EPR question
mediaglyphic
I am not sure about the real paradox in EPR, since the two particles have
the same genesis wouldn't how are we really effecting one when we measure
the other.
i understand that bell's inequality was shown to support the QM
interpretation of EPR in Aspects experiment but could the problem not be
with the way the presence of the particles was measured.
i am not a physicist but a lay engineer, so please be patient if these are
silly questions.
Hans Jud
mediaglyphic schrieb:
Hy
I have started a discussion about EPR in the group -de.sci.physik-. I'm not a
physicist eather.
I wasn't very successfull in getting answers that understand. I tried in
attacking the theme in different ways, I'm still trying, won't give up, and I
will monitor your question, maybe it will be more understandable.
Hans Jud
mediaglyphic
i have read a few books on EPR but i still feel that there are things i just
don;t get.
most importantly i would like to understand how these experiments were
conducted, exactly what was measured and how. i have read that some people
are unhappy with the way aspect conducted his experiment (too predictable or
something akin to a failure on a second order chi squared test or something
like this, you can tell that i am an amateur here!)
second if someone could really explain in detail how heisenberg's
uncertainty principle applies here, i get that if you measure something then
you affect it and that here you are measuring one particle and thus
affecting the particle pair. but the fact that the particle pairs were born
together tells me that they should infact contain some information about
each other, and that maybe when you measure one particle at a certain time
you get information about what's going on with the other particle at the
same time. this is where i get into problems, how are the particles marked
so we know that we are comparing results about the same ones? how do we know
that we are measuring the particles at the same time.
a third point that is unclear to me is in bells inequality, is sign a less
than and equal to or just a less than? i have seen both versions.
if anyone can help hear it would be greatly appreciated.
finall
"Hans Jud" <eh....@bluewin.ch> wrote in message
news:39634C03...@bluewin.ch...
and...@attglobal.net
>
> (not sure if this belongs in sci.phys.particle or in sci.phys.relativity)
>
> I am not sure about the real paradox in EPR, since the two particles have
> the same genesis wouldn't how are we really effecting one when we measure
> the other.
>
> i understand that bell's inequality was shown to support the QM
> interpretation of EPR in Aspects experiment but could the problem not be
> with the way the presence of the particles was measured.
>
> i am not a physicist but a lay engineer, so please be patient if these are
> silly questions.
The problem is that the two measurements are correlated but
the Copenhagen interpretation (CI) of QM says that you only determine
the result when you locally do the measurement on either particle.
So the CI says that if you do a measurement on either particle,
the result on the other particle is determined, but that the result
of the measurement on the first particle could be any one of a
number of results until you do the measurement.
The implication is that there's something passing between
the events at which the two particles are measured that is
going instantaneously in some frame of reference.
John Anderson
orton
http://www.fh-niederrhein.de/~physik07/knobelecke/k_elmodel.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_dorton.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_unified.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_unified2.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_haupt.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_why12a.htm
http://www.fh-niederrhein.de/~physik07/knobelecke/k_why12b.htm
http://www.fh-niederrhein.de/~physik07/index.html
http://www.fh-niederrhein.de/~physik07/knobelecke/k_dorton.htm
_the third side of every coin always gave me the edge, (orton).
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mediaglyphic
thanks for the response,
please see my questions below
> The problem is that the two measurements are correlated but
> the Copenhagen interpretation (CI) of QM says that you only determine
> the result when you locally do the measurement on either part
> So the CI says that if you do a measurement on either particle,
> the result on the other particle is determined, but that the result
> of the measurement on the first particle could be any one of a
> number of results until you do the measurement.
just because it could be one of any number of results does it necessarily
refute that it is precisely one of the results before you measure it?
>
> The implication is that there's something passing between
> the events at which the two particles are measured that is
> going instantaneously in some frame of reference.
>
the implication to me is that the pair of particles had a predfined value
and that we only discoved the value upon measurement.
