with ridiculous ad-hoc philosophical
maxims instead of any coherent explanation of what is going on.
We could add, as we do in quantum mechanics, social pressure -
"Don't waste your career on it"; "People who think about it
end up as crackpots or go mad"; "Philosophy, especially metaphysics,
is a disgusting business that no respectable person would engage
in - simlar to picking your nose in public - so don't question
the little incoherent philosophical maxims that we give you."
I imagine that such a poor child would quite readily just accept
the fact that there's something strange about that object; that the
normal rules don't apply for some reason which isn't completely
clear, and would repeat the incoherent philosophical snippets to
others who claimed that the object was black, as it seemed to be.
He might teach it to his children, and they to theirs. I imagine
we could even foster a whole community of people with such a
communicable mental disease; even a community of scientists.
>That is, your counterfactual assumption amounts to the same
>thing as assuming that each of the N particles has some unknown
>parameter lambda, and that there are three unknown functions
> P_A(lambda)
> P_B(lambda)
> P_C(lambda)
>where P_X(lambda) gives the probability of outcome +1 given that
>the particle has parameter lambda, and that the experimenter
>chooses setting X (X = A,B or C).
No; there is no probability involved in the proof at all.
R.
Eric Dennis
da...@atc-nycorp.com (Daryl McCullough) wrote in message news:<c8j3s...@drn.newsguy.com>...
> Eric Dennis says...
Your phrasing makes me think that I may have cited the wrong paper in
Speakable, which unfortunately I don't have in front of me right now.
I'm talking about the one that uses M, N, and /\ to label the past
light-cones of the two measurement events and the their overlap
respectively. In any case, the variables alpha or lambda, or whatever
you want to call them, are meant to denote all aspects of whatever
exists in this overlap, i.e. anything that could sub-luminally affect
both measurement outcomes at once. It looks like you're saying that
merely referring to such a set of things is already assuming some sort
of hidden variables -- I guess you would say "local states".
I would say that if you can't talk about things localized in a given
region in order to distinguish between hypothetical sources of local
influence and of non-local influence, then the whole idea of locality
isn't meaningful. Bell doesn't need to contemplate whether lambda is
"hidden" or not. He's just saying whatever is there, let's call it
lambda.
Phillip Helbig---remove CLOTHES to reply
In article <c8vgq2$r2$1...@lfa222122.richmond.edu>,
eb...@lfa221051.richmond.edu writes:
> In article <42c8441.04052...@posting.google.com>,
> Alex Green <drale...@yahoo.co.uk> wrote:
>
> >Tegmark and Wheeler have published a straw poll in:
> >http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0101/0101077.pdf
> >It seems that the many worlds interpretation is most popular amongst
> >quantum physicists who have a view.
>
> The results of this poll are interesting, but it's important to note
> that it was taken at a quantum computation conference. I wonder
> whether a poll of, say, atomic physicists would yield similar results.
Of course, as Penrose pointed out, there are more interpretations of
quantum mechanics than there are people working in the field. This is
not inconsistent, however, since it is possible to believe in more than
one interpretation at the same time. :-)
I think the key phrase is "who have a view". Most folks from the "shut
up and calculate" school probably wouldn't mention many worlds if asked,
and might go with the Copenhagen by default, since that is what many
standard textbooks espouse.
Charles J. Quarra
> Charles Francis <cha...@clef.demon.co.uk> writes:
>
> > In message <c6thrl$1b0b$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
> >writes
> >and which requires the instantaneous
> >propagation of non-local effects. That is not an explanation for
> >anything, or even a sensible interpretation.
>
> Well, what Bell's theorem showed was the non-locality of quantum
> mechanics itself. It's not entirely fair to complain abot Bohmian
> mechanics being non-local when experiments have shown that non-locality
> is a fact of life. Wavefunction collapse is non-local and so is
> the splitting of the universe into many worlds, but, of course,
> everybody will jump in here and claim that their personal interpretation
> or variant of Copenhagen or Everett isn't non-local. Inevitably,
> such "interpretations" merely amount to having a "way of thinking
> abuot it" which is equivalent to "never admit that it is non-local."
> It's the experiments which indicate non-locality; having a local
> interpretation of the qm formalism isn't a virtue.
>
Well, a point i suspect is not being made clear enough is that one of
the most important features of the MWI is that it removes the need of
think in non-local actions to explain quantum entanglement verified
thru Bell's unequalities
Recalling the EPR original experiment layout, you have a spin 0
initial state that splits into two entangled spin 1/2 states with
total spin 0. Then measurements done over one state inmediately
constrains the measurement done on its partner; this is usually
conceived as a "non-local" action
in the MWI, both spin 1/2 states (Bob and Alice) interact with their
respective measurememt devices and after that we have two entangled
states |entangled Bob> = |Bob spin+ > + |Bob spin- > which is
uncoupled (after the measurement) with the entangled state |entangled
Alice > = |Alice spin- > + |Alice spin+ >
Now, MWI says that both experimentalists, Alice and Bob are entangled
in a superposition of states with each possible result of spin
measurement (+/- 1/2) now when the two entangled states |entangled Bob
> and |entangled Alice> join and share their measurements, then
results represented on |Alice spin- > can interact _only_ with |Bob
spin+ > because its the only transition that preserves total angular
momentum. Likewise |Alice spin+ > can only interact with |Bob spin- >,
for the same reasons.
