entangled states
te...@nospam.sdf-eu.org
and help me to understand what people are saying
here? It has to do with the quantum computing literature.
I read somewhere that when two quantum states are
entangled, the measurement of one will cause the
instantaneous collapse of the other. Of course everyone
knows that the wavefunction collapses from a measurement,
but the `instantaneous' thing is what bothers me here.
It explicitly violates causality irregardless of arguments
about `information'. Let's see...
Special relativity tells us that there is no universal
notion of simultaneity. Suppose I perform a double slit
experiment with the screen located very far away.
There is an interference pattern. I then collapse the
state by performing a measurement on one of the slits.
Now, according to what I read, the collapse was instantaneous
throughout all space and so the interference pattern
`instantly' disappears. This means that in the frame
of the apparatus, the measurement and the disappearance
of the pattern were simultaneous. This implies that
there are frames in which the pattern disappears after
the measurement and that there are frames in which
the pattern disappears _before_ the measurement. The
latter is an explicit violation of causality.
I.e. If this relationship is `instant' then it is a
causal connection between spacelike separated events.
Impossible. So it cannot be instant. Why is it claimed to be?
PS: It seems that Einstein already mentioned this
problem in his `auto-biographical notes' written when
he was about 67.
-Terry
winton
First of all I don't think that you can use entanglement between
physically separated systems to send information from one system to the
other so that you need not worry about this violating causality. To
cause an effect information needs to be sent. The problem with the wave
function collapse being instantaneous, which does not make much sense
becuase simultaneity depends on which reference frame you are talking
about, is discussed (I think) in this paper by asher peres asher peres:
quant-ph/0212023.
-Winton
Arnold Neumaier
> Could someone please explain the following dilemma
> and help me to understand what people are saying
> here? It has to do with the quantum computing literature.
>
> I read somewhere that when two quantum states are
> entangled, the measurement of one will cause the
> instantaneous collapse of the other. Of course everyone
> knows that the wavefunction collapses from a measurement,
> but the `instantaneous' thing is what bothers me here.
The problem is ill understood, hence the confusion.
Real measurements take time, and are not instantaneous.
To treat the collapse as instantaneous is an idealization,
valid for many applications of quantum mechanics.
If relativistic effects play a role, one needs to use
quantum field theory. However, the measurement process in
quantum field theory is very poorly researched.
Thus statements about the conflict of instantaneous collapse
and relativity theory are based on very shaky grounds.
For measurement in the relativistic case (but without
invoking field theory) see quant-ph/9906034 and other papers
by Peres and/or Terno available in the arxiv.
They indicate the absence of problems, as far as such a
simplified analysis can be trusted.
Arnold Neumaier
Ben Rudiak-Gould
> I read somewhere that when two quantum states are
> entangled, the measurement of one will cause the
> instantaneous collapse of the other.
They still teach that to undergraduates, and it's taken for granted by
the popular press, but there aren't many physicists who believe it. In
fact I don't think there ever were, even in the early days of quantum
mechanics. Bohr believed in the rules of quantum mechanics, but he
didn't believe that the collapse rule mirrored a phenomenon in the real
world.
> the `instantaneous' thing is what bothers me here.
> It explicitly violates causality irregardless of arguments
> about `information'.
No, the collapse could be real without leading to any paradoxes of
causality (at least in the absence of general relativity).
> Suppose I perform a double slit
> experiment with the screen located very far away.
> There is an interference pattern. I then collapse the
> state by performing a measurement on one of the slits.
> Now, according to what I read, the collapse was instantaneous
> throughout all space and so the interference pattern
> `instantly' disappears.
It doesn't, because it's generated by different photons. The photons you
detect at the slits won't reach the screen until later. It's just as
though you simply covered one of the slits.
> I.e. If this relationship is `instant' then it is a
> causal connection between spacelike separated events.
> Impossible.
Not impossible, just unheard of. It's worth thinking about why causality
violation is considered such a bad thing. There's no inherent problem
with an effect preceding a cause with respect to some frame. The
problems show up when there are closed causal loops, i.e. when A causes
B causes ... causes Z causes A. Forbidding FTL communication is
sufficient but not necessary to prevent causal loops in special
relativity. A much weaker condition which suffices is that no effect may
precede its cause with respect to some particular inertial frame S.
Effects may still precede causes with respect to other frames, but
that's not a paradox, just a somewhat surprising result.
-- Ben
Igor Khavkine
> I read somewhere that when two quantum states are
> entangled, the measurement of one will cause the
> instantaneous collapse of the other. Of course everyone
> knows that the wavefunction collapses from a measurement,
> but the `instantaneous' thing is what bothers me here.
> It explicitly violates causality irregardless of arguments
> about `information'. Let's see...
The word `instantaneous' is easily thrown around in the popular
scientific literature, but must be used with much more care in any
serious discussion.
> Special relativity tells us that there is no universal
> notion of simultaneity. Suppose I perform a double slit
> experiment with the screen located very far away.
> There is an interference pattern. I then collapse the
> state by performing a measurement on one of the slits.
> Now, according to what I read, the collapse was instantaneous
> throughout all space and so the interference pattern
> `instantly' disappears. This means that in the frame
> of the apparatus, the measurement and the disappearance
> of the pattern were simultaneous. This implies that
> there are frames in which the pattern disappears after
> the measurement and that there are frames in which
> the pattern disappears _before_ the measurement. The
> latter is an explicit violation of causality.
>
> I.e. If this relationship is `instant' then it is a
> causal connection between spacelike separated events.
> Impossible. So it cannot be instant. Why is it claimed to be?
You have one right idea: simultaneity is only defined in special
relativity when a reference frame is specified. Thus, as you've pointed
out, when two measurements are made on space-like separated components
of an entangled system, each measurement can be seen as made either
before or after the other, depending on the frame of reference.
Together with the principle of causality, this should give you a hint
that nothing is actually transfered from the location of one
measurement to the other.
But you do have one idea wrong: correlation does not imply causation.
Quantum mechanics predicts that the outcomes of two measurements
performed on an entangled system may be correlated (knowing one will
tell you the other, and vice versa). However, it says nothing about one
measurement causing the outcome of another measurement. Especially, if
the two measurements are space-like separated, the ambiguity in their
temporal ordering should be enough to make the lack of such predictions
from QM self evident.
If we have to measurements, A and B, correlation is a symmetric
relationship. If A is correlated with B, then B is correlated with A.
On the other hand, causation is only one-way. If A causes B, then B
does not cause A. QM predicts a symmetric relationship between the
measurements, hence it can only refer to correlation. On the other
hand, there is nothing in special relativity that prevents correlation
at space-like separations, it only imposes restrictions on causation.
Hope this helps.
Igor
Nick Maclaren
winton <winton....@dartmouth.edu> writes:
|>
|> First of all I don't think that you can use entanglement between
|> physically separated systems to send information from one system to the
|> other so that you need not worry about this violating causality. To
|> cause an effect information needs to be sent.
That is correct, but is currently merely a belief based on minimal
evidence. There is, of course, NO evidence of the contrary :-)
|> The problem with the wave
|> function collapse being instantaneous, which does not make much sense
|> becuase simultaneity depends on which reference frame you are talking
|> about, is discussed (I think) in this paper by asher peres asher peres:
|> quant-ph/0212023.
Not so. There is a perfectly reasonable concept of simultaneity
between two frames, but it isn't the same as the naive one. The
case where it IS the same, is where the two measurements are taken
in spatially separated locations at rest with respect to each other.
Note that, in that case, instantaneous communication does not breach
causality.
Regards,
Nick Maclaren.
Nick Maclaren
In article <1136922276.3...@g43g2000cwa.googlegroups.com>,
"Igor Khavkine" <igo...@gmail.com> writes:
|>
|> But you do have one idea wrong: correlation does not imply causation.
|> Quantum mechanics predicts that the outcomes of two measurements
|> performed on an entangled system may be correlated (knowing one will
|> tell you the other, and vice versa). However, it says nothing about one
|> measurement causing the outcome of another measurement.
Agreed.
|> Especially, if
|> the two measurements are space-like separated, the ambiguity in their
|> temporal ordering should be enough to make the lack of such predictions
|> from QM self evident.
There is no ambiguity in the temporal ordering of events where
the measurements are separated solely by distance (i.e. are not
moving with respect to one another). There is a unique ordering
that is globally consistent.
Perhaps I should spell out in detail the experiment that I would
like to see done.
Take two experiments, A and B, each with a synchronised clock and
a copy of an entangled object, and separate them to a distance of
D light-seconds (and zero velocity), where D is at least 10 times
the temporal resolution of the state measurements.
Correct the clocks to allow for the relativistic effects, which
can be calculated consistently using the (known) accelerations
of A and B. A and B now have a consistent clock.
Take a (long) series of measurements of entangled states in A and
B, starting from an agreed moment. The times should be of the
form p+xD and q+xD, for all of p=0,q=D/5, p=D/5,q=0, p=0,q=0, and
for x=D/4 and x=4D. Or whatever - those numbers are arbitary, and
are chosen to avoid ambiguity.
Rejoin the experiments, and compare the time series, unshifted,
shifted by +D and -D and any others that take your fancy.
Provided that entanglement exists, SOMETHING interesting will come
out of that.
Regards,
Nick Maclaren.
Terry Pilling
there are many different ideas here. I have a couple of
points to make in response:
1) I don't like talking about `information' unless you
can define it for me and show me where it appears in
the relevant equations. The situation seems to me as this:
You have a photon field source in front of two screens, one
of them with two holes in it. When you place a measuring
apparatus around one of the holes you are introducing an
interaction vertex there. In other words you are placing
a new sink and source of the field there which did not
exist. This will destroy the correlation at the screen
and eliminate the pattern, but it still does not imply
anything happens instantaneously. In QFT everything obeys
relativity. No change in the field will propagate faster
than c. If I see a pattern disappear _before_ I introduce
the measurment at the slit (which is exactly what some
people seem to be claiming), I have then seen an _observable_
event occur before the _observable_ and known cause of it. This
is an explicit violation of causality regardless of how
you talk about it philosophically. It ain't philosophy,
it is observable physics here.
2) If you try to get out of the contradiction (not paradox, contradiction)
by assuming that all frames see the two events occurring simultaneously
then you again contradict relativity because simultaneity is not Lorentz
invariant. So you must be saying that relativity is wrong. Ridiculous.
3) Another way out could be for all frames to see
the interference pattern persist until they see the measurement.
But this would suggest a new group of transformations under
which nature must be invariant, since it cannot occur for frames
Lorentz related (a Lorentz transformation will not change a collapsed
interference pattern back into an interference pattern, for example,
as would be required for an observer that has seen the screen but not
yet the measurment) I find this difficult to accept.
4) Here is a different physical situation which exemplifies the
same underlying problem with the interpretation that a measurement
of an observable _causes_ an intantaneous change in the field
throughout all space (as opposed to a propagating change):
Suppose two so-called `entangled particles' (whatever that means)
are produced at a point and allowed to move freely until separated
by some distance (a well known situation).
By pre-arrangement, an observable is measured on one of them followed
a short time later by a measurement on the second (an experiment easily
set up). The two measurment events will be spacelike separated (i.e. _not_
causally connected) and so there will be observers for which either
measurement occurs first.
A commonly stated point of view is that the first measurement event
actually affects the second one and in fact is the physical cause
of the result of the second. This is impossible. Notice that
it _is_ possible if the two observables were determined at the
moment the two particles are produced so that the act of measurment
was merely passive observation. But this is not what is claimed.
The claim is that nothing is determined until the first measurement
is made and this _causes_ the other observable to be affected.
If this is the case, show me where, in QED, you have a field
variable propagating from one to the other and causing the change,
and show that this propagation is instant. You can't show this
because it is impossible in QED or any relativistic quantum
field theory. So what these people must be claiming is that
the creation of two photons can not be described in quantum
field theory! A suggestion that is ridiculous in light of the
successes of QED in describing that very thing.
--
-Terry
Ilja Schmelzer
> Could someone please explain the following dilemma
> and help me to understand what people are saying
> here? It has to do with the quantum computing literature.
> I read somewhere that when two quantum states are
> entangled, the measurement of one will cause the
> instantaneous collapse of the other. Of course everyone
> knows that the wavefunction collapses from a measurement,
> but the `instantaneous' thing is what bothers me here.
> It explicitly violates causality irregardless of arguments
> about `information'. Let's see...
Not causality, only Einstein causality.
> Special relativity tells us that there is no universal
> notion of simultaneity.
No, it tells there are many possible notions of simultaneity,
and looking at the observable effects we cannot tell which
is the correct one.
> Suppose I perform a double slit
> experiment with the screen located very far away.
> There is an interference pattern. I then collapse the
> state by performing a measurement on one of the slits.
> Now, according to what I read, the collapse was instantaneous
> throughout all space and so the interference pattern
> `instantly' disappears. This means that in the frame
> of the apparatus, the measurement and the disappearance
> of the pattern were simultaneous. This implies that
> there are frames in which the pattern disappears after
> the measurement and that there are frames in which
> the pattern disappears _before_ the measurement. The
> latter is an explicit violation of causality.
The problem is that the phrase "the interference pattern
disappears" suggests that something in the observable
results changes.
But the observable result, if you ignore correlations between
the two parts, is usually the sum of two interference patterns,
and looking at this sum alone (without knowing its
decomposition) you cannot observe any interference pattern.
Thus, the effect cannot be used to transfer any information
FTL.
> I.e. If this relationship is `instant' then it is a
> causal connection between spacelike separated events.
> Impossible.
Possible, if we go back to a preferred frame theory.
> So it cannot be instant. Why is it claimed to be?
The other problem is that in any realistic explanation/interpretation
of quantum entanglement you need a preferred frame. A consequence
of the violation of Bell's inequality. One way of a realistic
interpretation would be to assign the wave function some
status of reality. This is done in Bohmian mechanics, Nelsonian
stochastics as well as in realistic collapse pictures. But the wave
function (wave functional in field theory, to be distinguished
from Dirac psi fields) needs a preferred frame.
Note: There are different possible choices of simultaneity.
Each choice allows some realistic causal explanation in terms
of the preferred frame, that means, with something FTL or
instantaneous in this preferred time, violating Einstein causality,
but not absolute causality related with this choice of time t.
These different possible explanations disagree with each other.
Nonetheless, seeing only the observable effect we cannot tell
which of them is correct.
More specific: If t(A)<t(B) an explanation with A->B is
used, else with B->A. All explanations violate Einstein causality.
But classical causality remains intact.
Ilja
Ilja Schmelzer
> You have one right idea: simultaneity is only defined in special
> relativity when a reference frame is specified. Thus, as you've pointed
> out, when two measurements are made on space-like separated components
> of an entangled system, each measurement can be seen as made either
> before or after the other, depending on the frame of reference.
> Together with the principle of causality, this should give you a hint
> that nothing is actually transfered from the location of one
> measurement to the other.
A wrong hint. The situation can indeed be interpreted in two ways:
t(A) < t(B) and (for another choice of t) reverse. (From point of
view of Lorentz/Poincare two hypotheses about the actual
state of motion of the ether.)
But the description what _actually_ happens can,
of course, also depend on this _actual_ state, therefore,
depend on the choice of t. Thus, for every t we have an explanation:
A->B resp. (for the other choice of t) B->A.
(Bohmian mechanics, which depends on a preferred frame, gives
you an example of this scheme. BM1, using t1 as the preferred
frame, gives the deterministic, causal in t1, explanation A->B,
BM2, using t2 as the preferred frame, gives another deterministic
but causal in t2 explanation.)
Two explanations (and, as a consequence, no possibility to
use the effect for FTL information transfer, because each use
would contradict one of the explanations), but all
explanations violate Einstein causality. If something is wrong
in every realistic explanation it is wrong.
> But you do have one idea wrong: correlation does not imply causation.
Of course, but the correlations used in Bell's inequality are very
special ones, between the results of the measurements m_A, m_B
as well as the control parameters (choices of the experimenters)
c_A, c_B.
> Quantum mechanics predicts that the outcomes of two measurements
> performed on an entangled system may be correlated (knowing one will
> tell you the other, and vice versa). However, it says nothing about one
> measurement causing the outcome of another measurement.