> John Anderson
Hans Jud
mediaglyphic schrieb:
> (not sure if this belongs in sci.phys.particle or in sci.phys.relativity)
>
> I am not sure about the real paradox in EPR, since the two particles have
> the same genesis wouldn't how are we really effecting one when we measure
> the other.
>
> i understand that bell's inequality was shown to support the QM
> interpretation of EPR in Aspects experiment but could the problem not be
> with the way the presence of the particles was measured.
>
> i am not a physicist but a lay engineer, so please be patient if these are
> silly questions.
I would like to try another attempt
Lets say, I have a pair of gloves and put each in a box. My friend Bob takes
one box and travels 10000 miles.
A) living in our normal world:
I make the guess, that my box contains the left-handed glove. My chance to be
right is 50%.
After a while I open my box.
I see the left-handed glove. I was right with my guess and
I know, that my friend Bob must have the right-handed glove in his box.
B) living in Quantumworld (the pair of gloves acts like a pair of correlated
photons, the left-right-handed gloves are in a state of superposition.)
After a while I open my box.
I see the left-handed glove (the wave-function collapsed). I was right with my
guess and I know, that my friend Bob must have the right-handed glove in his
box.
Now, my first problem is not the question, if the wave-function of Bobs glove
collapsed immediately or not.... it even could be possible, that he already
had opened the box, before I did. Etc. etc.
I have a much SIMPLER problem:
WHAT IS THE BASIC OR MAIN REASON OF QT TO CREATE THE IDEA OF A SUPERPOSITIONED
STATE?
I always read, that the measurements lead to it. But what measurements? I
mean, the chances are 50% to be right or wrong. When I take 2 guesses, I have
a chance of 100% to be right. I almost get the idea, that in QT, adding
chances, you can get totals of more than 130% or so?
Regards
A half destroyed
Hans Jud
PS: forgive my bad language, I am Swiss-German
mediaglyphic
and your english is completely understandable so no need to apologize.
i believe that what you are stating when you say prob=130% is what is
implied by aspects experiment as applied to bell's inequality.
in order to really understand this though i believe that i will really have
to learn Quantum Physics from the bottom up.
my suspicion is that the way we measures creates the paradox. also i wonder
about this wave paricle duality, i wonder if quantum behaviour cannot best
be described by imagining quatnum events as something other than waves or
particles. i know the bootstrap theory is much discredited, but it always
had some elegance for me (it seems right to me that what we observe are not
particles but rather interactions amongst particles). i am afraid i may be
rambling!
if anyone can elaborate on the question about probability and bells
inequality or aspects experiment it would be much appreciated
"Hans Jud" <eh....@bluewin.ch> wrote in message
news:396751CE...@bluewin.ch...
Hans Jud
Hy,
its midnight here, but just a short replay. And when I ask questions, I know,
you cannot answer them, but maybe somebody else will be around.
>
> i believe that what you are stating when you say prob=130% is what is
> implied by aspects experiment as applied to bell's inequality.
>
> in order to really understand this though i believe that i will really have
> to learn Quantum Physics from the bottom up.
>
This is what I just cannot believe, is there really no choice, but to study the
whole thing? ( I cannot make it a profession) That would mean, that QM never
would be understood by normal folks. Again, I don' t mean to understand the
whole thing, but there are so many authors that try to explain the experiments,
that it makes me think, that at least these should be understandable. Basically
I understand (out of my guts) whats about illocality etc., but nobody can tell
me what makes such things necessary.
> my suspicion is that the way we measures creates the paradox.
I have some ideas about that too, but first I want to learn: Which paradox is
created?
> also i wonder
> about this wave paricle duality, i wonder if quantum behaviour cannot best
> be described by imagining quatnum events as something other than waves or
> particles.
Here too, I think I would have some ideas that fit in the whole thing..... but
how can I discuss, when I am not familiar in what way Bells inequality gets
proven to be wrong.