This means that the final state of the EPR experiment is
| PSI > = |Bob spin+ >|Alice spin- > + |Bob spin- >|Alice spin+ >
which essentially means that there is 50% probability that Alice or
Bob receives a particular spin state, but 100% probability that each
measure total spin 0
Note that in MWI, the transition occurs strictly _locally_ when
|entangled Bob > and |entangled Alice > share their measurements
this is important, since MWI is the only interpretation that makes
EPR a local action (without spooky action at a distance or hidden
variables), so in this sense, is elegant
Charlie Stromeyer Jr.
(Charles J. Quarra) wrote in message news:
> this is important, since MWI is the only interpretation that makes
> EPR a local action (without spooky action at a distance or hidden
> variables), so in this sense, is elegant
There is a problem, though, because MWI, the Copenhagen
interpretation, John Cramer's transactional interpretation, Bohmian
mechanics, etc. seem to have all been ruled out of existence three
years ago by this experiment:
http://arxiv.org/abs/quant-ph/0102109
Note that the inherent uncertainty here is clearly non-statistical or
non-probabilistic by any conventional probability theory, and so we
can perhaps interpret this bizarre finding as one definition of the
notion of "acausality".
Perhaps someone like John Baez knows of a weird type of fuzzy or
quantum logic that might be compatible with this experimental result.
If someone does have an idea about such an unusual logic then it might
also be interesting to see if this weird logic would somehow be
related to what John Baez has written before about the relationship
between quantum logic and non-associative mathematics.
If at first an idea does not seem crazy enough to be true then we
should scratch out the inside of whatever remains of our minds so that
we can start anew from scratch.
See, this is the kind of weird logic I'm talking about !-)
Arkadiusz Jadczyk
On 3 Jun 2004 05:16:49 -0400, cstr...@hotmail.com (Charlie Stromeyer
Jr.) wrote:
>
>There is a problem, though, because MWI, the Copenhagen
>interpretation, John Cramer's transactional interpretation, Bohmian
>mechanics, etc. seem to have all been ruled out of existence three
>years ago by this experiment:
>
>http://arxiv.org/abs/quant-ph/0102109
Photons, perhaps, should be treated as relativistic. There is no
sequentiality in EEQT, and there is even less sequentiality in
relativistic EEQT - see
http://www.cassiopaea.org/quantum_future/papers/garda.htm
for a review.
To understand that sequentiality is not needed, notice that "interaction
free experiments" are easily understood within EEQT, and they are easily
modeled. The very presence of detectors changes the evolution of the
wave function, whether they detect anything or not. Then, the wave
function may pass through the detector, without triggering it, it
changes its shape, it can then trigger some other detector. All depends
on details, detector characteristics, wave function shapes etc.
A typical effect, when there is a seeming "faster than light
communication" in quantum tunneling is when a wave function passes
through the initial detector, before the barrier, gets detected by the
second detector, after the barrier, gets reflected, and then triggers
the first detector. It looks as "superluminal". But is simply out of
sequence, due to reflections.
ark
--
Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm
--
Mike Stay
cstr...@hotmail.com (Charlie Stromeyer Jr.) wrote in message news:<61773ed7.0406...@posting.google.com>...
> (Charles J. Quarra) wrote in message news:
>
> > this is important, since MWI is the only interpretation that makes
> > EPR a local action (without spooky action at a distance or hidden
> > variables), so in this sense, is elegant
>
> There is a problem, though, because MWI, the Copenhagen
> interpretation, John Cramer's transactional interpretation, Bohmian
> mechanics, etc. seem to have all been ruled out of existence three
> years ago by this experiment:
>
> http://arxiv.org/abs/quant-ph/0102109
The experiment described there fits just fine within MWI. Why do you
believe it rules anything out?
[Moderator's note: In general different _intepretations_ of quantum mechanics
tend to be indistinguishable by experiment, otherwise they would be different
theories, not different ways to talk about the same theory. -usc]
--
Mike
r...@maths.tcd.ie
>r...@maths.tcd.ie wrote in message news:<c762c5$8qd$1...@lanczos.maths.tcd.ie>...
>> Charles Francis <cha...@clef.demon.co.uk> writes:
>>
>> > In message <c6thrl$1b0b$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie
>> >writes
>> >and which requires the instantaneous
>> >propagation of non-local effects. That is not an explanation for
>> >anything, or even a sensible interpretation.