No, the violation of Bell's inequality tells a lot, at least if we accept
the
necessity of realistic explanations. (Else, using phrases like
"nothing is _actually_ transfered", as you do, would be meaningless.)
> Especially, if
> the two measurements are space-like separated, the ambiguity in their
> temporal ordering should be enough to make the lack of such predictions
> from QM self evident.
It is far away from being self-evident. The violation of Bell's
inequality has to be considered as a classical example
of an indirect observation of a violation of Einstein causality:
Every reasonable explanation contains a violation of Einstein
causality.
> If we have to measurements, A and B, correlation is a symmetric
> relationship. If A is correlated with B, then B is correlated with A.
> On the other hand, causation is only one-way. If A causes B, then B
> does not cause A. QM predicts a symmetric relationship between the
> measurements, hence it can only refer to correlation.
The claim "There exists a causal connection A->B or B->A" (which
is the realistic consequence of violations of Bell's inequality) is
symmetric in A and B but refers to causation.
A correlation requires explanation. Realists accept three types of
explanations: A->B; B->A; C->A and C->B (common cause).
Bell's inequality excludes the common cause. A->B or B->A
remains.
For non-realists we have, instead, four explanations:
A->B; B->A; C->A and C->B; a quantum miracle happens.
> On the other
> hand, there is nothing in special relativity that prevents correlation
> at space-like separations, it only imposes restrictions on causation.
In a realistic interpretation, Einstein causality forbids violations of
Bell's inequality.
Ilja
Hendrik van Hees
> Suppose two so-called `entangled particles' (whatever that means)
> are produced at a point and allowed to move freely until separated
> by some distance (a well known situation).
> By pre-arrangement, an observable is measured on one of them followed
> a short time later by a measurement on the second (an experiment
> easily set up). The two measurment events will be spacelike separated
> (i.e. _not_ causally connected) and so there will be observers for
> which either measurement occurs first.
>
> A commonly stated point of view is that the first measurement event
> actually affects the second one and in fact is the physical cause
> of the result of the second. This is impossible.
It might be a commonly stated point of view, but it's wrong, at least it
is not the physics described by quantum theory. You pointed it out
correctly in your description above: The entangled two-particle state
was prepared at the very beginning, and this implies the strict
correlations of the entangled observables (e.g., the polarisation state
of two entangled photons in Zeilinger's famous "teleportation"
experiment). Although the single-particle observables are totally
undetermined, the correlation between the outcome of measurements is
100% sure. The measurement on one particle does *not* instantaneously
act on the other particle, which is far away, but the correlation
existed the whole time from the preparation of the particle pair.
> Notice that
> it _is_ possible if the two observables were determined at the
> moment the two particles are produced so that the act of measurment
> was merely passive observation.
As I said, that's exactly the case.
> But this is not what is claimed.
> The claim is that nothing is determined until the first measurement
> is made and this _causes_ the other observable to be affected.
Where is this claimed? I hope not in any quantum-mechanics textbook?
> If this is the case, show me where, in QED, you have a field
> variable propagating from one to the other and causing the change,
> and show that this propagation is instant. You can't show this
> because it is impossible in QED or any relativistic quantum
> field theory. So what these people must be claiming is that
> the creation of two photons can not be described in quantum
> field theory! A suggestion that is ridiculous in light of the
> successes of QED in describing that very thing.
FACK.
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:he...@comp.tamu.edu
Nick Maclaren
Ilja Schmelzer <Ilja.Sc...@FernUni-Hagen.de> wrote:
><te...@nospam.sdf-eu.org> schrieb
>> Could someone please explain the following dilemma
>> and help me to understand what people are saying
>> here? It has to do with the quantum computing literature.
>
>> I read somewhere that when two quantum states are
>> entangled, the measurement of one will cause the
>> instantaneous collapse of the other. Of course everyone
>> knows that the wavefunction collapses from a measurement,
>> but the `instantaneous' thing is what bothers me here.
>> It explicitly violates causality irregardless of arguments
>> about `information'. Let's see...
>
>Not causality, only Einstein causality.
By which I assume that you mean causality, with the cause required
to travel no faster than light. I am not sure that I like that
expression ....
Such nitpicking apart, you are quite right. To violate causality,
you need a lot more than is currently believed that entangled states
can provide. FTL information transfer does not necessarily violate
causality, despite the frequent claims that it does so.
Regards,
Nick Maclaren.
Blackbird
>[...]
> Special relativity tells us that there is no universal
> notion of simultaneity. Suppose I perform a double slit
> experiment with the screen located very far away.
> There is an interference pattern. I then collapse the
> state by performing a measurement on one of the slits.
> Now, according to what I read, the collapse was instantaneous
> throughout all space and so the interference pattern
> `instantly' disappears.
>[...]
No. In this frame (and all other frames), the interference pattern
disappears *after* you perform the measurement, and the delay is equal to
the time it takes light to travel from the slits to the screen. The setup
yot describe is not entaglement. There is no conceptual difference between
what you describe, and e.g. an experiment where you suddenly turn off a
flashlight. A screen some distance away will still be illuminated for some
time after the light is turned off.
Terry Pilling
> Terry Pilling wrote:
> > Suppose two so-called `entangled particles' (whatever that means)
> > are produced at a point and allowed to move freely until separated
> > by some distance (a well known situation).
> > By pre-arrangement, an observable is measured on one of them followed
> > a short time later by a measurement on the second (an experiment
> > easily set up). The two measurment events will be spacelike separated
> > (i.e. _not_ causally connected) and so there will be observers for
> > which either measurement occurs first.
> >
> > A commonly stated point of view is that the first measurement event
> > actually affects the second one and in fact is the physical cause
> > of the result of the second. This is impossible.
> It might be a commonly stated point of view, but it's wrong, at least it
> is not the physics described by quantum theory. You pointed it out
> correctly in your description above: The entangled two-particle state
> was prepared at the very beginning, and this implies the strict
> correlations of the entangled observables (e.g., the polarisation state
> of two entangled photons in Zeilinger's famous "teleportation"
Good! This kind of thing has always bothered me though. It seems
like you can always find two people who will have a philosophical
difference about what is going on here. However I don't see why.
Even in non-relativistic quantum mechanics the equations are completely
deterministic in terms of the amplitude. It is only in the last step,
interpreting the squared amplitude, where statical arguments come into play.
Of course the statistical measurements of two entangled states will
be correlated. It is a consequence of the underlying amplitudes
being determined by the equations of motion along with initial
and boundary conditions. The problem that I was having, and which
you have cleared up for me, is that some people have a different
viewpoint of how things work here and are quite convinced that they
are right and that it is me who is confused.
> Although the single-particle observables are totally
> undetermined, the correlation between the outcome of measurements is
> 100% sure. The measurement on one particle does *not* instantaneously
> act on the other particle, which is far away, but the correlation
> existed the whole time from the preparation of the particle pair.
Exactly how I have always viewed it.
> > But this is not what is claimed.
> > The claim is that nothing is determined until the first measurement
> > is made and this _causes_ the other observable to be affected.
> Where is this claimed? I hope not in any quantum-mechanics textbook?
I hope not also, but I have argued it with several people, seen
posts and discussions claiming this. I have even heard this statement:
"I know it doesn't make sense, but that is quantum mechanics,
you just have to accept it". To which I feel like replying "then you
had better learn some quantum theory, because it makes perfect sense and
it ain't anything like you seem to claim". Where are people being taught
that quantum theory doesn't make sense and has to be taken on faith?
Hopefully not in any physics departments.
I appreciate your reply Hendrik.
--
-Terry
---------------------------------------------------
Terry Pilling
Department of Physics
North Dakota State University
(701) 231-5780
terry[at]member.ams.org
http://www.physics.ndsu.nodak.edu/people/index.html
---------------------------------------------------
Ilja Schmelzer
> The entangled two-particle state
> was prepared at the very beginning, and this implies the strict
> correlations of the entangled observables (e.g., the polarisation state
> of two entangled photons in Zeilinger's famous "teleportation"
> experiment). Although the single-particle observables are totally
> undetermined, the correlation between the outcome of measurements is
> 100% sure. The measurement on one particle does *not* instantaneously
> act on the other particle, which is far away, but the correlation
> existed the whole time from the preparation of the particle pair.
That's wrong. As far as it is possible to make the notion "a correlation
existed" certain - that means, as far as we accept a notion of realism -
it is possible to prove that from this scenario (the correlation existed
the whole time) follows Bells inequality. But Bells inequality is
violated in quantum theory.
> > If this is the case, show me where, in QED, you have a field
> > variable propagating from one to the other and causing the change,
> > and show that this propagation is instant. You can't show this
> > because it is impossible in QED or any relativistic quantum
> > field theory.
I can show. Very easy. In any realistic theory.
(In other theories it is meaningless to talk about what really happens
and without that it is also meaningless to talk about causality. All you
have, if you reject realism, are correlations.)
Ilja
Andreas Most
> "Hendrik van Hees" <he...@comp.tamu.edu> schrieb
>
>>The entangled two-particle state
>>was prepared at the very beginning, and this implies the strict
>>correlations of the entangled observables (e.g., the polarisation state
>>of two entangled photons in Zeilinger's famous "teleportation"
>>experiment). Although the single-particle observables are totally
>>undetermined, the correlation between the outcome of measurements is
>>100% sure. The measurement on one particle does *not* instantaneously
>>act on the other particle, which is far away, but the correlation
>>existed the whole time from the preparation of the particle pair.
>
>
> That's wrong. As far as it is possible to make the notion "a correlation
> existed" certain - that means, as far as we accept a notion of realism -
> it is possible to prove that from this scenario (the correlation existed
> the whole time) follows Bells inequality. But Bells inequality is
> violated in quantum theory.
No! Saying "a correlation existed" does not mean that you accept a
sort of realism in the Bohmian meaning. It simply states that when
you perform a measurement of an observable A with the outcome x then
it is valid to say that if the measurement was performed earlier
(provided the wave function does not change) the outcome would have been
also x (and not y). So to say, the outcome is determined already when
the state is created. However, if you do not perform the measurement
this statement is meaningless because you do not even know what the
outcome of the measurement could have been.
The presumption for Bell's inequality is that the outcome of a
measurement is determined even if you do not perform the measurement.
Andreas.
Hendrik van Hees
> No! Saying "a correlation existed" does not mean that you accept a
> sort of realism in the Bohmian meaning. It simply states that when
> you perform a measurement of an observable A with the outcome x then
> it is valid to say that if the measurement was performed earlier
> (provided the wave function does not change) the outcome would have
> been also x (and not y). So to say, the outcome is determined already
> when the state is created. However, if you do not perform the
> measurement this statement is meaningless because you do not even know
> what the outcome of the measurement could have been.
> The presumption for Bell's inequality is that the outcome of a
> measurement is determined even if you do not perform the measurement.
Here, I think it is a little bit different. The correlation, described,
e.g., by the entangled two-photon polarisation state
|Psi>=1/sqrt(2)[|HV>-|VH>]
means that, if you find photon 1 (at position x) to be horizontally
polarised, then photon 2 (at position y) must be vertically polarized
and vice versa. It is not important whether you measure the
polarisation of photon 2 before or after photon 1 since these
correlations are already present at the preparation of the entangled
state (provided the entanglement is not destroyed while the photons
propagate to x and y).
This correlation does *not* imply that the polarization states are
predetermined by some hidden variables or the like. To the contrary,
these are maximally indetermined (see my answer to I. Schmelzer).
Hendrik van Hees
> That's wrong. As far as it is possible to make the notion "a
> correlation existed" certain - that means, as far as we accept a
> notion of realism - it is possible to prove that from this scenario
> (the correlation existed
> the whole time) follows Bells inequality. But Bells inequality is
> violated in quantum theory.
Here you misunderstood my previous explanation. If I understood your
conception of realism right (mainly from previous discussions in the
German newsgroups), my notion of the meaning of "quantum state" is not
a realistic view after all, since I think the only consistent
interpretation of quantum theory so far is Ballentine's minimal
statistical interpretation which assigns the quantum state to ensembles
of independently equally prepared systems rather than to an individual
system.
In this interpretation, for a correlation of single-particle observables
(say the polarisation states of the single photons in an
polarisation-entangled state), you do not need determined
single-particle observables at all.
Let's take this most simple example of polarisation-entangled photons.
The normalised polarisation state of the two-photon system is given by
|Psi>=1/sqrt(2)[|HV>-|VH>]
For each of the photons, the polarisation state is maximally
indetermined, since according to quantum statistics, to the single
photon we have to assign the statistical operator
R_{1}=Tr_2 |Psi><Psi|=1/2 (|H><H|+|V><V|),
i.e. measuring the single photon's polarisation, you find it with
probability 1/2 horizontally and with probability 1/2 vertically
polarised. Our knowledge about the polarisation state is thus minimal
(i.e. the Shannon-Jaynes-von Neumann-entropy is maximal).
Another point is that you cannot derive Bell's equality within this
interpretation of quantum theory (i.e., the minimal interpretation). To
the contrary, it is violated exactly for such entangled states. See for
instance, Gottfried's book (new edition) on quantum mechanics, which
uses the joint probability to measure the polarisation of one photon
and the polarisation of the other photon in the entangled pair with
polarisation filters with an arbitrary angle relative to each other.
Then one finds a violation of Bell's inequality, which follows only
under the assumption of the predetermination of the single-photon
polarisation within local hidden-variable theories.
> I can show. Very easy. In any realistic theory.
>
> (In other theories it is meaningless to talk about what really happens
> and without that it is also meaningless to talk about causality. All
> you have, if you reject realism, are correlations.)
Quantum theory is a causal theory in that the knowledge of the state of
a system (and the knowledge of the dynamics, "encoded" in the system's
Hamilton operator) determines its state completely at later times. The
knowledge of the state itself contains indeed only statistical
knowledge about the system, i.e., it cannot describe a single quantum
system but only ensembles of independently prepared systems. In this
sense quantum theory is not "realistic", because it cannot describe the
space-time evolution of single systems but only its stochastic
properties, we can principally have knowledge about. According to
quantum theory, we cannot have more than that probabilistic knowledge.
Of course, you may argue that quantum theory is not complete, and I
agree with that insofar the quantum theory is still not consistent with
general relativity.
Andreas Most
> Not impossible, just unheard of. It's worth thinking about why causality
> violation is considered such a bad thing. There's no inherent problem
> with an effect preceding a cause with respect to some frame. The
> problems show up when there are closed causal loops, i.e. when A causes
> B causes ... causes Z causes A. Forbidding FTL communication is
> sufficient but not necessary to prevent causal loops in special
> relativity. A much weaker condition which suffices is that no effect may
> precede its cause with respect to some particular inertial frame S.
> Effects may still precede causes with respect to other frames, but
> that's not a paradox, just a somewhat surprising result.
>
Hi Ben,
great analysis again. I always enjoy reading your postings.
However, you lost me with your last statement.
I agree that "forbidding FTL communication" is not the necessary
condition to prevent causal loops. But, as of my understanding,
the weaker condition, that no effect may precede its cause in some
inertial frame, directly implies that information cannot be communicated
faster than light. Otherwise you could use tachyons to send some
information into your own past.
Andreas.
Ilja Schmelzer
> Ilja Schmelzer wrote:
> > "Hendrik van Hees" <he...@comp.tamu.edu> schrieb
> >>The entangled two-particle state
> >>was prepared at the very beginning, and this implies the strict
> >>correlations of the entangled observables (e.g., the polarisation state
> >>of two entangled photons in Zeilinger's famous "teleportation"
> >>experiment). Although the single-particle observables are totally
> >>undetermined, the correlation between the outcome of measurements is
> >>100% sure. The measurement on one particle does *not* instantaneously
> >>act on the other particle, which is far away, but the correlation
> >>existed the whole time from the preparation of the particle pair.
> >
> > That's wrong. As far as it is possible to make the notion "a
correlation
> > existed" certain - that means, as far as we accept a notion of realism -
> > it is possible to prove that from this scenario (the correlation existed
> > the whole time) follows Bells inequality. But Bells inequality is
> > violated in quantum theory.
>
> No! Saying "a correlation existed" does not mean that you accept a
> sort of realism in the Bohmian meaning.
I see, the phrase "a correlation existed" may be meaningful also from
a purely positivistic point of view, where only observables are relevant.