>I know the bootstrap theory is much discredited, but it always had some
elegance for me (it seems right to me that what we observe are not
> particles but rather interactions amongst particles). i am afraid i may be
> rambling!
>
> if anyone can elaborate on the question about probability and bells
> inequality or aspects experiment it would be much appreciated
>
>
I hope somebody is out there hearing our problems and despair
Good night
Hans Jud
By the way, what is your name?
>
Frank Wappler
> Let's say, I have a pair of gloves and put each in a box.
> A) living in our normal world:
> [...] After a while I open my box.
> I see the left-handed glove.
> [...] I know, that my friend Bob must have
> the right-handed glove in his box.
> B) living in Quantumworld:
.. an equal experimental description, with additional nomenclature ...
> (the pair of gloves acts like a pair of correlated photons,
> the left-right-handed gloves are in a state of superposition.)
> [...] After a while I open my box.
> I see the left-handed glove (the wave-function collapsed).
> [...] I know, that my friend Bob must have
> the right-handed glove in his box.
> WHAT IS THE BASIC OR MAIN REASON OF QT TO CREATE THE IDEA
> OF A SUPERPOSITIONED STATE?
AFAIU:
to concisely describe the set of all admissible outcomes of one trial:
in each trial you might find either a left or a right
(that's unless you'd _admit_ only the trials in which you find left -
since that's the only trial you've described);
or to concisely summarize all actual outcomes of a set of trials:
you may have found a certain ratio of left and right
(that's unless you've _only_ found left -
as in the only trial you've described).
The admissible outcomes are often derived from actual outcomes
obtained in previous trials;
one would expect that a setup "doesn't change a lot, soon".
The described state of the glove pair is also "entangled":
Bob individually could find { left, or right },
you individually could find { left, or right },
but (Bob and you) collectively could only find
{ (left and right), or (right and left) }
while "finds" of
{ (left and left), or (right and right) }
are not admissable a priori, by the above prescription.
However, your example also misses an important point:
apparently it is assumed that Bob and you agree a priori
on what you both find "left", and what "right", trial by trial.
Usually such relations between coordinate systems
(their orientation_angle wrt. each other) are not known a priori
but are _results_ of experiments that have to be derived
from correlating the individual observations.
Surely the EPR/Aspect/Gisin-type experiments make the best examples
themselves; let me still try to make up an analogy:
Suppose that you take N pennies and N aspirins,
and put them in two cups:
0 =< k =< N pennies and N - k aspirins in one cup, and
the remaining N - k pennies and k aspirins in the other cup.
Send the filled cups to two detectors, A and B, who both report
their observations in terms of the labels "good" or "not-so-good".
Correlating the results by the (calibrated) trial number
allows you, as well as everyone else, incl. A and B themselves,
to determine the relation/orientation between the two coordinate
systems { good, or not-so-good }_A and { good, or not-so-good }_B
in the first place:
- the reported observations might be highly anti-correlated,
i.e. if one finds the received cup good, then the other does not,
and vice versa. The two coordinate systems would be closely alinged.
(For instance: if both detectors might be kids who rather
get enough pennies to afford a movie ticket,
but have no use for aspirins.) Or
- the reported observations might be highly correlated,
i.e. both tend to agree on their finds.
The two coordinate systems would correspondingly be anti-alinged.
(For instance: if one detector is a kid as described above,
and the other detector is a crew of people stranded on a desert
island, how'd each dearly needed an asprin.
Let's say you conduct one trial a day, and that all tic-tacs
are consumed and all pennies are spent or still useless
when the next cup arrives.) Or
- the reported observations might not be correlated,
the finds being statistically independend.
The two coordinate systems would correspondingly be orthogonal.
(For instance: if one detector is a kid or a crew as described above
and the other equates the coordinate system { good, or not-so-good }
with { even_number_of_pennies, or odd_number_of_pennies },
for some reason.) Etc.