>>
>> Well, what Bell's theorem showed was the non-locality of quantum
>> mechanics itself. It's not entirely fair to complain abot Bohmian
>> mechanics being non-local when experiments have shown that non-locality
>> is a fact of life. Wavefunction collapse is non-local and so is
>> the splitting of the universe into many worlds, but, of course,
>> everybody will jump in here and claim that their personal interpretation
>> or variant of Copenhagen or Everett isn't non-local. Inevitably,
>> such "interpretations" merely amount to having a "way of thinking
>> abuot it" which is equivalent to "never admit that it is non-local."
>> It's the experiments which indicate non-locality; having a local
>> interpretation of the qm formalism isn't a virtue.
>>
>Well, a point i suspect is not being made clear enough is that one of
>the most important features of the MWI is that it removes the need of
>think in non-local actions to explain quantum entanglement verified
>thru Bell's unequalities
What Aspect's experiment showed was that if the results of the
measurements depended on anything, they depended on the settings
of distant devices. MWI asserts that the results didn't depend
on anything, which is how it escapes the conclusion.
This is not an explanation; it is simply giving up and refusing
to investigate further. Whenever we lack an explanation for why a given
measurement result was what it was (as opposed to something
else), anybody can step in with the "explanation" that every
possible measurement result actually occurred, each in its
own universe with a unique copy of the observer. If we couldn't
explain why things fall down instead of up, a many worlds
enthusiast will be ready to speculate about another world
where everything falls up. However, he has no evidence at all
that such a world exists, and those who adopt the many worlds
interpretation of quantum mechanics have no more justification
for their assertion that parallel worlds exist than does the
person who asserts the existence of the falling-upwards world.
The supposed restoration of locality in the many worlds
interpretation is highly unimpressive as well. The
multiverse is supposedly local in an algebraic way:
we write |me>(|you_1>+|you_2>) and say that you have
split but not I, instead of writing |me>|you_1>+|me>|you_2>
and saying that the entire universe has split. Distributivity
of multiplication over addition is trumpeted as a profound
insight. Still, regardless of this, the observers who
are confined to a single universe _still_ observe nonlocal
physics. Claiming that locality is restored in this
interpretation is exactly analogous to claiming that
one can demonstrate that the universe is rotationally invariant
about the centre of the Earth by considering an ensemble of
many worlds which differ from each other by rotations about
the centre of the Earth and claiming that the each member of the
ensemble really exists.
Anyway, the entire many worlds mentality is founded upon
the unjustified dogmatic assertion that the state vector is
a complete description of the system, combined with the
other spurious and equally unjustified dogmatic assertion
that the state vector represents the system itself rather
than knowledge of the system. One can only be led to the
many worlds interpretation by adhering doggedly to these
two assertions, which have never been supported by any
consistent argument.
The "wavefunction is a complete description" proofs
turned out to be incorrect, and Bohm's theory is a counterexample.
The assertion that the state vector describes only the system
itself rather than incorporating some element of subjective
knowledge can be seen to be undermined by the following example:
Let Alice and Bob be taking part in an EPR-type experiment using
spin-1/2 particles, with Alice receiving her particle a few moments
before Bob receives his. By choosing to measure the spin of her
particle along the Z-axis or the X-axis, Alice can choose whether
Bob receives one of |up_z> or |down_z>, or one of |up_x> or |down_x>,
respectively. Now, Bob cannot, even in principle, determine which
it is that Alice has chosen (otherwise he would have received a message
from her, and the message could be sent faster than light), so we
have the result that there is no physical experiment, even in
principle, which can distinguish whether a given particle has a
state vector chosen from {|up_z>,|down_z>} or {|up_x>,|down_x>}.
Thus, if you assert that the state vector is a real physical thing
which does not express anything related to the information available,
you come up against the seemingly contradictory fact that supposedly
distinct "physical" states cannot be distinguished by any physical
experiment, even in principle (a state chosen from {|up_z>,|down_z>}
will definitely be distinct from a state chosen from {|up_x>,|down_x>}).
One might have thought that two things which cannot be distinguished
from each other, even in principle, should be considered the same.
I am not here claiming that the wavefunction represents
knowledge alone, only drawing attention to the fact that
there are good reasons to believe that it is not _entirely_
a description of the system alone.
Anyway, back to many worlds. The final, and decisive, argument
against many worlds is that, if we do cling without reason to the dogmatic
assertions that the state vector is the complete description and
that it represents the system itself, then we have to face the
fact that the Hamiltonian and the state vector in the Hilbert
space formulation do not provide enough information to reconstruct
a picture of the system which is supposedly being described.
For example, the group of translations, R^3, acts on the set of states
of the physical system, hence we have space and location and so on.