But the full phrase was "existed the whole time from the preparation
of the particle pair", which already refers to something not observed,
thus, to some not purely positivistic idea of reality.
> It simply states that when
> you perform a measurement of an observable A with the outcome x then
> it is valid to say that if the measurement was performed earlier
> (provided the wave function does not change) the outcome would have been
> also x (and not y). So to say, the outcome is determined already when
> the state is created.
That's what I need. At least, I would interpret the notion "the outcome
is determined already when the state is created" in the following way:
The outcomes (m_A, m_B) in M={-1,1}x{-1,1} are determined by the
two-particle state (some x in some set X of possible two-particle states)
and the choice of the two experimenters in which direction they want to
measure, c_A, c_B in the subset of three directions {0,60 degree,120
degree}.
Means, there exists some function m_A(x,c_A,c_B) and m_B(x,c_A,c_B),
so that the expectation value of some function f on M is
E(f|c_A,c_B) = int f(m_A(x,c_A,c_B),m_B(x,c_A,c_B)) rho(x) dx
(That's what I have named "to make the notion certain".)
> However, if you do not perform the measurement
> this statement is meaningless because you do not even know what the
> outcome of the measurement could have been.
But a notion of _existence_ of something (the value or the correlation
observed later) at some moment of time t0 should not depend on
human decisions made at later time t>t0.
Moreover, a notion of a theory is not meaningless if it is possible to
derive physical predictions based on this notion. For the notion of
realism defined here this is possible. Especially we can derive the
prediction
Einstein causality (no dependence of m_A on c_B, m_B on c_A)
=> Bell's inequality.
That's the same sort of reasoning which we have to use to justify
quarks and colors - we do not see the colors, all what we see is
white, but this does not make color meaningless, because based on
the theory of color we can derive testable predictions.
> The presumption for Bell's inequality is that the outcome of a
> measurement is determined even if you do not perform the
> measurement.
Correct.
Ilja
Andreas Most
I fully agree with you. The point I was trying to make is, that
if (and only then) you find photon 1 (at position x) to be horizontally
polarised, it is legitimate to say you would have found the same result
if you had made the measurement earlier, even back to the creation time.
It would be a contradiction to assume the result could have been a
vertically polarised photon simply because you could have measured the
polarisation of photon 2 (which must be vertically polarised according
to our measurement) right after its creation.
I think that the outcome of the polarisation measurement is independent
of when the measurement is performed and is therefore in some sense
determined since its creation time. However, if you do not perform the
the measurement at all, the polarisation is maximally indetermined and
any (hidden) value has no sort of realism in the Bohmian meaning.
Andreas.
Nick Maclaren
>e.g., by the entangled two-photon polarisation state
>
>|Psi>=1/sqrt(2)[|HV>-|VH>]
>
>means that, if you find photon 1 (at position x) to be horizontally
>polarised, then photon 2 (at position y) must be vertically polarized
>and vice versa. It is not important whether you measure the
>polarisation of photon 2 before or after photon 1 since these
>correlations are already present at the preparation of the entangled
>state (provided the entanglement is not destroyed while the photons
>propagate to x and y).
Or by the process of measurement. This is at the heart of my question
about repeated measurements - unless you can measure without destroying
entanglement (even if possibly changing the state in unpredictable ways),
entanglement is theoretically pretty uninteresting and completely useless
for practical communication.
The standard claims by the quantum communication brigade definitely
do assume multiple measurements.
>This correlation does *not* imply that the polarization states are
>predetermined by some hidden variables or the like. To the contrary,
>these are maximally indetermined (see my answer to I. Schmelzer).
Grrk. Are you sure about the second sentence? What about location
A setting up entangled photons with known polarization states, and
then propagating the pair to locations B and C? Isn't that feasible?
Regards,
Nick Maclaren.
Hendrik van Hees
> I see, the phrase "a correlation existed" may be meaningful also from
> a purely positivistic point of view, where only observables are
> relevant. But the full phrase was "existed the whole time from the
> preparation of the particle pair", which already refers to something
> not observed, thus, to some not purely positivistic idea of reality.
The only thing I wanted to stress is that the two-photon
polarisation-entangled state
|Psi> \propto |HV>-|VH>
describes the 100% correlation of the single-photon polarisations
although those single-photon polarisations are *not* predetermined in
any way. They are "maximally unknown" in the sense of information
theory (Shannon-Jaynes-von Neumannentropie):
R_{single-photon polarisation}=1/2(|H><H|+|V><V|)=1/2 I.
Nick Maclaren
Ben Rudiak-Gould <br276d...@cam.ac.uk> wrote:
>
>Not impossible, just unheard of. It's worth thinking about why causality
>violation is considered such a bad thing. There's no inherent problem
>with an effect preceding a cause with respect to some frame.
I don't understand why that is regarded as a causality violation,
anyway. It seems a bizarre use of terminology. Whatever. As you say,
the fact that frame A gets a little confused about what is going on in
frames B and C is a mere oddity.
>The problems show up when there are closed causal loops, i.e. when A
>causes B causes ... causes Z causes A. Forbidding FTL communication is
>sufficient but not necessary to prevent causal loops in special
>relativity. A much weaker condition which suffices is that no effect may
>precede its cause with respect to some particular inertial frame S.
Yes. And that is a real causality violation, and would cause the
whole of modern philosophy and science to fall apart. But there is an
even weaker condition which is relevant here, in that it need apply
only to causes and effects that can be used to transfer information.
For example, consider frames A, B and C. It is possible to have a
causal loop A -> B -> C -> A but, if the loop affects probabilities
in such a way that A cannot detect whether the loop has taken place
or not, it doesn't matter that the effect transfers round the loop
backwards in time. Yes, the three of them can prove that causal
violation (of a sort) has taken place, but only by passing messages
using ordinary light - which means that it is too late to use the
information by the time they have found out!
The key here is distributions that are pairwise associated, but where
the association doesn't transfer to a third location.
>Effects may still precede causes with respect to other frames, but
>that's not a paradox, just a somewhat surprising result.
It isn't even surprising, to those of us who grew up in environments
where communications were slow. It wasn't rare to hear of a result
in advance of hearing of its announcement.
Regards,
Nick Maclaren.
Hendrik van Hees
>>This correlation does *not* imply that the polarization states are
>>predetermined by some hidden variables or the like. To the contrary,
>>these are maximally indetermined (see my answer to I. Schmelzer).
>
> Grrk. Are you sure about the second sentence? What about location
> A setting up entangled photons with known polarization states, and
> then propagating the pair to locations B and C? Isn't that feasible?
Sure, that's what's usually done in these kind of experiments (most
famous is perhaps Zeilinger's "teleportation" experiment).
The point is that the single-photon polarisation is kompletely unknown
for each of the photons in the two-photon entangled state, e.g., the
singlet state |HV>-|VH>.
Ilja Schmelzer
"Andreas Most" <Andrea...@nospam.de> schrieb
> Ben Rudiak-Gould wrote:
> > Not impossible, just unheard of. It's worth thinking about why causality
> > violation is considered such a bad thing. There's no inherent problem
> > with an effect preceding a cause with respect to some frame. The
> > problems show up when there are closed causal loops, i.e. when A causes
> > B causes ... causes Z causes A. Forbidding FTL communication is
> > sufficient but not necessary to prevent causal loops in special
> > relativity. A much weaker condition which suffices is that no effect may
> > precede its cause with respect to some particular inertial frame S.
> > Effects may still precede causes with respect to other frames, but
> > that's not a paradox, just a somewhat surprising result.
> great analysis again. I always enjoy reading your postings.
> However, you lost me with your last statement.
> I agree that "forbidding FTL communication" is not the necessary
> condition to prevent causal loops. But, as of my understanding,
> the weaker condition, that no effect may precede its cause in some
> inertial frame, directly implies that information cannot be communicated
> faster than light. Otherwise you could use tachyons to send some
> information into your own past.
The weaker condition requires a fixed choice of a preferred frame
or preferred time t. Then, causal connection A->B is possible
if t(A)<t(B).
That means that from point of view of other Lorentz frames t' it
may happen that t'(A)>t'(B), thus, information is send into the
"past" of "time" t'. But the "time" t' is in this interpretation only
some artificial local time-like coordinate with no fundamental
importance. Fundamental, and related with causality, is only
one time coordinate t.
Note that the mechanism which describes the FTL information
transfer necessarily violates Lorentz covariance, depends on
the preferred time.
Ilja
Andreas Most
> "Andreas Most" <Andrea...@nospam.de> schrieb
>> Ben Rudiak-Gould wrote:
>>> Not impossible, just unheard of. It's worth thinking about why causality
>>> violation is considered such a bad thing. There's no inherent problem
>>> with an effect preceding a cause with respect to some frame. The
>>> problems show up when there are closed causal loops, i.e. when A causes
>>> B causes ... causes Z causes A. Forbidding FTL communication is
>>> sufficient but not necessary to prevent causal loops in special
>>> relativity. A much weaker condition which suffices is that no effect may
>>> precede its cause with respect to some particular inertial frame S.
>>> Effects may still precede causes with respect to other frames, but
>>> that's not a paradox, just a somewhat surprising result.
>
>> great analysis again. I always enjoy reading your postings.
>> However, you lost me with your last statement.
>> I agree that "forbidding FTL communication" is not the necessary
>> condition to prevent causal loops. But, as of my understanding,
>> the weaker condition, that no effect may precede its cause in some
>> inertial frame, directly implies that information cannot be communicated
>> faster than light. Otherwise you could use tachyons to send some
>> information into your own past.
>
> The weaker condition requires a fixed choice of a preferred frame
> or preferred time t. Then, causal connection A->B is possible
> if t(A)<t(B).
I don't think this was Bens point.
> That means that from point of view of other Lorentz frames t' it
> may happen that t'(A)>t'(B), thus, information is send into the
> "past" of "time" t'. But the "time" t' is in this interpretation only
> some artificial local time-like coordinate with no fundamental
> importance. Fundamental, and related with causality, is only
> one time coordinate t.
Apart from the fact, that you obviously reject the relativity principle,
what exactly is the preferred frame and how can I identify it?
Is the preferred frame globally valid (in our universe) and static?
> Note that the mechanism which describes the FTL information
> transfer necessarily violates Lorentz covariance, depends on
> the preferred time.
FTL communication does not violate Lorentz covariance at all.
Tachyons are described perfectly well in a covariant way.
The problem is causality.
>
> Ilja
Andreas.
Ilja Schmelzer
> > That's wrong. As far as it is possible to make the notion "a
> > correlation existed" certain - that means, as far as we accept a
> > notion of realism - it is possible to prove that from this scenario
> > (the correlation existed
> > the whole time) follows Bells inequality. But Bells inequality is
> > violated in quantum theory.
>
> Here you misunderstood my previous explanation. If I understood your
> conception of realism right (mainly from previous discussions in the
> German newsgroups), my notion of the meaning of "quantum state" is not
> a realistic view after all, since I think the only consistent
> interpretation of quantum theory so far is Ballentine's minimal
> statistical interpretation which assigns the quantum state to ensembles
> of independently equally prepared systems rather than to an individual
> system.
Ok. But, in this case, if you want to be consistent, you should be careful
not to use realistic terminology.
I know thats hard. And that it is that hard is IMHO also an argument
in favour of realism.
> In this interpretation, for a correlation of single-particle observables
> (say the polarisation states of the single photons in an
> polarisation-entangled state), you do not need determined
> single-particle observables at all.
But what we observe in reality ;-) are single events. Only later we
combine all our single observations into a statistical picture, which
may be compared with QM predictions. In this sense, QM
is obviously incomplete.
(To say "there are single events, but it is impossible to make
predictions about them" already uses realistic language and
therefore presupposes some notion of realism.)
> Let's take this most simple example of polarisation-entangled photons.
There is no disagreement about the math.
> Another point is that you cannot derive Bell's equality within this
> interpretation of quantum theory (i.e., the minimal interpretation). To
> the contrary, it is violated exactly for such entangled states. See for
> instance, Gottfried's book (new edition) on quantum mechanics,
No necessity, because I have never questioned that to prove
Bell's inequality you need some notion of reality.
In the theory "Gods Will is unpredictable and unexplainable" I
cannot prove Bell's inequality too.
> Then one finds a violation of Bell's inequality,
It has also never been questioned that Bell's inequality is
violated in QM.
> > I can show. Very easy. In any realistic theory.
> >
> > (In other theories it is meaningless to talk about what really happens
> > and without that it is also meaningless to talk about causality. All
> > you have, if you reject realism, are correlations.)
>
> Quantum theory is a causal theory in that the knowledge of the state of
> a system (and the knowledge of the dynamics, "encoded" in the system's
> Hamilton operator) determines its state completely at later times.
As well, the state in later times determines the state in the past, at least
as long as we look only at unitary evolution, not on the collapse.
Moreover, I don't think it makes much sense to talk about
causality in a theory where we cannot even talk about single events.
The notion named "causality" in QM literature is IMHO better called
statistical correlation.
> The
> knowledge of the state itself contains indeed only statistical
> knowledge about the system, i.e., it cannot describe a single quantum
> system but only ensembles of independently prepared systems. In this
> sense quantum theory is not "realistic", because it cannot describe the
> space-time evolution of single systems but only its stochastic
> properties, we can principally have knowledge about.
I would insert "the minimal interpretation of" before "quantum theory".
> According to
> quantum theory, we cannot have more than that probabilistic knowledge.
That's already beyond the minimal interpretation. The minimal
interpretation simply remains silent. (Else, it would not be minimal,
and I would define a more minimal interpretation.)
Ilja
Ralph Hartley
> ... my question
> about repeated measurements - unless you can measure without destroying
> entanglement (even if possibly changing the state in unpredictable ways),
> entanglement is theoretically pretty uninteresting and completely useless
> for practical communication.
I won't argue with what you consider "uninteresting", but it isn't
*completely* useless.
Consider the application that is closest to practical use: quantum
cryptography.
Each entangled pair is measured exactly once by Alice and once by Bob.
After the first of those measurements the *quantum* entanglement is used
up, what is left is ordinary classical correlation i.e. Alice and Bob
both have the same key.
The fact that measurement destroys quantum entanglement is *essential*
to this application. That's what prevents Eve from making her own
measurements without being discovered.
Similarly in quantum "teleportation" (what a bad name). Each entangled
pair is used just once. The quantum entanglement is used up by the process.
> The standard claims by the quantum communication brigade definitely
> do assume multiple measurements.
I don't know what you mean. The above two examples do not assume that
(they do use multiple pairs), and most of the real communications
applications I am familiar with are variations on them.
If you mean claims of instantaneous communication etc., well they assume
a variety of untrue things.
Ralph Hartley
Andreas Most
> ...
> I see, the phrase "a correlation existed" may be meaningful also from
> a purely positivistic point of view, where only observables are relevant.
> But the full phrase was "existed the whole time from the preparation
> of the particle pair", which already refers to something not observed,
> thus, to some not purely positivistic idea of reality.
The correlation existed, not the outcome of the measurement.
If you start from an entangled state
|Psi>=1/sqrt(2)[|HV>-|VH>]
and you find photon 1 to be horizontally polarised you could have
as well started off with a wave function
|Psi>=|HV>
for this single photon pair. I.e., you would have found a horizontal
polarisation for photon 1, even if you had performed the measurement
earlier. But if you don't perform the measurement at all (i.e. the setup
does not force the state into the base {|H>,|V>} ) this reduction is
not only meaningless but also wrong, because you might e.g. decide to
measure the circular polarisation (i.e. the setup forces the state
into a different base).
> ...
> But a notion of _existence_ of something (the value or the correlation
> observed later) at some moment of time t0 should not depend on
> human decisions made at later time t>t0.
Existence is a pretty philosophical term. The question would be
what is the meaning of the existence of something that has no impact
on our universe at all as e.g. the unmeasured linear polarisation of
a photon. I could assume its existence as well as its nonexistence
without any change to the description of our world.
Andreas.
Oz
>
>|Psi>=1/sqrt(2)[|HV>-|VH>]
>
>polarised, then photon 2 (at position y) must be vertically polarized
>and vice versa. It is not important whether you measure the
>polarisation of photon 2 before or after photon 1 since these
>correlations are already present at the preparation of the entangled
>state (provided the entanglement is not destroyed while the photons
>propagate to x and y).