Similarly, in the Aspect/Gisin experiments the orientation_angles
of various detector pairs wrt. each other are results that are
only derived _from_ their individual observations
in two-valued coordinate systems e.g.
{ (Ah = 1 and Av = 0), (Ah = 0 and Av = 1) } and
{ (Bu = 1 and Bf = 0), (Bu = 0 and Bf = 1) },
through Malus' definition:
orientation/angle( A, B, { trials k } ) ==
1/2 arccos( Sum_{ trials k }_(
(Ah_k Bu_k + Av_k Bf_k - Ah_k Bf_k - Av_k Bu_k) /
(Ah_k Bu_k + Av_k Bf_k + Ah_k Bf_k + Av_k Bu_k) ).
Note that this can only be evaluated by someone who has obtained
both individual sets of observations of the two detectors,
i.e. _not_ instantaneously by any one detector alone.
(The original EPR experiment involves of course trial by trial
measurements of the velocity of the various detectors wrt. each other
which requires light signal roundtrips.)
Hope this helps. Frank W ~@) R
> PS: forgive my bad language
That's quite allright, IMHYPO. Only: your question was pretty LOUD.
Stephen Speicher
>
> Lets say, I have a pair of gloves and put each in a box. My
> friend Bob takes one box and travels 10000 miles.
> A) living in our normal world: I make the guess, that my box
> contains the left-handed glove. My chance to be right is 50%.
> After a while I open my box. I see the left-handed glove. I
> was right with my guess and I know, that my friend Bob must
> have the right-handed glove in his box.
> B) living in Quantumworld (the pair of gloves acts like a pair
> of correlated photons, the left-right-handed gloves are in a
> state of superposition.) After a while I open my box. I see
> the left-handed glove (the wave-function collapsed). I was
> right with my guess and I know, that my friend Bob must have
> the right-handed glove in his box.
>
This is a very poor analogy. Here you use superposition as
focusing on the state of your knowledge, while the standard
theory, the Copenhagen interpretation, uses the term to focus on
the state of existence. Here is one of the founding fathers of
the theory, Werner Heisenberg, expressing the standard notion.
"Therefore, the transition from the 'possible' to the
'actual' takes place during the act of observation. If
we want to describe what happens in an atomic event, we
have to realize that the word 'happens' can apply only
to the observation, not to the state of affairs between
two observations. It applies to the physical, not the
psychical act of observation, and we may say that the
transition from the 'possible' to the 'actual' takes
place as soon as the interaction of the object with the
measuring device, and thereby with the rest of the
world, has come into play: it is not connected with the
act of registration of the result by the mind of the
observer."
---Werner Heisenberg, _Physics and Philosophy_, 1948.
>
> I have a much SIMPLER problem:
>
> WHAT IS THE BASIC OR MAIN REASON OF QT TO CREATE THE IDEA OF A
> SUPERPOSITIONED STATE?
>
There are two reasons for this: one philosophical, and the other
scientific.
To understand the choices made, you must study the postivist
philosophy of Neils Bohr and his colleagues in the Vienna Circle.
This is the foundation for the interpretation given to quantum
events. In short, the postivists accepted a form of empirical
reality, but made it dependent on observation and experiment. In
effect, they believed we cannot verify the existence of an
observer-independent reality.
Simply put, the scientific reason has to do with Schroedinger's
wave equation for a free particle. A general mathematical
principle applied to this equation states that any function
psi(x,t), a solution to the equation, can be written as a
linear superposition of some number of complex waves of a certain
form. The idea, then, of a superposition state corresponds well
with the philosophical ideas of the founders of the Copenhagen
interpretation, insofar as it is the collapse of the wavefunction
by measurement which corresponds to Heisenberg's transition from
the possible to the actual.
> I always read, that the measurements lead to it. But what
> measurements? I mean, the chances are 50% to be right or wrong.