Using only the Hamiltonian and state vector, a natural action of R^3 on
the Hilbert space cannot be constructed. What this means is that
the information contained in the Hamiltonian and state vector is
not enough to describe anything spatial. If you do not already know
about space, you will not learn about it by studying the Hamiltonian
and state vector, which are the only thing that many worlders believe
to exist. The universe described by many worlds is not one in which
space appears, let alone locality.
R.
Frank Hellmann
> r...@maths.tcd.ie wrote in message news:<c762c5$8qd$1...@lanczos.maths.tcd.ie>...
> > Charles Francis <cha...@clef.demon.co.uk> writes:
> >
Of course if we have an anisotropic system with a higher amplitude for
+ for Bob and - for Alice, the end result will be
c_1 |Alice - >|Bob + > + c_2 |Alice + >|Bob - >
Now both of these non interacting branches exist if we take MWI
serious and it is pure chance in which we happen to talk about it. The
amplitudes don't translate into propabilities.
So the theory requires a non local comparsion of the branches to
insert by hand the observed propabilities and thus you get non
locality again.
---
frank.
Oliver Jennrich
> (Charles J. Quarra) wrote in message news:
>> this is important, since MWI is the only interpretation that makes
>> EPR a local action (without spooky action at a distance or hidden
>> variables), so in this sense, is elegant
> There is a problem, though, because MWI, the Copenhagen
> interpretation, John Cramer's transactional interpretation, Bohmian
> mechanics, etc. seem to have all been ruled out of existence three
> years ago by this experiment:
> http://arxiv.org/abs/quant-ph/0102109
The problem with this paper, though, is that it doesn't describe a
real experiment, much less presents any measurements, data, anything,
that is likely to show the postulated effects.
What's worse, passages like
| Nevertheless, the photon has not
| been [permanently] absorbed by the atom, so no interaction between
| the photon and the atom seems to have taken place.
makes me wonder if the authors really think that an absorption with a
re-emission can be considered as "no interaction".
--
Space - the final frontier
Alan Forrester
> > this is important, since MWI is the only interpretation that makes
> > EPR a local action (without spooky action at a distance or hidden
> > variables), so in this sense, is elegant
>
> There is a problem, though, because MWI, the Copenhagen
> interpretation, John Cramer's transactional interpretation, Bohmian
> mechanics, etc. seem to have all been ruled out of existence three
> years ago by this experiment:
>
> http://arxiv.org/abs/quant-ph/0102109
>
> Note that the inherent uncertainty here is clearly non-statistical or
> non-probabilistic by any conventional probability theory, and so we
> can perhaps interpret this bizarre finding as one definition of the
> notion of "acausality".
>
> Perhaps someone like John Baez knows of a weird type of fuzzy or
> quantum logic that might be compatible with this experimental result.
> If someone does have an idea about such an unusual logic then it might
> also be interesting to see if this weird logic would somehow be
> related to what John Baez has written before about the relationship
> between quantum logic and non-associative mathematics.
I don't see any problem under the MWI. Let's recap the experiment. You
have an MZ interferometer with three atoms in one arm arm 1 and none
in the other.
Let the state of a photon in Arm 1 be written |1> and the state of a
phton in the other arm be |2>. Let the state of atom j with spin Z+ be
|Z+(j)>. Let the state of the atoms and photon at time t be |pa(t)>.
We trace the evolution of this state without assuming collapse as per
the MWI.
Now, as I understand it, an atom with Z+ spin absorbs a photon and one
in Z- does not, I shall assume that no other interactions take place.
Let all three atoms be in a superposed state of Z+ and Z- with equal
real amplitude at the start of the experiment. We send the photon
through a beamsplitter and a suitable phase shifter so that it is in a
similar state wrt which arm it is in, i.e. - equal superposition with
real amplitudes. We will dub this time t=0 and so we have
|pa(0)> = a(|1> + |2>)(|Z+(1)> + |Z-(1)>)(|Z+(2)> + |Z-(2)>)(|Z+(3)> +
|Z-(3)>)
with a = 1/2sqrt(2)
Now the photon comes to the first atom. If the atom has spin Z+ and
the photon is in branch 1 (of the interferometer) then the atom goes
off. We will denote this state by |bangj> for atom j. Otherwise the
photon continues on its merry way as does the atom. We dub this t = 1
So we have
|pa(1)> = a(|bang1> + |1>|Z-(1)> + |2>|Z+(1)> + |2>|Z-(1)>)(|Z+(2)> +
|Z-(2)>)(|Z+(3)> + |Z-(3)>)
So the photon in the |1> arm is present in two versions after the
interaction, one of which keeps going while the other does not because
it has been absorbed by atom 1. Now, if the photon has been absorbed
by atom 1 then obviously it can't interact with atom 2 or 3. This
interaction and so the generation of these two versions is perfectly
local, as can be seen from the fact that nothing has happened to atoms
2 or 3 yet, or to the |2> version of the photon.