>
>predetermined by some hidden variables or the like. To the contrary,
>these are maximally indetermined (see my answer to I. Schmelzer).
Some years ago I attempted to understand bells inequality.
My proposal (for knocking down) envisaged a thought experiment where the
two particles had a circular polarisation that was (say) 180 deg out of
phase.
Now putting to one side any differing frame of reference, ie take it as
newtonian space. And allowing that the entangled particles were (in
effect) a single particle so that the *only* way you could extract a
sub-particle of spin up would be if it decomposed into a spin up and a
spin down particle.
I have undoubtedly made reams of faux pas here, but if you can read
between the lines a bit and point out that bell's inequality still
doesn't hold in this situation.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
Use o...@farmeroz.port995.com [ozac...@despammed.com functions].
BTOPENWORLD address has ceased. DEMON address has ceased.
Oz
>No! Saying "a correlation existed" does not mean that you accept a
>sort of realism in the Bohmian meaning. It simply states that when
>you perform a measurement of an observable A with the outcome x then
>it is valid to say that if the measurement was performed earlier
>(provided the wave function does not change) the outcome would have been
>also x (and not y). So to say, the outcome is determined already when
>the state is created.
Is this what bell's inequality states?
I don't know because, despite asking over a period of years, nobody has
ever come back with a clear description. For such a critical piece of
information I find this disturbing, its as if people don't really
properly understand it.
>However, if you do not perform the measurement
>this statement is meaningless because you do not even know what the
>outcome of the measurement could have been.
To be frank since the outcome was random and the only result statistical
you can't even give a result with most interactions when both particles
are prepared to be identical. So the above comment of yours surely can't
be true.
Nick Maclaren
Ralph Hartley <har...@aic.nrl.navy.mil> wrote:
>
>I won't argue with what you consider "uninteresting", but it isn't
>*completely* useless.
If it requires the physical transfer of one of each of a pair of
somethings to the two locations, and can provide only a bounded,
small number of 'entangled bits' for each physical transfer, then
I can justify why it is completely useless in a practical sense.
I.e. it provides no security advantages over a one-time pad.
That this is not just a matter of judgement, but a statement that
any class of attack against a one-time pad has an exact analogue
in an attack against quantum communication. I believe that this
statement could be made mathematically rigorous, and have drafted
such a proof (but lack the ability to make it watertight).
Note that the papers that demonstrate a provable security over a
one-time pad all use quantum communication for the data transfer
as well as the key (see below), and I am perfectly happy with that
proof. Yes, THAT usage is solid, but it implies that you can read
approximately as many entangled bits as the TOTAL number of bits in
ALL messages sent between the sites between physical resynchronisations.
And that, in a modern environment, is a large number.
For current IT, below 10^15 bits is sometimes small in this context,
and below 10^9 always is.
>The fact that measurement destroys quantum entanglement is *essential*
>to this application. That's what prevents Eve from making her own
>measurements without being discovered.
Yes, but what people who don't know about cryptanalysis often fail to
realise is that must apply to the DATA as well as the KEY. Hence the
requirement for a very large number, preferably an indefinite number,
of bits - a.k.a. an entangled channel.
As I told you by Email, I have looked at a fair number of papers,
been to several presentations, and have dismally failed to get a
clear answer to exactly what physical transfers are needed, and how
many entangled bits each one will provide. So far, nobody at a
seminar has responded by telling me that is not an interesting
question or that anyone with a clue would know the answer.
While this isn't shaping up to be another cold fusion, it definitely
has the feel of hot fusion (c. 1960). Some of those old documents
are worth reading, as antidotes against hubris.
Regards,
Nick Maclaren.
Hendrik van Hees
> Ok. But, in this case, if you want to be consistent, you should be
> careful not to use realistic terminology.
I try to use consistent terminology. For me an experimental setup in the
lab *is* realistic, and I use common language to describe it. Quantum
theory tells us that we cannot know all observables of a system with
certainty, and we cannot know the outcome of a measurement, when
measuring an observable which is not determined by the preparation of
the system in its actual quantum state, but we know probabilities about
the outcome of such a measurement. Of course we can test such
statements only on an ensemble of single systems, prepared in the
quantum state in question.
You may dream of a deterministic theory, where the outcome of all
measurements is predetermined by the preparation of the state, but
that's still a dream, and the success of quantum theory makes it very
difficult to make that dream come true ;-). Here we discuss physics,
not dreams!
> But what we observe in reality ;-) are single events. Only later we
> combine all our single observations into a statistical picture, which
> may be compared with QM predictions. In this sense, QM
> is obviously incomplete.
So far, no physical theory is complete. So what? Up to now QM describes
all outcomes of experiments very well. Maybe further scientific
progress comes up with a more satisfying explanation for the phenomeno.
So far it's not!
>
> (To say "there are single events, but it is impossible to make
> predictions about them" already uses realistic language and
> therefore presupposes some notion of realism.)
As I said, for me an experimental setup in the lab is real. Your notion
of "realism" is too narrow. One cannot talk about experiments without
that minimal "realistic language".
>
>> Let's take this most simple example of polarisation-entangled
>> photons.
>
> There is no disagreement about the math.
The math describes the outcome of experiments very well. So it's a
successful physical theory. I don't know, what you disagree about,
except a dream about a special philosophical conception about nature,
but nature does not care about our philosophical prejudices, but
behaves as she likes.
> No necessity, because I have never questioned that to prove
> Bell's inequality you need some notion of reality.
>
> In the theory "Gods Will is unpredictable and unexplainable" I
> cannot prove Bell's inequality too.
Quantum theory is much more than such religious conceptions. It's an
experimentally very success model about the objectively observable
"reality" as observed in the lab or everywhere else.
>
>> Then one finds a violation of Bell's inequality,
>
> It has also never been questioned that Bell's inequality is
> violated in QM.
It is violated in a way agreeing with QM, and thus it's very difficult
to think of a deterministic theory agreeing with all the observations,
QM describes successfully.
> As well, the state in later times determines the state in the past, at
> least as long as we look only at unitary evolution, not on the
> collapse.
There is no collapse. What should collapse? That's Copenhagen esoterics,
not quantum mechanics in its minimal interpretation.
>
> Moreover, I don't think it makes much sense to talk about
> causality in a theory where we cannot even talk about single events.
> The notion named "causality" in QM literature is IMHO better called
> statistical correlation.
The state (statistical operator) evolves according to causal laws.
That's why I call QM a causal theory. Without causality you'd really
need not do science at all. In my language QM is an indeterministic but
causal theory.
>
>> The
>> knowledge of the state itself contains indeed only statistical
>> knowledge about the system, i.e., it cannot describe a single quantum
>> system but only ensembles of independently prepared systems. In this
>> sense quantum theory is not "realistic", because it cannot describe
>> the space-time evolution of single systems but only its stochastic
>> properties, we can principally have knowledge about.
>
> I would insert "the minimal interpretation of" before "quantum
> theory".
Yes, and one should not interpret more into the theory than there is
contained in it.
>
>> According to
>> quantum theory, we cannot have more than that probabilistic
>> knowledge.
>
> That's already beyond the minimal interpretation. The minimal
> interpretation simply remains silent. (Else, it would not be minimal,
> and I would define a more minimal interpretation.)
This I do not understand. Minimal interpretation contains the
probabilistic interpretation of the state and takes this stochastic
nature of the QM description serious.
Ilja Schmelzer
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andrea...@nospam.de> schrieb
> >> Ben Rudiak-Gould wrote:
> >>> Not impossible, just unheard of. It's worth thinking about why
causality
> >>> violation is considered such a bad thing. There's no inherent problem
> >>> with an effect preceding a cause with respect to some frame. The
> >>> problems show up when there are closed causal loops, i.e. when A
causes
> >>> B causes ... causes Z causes A. Forbidding FTL communication is
> >>> sufficient but not necessary to prevent causal loops in special
> >>> relativity. A much weaker condition which suffices is that no effect
may
> >>> precede its cause with respect to some particular inertial frame S.
> >>> Effects may still precede causes with respect to other frames, but
> >>> that's not a paradox, just a somewhat surprising result.
> >> However, you lost me with your last statement.
> >> I agree that "forbidding FTL communication" is not the necessary
> >> condition to prevent causal loops. But, as of my understanding,
> >> the weaker condition, that no effect may precede its cause in some
> >> inertial frame, directly implies that information cannot be
communicated
> >> faster than light. Otherwise you could use tachyons to send some
> >> information into your own past.
> >
> > The weaker condition requires a fixed choice of a preferred frame
> > or preferred time t. Then, causal connection A->B is possible
> > if t(A)<t(B).
>
> I don't think this was Bens point.
The point is that there _is_ a condition weaker than "forbidding FTL
communication" which allows to prevent causal loops. (BTW, this
remains true even if you don't like this condition because it violates
a strong form of the relativity principle.)
> > That means that from point of view of other Lorentz frames t' it
> > may happen that t'(A)>t'(B), thus, information is send into the
> > "past" of "time" t'. But the "time" t' is in this interpretation only
> > some artificial local time-like coordinate with no fundamental
> > importance. Fundamental, and related with causality, is only
> > one time coordinate t.
>
> Apart from the fact, that you obviously reject the relativity principle,
I reject a strong form of the relativity principle. The weaker
form of the relativity principle, which is only about observables,
remains valid. (At least for distances large compared with the
critical length of unification of SM with gravity.)
> what exactly is the preferred frame and how can I identify it?
You can roughly identify it as the rest frame of CMBR.
> Is the preferred frame globally valid (in our universe) and static?
Yes. (You need a theory of gravity with preferred frame
for this purpose, see gr-qc/0205035.)
> > Note that the mechanism which describes the FTL information
> > transfer necessarily violates Lorentz covariance, depends on
> > the preferred time.
>
> FTL communication does not violate Lorentz covariance at all.
> Tachyons are described perfectly well in a covariant way.
> The problem is causality.
Ok, but if we include a reasonable notion of causality, without
causal loops, as an additional requirement for the mechanism,
my statement holds.
Ilja
Ilja Schmelzer
> > Ok. But, in this case, if you want to be consistent, you should be
> > careful not to use realistic terminology.
>
> I try to use consistent terminology. For me an experimental setup in the
> lab *is* realistic, and I use common language to describe it. Quantum
> theory tells us that we cannot know all observables of a system with
> certainty,
To know something with certainty is quite irrelevant for a realist if
the question is if something really exists.
If you reject realism, you not only give up some hope to know some
state of reality with certainty (or without certainty). In this case, you
nonetheless would be allowed to use realistic terminology.
> You may dream of a deterministic theory, where the outcome of all
> measurements is predetermined by the preparation of the state, but
> that's still a dream, and the success of quantum theory makes it very
> difficult to make that dream come true ;-). Here we discuss physics,
> not dreams!
I don't dream about a theory where everything may be predetermined
by some human preparation of the state. Realism is much weaker -
the hypothesis that there exists something out there which determines
the result of the measurement.
> > But what we observe in reality ;-) are single events. Only later we
> > combine all our single observations into a statistical picture, which
> > may be compared with QM predictions. In this sense, QM
> > is obviously incomplete.
>
> So far, no physical theory is complete. So what?
In this sense - that it describes what happens for single events -
Bohmian mechanics (and Nelsonian stochastics - determinism is
not the relevant point) are complete.
> Up to now QM describes
> all outcomes of experiments very well. Maybe further scientific
> progress comes up with a more satisfying explanation for the phenomeno.
> So far it's not!
Bohmian mechanics and Nelsonian stochastics are more satisfying
explanations, simply because they are realistic explanations, while
minimal QM refuses to explain anything.
> > (To say "there are single events, but it is impossible to make
> > predictions about them" already uses realistic language and
> > therefore presupposes some notion of realism.)
>
> As I said, for me an experimental setup in the lab is real. Your notion
> of "realism" is too narrow. One cannot talk about experiments without
> that minimal "realistic language".
Too narrow?
For an experiment, we measure expectation values E(f|c) for functions
f on measurement results M in dependence of control parameters c in C.
There exists some reality X with probability distribution rho(x)dx so
that E(f|c)= int f(m(x,c)) rho(x) dx.
> >> Let's take this most simple example of polarisation-entangled
> >> photons.
> >
> > There is no disagreement about the math.
>
> The math describes the outcome of experiments very well. So it's a
> successful physical theory. I don't know, what you disagree about,
> except a dream about a special philosophical conception about nature,
> but nature does not care about our philosophical prejudices, but
> behaves as she likes.
The hypothesis about the existence of some state of reality x in X so
that the preparation of the experiment defines some probability
distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
of course, a special philosophical conception of nature named realism.
But Nature does not seem to object against this philosophical
conception. We have realistic theories in agreement with
observation.
> > No necessity, because I have never questioned that to prove
> > Bell's inequality you need some notion of reality.
> > In the theory "Gods Will is unpredictable and unexplainable" I
> > cannot prove Bell's inequality too.
>
> Quantum theory is much more than such religious conceptions.
Of course. But the part which is useful remains valid in realistic
theories.
The rejection of the search for realistic explanation the minimal
interpretation shares with this religious conception.
> >> Then one finds a violation of Bell's inequality,
> >
> > It has also never been questioned that Bell's inequality is
> > violated in QM.
>
> It is violated in a way agreeing with QM, and thus it's very difficult
> to think of a deterministic theory agreeing with all the observations,
> QM describes successfully.
No, it is simple, and well-known how to do this. BM, NS.
> > Moreover, I don't think it makes much sense to talk about
> > causality in a theory where we cannot even talk about single events.
> > The notion named "causality" in QM literature is IMHO better called
> > statistical correlation.
>
> The state (statistical operator) evolves according to causal laws.
> That's why I call QM a causal theory. Without causality you'd really
> need not do science at all. In my language QM is an indeterministic but
> causal theory.
Again, I see no justification to talk about causality in a
nonrealistic theory. In statistics, as long as you don't care
about realistic explanation, you have to use, instead, the
notion of correlation.
QM is in this sense not causal, but a scheme which allows
to compute correlations.
> > I would insert "the minimal interpretation of" before "quantum
> > theory".
>
> Yes, and one should not interpret more into the theory than there is
> contained in it.
The minimal interpretation is, in some sense, not an interpretation
but a refusal to interprete.
> >> According to
> >> quantum theory, we cannot have more than that probabilistic
> >> knowledge.
> >
> > That's already beyond the minimal interpretation. The minimal
> > interpretation simply remains silent. (Else, it would not be minimal,
> > and I would define a more minimal interpretation.)
>
> This I do not understand. Minimal interpretation contains the
> probabilistic interpretation of the state
Yes.
> and takes this stochastic nature of the QM description serious.
No. The minimal interpretation is not in conflict with
other, non-minimal interpretations, but defines the common
part of various interpretations. In all questions where
different interpretations give different answers the minimal
interpretation remains silent.
(If not, I simply define another interpretation which
remains silent about this question. This new interpretation is
smaller than your "minimal" interpretation, therefore I can
claim that your choice of denotation of your interpretation
is incorrect, and my new interpretation is the minimal one.)
Ilja
Ilja Schmelzer
"Andreas Most" <Andrea...@nospam.de> schrieb
> Ilja Schmelzer wrote:
> > ...
> > I see, the phrase "a correlation existed" may be meaningful also from
> > a purely positivistic point of view, where only observables are
relevant.
> > But the full phrase was "existed the whole time from the preparation
> > of the particle pair", which already refers to something not observed,
> > thus, to some not purely positivistic idea of reality.
>
> The correlation existed, not the outcome of the measurement.
That's meaningless without a concept of realism beyond pure
positivism.
> If you start from an entangled state
>
> |Psi>=1/sqrt(2)[|HV>-|VH>]
>
> and you find photon 1 to be horizontally polarised you could have
> as well started off with a wave function
>
> |Psi>=|HV>
>
> for this single photon pair. I.e., you would have found a horizontal
> polarisation for photon 1, even if you had performed the measurement
> earlier.
A counterfactual statement. Such statements are meaningless outside
a concept of realism beyond positivism.
There is a meaningful notion of realism, there such claims make sense.