> When I take 2 guesses, I have a chance of 100% to be right. I
> almost get the idea, that in QT, adding chances, you can get
> totals of more than 130% or so?
>
For a simple EPR-type thought experiment, quantum theory predicts
a cos^2 dependence on the coincidence rate between angular
settings of two differently oriented polarizers (actually, it is
the difference angle between the polarizer settings which is
important). In two experiments performed in 1981 and 1982, Alain
Aspect confirmed the quantum predictions, measuring the
coincidence rates under various polarizer settings. More recent
experiments at Innsbruck have given a fine-tuning to this type of
experiment (under more stringent conditions) and found a similar
violation of expected values. Normal coincidences should be <= 2,
theoretical predictions are 2.83, and the Innsbruck experiments
found typical values around 2.73.
Stephen
s...@compbio.caltech.edu
You can always tell a pioneer by the arrows in his back.
Printed using 100% recycled electrons.
--------------------------------------------------------
Ron House
>
> > in order to really understand this though i
> > believe that i will really have
> > to learn Quantum Physics from the bottom up.
>
> This is what I just cannot believe, is there really
> no choice, but to study the whole thing? ( I cannot make
> it a profession) That would mean, that QM never
> would be understood by normal folks. Again, I don' t mean
> to understand the whole thing, but there are so many authors
> that try to explain the experiments, that it makes me think,
> that at least these should be understandable.
They are. Let me have a crack at it.
You have two atomic particles that annihilate each other, resulting in
two photons going in opposite directions. Now let's say that the wave
function of this pair basically says "These two photons have the same
polarisation". Note carefully, this particular wave fn doesn't tell us
what the angle of polarisation is, just that, whatever it is, it is the
same for both.
Now as you will be aware, if you are wearing polarised sunglasses (the
polarisers oriented at 0 degrees, and polarised light reflects off the
road with angle 90deg, then none of the light gets through. If you turn
your glasses through 90deg, so that both the glasses and the oncoming
light have polarisation angle 0deg, then all of the light gets through.
What if the polarising filter is at some other angle to the plane of
polarisation? It turns out that the intensity of polarised light passing
through a filter is cos^2 theta (where theta is the angle between the
plane of polarisation and the angle of the filter).
OK, back to our two photons. Remember, the wave fn doesn't say what the
polarisation angles are, only that they are the same. So let's place
polarisers in the paths of our two photons. Say we put polariser A in
the path of photon 1, at angle 45deg, and photon 1 passes through the
filter. We now know that photon 1 is polarised at 45deg. Therefore so
must photon 2 also be. So if we place polariser B in the path of photon
2, also at 45deg, 2 is guaranteed to pass through.
So far so good.
But what if we place polariser B at, say, 20deg? The probability that
photon 2 goes through must be cos^2 ((45-20)*pi/180). That is greater
than 1/2. How does photon 2 'know' that is should go through with
greater than 1/2 probability? I mean, it doesn't know that I will place
polariser A at 45deg, does it? If I had place polariser A at 65deg, the
the angle between polariser A at 65deg and B at 20deg is 45deg, for
which angle cos^2 theta is exactly 1/2.
So the probability with which photon 2 goes through filter B at 20deg is
1/2 if I put filter A at 65deg, and more than 1/2 if I put filter A at
45deg.
Of course, for the photons that block at A, the probabilities for the
photons at B are 1 minus the probability for the companions of those
that pass at A (head spins, but it makes sense, as the total probability
of a pass is always 1/2).
We don't notice anything odd at either A or B, because half the photons
go through and half don't, no matter what the polarisation angles.
However, when we bring the two sets of records together and compare them
photon by photon, we notice the strange dependence at B upon the angle
of the filter at A. This is what is causing all the fuss. If it doesn't
strike you that there is anything remarkable here, then try to simulate
it. Let's assume a local realistic theory: no effect depends on remote
causes unless information can travel from one to the other at the speed
of light. Try to 'cook up' a predetermined rule for whether photons 1
and 2 pass through their filters; invent any rule you like, so long as
photon 2's rule doesn't mention filter A, and photon 1's rule doesn't
mention filter B. Try to get the cos^2 theta relationship at all
possible angles between A and B. You'll find it can't be done.