Let |S(j)> = (|Z+(3)> + |Z-(3)>) just for notational convenience since
the terms will soon become complicated otherwise. Another local
interaction between |1> and atom 2 produces
|pa(2)> = a(|bang1>|S(2)> + |S(1)>|bang2> + |1>|Z-(1)>|Z-(2)>
+ |2>|S(1)>|S(2)>) |S(3)>
It's fairly obvious what the state at time t = 3 after the interaction
with atom 3 will be
|pa(3)> = a(|bang1>|S(2)>|S(3)> + |S(1)>|bang2>|S(3)>
+|S(1)>|S(2)>|bang3>
+ |1>|Z-(1)>|Z-(2)>|Z-(3)> + |2>|S(1)>|S(2)>|S(3)>)
I shall assume that at the end of the experiment we measure the Z spin
of the atom and position of the photon in a destructive way so that
they decohere. Presumably by putting CCDs in both arms so that the
photon will reach them at t = 4 and destructively measuring the Z spin
of atoms at t = 4 regardless of the outcome of the experiment. This
would prevent interference between the different terms.
After each experiment there will be 1 world in which atom 1 interacted
with the photon, another in which atoms 2 did so and another in which
atom 3 did so. In none of these worlds will we see two atoms go off.
Then there will be the world in which the photon didn't interact with
any of the atoms despite being in the first branch of the
interferometer. Finally, there are 8 branches with the photon in the
second arm, one for each possible measuring result on the atom. To
compare the readings on all the detectors we have to bring the
relevant information together.
If you really want to you can confirm that the six detectors (one CCD
to detect photons for each arm of the interferometer gives 2, one for
each atom adds three and then we need to bring the information from
these five together to a sixth detector) exhibit the appropriate
correlations. Bear in mind that you can't carelessly cross out terms
as in the article you referenced above and there won't be a problem.
You might want to read my contribution to the thread on the MWI, which
has good references.
Alan
Tony Smith
> interpretation, John Cramer's transactional interpretation, Bohmian
> mechanics, etc. seem to have all been ruled out of existence three
> years ago by this experiment:
> http://arxiv.org/abs/quant-ph/0102109
The paper cited by Charlie Stromeyer Jr. (Zirkus) was written
by Elitzur and Dolev who in a subsequent paper at
http://xxx.lanl.gov/abs/quant-ph/0207029
seem to me to state that the general approach of the transactional
interpretation is not ruled out if it is interpreted as affecting
"... not only events but also entire histories ...".
Perhaps such a history (as opposed to mere event) interpretation
could also validate MWI, Bohm, etc.
Here are some excerpts from
http://xxx.lanl.gov/abs/quant-ph/0207029
by Elitzur and Dolev:
"... the results ... demonstrated an even more intriguing effect. ...
if the photon indicates that interference was disrupted,
then, with 100% certainty, one of the atoms has "collapsed"
into the intersecting box.
However, it can be any of the N atoms, not necessarily the first.
Worse, once we have measured one of the atoms
and found it in the intersecting box,
all the other atoms return to their original,
undisrupted, superposition state.
Consequently,
if we do not measure these atoms' positions
but reunite the boxes and perform an "interference" measurement,
the atoms will always exhibit full interference,
as if no photon has ever interacted with them!
... If one assumes that the photon's wave function has interacted
with the particular atom we've measured so as to ruin its interference,
how come that all the other atoms in the row, positioned before and after
that particular atom, seem to have never been affected?
...
Another offence to the ordinary temporal notions comes from our
... inverse EPR experiment ... In 44% (e.g., 4/9 ) of the cases
... one of the atoms will be subjected to z measurement ... while
the other atom will be subjected to x or y ...
Suppose, then, that the first atom was found in the intersecting box.
This means that no photon has ever crossed that path.
But then, by Bell's proof, the other atom is still affected nonlocally
by the measurement of the first atom.
But then again, if no photon has interacted with the first atom ... the
two atoms share no causal connection, in either past of future!
... this experiment yields a history that is not consistent:
One atom indicates that the photon has taken only one path,
while the other atom's state proves that both atoms have been visited
by the same photon.
...
the still unexplained CP violation exhibited by neutral kaons,
which, by CPT invariance, entails a fundamental violation of T.
Consequently, if a subtle time-asymmetry is inherent to physical
interactions themselves, the orthodox picture of time as a mere
dimension looses much of its conviction.
...
the "transactional" interpretations ... by invoking retarded-plus-
advanced actions, offer a simple and elegant explanation for many
spatial and temporal peculiarities manifested by QM. ...
we ... propos[e]... that this spacetime is not static.
Perhaps it, too, is subject to some subtle dynamics,
that is changes affect not only events but also entire histories.
Then,
time's asymmetry will be anchored in that dynamics governing
spacetime itself ...
Also, quantum mechanical experiments yielding apparently inconsistent
histories, as those described above, would give rise to an account like
"first a retarded interaction brings about history t1x1, t2x2, ...
and then
an advanced interaction transforms this history into t1x'1, t2x'2, ...."