I like it, and I defend it. But if you reject it, without defining an
alternative
concept of realism which makes such claims meaningful, you are simply
inconsistent.
> > But a notion of _existence_ of something (the value or the correlation
> > observed later) at some moment of time t0 should not depend on
> > human decisions made at later time t>t0.
>
> Existence is a pretty philosophical term.
No, it is a well-defined notion, which allows you to prove theorems
if you accept it.
> The question would be
> what is the meaning of the existence of something that has no impact
> on our universe at all
Very simple. What is real has to be specified by a realistic physical
theory. Realism simply means that we search for scientific truth only
among realistic theories.
More specific: you have experiments which measure expectation values
E(f|c) of functions on measurement results f: M->R depending on
control parameters C. A realistic theory has to explain this using
a state of reality x in X which defines the measurement results
m=m(x,c) and a probability distribution rho(x) so that
E(f|c)= int f(m(x,c)) rho(x) dx.
The question "what is real" has the answer "if this explanation
is correct, x is real".
Once we also use Ockhams razor to choose among theories, things
which have no impact on our universe will not be part of the preferred
realistic theory.
> I could assume its existence as well as its nonexistence
> without any change to the description of our world.
You cannot assume the nonexistence of a preferred frame.
Because no realistic description of the world is possible
without some real effects happening FTL. That's because
realism is not a pretty philosophical theory but a well-defined
concept which allows to prove theorems.
Ilja
Ilja Schmelzer
"Oz" <O...@farmeroz.port995.com> schrieb
> Is this what bell's inequality states?
Current state of a text explaining it:
Definition of statistical observation:
A statistical experiment gives a probality
distribution rho(m|c) of measurement results
m in M which depends on control parameters
c in C which may be defined by free decisions
of the experimenters. Expectation values for
functions f: M->R are defined by
E(f|c) =int f(m) rho(m|c) dm
Definition of statistical dependence:
A dependence of rho(m|c) or E(f|c) on c in C
or some subset c' in C', C = C'x C'', this is
called statistical dependence.
Definition of realistic explanation:
A realistic explanation consists of a probability
description rho(x) of "states of reality" x in X
and a function m(x,c) so that
E(f|c)= int f(m(x,c)) rho(x) dx.
Definition of causal dependence:
If m(x,c) depend on c in C or some subset
c' in C', C = C'x C'', this is called
causal dependence.
Definition of Einstein causality:
There are two possibilities to understand
Einstein causality. The weak (statistical)
notion of Einstein causality forbids only
statistical dependencies between spacelike
separated events.
Instead, realistic Einstein causality
predicts that for every observation exists
a realistic explanation which does not
contain causal dependencies between spacelike
separated event.
Proof of Bell's inequality:
Situation: We have two space-like separated
regions of spacetime A and B. We have
M = M_A x M_B, C = C_A x C_B,
M_A = M_B = {-1,1}, C_A = C_B = {1,2,3}
We denote the expectation value E(f|C) of the
product f(m_A,m_B) = m_A m_B with P(c_A,c_B) so that
P(c_A,c_B) = int m_A(x,c_A,c_B) m_B(x,c_A,c_B) rho(x) dx.
Now Einstein causality forbids m_A to depend on c_B
and reverse, so that
P(c_A,c_B) = int m_A(x,c_A) m_B(x,c_B) rho(x) dx.
Now, for c_A = c_B we observe m_A = m_B. This
is possible only if m_A(x,.) = m_B(x,.) are the same
function m(x,.). (This is the EPR argument.) Thus,
P(c_A,c_B) = int m(x,c_A) m(x,c_B) rho(x) dx.
For the three function values m(x,1),m(x,2),m(x,3)
at most two of the following statements may be true:
m(x,1)==m(x,2); m(x,2)==m(x,3); m(x,1)=/=m(x,3)
(Indeed, if two are true, the third must be false.)
Thus, m(x,1)m(x,2)+m(x,2)m(x,3)-m(x,1)m(x,3)<=1.
(Each part is 1 if one statement is true, else -1.)
It follows that
P(1,2) + P(2,3) - P(1,3) <= int rho(x)dx = 1.
which is Bell's inequality.
Consequences of the violation:
Once Bell's inequality is violated, every realistic
explanations contains:
or a causal dependence m_A(x,c_A,c_B) of m_A on c_B,
or a causal dependence m_B(x,c_A,c_B) of m_B on c_A.
In other words, we have some causal connection,
A->B or B->A, but don't know its direction. It is
easy to see that, indeed, realistic explanations
with causal connections of above types exist.
If A and B are spacelike separated, above causal
connections are forbidden by realistic Einstein
causality, thus, realistic Einstein causality is
falsified by violations of Bell's inequality.
On the other hand, the existence of two realistic
explanations with different causal connections
has consequences:
First, we can immediately prove that the violation
of Bell's inequality cannot be used for information
transfer. Indeed, an application for information
transfer A->B contradicts the explanation B->A,
and reverse. Thus, weak Einstein causality is
not falsified.
Second, classical causality based on a preferred
frame is not falsified too. For every choice of
absolute time t we have a realistic explanation
compatible with classical causality: If t(A)<t(B)
we choose the explanation A->B, and reverse.
Moreover, assume that for every pair of open
spacetime regions A, B we have violations
of Bell's inequality. Now, assume we have a
general realistic theory which allows to explain
all these violations. Assume that its notion
of causality does not contain closed causal loops.
Then the realistic theory contains a preferred
foliation of spacetime. The construction of this
foliation is quite straightforward: We decide
p1<p2 if there exists some environments U1, U2
of p1, p2 so that all causal explanations
of violations of Bell's inequality between
U1 and U2 are of type U1 -> U2. This order
defines the preferred foliation.
Of course, the preferred foliation depends on
the choice of explanation. Other explanations
lead to other preferred foliations. But each
realistic explanation contains a preferred
foliation.
Ilja
Hendrik van Hees
> I don't dream about a theory where everything may be predetermined
> by some human preparation of the state. Realism is much weaker -
> the hypothesis that there exists something out there which determines
> the result of the measurement.
But that's determinism again. You may say that there are no really
closed systems, but everything interacts with everything else in the
universe and that the indeterminism of quantum mechanics is just lack
of knowledge about the "rest of the universe". I'm not sure whether
this possibility is or is not in contradiction to the violation of
Bell's unequality, because this seems to be a concept introducing
nonlocal interactions, which have to be strictly distinguished from the
nonlocal correlations which are encoded in entangled states (EPR
states).
> In this sense - that it describes what happens for single events -
> Bohmian mechanics (and Nelsonian stochastics - determinism is
> not the relevant point) are complete.
Ok, now we shall again enter our old battle about what are different
theories. For me Bohmian mechanics is, insofar it is formulated
successfully in non-relativistich quantum mechnaics, the same theory as
quantum mechanics with an ugly additional concept, because also Bohmian
mechanics cannot tell me which polarisation state I will measure for a
single photon in an entangled state. Bohm's "trajectories" are well
hidden from our observations, and they cannot tell us about the outcome
of measurements beyond what we can already know about the system within
the minimal interpretation. Thus, Bohmian Mechanics does not help to
make quantum mechanics more complete than it already is in the much
simpler minimal interpretation.
> Too narrow?
>
> For an experiment, we measure expectation values E(f|c) for functions
> f on measurement results M in dependence of control parameters c in C.
Let's get it a little cleaned up. We measure observables which (in the
sense of the minimal interpretation) are not determined by the state,
we have prepared before doing the measurement. Thus the outcome of
these measurements for an ensemble of identically prepared systems show
variations, and the only thing quantum mechanics tells me is the
probability distribution about the outcome of these measurements.
To say, we measure expectation values for observables also implies that
I have to repeat the experiments sufficiently often to obtain this
expectation value with a given accuracy. So you have the same trouble
as with minimally interpreted QT: You do not make any statement about
the outcome of a single measurement. You cannot tell with certainty
which value you will measure before you actually measure it.
> The hypothesis about the existence of some state of reality x in X so
> that the preparation of the experiment defines some probability
> distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
> of course, a special philosophical conception of nature named realism.
Could you remind me about your mathematical notation? What means X and x
in X etc.
>
> But Nature does not seem to object against this philosophical
> conception. We have realistic theories in agreement with
> observation.
Before I though I have understood, what you mean by "realistic theory".
Now again this notion slipped away. If it's not predeterminism of all
observables as in good old classical physics, I do not understand yet
what you mean.
> Of course. But the part which is useful remains valid in realistic
> theories.
>
> The rejection of the search for realistic explanation the minimal
> interpretation shares with this religious conception.
You are right in the sense, that we have not yet a proof that there does
not exist a deterministic theory, which is as successful as QT to
explain the phenomena.
>> It is violated in a way agreeing with QM, and thus it's very
>> difficult to think of a deterministic theory agreeing with all the
>> observations, QM describes successfully.
>
> No, it is simple, and well-known how to do this. BM, NS.
See my objection against BM above. I have to think about NS again, but I
thought that even Nelson himself doesn't believe anymore in his own
concept.
> Again, I see no justification to talk about causality in a
> nonrealistic theory. In statistics, as long as you don't care
> about realistic explanation, you have to use, instead, the
> notion of correlation.
Again, I need to understand, what is a "realistic explanation" if it is
not determinism.
>
> QM is in this sense not causal, but a scheme which allows
> to compute correlations.
The trouble is, that we use different language. The best essay about the
subject "determinism vs. causality" is in Schwinger's book "Quantum
Mechanics, symbolism for atomistic measurements".
> The minimal interpretation is, in some sense, not an interpretation
> but a refusal to interprete.
Not at all. It takes the probabilistic nature of QT seriously not more
and not less.
> No. The minimal interpretation is not in conflict with
> other, non-minimal interpretations, but defines the common
> part of various interpretations. In all questions where
> different interpretations give different answers the minimal
> interpretation remains silent.
Where give different interpretation different answers? Can I
experimentally decide about the success or failure of one or the other
interpretation? If so, then you have not only a new interpretation but
a new theory!
>
> (If not, I simply define another interpretation which
> remains silent about this question. This new interpretation is
> smaller than your "minimal" interpretation, therefore I can
> claim that your choice of denotation of your interpretation
> is incorrect, and my new interpretation is the minimal one.)
As I said, don't interpret more into QT than it contains!
Andreas Most
Things are perfectly consistent if you consider the wave function as a
mathematical object in which all information we have about a quantum
state is encoded. A measurement changes the knowledge about the quantum
state and thus the wave function.
Then it is also obvious that different obervers may have different
description (wave function) of a quantum state based on their specific
knowledge about a state (consider e.g. the thought experiment about
"Wigner's friend")
And actually, the correlation of observables of an entangled system is
to me as mysterious as is in Newtonian mechanics an object moving on
a straight line forever if no forces are present. ;-)
In order to not be in the urge of assuming such a preferred frame
I avoid using hidden variables. Apart from this I do not see that
Bohmian mechanics makes any testable (by experiment) prediction that
goes beyond the predictions of QM. (Also your paper makes no testable
predictions as far as I have read it).
I agree that the Bohmian interpretation does not contradict experiment.
But I think you give up to many well-established principles without
gaining anything new in terms of testable predictions.
Andreas.
>
> Ilja
>
>
Hendrik van Hees
> Things are perfectly consistent if you consider the wave function as a
> mathematical object in which all information we have about a quantum
> state is encoded. A measurement changes the knowledge about the
> quantum state and thus the wave function.
So far I can agree.
> Then it is also obvious that different obervers may have different
> description (wave function) of a quantum state based on their specific
> knowledge about a state (consider e.g. the thought experiment about
> "Wigner's friend").
I think that's not what is meant when we say: "We assign the state [psi]
(let [psi] denote a ray in Hilbert space represented by a vector |psi>)
to a system." It's too subjectivistic a view.
I think, what is meant by this statement is that a system was prepared
by the experimenter in this state [psi]. Within the minimal
interpretation that's a little bit unprecise, because the information,
encoded in [psi] is only probabilistic. So what it really means is,
that the system under consideration belongs to a (really prepared or at
least in principle preparable) ensemble of independent systems which
shows the statistic features encoded in [psi]. Different observers all
assign this state [psi] and not any other to it, although one observer
may use another observer's states mapped by a unitary (or antiunitary)
operator. This covers also the case of observers in different frames of
reference or using different pictures of time evolution (Schroedinger,
Heisenberg, or Dirac).
Of course, one also has the more common case of an incomplete knowledge
about the system, and then different observers might assign different
impure states (statistical operators) to the system, based on their
knowledge of the system.
> And actually, the correlation of observables of an entangled system is
> to me as mysterious as is in Newtonian mechanics an object moving on
> a straight line forever if no forces are present. ;-)
In fact, physics does not give an "explanation" for this. It's just an
experimental fact about moving bodies which Galileo and Newton used to
base their further analysis on. The principle of inertia is a basic
observation, we cannot deduce from more basic observations (despite the
fact that general relativity refines the principle of inertia in a
subtle way).
> In order to not be in the urge of assuming such a preferred frame
> I avoid using hidden variables. Apart from this I do not see that
> Bohmian mechanics makes any testable (by experiment) prediction that
> goes beyond the predictions of QM. (Also your paper makes no testable
> predictions as far as I have read it).
I agree completely.
> I agree that the Bohmian interpretation does not contradict
> experiment. But I think you give up to many well-established
> principles without gaining anything new in terms of testable
> predictions.
You make an already complecated subject even more complicated by
introducing unobservable "elements of reality" and name them
trajectories to make QT sound a little bit more like classical
mechanics.
Ralph Hartley
>>contained in it.
>
> The minimal interpretation is, in some sense, not an interpretation
> but a refusal to interprete.
A *justified* refusal to interpret. Because all other interpretations
interpret more into the theory than is contained in it.
> ... The minimal interpretation is not in conflict with
> other, non-minimal interpretations, but defines the common
> part of various interpretations. In all questions where
> different interpretations give different answers the minimal
> interpretation remains silent.
Just so. But that's only *one* of it's good properties.
Another it that it *is* complete, in the sense that it answers all
questions that are experimentally testable. (Ignoring the fact that
Quantum Mechanics is really a framework not a particular theory)
No one ever promised you answers to any other questions.
No one promised that any others even *have* answers.
Certainly there are questions that do not have answers, e.g. "What color
are electrons?"
Other interpretations are useful aids to thought, for example they make
the causal properties easier to see, but they all contain something
unneeded.
Suppose someone suggested a bet on what the "correct" interpretation is.
How would you *settle* such a bet? Even if there were a "correct"
interpretation, what would it be good for? It would not predict the
results of even one more experiment.
> The question "what is real" has the answer "if this explanation
> is correct, x is real".
>
> Once we also use Ockhams razor to choose among theories, things
> which have no impact on our universe will not be part of the preferred
> realistic theory.
The answer to the question "what is real" does not have any impact on
our observable universe. I would be willing to let that one slide,
except for:
> You cannot assume the nonexistence of a preferred frame.
> Because no realistic description of the world is possible
> without some real effects happening FTL.
Therefore *all* realistic (in your narrow sense) theories contain
something with no impact on our universe.
In a broader sense, "many worlds", if taken literally (which I do *not*
normally recommend), is completely realistic. If it is correct, all
those worlds are real (the ones with nonzero amplitude). There is an
absolutely real independent reality which really determines everything
that really is determined.
Individual outcomes are an illusion. They don't happen, so they don't
need to be determined by anything.
There is no preferred frame, and the universe is locally causal. In fact
it is even deterministic. We don't remember things happening that way,
but we wouldn't be expected to. In each world we remember only one
particular outcome, and wonder what determined it, or why our
"consciousness", whatever that is, ended up in that particular world.
Science consists of finding realistic (in the broad sense), local
deterministic, theories. Many worlds has those properties, and BM does
not, so BM should not even be considered.
Do I really think that? No. But if I did, I would be just as consistent
in using realistic language, and in calling myself a realist, as you are.
I don't actually prefer any interpretation, except as aids to intuition.
Questions that cannot be answered *should* not be answered.
Ralph Hartley
Andreas Most
I didn't say I don't like it. I just wanted to understand Ben's
argument.