This experiment has been done with the two measurements close enough in
time to rule out transmission of information at the speed of light. Some
suggestive experiments (of a different construction) even suggest that
such correlations can have an effect backwards in time!
So one of two things must be happening: either there is nonlocal
causation faster than light, or the photons don't have a definite
polarisation angle as they travel apart. This is what causes the
consternation.
I don't find this a problem because I believe reality to be mental, not
material. That is, reality exists, but that reality IS the logical
relationships expressed by the wave function, whereas "material" is
merely an appearance that manifests on our human scale of observation.
The wave function is the primary reality, not the "particles" or the
"waves" whose duality has caused so much fog to so many.
> I hope somebody is out there hearing our problems and despair
>
> Good night
>
> Hans Jud
Hope the above helps. Best wishes,
--
Ron House ho...@usq.edu.au
http://www.sci.usq.edu.au/staff/house
Goodness trumps ideologies.
Frank Wappler
I hope you'll have no problems aligning the letters
that were ordered incorrectly in
Frank Wappler wrote:
> The two coordinate systems would be closely alinged.
and that my example how quantum mechanics describes
the measurement of relatios between coordinate systems
is invariant under interchange of
> tic-tacs
for
> aspirins
.
Frank Wappler
> For a simple EPR-type thought experiment, quantum theory
> predicts a cos^2 dependence on the coincidence rate
> between angular settings of two differently oriented polarizers
> (actually, it is the difference angle between the polarizer
> settings which is important).
That's not a prediction, but unambiguously implied
through the measurement procedure (Malus' procedure)
by which the orientation_angle of a pair of polarizers
wrt. each other is being determined in the first place.
Having measured values of the pairwise orientation_angle
(over any particular set of trials),
they may of course be further correlated with various
other observations, e.g. of individual "settings".
> In two experiments performed in 1981 and 1982, Alain Aspect
> confirmed the quantum predictions, measuring the
> coincidence rates under various polarizer settings.
How, if at all, did Aspect et. al. determine the orientation_angle
of particular polarizer pairs in particular sets of trials
in the first place,
and its relation and their "settings" in those trials?
> More recent experiments at Innsbruck have given a fine-tuning
> to this type of experiment (under more stringent conditions)
How, if at all, was the orientation_angle of particular
polarizer pairs in particular sets of trials be determined
in those experiments in the first place,
and its relation and their "settings" in those trials?
> Normal coincidences should be <= 2
Please explain how one would arrive at such an expectation.
Thanks, Frank W ~@) R
Stephen Speicher
> Stephen Speicher wrote:
>
> > For a simple EPR-type thought experiment, quantum theory
> > predicts a cos^2 dependence on the coincidence rate
> > between angular settings of two differently oriented polarizers
> > (actually, it is the difference angle between the polarizer
> > settings which is important).
>
> That's not a prediction, but unambiguously implied
> through the measurement procedure (Malus' procedure)
> by which the orientation_angle of a pair of polarizers
> wrt. each other is being determined in the first place.
>
The results of a mathematical analysis _predicts_ what
experiments confirm. So, for instance, if one polarizer, A, is
oriented at angle a, its eigenstates are |psi_A_v> and |psi_A_h>
(the notation should be clear -- polarizer A with vertical or
horizontal) and likewise for polarizer B, with primed directions,
|psi_B_v'> and |psi_B_h'>. The difference angle, b-a, is taken
as the angle between the vertical axes of the polarizers. For
simplicity, I'll just calculate one of the four eigenstates of
the difference angle (b-a), and the other three, psi__, psi++,
psi+-, follow in the same manner.