Such a model will be better capable of explaining quantum peculiarities
of the kind described above, as well as a few other surprising results
discovered lately by similar techniques ...".
I should note that, although Elitzur and Dolev describe CP violation
as "still unexplained", that phenomenon might be explainable by the
complex phase of Kobayashi-Maskawa parameters - see for example
http://www.physicstoday.org/pt/vol-54/iss-5/p17.html
Tony Smith
Daryl McCullough
comment.
>[Moderator's note: In general different _intepretations_ of quantum mechanics
>tend to be indistinguishable by experiment, otherwise they would be different
>theories, not different ways to talk about the same theory. -usc]
It isn't that clear-cut. The problem is that every theory has a few
loose ends---details that are not completely spelled out by the theory.
Different interpretations may fill in these details differently. In
the case of quantum mechanics, the unitary evolution of the wavefunction
is pretty uncontroversial---every interpretation of quantum mechanics
must give equivalent results. On the other hand, exactly what happens
when a measurement is made is difficult to get a firm grasp of, and different
interpretations of quantum mechanics fill in these details in different
ways. I suppose you could call the VonNeumann assumption that measurement
collapses the wave function a different theory than the MWI assumption that
the wave function never collapses, but I think most people would say that
these are different interpretations of the same theory.
Italo Vecchi
> > http://arxiv.org/abs/quant-ph/0102109
>
> The experiment described there fits just fine within MWI. Why do you
> believe it rules anything out?
>
>
> [Moderator's note: In general different _intepretations_ of quantum mechanics
> tend to be indistinguishable by experiment, otherwise they would be different
> theories, not different ways to talk about the same theory. -usc]
By the way, afaiu, what's described in
http://arxiv.org/abs/quant-ph/0102109 is a thought experiment. It
hasn't been actually carried out.
IV
Charlie Stromeyer Jr.
> The paper cited by Charlie Stromeyer Jr. (Zirkus) was written
> by Elitzur and Dolev who in a subsequent paper at
> http://xxx.lanl.gov/abs/quant-ph/0207029
> seem to me to state that the general approach of the transactional
> interpretation is not ruled out if it is interpreted as affecting
> "... not only events but also entire histories ...".
Tony, many thanks for mentioning this paper which I myself had not
bothered to check for. It will take me some time to think about the
questions raised in this thread because there is a variety of related
literature that I should look at first.
For now, I will mention that the views within the above paper such as
the ideas of an emergent and intrinsic time arrow, the lack of
dependence upon initial conditions, that time asymmetry is inherent
for all physical processes rather than an artefact of boundary
conditions etc. are similar to the ideas of Stephen Wolfram (and maybe
Ed Fredkin and others) as you can see e.g. with the NKS book and
perhaps also within some of the academic papers recently posted in the
"Bibliography" section:
http://www.wolframscience.com/reference/
(Btw, I earlier took the pseudonym "zirkus" from Monty Python's
Fleigender Zirkus and from the book title "Fleigender Zirkus der
Physique")
Charles J. Quarra
r...@maths.tcd.ie wrote in message news:<c9irnv$2vbh$1...@lanczos.maths.tcd.ie>...
> disposablemail...@yahoo.com.ar (Charles J. Quarra) writes:
> .....
> >r...@maths.tcd.ie wrote in message news:<c762c5$8qd$1...@lanczos.maths.tcd.ie>...
> >> Charles Francis <cha...@clef.demon.co.uk> writes:
>
> What Aspect's experiment showed was that if the results of the
> measurements depended on anything, they depended on the settings
> of distant devices. MWI asserts that the results didn't depend
> on anything, which is how it escapes the conclusion.
>
> This is not an explanation; it is simply giving up and refusing
> to investigate further. Whenever we lack an explanation for why a given
> measurement result was what it was (as opposed to something
> else), anybody can step in with the "explanation" that every
> possible measurement result actually occurred, each in its
> own universe with a unique copy of the observer. If we couldn't
> explain why things fall down instead of up, a many worlds
> enthusiast will be ready to speculate about another world
> where everything falls up. However, he has no evidence at all
> that such a world exists, and those who adopt the many worlds
> interpretation of quantum mechanics have no more justification
> for their assertion that parallel worlds exist than does the
> person who asserts the existence of the falling-upwards world.