>>>That means that from point of view of other Lorentz frames t' it
>>>may happen that t'(A)>t'(B), thus, information is send into the
>>>"past" of "time" t'. But the "time" t' is in this interpretation only
>>>some artificial local time-like coordinate with no fundamental
>>>importance. Fundamental, and related with causality, is only
>>>one time coordinate t.
>>
>>Apart from the fact, that you obviously reject the relativity principle,
>
>
> I reject a strong form of the relativity principle. The weaker
> form of the relativity principle, which is only about observables,
> remains valid. (At least for distances large compared with the
> critical length of unification of SM with gravity.)
>
>
>>what exactly is the preferred frame and how can I identify it?
>
>
> You can roughly identify it as the rest frame of CMBR.
>
>
>>Is the preferred frame globally valid (in our universe) and static?
>
>
> Yes. (You need a theory of gravity with preferred frame
> for this purpose, see gr-qc/0205035.)
As of my understanding, if you have two observers being at different
locations and each being at rest relative to the CMBR at their position,
the two observers move relative to one another.
That is you cannot define a preferred frame globally.
(BTW: I read in your paper that you can prove a flat
universe in your GLET. How would you then explain the redshift of
objects being far away if not by an expanding universe?)
>>>Note that the mechanism which describes the FTL information
>>>transfer necessarily violates Lorentz covariance, depends on
>>>the preferred time.
>>
>>FTL communication does not violate Lorentz covariance at all.
>>Tachyons are described perfectly well in a covariant way.
>>The problem is causality.
>
>
> Ok, but if we include a reasonable notion of causality, without
> causal loops, as an additional requirement for the mechanism,
> my statement holds.
Again, causality has nothing to do with covariance.
Instead, causality considerations tell us which (covariant) solution
makes physically sense. For example, a spacelike line cannot be the
world line of anything that interacts with our observable world.
Excluding mathematical possible solutions to physics equations based on
such considerations is also done elsewhere (E.g. the broken cup that
does not recompile or using retarded solutions in electrodynamics and
rejecting advanced ones). But these exclusion schemes do not change the
properties of the physics equation (properties like e.g. covariance)
Ilja Schmelzer
news:43D7FD27...@aic.nrl.navy.mil...
> Ilja Schmelzer wrote:
> > "Hendrik van Hees" <he...@comp.tamu.edu> schrieb
> >>... one should not interpret more into the theory than there is
> >>contained in it.
> >
> > The minimal interpretation is, in some sense, not an interpretation
> > but a refusal to interprete.
>
> A *justified* refusal to interpret. Because all other interpretations
> interpret more into the theory than is contained in it.
In a situation where different theories are undistinguishable by
observation, they are considered to be equivalent and named
interpretations of the same theory. Then it is also reasonable to
define a "minimal interpretation" which contains only those
parts shared by all theories.
Then, by construction, all other interpretations interpret more
into "the theory" than is contained in it.
> > ... The minimal interpretation is not in conflict with other,
> > non-minimal interpretations, but defines the common part of various
> > interpretations. In all questions where different interpretations
> > give different answers the minimal interpretation remains silent.
> Just so. But that's only *one* of it's good properties.
> Another it that it *is* complete, in the sense that it answers all
> questions that are experimentally testable.
Also a consequence of the construction principle.
> No one ever promised you answers to any other questions.
> No one promised that any others even *have* answers.
So what? No one promised me anything. No one promised
me that there exists a unified theory. No one promised me
I have a chance to find it. Nonetheless I try to find it.
> Other interpretations are useful aids to thought, for example they
> make the causal properties easier to see, but they all contain
> something unneeded.
Unneeded? Depends on what you want. If you want to know some
scattering amplitudes of some very unstable particles, these
interpretations contain something unneeded. But if you simply
want to understand how the univers works, and experimental
tests are only a tool to reject wrong theories?
> Suppose someone suggested a bet on what the "correct" interpretation
> is. How would you *settle* such a bet?
There are lots of different criteria, like simplicity, beauty.
> Even if there were a "correct"
> interpretation, what would it be good for?
It helps me to understand how the universe works. I'm
just curious how this funny thing named universe works.
> It would not predict the results of even one more experiment.
I'm not really interested in scattering amplitudes themself.
For me they are only a tool to recognize some wrong theories
as wrong.
> The answer to the question "what is real" does not have any impact on
> our observable universe. I would be willing to let that one slide,
> except for:
>
> > You cannot assume the nonexistence of a preferred frame. Because no
> > realistic description of the world is possible without some real
> > effects happening FTL.
>
> Therefore *all* realistic (in your narrow sense) theories contain
> something with no impact on our universe.
No. The impact can be seen (the CMBR). I believe that the
theory we need to understand the initial conditions of our universe
- a quantum TOE - will not have relativistic symmetry.
> In a broader sense, "many worlds", if taken literally (which I do
> *not* normally recommend), is completely realistic.
I see no reason to weaken the notion of realism used by EPR
and Bell. In this sense, MWI is not a realistic interpretation.
I follow Bell who has characterized it as "extravagant, and
above all extravagantly vague" which he "could almost
dismiss as silly".
> If it is correct, ...
> ...We don't remember things happening that way,
> but we wouldn't be expected to. In each world we remember only one
> particular outcome, and wonder what determined it, or why our
> "consciousness", whatever that is, ended up in that particular world.
I wonder only what distinguishes this sort of "explanation" from
"Gods Will is unexplainable".
> Science consists of finding realistic (in the broad sense), local
> deterministic, theories. Many worlds has those properties, and BM does
> not, so BM should not even be considered.
According to this methodology, Newtonian gravity should not have been
considered, for the same reason you propose not to consider BM:
nonlocality. Fortunately, Newton's decision was different.
> Do I really think that? No. But if I did, I would be just as consistent
> in using realistic language, and in calling myself a realist, as you are.
There is a difference. My notion of realism is well-defined, MWI is instead
vague. It is hard to prove inconsistence if everything is vague.
> I don't actually prefer any interpretation, except as aids to intuition.
> Questions that cannot be answered *should* not be answered.
"cannot be answered" is very different from "there are many possible
answers, and it is hard to say which answer is preferable".
Ilja
Ilja Schmelzer
> > I don't dream about a theory where everything may be predetermined
> > by some human preparation of the state. Realism is much weaker -
> > the hypothesis that there exists something out there which determines
> > the result of the measurement.
>
> But that's determinism again.
Determinism is not the point. Random number generators may
be involved.
> You may say that there are no really
> closed systems, but everything interacts with everything else in the
> universe and that the indeterminism of quantum mechanics is just lack
> of knowledge about the "rest of the universe". I'm not sure whether
> this possibility is or is not in contradiction to the violation of
> Bell's unequality,
This possibility is certainly inside the domain of common sense
realism and also within EPR-Bell realism. The main formula
is
E(f|c)= int f(m(x,c)) rho(x) dx.
for the expectation values E(f) of some function f M->R on
the results of the measurement. x in X describes reality outside,
our lack of knowledge about it, as well as, possibly, some
inherent indeterminism, is included in the probability distribution
rho(x).
> because this seems to be a concept introducing
> nonlocal interactions, which have to be strictly distinguished from the
> nonlocal correlations which are encoded in entangled states (EPR
> states).
The nonlocality is only about the dependence of the localized
macroscopic measurement results m from the localized
macroscopic preparation parameters c in the function m(x,c).
x in X may be nonlocal or whatever you like, it doesn't matter.
All we need is the _existence_ of some X, rho(x), m(x,c)
If the dependence of m on c is Einstein-local, Bell's inequality
may be proven.
> > In this sense - that it describes what happens for single events -
> > Bohmian mechanics (and Nelsonian stochastics - determinism is
> > not the relevant point) are complete.
> Ok, now we shall again enter our old battle about what are different
> theories. For me Bohmian mechanics is, insofar it is formulated
> successfully in non-relativistich quantum mechnaics, the same theory as
> quantum mechanics with an ugly additional concept, because also Bohmian
> mechanics cannot tell me which polarisation state I will measure for a
> single photon in an entangled state. Bohm's "trajectories" are well
> hidden from our observations, and they cannot tell us about the outcome
> of measurements beyond what we can already know about the system within
> the minimal interpretation.
No problem. I do not want to suggest you to compute Bohmian trajectories.
(Moreover, I tend to think that Nelsonian stochastics is closer to truth.)
> Thus, Bohmian Mechanics does not help to
> make quantum mechanics more complete than it already is in the much
> simpler minimal interpretation.
You have to distinguish a complete description of reality from a
complete description of our observable expectation values. Last not least,
expectation values we observe only indirectly, combining lots of particular
real observations.
> > Too narrow?
> >
> > For an experiment, we measure expectation values E(f|c) for functions
> > f on measurement results M in dependence of control parameters c in C.
>
> Let's get it a little cleaned up. We measure observables which (in the
> sense of the minimal interpretation) are not determined by the state,
> we have prepared before doing the measurement. Thus the outcome of
> these measurements for an ensemble of identically prepared systems show
> variations, and the only thing quantum mechanics tells me is the
> probability distribution about the outcome of these measurements.
Correct.
> To say, we measure expectation values for observables also implies that
> I have to repeat the experiments sufficiently often to obtain this
> expectation value with a given accuracy. So you have the same trouble
> as with minimally interpreted QT: You do not make any statement about
> the outcome of a single measurement. You cannot tell with certainty
> which value you will measure before you actually measure it.
Indeed. I'm unable to prepare pure states of reality x. Our preparation
procedures only allow to prepare some subset of probabilistic states
rho(x)dx.
> > The hypothesis about the existence of some state of reality x in X so
> > that the preparation of the experiment defines some probability
> > distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
> > of course, a special philosophical conception of nature named realism.
>
> Could you remind me about your mathematical notation? What means X and x
> in X etc.
X means the set of all states of reality. This set has to be defined by
a realistic theory/interpretation.
x means a particular state of reality which is realized in a particular
experiment.
c in C describes the control or input parameters of the experiment -
parameters
which may be set by a free will decision of the experimenter.
rho(x)dx is the probability distribution of the states of reality defined
by the preparation procedure. (Better, the part of preparation
procedure before the choice of the control parameters c.)
> > But Nature does not seem to object against this philosophical
> > conception. We have realistic theories in agreement with
> > observation.
>
> Before I though I have understood, what you mean by "realistic theory".
> Now again this notion slipped away. If it's not predeterminism of all
> observables as in good old classical physics, I do not understand yet
> what you mean.
If you like, you can intepret the function m(x,c) as some deterministic
rule which describes how the unknown state of reality x, together with
the control parameters, defines the measurement result. But, again, I
don't think determinism is the point. A classical stochastic process is
described in the same way.
> > Of course. But the part which is useful remains valid in realistic
> > theories.
> > The rejection of the search for realistic explanation the minimal
> > interpretation shares with this religious conception.
> You are right in the sense, that we have not yet a proof that there does
> not exist a deterministic theory, which is as successful as QT to
> explain the phenomena.
Here I disagree. BT is a general scheme, as general as QT, and
may be applied in field theory in a similar way. As usual I refer you
to Bell, beables for QFT.
> >> It is violated in a way agreeing with QM, and thus it's very
> >> difficult to think of a deterministic theory agreeing with all the
> >> observations, QM describes successfully.
> >
> > No, it is simple, and well-known how to do this. BM, NS.
>
> See my objection against BM above.
I see, but your objection about an "ugly additional concept" in BM
does not prevent BM from being a deterministic theory agreeing
with all the observations QM describes successfully.
But the "ugly additional concept" is what I want to have. I impose
the restriction "realistic theory" to QM and observe that to make them
compatible I have to introduce some additional concepts. Fine. Now,
we cannot observe these additional things in detail, not fine. And
there may be (are) different proposals for these additional concepts,
which cannot be distinguished by observation. Also not fine.
But considerations about simplicity and beauty of theories have
to be applied in science anyway, and they may be applied here too.
Thus, not that problematic.
But, even much better, we can _prove_, that all these different
"ugly additioal concepts" have something in _common_. Thus,
there is no necessity to care about the ugly details of the ugly
additional concept - we know for sure about this common property.
This common property is a preferred foliation.
> I have to think about NS again, but I
> thought that even Nelson himself doesn't believe anymore in his own
> concept.
AFAIK after he has recognized that the wave function lives
on configuration space instead of 3D space.
> > Again, I see no justification to talk about causality in a
> > nonrealistic theory. In statistics, as long as you don't care
> > about realistic explanation, you have to use, instead, the
> > notion of correlation.
>
> Again, I need to understand, what is a "realistic explanation" if it is
> not determinism.
Determinism or classical stochastics. (Classical stochastics
may be, in principle, interpreted as a combination of determinism
and lack of knowledge. But this question as well may be left open.
If there is some "inherent nondeterminism" in Nature, but as far as
this "inherent nondeterminism" - whatever this means - may be
described with the math of classical stochastics, it is covered too.)
Observation gives you E(f|c)= int f(m) rho(m|c)dm.
Realism requires to explain this in the form
E(f|c)= int f(m(x,c)) rho(x) dx
for some hypothetical X, rho(x)dx, m(x,c), which the realistic
theory has to construct from rho(m|c)dm on M.
> > The minimal interpretation is, in some sense, not an interpretation
> > but a refusal to interprete.
>
> Not at all. It takes the probabilistic nature of QT seriously not more
> and not less.
If it would, it would not be minimal. The minimal interpretation
clarifies that |psi|^2 is a probabity distribution and leaves anything
else unanswered.
> > No. The minimal interpretation is not in conflict with
> > other, non-minimal interpretations, but defines the common
> > part of various interpretations. In all questions where
> > different interpretations give different answers the minimal
> > interpretation remains silent.
>
> Where give different interpretation different answers?
For example, in BM we have determinism, in NS classical stochastics
(Wiener process).
> Can I
> experimentally decide about the success or failure of one or the other
> interpretation?
No.
> > (If not, I simply define another interpretation which
> > remains silent about this question. This new interpretation is
> > smaller than your "minimal" interpretation, therefore I can
> > claim that your choice of denotation of your interpretation
> > is incorrect, and my new interpretation is the minimal one.)
> As I said, don't interpret more into QT than it contains!
Do it yourself. QT doesn't tell that you have to take
the probabilistic nature of QT seriously (that means, it
doesn't tell that its probabilistic nature is more
complex/deep/serious than that of classical probabilistic
theories like thermodynamics.)
Ilja
Ilja Schmelzer
Yes. But it may be interpreted as well as a shortage of our rulers.
> That is you cannot define a preferred frame globally.
> (BTW: I read in your paper that you can prove a flat
> universe in your GLET.
Flat only in the approximation of a homongeneous universe.
The other homongeneous solutions with constant curvature
are not homogeneous in GLET.
> How would you then explain the redshift of
> objects being far away if not by an expanding universe?)
By an interpretation of the _observed_ increase of distances
between far away points by shrinking rulers.
> > Ok, but if we include a reasonable notion of causality, without
> > causal loops, as an additional requirement for the mechanism,
> > my statement holds.
> Again, causality has nothing to do with covariance.
> Instead, causality considerations tell us which (covariant) solution
> makes physically sense. For example, a spacelike line cannot be the
> world line of anything that interacts with our observable world.
> Excluding mathematical possible solutions to physics equations based on
> such considerations is also done elsewhere (E.g. the broken cup that
> does not recompile or using retarded solutions in electrodynamics and
> rejecting advanced ones). But these exclusion schemes do not change the
> properties of the physics equation (properties like e.g. covariance)
Causality is a word with different meanings. Your concept of causality
is also useful, but not what I'm talking about.
What I name causality is simply a partial order among events: A->B
if some (human) decision at A can influence the outcome of a
(macroscopic) measurement at B. This relation should be transitive
and should not allow closed causal loops.
Now, we have x(t1)->x(t2) for t1<t2 along usual worldlines x(t).
But, according to my realistic interpretation of violations of Bell's
inequality, we have also "A->B or B->A" for space-like separated
events.
Despite the fact that all these observational facts are covariant,
there exists no covariant relation A->B with these properties.
Ilja
Andreas Most
I agree with you so far. But I was heading into a different direction.
Consider an EPR-like setup with an entangled photon pair ("diphoton"
as it was mentioned in d.s.physik ;-) ) with the previously mentioned
wave function |psi> = 1/sqrt(2) (|HV> - |VH>)
Let Alice and Bob each receive one of these photons (Maybe they are
doing some quantum cryptography). If Alice has performed a measurement
and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
function would Bob use to describe the system?