>
An example i use sometimes to visualize what is the meaning between
an "objective" universe between a "continually-branching" universe is
usually draw from the classical physics box: I guess you can call it a
gedanken teletransporter classical machine (ie: [p,q]=0, dp/dt=-dH/dq
, dq/dt=dH/dp ). In principle this gedanken is just a toy-idea with no
further validity to understand any true physics, just to get insight
into the perspective of the "observer observing an observer observe
quantum phenomena" vs. "observer observing quantum phenomena"
Lets suppose we live in a classical world, where particles positions
and momenta can simultaneously be known with infinite accuracy. Lets
suppose we have a machine that can read all microscopic relevant
information from a macroscopic object to generate a full replica. Then
the experiment is arranged with a reading pod is connected to two
recomposing pods in separate equal rooms, with a single difference: in
front of the chair pod of one of the rooms there is a poster with a
big "A", and a big "B" in the poster in the other room. Then a
willingful self-experimentalist enters the reading pod (that will
disintegrate it completely while reading the useful info for
duplicating, using the atoms for recycling/agriculture purposes) and
after some Zaps, two copies of the same person appear in two separate
rooms. One of the copied persons has seen just after being teleported
a big "A", the other copy has seen a big "B".
This account was what an observer observing an observer would have
seen. The question i drop now is: what does the observer in first
place see?
I personally quickly can dismiss ill-formed answers like "he doesnt
see anything because he died when he was disintegrated in the reading
pod" or "he see boths because he is two persons know", but i'll do the
strong assumption most people following the argument can get a pass on
that
Another, more appealing, but still temptative answer is: "he enters
into a reading pod, then after being teleported, he sees a big "A"
with 50% probability, and a big "B" with 50% probability."
Its possible to enter into interesting (but still COMPLETELY
physically irrelevant) disgresions about consciousness tunneling
fairies now, but i will pass :)
the point im badly trying to make here is that under a perfect
classical world, even if we have a physically deterministic system
(two classical copies of a human made, original evaporated) can be
understood as probabilistic when seen by a part of the system,
specially when that is a self-conscious part that is going to
interpret what he sees as a measurement and advocate this or that
measurement theory)
the problem that poses QM is esentially that we cannot understand the
"true physics behind" without solving the QM system of system +
measurement device + experimenter, unless we appeal to strong but
effective concepts as collapse of wavefunctions. In this sense, MWI is
not even a theory in itself, is just a loud statement saying "We have
to include the observer as part of the full wavefunction to solve!",
which i think is not trivial
Daniel Elander
> Of course if we have an anisotropic system with a higher amplitude for
> + for Bob and - for Alice, the end result will be
>
> c_1 |Alice - >|Bob + > + c_2 |Alice + >|Bob - >
>
> Now both of these non interacting branches exist if we take MWI
> serious and it is pure chance in which we happen to talk about it. The
> amplitudes don't translate into propabilities.
Why not? You stated that the branches are non-interacting, so they
ought to be orthogonal. It seems to me that you just need to square
the amplitudes to get the probability.
> So the theory requires a non local comparsion of the branches to
> insert by hand the observed propabilities and thus you get non
> locality again.
What do you mean by a non-local comparison of the branches? How would
you experimentally compare the branches?
Jerzy Karczmarczuk
Oliver Jennrich wrote:
//About the thought experiment on "sequentiality" of photons//
> What's worse, passages like
>
> | Nevertheless, the photon has not
> | been [permanently] absorbed by the atom, so no interaction between
> | the photon and the atom seems to have taken place.
>
> makes me wonder if the authors really think that an absorption with a
> re-emission can be considered as "no interaction".
Sometimes there are even more nasty fallacious arguments in the literature.
Some yeons ago I have read about an experiment whose authors considered
that the beam particles interacting with a target, and continuing their
paths *exactly* forward, in fact didn't interact at all.
I was shocked, since I thought that the fundamentals of the optical
theorem is taught to everybody studying physics, including hard
experimentalists...
Jerzy Karczmarczuk
scerir
"Daryl McCullough"
> The problem is that every theory has a few
> loose ends---details that are not completely
> spelled out by the theory. Different interpretations
> may fill in these details differently.
EPR wrote that "if, without in any way disturbing
a system, we can predict with certainty (i.e. with
probability equal to unity) the value of a physical
quantity, then there exists an element of physical
reality corresponding to this physical quantity."
Notice that they use the term "predict", which is
different, of course, from conditional probabilities.
Now the question seems to be: is the above condition
("realism") fulfilled by one of those many interpretations
of QM? What about - paradoxically - the MWI?
s.
backdoorstudent
> > (Charles J. Quarra) wrote in message news:
>
> The experiment described there fits just fine within MWI. Why do you
> believe it rules anything out?
>
>
> [Moderator's note: In general different _intepretations_ of quantum mechanics
> tend to be indistinguishable by experiment, otherwise they would be different
> theories, not different ways to talk about the same theory. -usc]
This is not entirely correct. There are different interpretations
(theories) of quantum mechanics that are in principle physically
distinguishible. For example, the deBroglie-Bohm (and other stochastic
theories based on a quantum potential) and the
Ghirardi-Rimini-Weber-Pearle spontaneous localization interpretations
differ from standard quantum theory in specific instances. Indeed,
their proponents actually call them "theories". As the technology
progresses experiments are expected to actually test these ideas.
Sorry to diverge from the topic a little here, but I think the terms
"interpretation" and "theory" have become hideously blurred in quantum
mechanics. Even the people who claim to use QM without interpretation
tend to sneak in assumptions unconsciously. And in my opinion, it has
become too dogmatic and fashionable to accuse those who want a
conceptually coherent quantum theory of being "classically
predjudiced" or practising metaphysics.
Charlie Stromeyer Jr.
> > http://arxiv.org/abs/quant-ph/0102109
>
> The problem with this paper, though, is that it doesn't describe a
> real experiment, much less presents any measurements, data, anything,
> that is likely to show the postulated effects.
Neither Newton nor Einstein themselves did actual experiments to
measure the effects of gravity but this did not prevent their ideas
from being correct!
Either the above paper is mathematically valid within the formalism of
quantum theory or it is not. So far, I do not see a flaw in the paper,
but this issue will take me some time to think about. Of course, there
remains the possibilty if such an experiment were actually performed
that there would be some new effect introduced which I am currently
not intuiting, e.g. superconductivity was discovered by accident and
nuclear fission would have been discovered by accident in 1935 by
Emilio Segre if a piece of metal like tinfoil had not been blocking
the tell-tale signal.
> What's worse, passages like
>
> | Nevertheless, the photon has not
> | been [permanently] absorbed by the atom, so no interaction between
> | the photon and the atom seems to have taken place.
>
> makes me wonder if the authors really think that an absorption with a
> re-emission can be considered as "no interaction".
Ah, but this is why it is called "interaction free measurement" (IFM),
and the authors are not discussing here what they might think per se,
but are instead discussing work done a decade previously by L. Hardy.
Frank Hellmann
dan...@elit.net (Daniel Elander) wrote in message news:<37d84b42.04060...@posting.google.com>...
> > Of course if we have an anisotropic system with a higher amplitude for
> > + for Bob and - for Alice, the end result will be
> >
> > c_1 |Alice - >|Bob + > + c_2 |Alice + >|Bob - >
> >
> > Now both of these non interacting branches exist if we take MWI
> > serious and it is pure chance in which we happen to talk about it. The
> > amplitudes don't translate into propabilities.
>
> Why not? You stated that the branches are non-interacting, so they
> ought to be orthogonal. It seems to me that you just need to square
> the amplitudes to get the probability.
>
But in MWI you don't have collapse or anything like it. If both
branches with different amplitudes exist then what makes it more
likely for us to be in one then in the other branch? Nothing both are
equally likely.
The square of the amplitudes has no meaning in the MWI analysis of the
meassurment process (neccesarily, it's all firmly based on linear QM
after all), and thus the meassurment process can according to this
analysis not depend on the amplitude either.
The only thing that could work would be if we split up into enough
branches to create the propabilities.
for a 100/1 propability we would split in a hundred and one branches
out of which only one carries the unlikely result.
But that would interfere with the orthogonality of the states (at
least on a naive level).
> > So the theory requires a non local comparsion of the branches to
> > insert by hand the observed propabilities and thus you get non
> > locality again.
>
> What do you mean by a non-local comparison of the branches? How would
> you experimentally compare the branches?
You couldn't which is why (at least naive) MWI falls flat. You have to
put in propabilities by hand in a non local way where the formalism
has no clear point where to insert them.
To make things a bit clearer, imagine a MWI experiment with an
experiment that has a 90% chance for result (1) and a 10% chance for
result (2).
A physicist repeats the experiment 5 times.
after the experiment you will have 2^5 branches and 2^5 physicists you
will have just as many physicists who observed 4 (1)s and 1 (2)s as
who observed 1 (1)s and 4 (2)s you get one physicist who observed only
(1)s and one who observed only (2)s
However it should of course be that the likelyhood to get 5 (1)s is
0.9^5 ~ 0.6 and 5 (2)s is 0.1^5 = 0.00001.
(this propabilities are encoded in the amplitude of course)
Now which are we in? It's random all branches exist after all.
If you want to recover the right behaviour at all you have to somehow
postulate that it's more likely we are in a higher intensity branch
(whatever that means, it doesn't actually make sense), to do that you
have to compare the branches (you can not even find out what the
propability for one branch is by just looking at that branch since you
can not assume that the whole thing was normalized before the
meassurement, after all we already are in a branch of a branch of a
branch).
Of course you can not even tell from within the system what the
amplitude is except by the propabilities you derive from them since
everything is linear!
Bottom line: (naive) MWI doesn't make any sense either.
I've heared people allude to a less naive MWI but I haven't seen
anything like that anywhere yet.
BTW this same analysis kills Bohmiam Mechanics as of course in it, too
both branches exist and crucially in every branch a Bohmian mechanicst
exists who calculates that the relevant particle is moving in his own
wave packet, therefore it is an MWI (with a bookeeping particle) and
actually subject to the same problem.
---
frank.