If Bob is spacelike separated, he cannot
possibly know whether Alice has performed the measurement at all.
And as long as he leaves the system unchanged and does not get
information from Alice, he must describe the system as
|psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
knowledge would lead to contradictions (I think GHZ like setups
would show contradictions.)
As soon as he gets to know about Alice measurement, he can use
(so to say with 20/20 hindsight) |psi> = |HV> to interpret his
previous observations (measurements).
I am simply trying to say that spacelike separated observers might have
different descriptions for a quantum mechanical system. It might be even
possible for timelike connected events, if you do not receive any
information about a measurement like in the "Wigner's friend" thought
experiment, though I think that decoherence effects play a bigger role here.
>> And actually, the correlation of observables of an entangled system is
>> to me as mysterious as is in Newtonian mechanics an object moving on
>> a straight line forever if no forces are present. ;-)
>
> In fact, physics does not give an "explanation" for this. It's just an
> experimental fact about moving bodies which Galileo and Newton used to
> base their further analysis on. The principle of inertia is a basic
> observation, we cannot deduce from more basic observations (despite the
> fact that general relativity refines the principle of inertia in a
> subtle way).
Yes, and I think that quantum mechanical behaviour is fundamental in a
similar manner. There is maybe no explanation for it.
However, just to add "my two cents": I have the impression that the
so-called collapse of the wave function being related to information
gain has to do with the arrow of time (because of entropy...).
Maybe, If we sometime solve the "arrow of time" puzzle,
we might be able to solve also the so-called "measurement problem".
(please don't flame me on this. It's just my personal opinion...)
>
>> In order to not be in the urge of assuming such a preferred frame
>> I avoid using hidden variables. Apart from this I do not see that
>> Bohmian mechanics makes any testable (by experiment) prediction that
>> goes beyond the predictions of QM. (Also your paper makes no testable
>> predictions as far as I have read it).
>
> I agree completely.
>
>> I agree that the Bohmian interpretation does not contradict
>> experiment. But I think you give up to many well-established
>> principles without gaining anything new in terms of testable
>> predictions.
>
> You make an already complecated subject even more complicated by
> introducing unobservable "elements of reality" and name them
> trajectories to make QT sound a little bit more like classical
> mechanics.
Yes!
Regards,
Andreas.
Ilja Schmelzer
"Andreas Most" <Andrea...@t-online.de> schrieb
> >>polarisation for photon 1, even if you had performed the measurement
> >>earlier.
> > A counterfactual statement. Such statements are meaningless outside
> > a concept of realism beyond positivism.
> > There is a meaningful notion of realism, there such claims make sense.
> > I like it, and I defend it. But if you reject it, without defining an
> > alternative
> > concept of realism which makes such claims meaningful, you are simply
> > inconsistent.
>
> Things are perfectly consistent if you consider the wave function as a
> mathematical object in which all information we have about a quantum
> state is encoded.
I'm not talking about consistence. I accept that the minimal interpretation
is consistent and that there may be other, nonrealistic but consistent
interpretations.
> A measurement changes the knowledge about the quantum
> state and thus the wave function.
An interpretation which talks about human knowledge without
talking about states of reality is certainly not a realistic interpretation.
> And actually, the correlation of observables of an entangled system is
> to me as mysterious as is in Newtonian mechanics an object moving on
> a straight line forever if no forces are present. ;-)
As well, there is nothing mysterious in our world for somebody
who believes "Gods Will is unexplainable".
> > You cannot assume the nonexistence of a preferred frame.
> > Because no realistic description of the world is possible
> > without some real effects happening FTL. That's because
> > realism is not a pretty philosophical theory but a well-defined
> > concept which allows to prove theorems.
>
> In order to not be in the urge of assuming such a preferred frame
> I avoid using hidden variables.
A common but IMHO wrong decision - the rejection of reality
once reality does not behave according to your prejdices (against
the preferred frame).
> Apart from this I do not see that
> Bohmian mechanics makes any testable (by experiment) prediction that
> goes beyond the predictions of QM.
That's not the aim of BM. The aim is to provide a realistic
(even deterministic) interpretation of QM.
> (Also your paper makes no testable predictions as far as I have read it).
GLET includes additional terms, and makes different predictions
(inflation, some dark matter term, stable "frozen stars" slightly greater
than their BH horizons).
> I agree that the Bohmian interpretation does not contradict experiment.
> But I think you give up to many well-established principles without
> gaining anything new in terms of testable predictions.
The other choice is to give up an even much more fundamental
principle: realism.
On the other hand, the acceptance of a hidden preferred frame
is not dangerous at all. Instead, it allows to revive lots of
other principles which are incompatible with the underlying
philosophy of GR. (Local energy and momentum conservation,
the interpretation of the wave function as real, positive
definiteness in the "big" space of quantum gauge theories,
canonical quantization using a Hamiltonian formalism.)
Ilja
Andreas Most
> "Andreas Most" <Andrea...@t-online.de> schrieb
> ...
>>>>what exactly is the preferred frame and how can I identify it?
>>>
>>>You can roughly identify it as the rest frame of CMBR.
>>>
>>>
>>>>Is the preferred frame globally valid (in our universe) and static?
>>>
>>>Yes. (You need a theory of gravity with preferred frame
>>>for this purpose, see gr-qc/0205035.)
>>
>>As of my understanding, if you have two observers being at different
>>locations and each being at rest relative to the CMBR at their position,
>>the two observers move relative to one another.
>
>
> Yes. But it may be interpreted as well as a shortage of our rulers.
That's about what GR says about the expanding universe. So where is the
difference?
>>That is you cannot define a preferred frame globally.
>>(BTW: I read in your paper that you can prove a flat
>>universe in your GLET.
>
>
> Flat only in the approximation of a homongeneous universe.
> The other homongeneous solutions with constant curvature
> are not homogeneous in GLET.
>
>
>>How would you then explain the redshift of
>>objects being far away if not by an expanding universe?)
>
>
> By an interpretation of the _observed_ increase of distances
> between far away points by shrinking rulers.
As I said, this is the interpretation of GR.
>>>Ok, but if we include a reasonable notion of causality, without
>>>causal loops, as an additional requirement for the mechanism,
>>>my statement holds.
>>Again, causality has nothing to do with covariance.
>>Instead, causality considerations tell us which (covariant) solution
>>makes physically sense. For example, a spacelike line cannot be the
>>world line of anything that interacts with our observable world.
>>Excluding mathematical possible solutions to physics equations based on
>>such considerations is also done elsewhere (E.g. the broken cup that
>>does not recompile or using retarded solutions in electrodynamics and
>>rejecting advanced ones). But these exclusion schemes do not change the
>>properties of the physics equation (properties like e.g. covariance)
>
> Causality is a word with different meanings. Your concept of causality
> is also useful, but not what I'm talking about.
>
> What I name causality is simply a partial order among events: A->B
> if some (human) decision at A can influence the outcome of a
> (macroscopic) measurement at B. This relation should be transitive
> and should not allow closed causal loops.
>
> Now, we have x(t1)->x(t2) for t1<t2 along usual worldlines x(t).
> But, according to my realistic interpretation of violations of Bell's
> inequality, we have also "A->B or B->A" for space-like separated
> events.
What about the closed causal loops?
( I assume it is your definition of "causal" as above )
If there are three space-like seperated events A,B,C you have:
A->B or B->A
A->C or C->A
B->C or C->B
So it might be possible to have A->B->C->A. You will always be left with
causal loops.
> Despite the fact that all these observational facts are covariant,
> there exists no covariant relation A->B with these properties.
Still, tachyons would do the job and they are perfectly covariant!
>
> Ilja
>
Hendrik van Hees
> Let Alice and Bob each receive one of these photons (Maybe they are
> doing some quantum cryptography). If Alice has performed a measurement
> and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
> function would Bob use to describe the system?
He should not use a wave function at all, but the reduced state, based
on his knowledge, i.e.,
Tr_A {|Psi><Psi|}=1/2 (|H><H|+|V><V|).
>
> If Bob is spacelike separated, he cannot
> possibly know whether Alice has performed the measurement at all.
Right, and as the above state tells us, whether or not Alice measures
the polarisation of her photon, he will find always the same outcome,
namely in 50% of all cases he'll get a horizontally or a vertically
polarised photon. That's why there is no contradiction to causality in
this setting: He cannot even know whether Alice has measured the
polarisation of her photon or not. He also can not check whether his
photon was entangled with Alice's or not.
This they only can do by comparing there measurement protocols (i.e.,
they also need to note precisely enough which photon was measured,
i.e., by taking the precise time of their measurements) and look
whether there is the correlation encoded in |Psi> or not.
That makes the whole thing also good for cryptography, because by
measuring a single photon of an entangled pair tells you nothing, but
if a spy measured one of the photons, Alice and Bob will know
immediately, because then the entanglement was destroyed before they
measured the state of their photons, and there will be no correlation.
> And as long as he leaves the system unchanged and does not get
> information from Alice, he must describe the system as
> |psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
> knowledge would lead to contradictions (I think GHZ like setups
> would show contradictions.)
As I said, the single photons must be described by reduced states
(tracing over the part of the system, not accesible by Bob).
> Yes, and I think that quantum mechanical behaviour is fundamental in a
> similar manner. There is maybe no explanation for it.
>
> However, just to add "my two cents": I have the impression that the
> so-called collapse of the wave function being related to information
> gain has to do with the arrow of time (because of entropy...).
> Maybe, If we sometime solve the "arrow of time" puzzle,
> we might be able to solve also the so-called "measurement problem".
> (please don't flame me on this. It's just my personal opinion...)
Well that all may be true, but I have my doubts about the collapse
business. I don't think that the collapse is a physical process
happening to an individual system when we measure it.
Andreas Most
> "Andreas Most" <Andrea...@t-online.de> schrieb
>> Ilja Schmelzer wrote:
>>> "Andreas Most" <Andrea...@nospam.de> schrieb
>>>> I.e., you would have found a horizontal
>>>> polarisation for photon 1, even if you had performed the measurement
>>>> earlier.
>
>>> A counterfactual statement. Such statements are meaningless outside
>>> a concept of realism beyond positivism.
>>> There is a meaningful notion of realism, there such claims make sense.
>>> I like it, and I defend it. But if you reject it, without defining an
>>> alternative
>>> concept of realism which makes such claims meaningful, you are simply
>>> inconsistent.
>> Things are perfectly consistent if you consider the wave function as a
>> mathematical object in which all information we have about a quantum
>> state is encoded.
>
> I'm not talking about consistence. I accept that the minimal interpretation
> is consistent and that there may be other, nonrealistic but consistent
> interpretations.
>
>> A measurement changes the knowledge about the quantum
>> state and thus the wave function.
>
> An interpretation which talks about human knowledge without
> talking about states of reality is certainly not a realistic interpretation.
I didn't say human knowledge. This could imply that it is the human mind
which causes the collapse of the the wave function.
The wave function is the description of a quantum mechanical system.
(knowingly letting aside more complex situations where you would need
a statistical operator to describe a system)
It is thus just a mathematical object and not physical one.
The information about the outcome of a measurement changes this
description. This is different from classical physics where, e.g.
the observation of the moon does not change its orbit.
The physical entities in QM are things like position, energy, spin, etc.
There are however physical limits on having the knowledge about all of
them and I don't see a reason to assign them some sort of "existence" or
"realism" while I cannot possibly know them nor describe them.
>
>> And actually, the correlation of observables of an entangled system is
>> to me as mysterious as is in Newtonian mechanics an object moving on
>> a straight line forever if no forces are present. ;-)
>
> As well, there is nothing mysterious in our world for somebody
> who believes "Gods Will is unexplainable".
Well, using BM to fit QM into our classical educated picture of the
world and introducing an ether to make EM comply with Newtonian physics
while not questioning the classical conception, is to me pretty
narrow-minded.
>>> You cannot assume the nonexistence of a preferred frame.
>>> Because no realistic description of the world is possible
>>> without some real effects happening FTL. That's because
>>> realism is not a pretty philosophical theory but a well-defined
>>> concept which allows to prove theorems.
>> In order to not be in the urge of assuming such a preferred frame
>> I avoid using hidden variables.
>
> A common but IMHO wrong decision - the rejection of reality
> once reality does not behave according to your prejdices (against
> the preferred frame).
>
>> Apart from this I do not see that
>> Bohmian mechanics makes any testable (by experiment) prediction that
>> goes beyond the predictions of QM.
>
> That's not the aim of BM. The aim is to provide a realistic
> (even deterministic) interpretation of QM.
You mean "realistic" in terms of what we call "realistic" being biased
by classical physics.
>> (Also your paper makes no testable predictions as far as I have read it).
>
> GLET includes additional terms, and makes different predictions
> (inflation, some dark matter term, stable "frozen stars" slightly greater
> than their BH horizons).
That is so far not very convincing, even because there are still two
parameters in your GLET which have to be determined.
You could as well add higher order terms to GR to make such predictions.
>> I agree that the Bohmian interpretation does not contradict experiment.
>> But I think you give up to many well-established principles without
>> gaining anything new in terms of testable predictions.
>
> The other choice is to give up an even much more fundamental
> principle: realism.
>
> On the other hand, the acceptance of a hidden preferred frame
> is not dangerous at all. Instead, it allows to revive lots of
> other principles which are incompatible with the underlying
> philosophy of GR. (Local energy and momentum conservation,
Are you trying to claim that there is no (local) energy and momentum
conservation in GR ???
> the interpretation of the wave function as real, positive
> definiteness in the "big" space of quantum gauge theories,
> canonical quantization using a Hamiltonian formalism.)
Mathematical simplicity is nowadays not considered to be
a necessary criterion.
>
> Ilja
>
>
Andreas.
Ilja Schmelzer
> >>>
> >>>Yes. (You need a theory of gravity with preferred frame
> >>>for this purpose, see gr-qc/0205035.)
> >>As of my understanding, if you have two observers being at different
> >>locations and each being at rest relative to the CMBR at their position,
> >>the two observers move relative to one another.
> > Yes. But it may be interpreted as well as a shortage of our rulers.
> That's about what GR says about the expanding universe. So where is the
> difference?
You can use the CMBR frame and consider it as globally valid and
static (relative to the preferred background or the ether).
> >>How would you then explain the redshift of
> >>objects being far away if not by an expanding universe?)
> > By an interpretation of the _observed_ increase of distances
> > between far away points by shrinking rulers.
>
> As I said, this is the interpretation of GR.
It is a common property of many metric theories of gravity.
The point is that a realistic interpretation has to define which of the
alternatives are correct. Some attempts for explanation may have
causal loops, in this case they have to be rejected as inconsistent
explanations. But other have no causal loops.
For example, the time order t(A) < t(B) < t(C) defines one consistent
explanation of all three observations without closed causal loops.
Thus, there exists a realistic explanation without closed causal loops,
contrary to your claim.
> > Despite the fact that all these observational facts are covariant,
> > there exists no covariant relation A->B with these properties.
> Still, tachyons would do the job and they are perfectly covariant!
Which job? To describe which of the alternatives holds in
> A->B or B->A
> A->C or C->A
> B->C or C->B
without closed causal loops? I don't think so.
Ilja
Andreas Most
> Andreas Most wrote:
>
>
>>Let Alice and Bob each receive one of these photons (Maybe they are
>>doing some quantum cryptography). If Alice has performed a measurement
>>and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
>>function would Bob use to describe the system?
>
>
> He should not use a wave function at all, but the reduced state, based
> on his knowledge, i.e.,
>
> Tr_A {|Psi><Psi|}=1/2 (|H><H|+|V><V|).
I was referring to the two-photon system, not just the photon that Bob
has.
>>If Bob is spacelike separated, he cannot
>>possibly know whether Alice has performed the measurement at all.
>
>
> Right, and as the above state tells us, whether or not Alice measures
> the polarisation of her photon, he will find always the same outcome,
> namely in 50% of all cases he'll get a horizontally or a vertically
> polarised photon. That's why there is no contradiction to causality in
> this setting: He cannot even know whether Alice has measured the
> polarisation of her photon or not.
Yes, absolutely right.
> He also can not check whether his
> photon was entangled with Alice's or not.
This was actually the precondition of the thought experiment.
>
> This they only can do by comparing there measurement protocols (i.e.,
> they also need to note precisely enough which photon was measured,
> i.e., by taking the precise time of their measurements) and look
> whether there is the correlation encoded in |Psi> or not.
I cannot see what role time might play here, apart from identifying
the photon pairs if there is more than one. Anyway, I was looking only
at one pair.
> That makes the whole thing also good for cryptography, because by
> measuring a single photon of an entangled pair tells you nothing, but
> if a spy measured one of the photons, Alice and Bob will know
> immediately, because then the entanglement was destroyed before they
> measured the state of their photons, and there will be no correlation.
>
>
>>And as long as he leaves the system unchanged and does not get
>>information from Alice, he must describe the system as
>>|psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
>>knowledge would lead to contradictions (I think GHZ like setups
>>would show contradictions.)
>
>
> As I said, the single photons must be described by reduced states
> (tracing over the part of the system, not accesible by Bob).
Yes, but I talk about the wave function for the two-photon system being
initially entangled.
I was trying to make the point that Alice and Bob might have different
wave functions for the description of this "biphoton" depending on there
knowledge.
>
>
>>Yes, and I think that quantum mechanical behaviour is fundamental in a
>>similar manner. There is maybe no explanation for it.
>>
>>However, just to add "my two cents": I have the impression that the
>>so-called collapse of the wave function being related to information
>>gain has to do with the arrow of time (because of entropy...).
>>Maybe, If we sometime solve the "arrow of time" puzzle,
>>we might be able to solve also the so-called "measurement problem".
>>(please don't flame me on this. It's just my personal opinion...)
>
>
> Well that all may be true, but I have my doubts about the collapse
> business. I don't think that the collapse is a physical process
> happening to an individual system when we measure it.
I agree so far as I don't think that the collapse is a physical process.
IMHO the collapse of the wave function simply represents a change of
information about a system.
And this is where our discussion started, when I called the wave
function simply a mathematical object in that all the possibly available
information about a system is encoded. A change of information (the
result of a measurement) thus changes the wave function.
Others would call this the collapse.
Andreas.
Hendrik van Hees
> Yes, but I talk about the wave function for the two-photon system
> being initially entangled.
> I was trying to make the point that Alice and Bob might have different
> wave functions for the description of this "biphoton" depending on
> there knowledge.
What do you mean by that? Either they both know the exact state, i.e.,
that they have the entangled helicity-0 photon state (then both
describe it by the same state |Psi>) or Bob knows only about an
electron hitting is polarisation foil, and then he describes it by the
reduced density matrix.
I.Vecchi
..
>
> I agree so far as I don't think that the collapse is a physical process.
> IMHO the collapse of the wave function simply represents a change of
> information about a system.
Yes, but one may argue, as I do, that information about measurement
outcomes is what physics is about. In other words, that the distinction
between epistemic and physical is spurious.
>
> And this is where our discussion started, when I called the wave
> function simply a mathematical object in that all the possibly available
> information about a system is encoded. A change of information (the
> result of a measurement) thus changes the wave function.
> Others would call this the collapse.
Indeed. If the state vector encodes observer's knowledge about
measurement outcomes, then Bob's and Alice's knowledge is encoded by
two distinct state vectors. Measurement-induced changes in one of them
will not affect the other as long as no information is exchanged
between Bob and Alice. It is only when information is
compared/exchanged that entanglement comes into play.
The point being discussed here is not purely philosophical. The
implicit and erroneous assumption that distinct observers share the
same state vector is at the core of Altschul and Rebbi's ([1])
objections against Maris' electrino model.
Cheers,
IV
[1] B. Altschul, C. Rebbi "Analysis of a toy model of electron
splitting" Phys. Rev. A 69, 032111 (2004) . They supplement their
"anti-superluminal" objection with a crude misrepresentation of Maris'
arguments and with an olympic indifference to experimental results, but
that is another story.
Ilja Schmelzer
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andrea...@t-online.de> schrieb
> >> Ilja Schmelzer wrote:
> >> A measurement changes the knowledge about the quantum
> >> state and thus the wave function.
> >
> > An interpretation which talks about human knowledge without
> > talking about states of reality is certainly not a realistic
interpretation.
>
> I didn't say human knowledge. This could imply that it is the human mind
> which causes the collapse of the the wave function.
If we omit the word "human" my argument does not change.
> The wave function is the description of a quantum mechanical system.
> It is thus just a mathematical object and not physical one.
Of course. The objects of realistic theories are also mathematical
objects and not physical ones. The difference is what is described
(unsing mathematical words): States of reality or something else
(states of knowledge, algorithms for computations of probability
distributions and so on.)
> The information about the outcome of a measurement changes this
> description. This is different from classical physics where, e.g.
> the observation of the moon does not change its orbit.
Of course, if we describe in classical physics states of knowledge,
they also change if we receive information.
> The physical entities in QM are things like position, energy, spin, etc.
> There are however physical limits on having the knowledge about all of
> them and I don't see a reason to assign them some sort of "existence" or
> "realism" while I cannot possibly know them nor describe them.
How do you know there are limits? If you don't search for a realistic
theory you will never find one, of course. But these are only limits
of your approach to science.
> >> And actually, the correlation of observables of an entangled system is
> >> to me as mysterious as is in Newtonian mechanics an object moving on
> >> a straight line forever if no forces are present. ;-)
> >
> > As well, there is nothing mysterious in our world for somebody
> > who believes "Gods Will is unexplainable".
>
> Well, using BM to fit QM into our classical educated picture of the
> world and introducing an ether to make EM comply with Newtonian physics
> while not questioning the classical conception, is to me pretty
> narrow-minded.
Anything else except name-calling?
As Lorentz-invariance, as the "classical educated picture of the world"
refers to some set of principles. If they appear to be in conflict, we
should
search for possibilities to solve this conflict. Above possibilities has to
be
tried out. To consider Lorentz-invariance as a dogma is as well
narrow-minded.
I'm open for questioning the classical conceptions. But questioning is
different from rejection without question, in favour of some "modern"
but also over a century old principle.
> >> Apart from this I do not see that
> >> Bohmian mechanics makes any testable (by experiment) prediction that
> >> goes beyond the predictions of QM.
> >
> > That's not the aim of BM. The aim is to provide a realistic
> > (even deterministic) interpretation of QM.
>
> You mean "realistic" in terms of what we call "realistic" being biased
> by classical physics.
I mean "realistic" in terms of a well-defined formal criterion. Observed
expectation values should be explained by some (X, rho(x)dx,m(x,c))
with
E(f|c)= int f(m(x,c)) rho(x) dx.
> >> (Also your paper makes no testable predictions as far as I have read
it).
> >
> > GLET includes additional terms, and makes different predictions
> > (inflation, some dark matter term, stable "frozen stars" slightly
greater
> > than their BH horizons).
>
> That is so far not very convincing, even because there are still two
> parameters in your GLET which have to be determined.
> You could as well add higher order terms to GR to make such predictions.
Your point being? I have not invented the additional terms to
make some different predictions, but they are the natural result of the
sufficiently simple and natural axioms of my theory.
BTW, by adding appropriate dark matter you can make whatever
prediction you like in standard GR.
> >> I agree that the Bohmian interpretation does not contradict experiment.
> >> But I think you give up to many well-established principles without
> >> gaining anything new in terms of testable predictions.
> >
> > The other choice is to give up an even much more fundamental
> > principle: realism.
> >
> > On the other hand, the acceptance of a hidden preferred frame
> > is not dangerous at all. Instead, it allows to revive lots of
> > other principles which are incompatible with the underlying
> > philosophy of GR. (Local energy and momentum conservation,
>
> Are you trying to claim that there is no (local) energy and momentum
> conservation in GR ???
Correct. It is impossible to define a energy and momentum density
for the energy of the gravitational field in a covariant way.
It is, instead, possible to define such a thing in a coordinate-depending
way (so called pseudo-tensors). But this way has to be rejected because
it is in conflict with the metaphysical principles of GR.
Ways to define some sort of global energy conservation depend in
sufficiently obvious ways on the choice of boundary conditions which
are equivalent to fixing, with sufficient accuracy, the coordinates "in the
infinite point" and using, then, some pseudo-tensor.
> > the interpretation of the wave function as real, positive
> > definiteness in the "big" space of quantum gauge theories,
> > canonical quantization using a Hamiltonian formalism.)
>
> Mathematical simplicity is nowadays not considered to be
> a necessary criterion.
You propose to reject Ockhams razor as well? Too old, too
classical?
Ilja
Andreas Most
> Andreas Most ha scritto:
> ..
>
>>I agree so far as I don't think that the collapse is a physical process.
>>IMHO the collapse of the wave function simply represents a change of
>>information about a system.
>
>
> Yes, but one may argue, as I do, that information about measurement
> outcomes is what physics is about. In other words, that the distinction
> between epistemic and physical is spurious.
>
>
>>And this is where our discussion started, when I called the wave
>>function simply a mathematical object in that all the possibly available
>>information about a system is encoded. A change of information (the
>>result of a measurement) thus changes the wave function.
>>Others would call this the collapse.
>
>
> Indeed. If the state vector encodes observer's knowledge about
> measurement outcomes, then Bob's and Alice's knowledge is encoded by
> two distinct state vectors. Measurement-induced changes in one of them
> will not affect the other as long as no information is exchanged
> between Bob and Alice. It is only when information is
> compared/exchanged that entanglement comes into play.
Very interesting point. That is why we usually do not need to take
the universe's wave function, when we only want to describe a couple
of electrons ;-)
>
> The point being discussed here is not purely philosophical. The
> implicit and erroneous assumption that distinct observers share the
> same state vector is at the core of Altschul and Rebbi's ([1])
> objections against Maris' electrino model.
>
> Cheers,
>
> IV
>
> [1] B. Altschul, C. Rebbi "Analysis of a toy model of electron
> splitting" Phys. Rev. A 69, 032111 (2004) . They supplement their
> "anti-superluminal" objection with a crude misrepresentation of Maris'
> arguments and with an olympic indifference to experimental results, but
> that is another story.
>
Also available at http://www.arxiv.org/abs/cond-mat/0211096
Andreas.
Andreas Most
> Andreas Most wrote:
>
>
>>Yes, but I talk about the wave function for the two-photon system
>>being initially entangled.
>>I was trying to make the point that Alice and Bob might have different
>>wave functions for the description of this "biphoton" depending on
>>there knowledge.
>
>
> What do you mean by that? Either they both know the exact state, i.e.,
> that they have the entangled helicity-0 photon state (then both
> describe it by the same state |Psi>) or Bob knows only about an
> electron hitting is polarisation foil, and then he describes it by the
> reduced density matrix.
>
Initially Alice and Bob use the same wave function to describe this
entangled photon state.
Consider now the case where Alice perfoms a measurement on her photon
while Bob does not. Alice can now describe the two photons with seperate
wave functions according to her measurement. However, as long as Bob is
spatially seperated from Alice's measurement event, he cannot possibly
know what the outcome of her measurement is nor whether she performed
the measurement at all. His description of the biphoton is still the
entangled two-photon state. That is, Alice and Bob may have a different
wave function for the two-photon system. Only when Bob also performs
a measurement on his photon or receives Alice's measurement results,
he will change his wave function accordingly.
There is no contradiction in here because it is not the wave function
that is measured. IMHO the so-called wave function
collapse coincides with the gain of information about, say, a
measurement result. The wave function could thus be considered as
an information container about a quantum mechanical system.
Different observers might have different wave functions for the
same system.
I know this is a pretty simplified description not regarding more
complex states where you would need a statistical operator. But this
interpretation (if you can call it that) helped me understanding the
popular quantum mechanical paradoxons ;-)
Andreas.
I.Vecchi
http://128.148.60.98/physics/researchpages/cme/bubble/jltp.pdf
IV
I.Vecchi
Andreas Most wrote:
> I.Vecchi wrote:
> > The
> > implicit and erroneous assumption that distinct observers share the
> > same state vector is at the core of Altschul and Rebbi's ([1])
> > objections against Maris' electrino model.
> >
> > Cheers,
> >
> > IV
> >
> > [1] B. Altschul, C. Rebbi "Analysis of a toy model of electron
> > splitting" Phys. Rev. A 69, 032111 (2004) . They supplement their
> > "anti-superluminal" objection with a crude misrepresentation of Maris'
> > arguments and with an olympic indifference to experimental results, but
> > that is another story.
> >
>
> Also available at http://www.arxiv.org/abs/cond-mat/0211096
Some more on this.
In [1] Maris aims to "bring into very sharp focus some of the
uncertainties of quantum measurement theory" and argues that "quantum
mechanics does not make clear predictions for the results of
measurements on systems" like those he examines. I happen to concur
with him. Actually I have been claiming that, once one recognises
entanglement as a property of the measurement process enforcing
constraints on distinct measurement outcomes, the prevailing usage of
entanglement may be inadequate (cf. [2]).
In [3] Altschul and Rebbi dismiss Maris' model, ignoring the relevant
experimental data, which are not even cited in their paper. In fact
their model contemplates "full sized bubbles" which are incompatible
with the observed phonomena. The thrust of their argument, beside
their irrelevant 1-dimensional construct, is that Maris' model would
enable superluminal signalling. I contend that their argument is
flawed. The key point is that, while the electrino bubbles are
entangled, the energy they carry is not. In other words, upon
measurement a fractional-amplitude bubble will release photons locally,
regardless of whether the fractional-amplitude electron spawning it is
detected or found to be locally absent. Similarly, other bubbles
entangled with the one being measured will release their photons
locally only when they will be subjected to measurement.
I stress that this is not just an interpretational issue. It is an
experimentally relevant one, with the measurement problem at its core.
IV
[1] H.J. Maris "On the Fission of Elementary Particles and the Evidence
for Fractional Electrons in Liquid Helium" Journal of Low Temperature
Physics , 120, 3/4 (2000) pp. 173-204 at
http://128.148.60.98/physics/researchpages/cme/bubble/jltp.pdf
[2]
http://groups.google.com/group/sci.physics.research/msg/6a73a0f2cbdfa344
[3] B. Altschul, C. Rebbi "Analysis of a Toy Model of Electron
'Splitting' at
http://www.arxiv.org/abs/cond-mat/0211096
Peter
> The measurement on one particle does *not* instantaneously
> act on the other particle, which is far away, but the correlation
> existed the whole time from the preparation of the particle pair.
>
If the measurements on the two particles was just a matter of observing
two pre-set values, then I would agree, but what I have read suggests the
situation is more complicated than this.
Eg from:
http://en.wikipedia.org/wiki/Quantum_entanglement
<<<
One apparent way to explain quantum entanglement is an approach known
as "hidden variable theory", in which unknown deterministic microscopic
parameters would cause the correlations. However, in 1964 Bell showed that
such a theory could not be "local", the quantum entanglement predicted by
quantum mechanics being experimentally distinguishable from a broad class
of local hidden-variable theories. Results of subsequent experiments have
overwhelmingly supported quantum mechanics.
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Terry Pilling wrote:
>> If this is the case, show me where, in QED, you have a field variable
>> propagating from one to the other and causing the change, and show that
>> this propagation is instant. You can't show this because it is
>> impossible in QED or any relativistic quantum field theory. So what
>> these people must be claiming is that the creation of two photons can
>> not be described in quantum field theory! A suggestion that is
>> ridiculous in light of the successes of QED in describing that very
>> thing.
>>
Thats an interesting point. But I wonder if QED can describe
the creation of two entangled photons?
Regards,
Peter
FrediFizzx
news:pan.2006.02.27....@please.net...
Yes it can. The annihilation of an electron and positron coming
together slowly can produce an entangled pair of photons. In that case,
I agree with what Hendrik van Hees said above.
FrediFizzx
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
Roland Franzius
I doubt one can produce an entangled pair of photons if the leptons are
not prepared as an entangled (anti)pair state. You dont get something
entangled from a two particle product state. Something has to reduce the
incoming state to a pure two particle spin eigenstate to have entangled
photon pairs in the zero spin channel. The mystery how to physically
project uncorrelates states to strongly correlated pair states remains.
--
Roland Franzius