<psi'++|psi> = 1/sqrt(2) <psi_A_v|<psi_B_v'|(|psi_A_L|psi_B_L> +
+|psi_A_R|psi_B_R)
= 1/sqrt(2) (<psi_A_v|psi_A_L> <psi_B_v'|psi_B_L> +
+<psi_A_v|psi_A_R> <psi_B_v'|psi_B_R>)
= 1/sqrt(2) [ 1 e^i(b-a) + 1 e^-i(b-a) ]
------- -------- ------- --------
sqrt(2) sqrt(2) sqrt(2) sqrt(2)
= 1/sqrt(2) cos(b-a)
So, the probability for
P++(a,b) = |psi'++|psi|^2 = 1/2 cos^2(b-a)
A similar calculation will reveal
P-- = 1/2 cos^2(b-a)
P+- = 1/2 sin^2(b-a)
P_+ = 1/2 sin^2(b-a)
Hence, the prediction of a cos^2 dependence.
> > In two experiments performed in 1981 and 1982, Alain Aspect
> > confirmed the quantum predictions, measuring the
> > coincidence rates under various polarizer settings.
>
> How, if at all, did Aspect et. al. determine the orientation_angle
> of particular polarizer pairs in particular sets of trials
> in the first place,
> and its relation and their "settings" in those trials?
>
Read the literature.
A. Aspect et al.,"Experimental Realization of
Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation
of Bell's Inequalities.", _Physical Review Letters_, V 49, Num 2,
pp 91-94, 1982.
A. Aspect et al.,"Experimental Test of Bell's Inequalities Using
Time-Varying Analyzers", _Physical Review Letters_, V 49, Num 25,
pp 1804-1807, 1982.
> > More recent experiments at Innsbruck have given a fine-tuning
> > to this type of experiment (under more stringent conditions)
>
> How, if at all, was the orientation_angle of particular
> polarizer pairs in particular sets of trials be determined
> in those experiments in the first place,
> and its relation and their "settings" in those trials?
>
Read the literature.
G. Weihs et al, "Violation of Bell's Inequality under Strict
Einstein Locality Conditions", _Physical Review Letters_, V 81,
Num 23, pp 5039-5042, 1998.
> >
> > Normal coincidences should be <= 2
> >
>
> Please explain how one would arrive at such an expectation.
>
Assume two polarizers, A and B, where A switches orientation
between a and c, and B switches orientation between b and d, and
a measurement distribution function p(L), normalized so that
int{p(L)dL} = 1. The expectation value for photon A entering the
polarizer with orientation a is denoted A(a,L), and the
expectation of photon B entering the polarizer with orientation b
is denoted B(b,L). A +/- 1 corresponds to detection in the
vertical or horizontal channels, respectively. Therefore,
|A(a,L)| and |B(b,L)| <= 1. equ(1).
For any joint measurement, say a and b, the expectation value is:
E(a,b) = int{A(a,L) B(b,L) dL}
Similarly,
E(a,b) - E(a,d) = int{A(a,L) B(b,L) - A(a,L) B(d,L) p(L) dL}
= int{A(a,L)[B(b,L) - B(d,L)] p(L) dL}
But, |A(a,L)| <= 1, so
E(a,b) -E(a,d)| <= int{|B(b,L) -B(d,L)| p(L) dL}
A similar analysis reveals
|E(c,b) + E(c,d) <= int{|B(b,L) + B(d,L)| p(L) dL}
combining these last two,
|E(a,b) - E(a,d)| + |E(c,b) + E(c,d)| <= Int{[|B(b,L) - B(d,L)| +
+|B(b,L) + B(d,L)|] p(L) dL}
But, from equ(1), |B(b,L) - B(d,L)| + |B(b,L) + B(d,L)|
must be <= 2, so
|E(a,b) - E(a,d)| + |E(c,b) + E(c,d)| <= 2 int{p(L) dL}
But, int{p(L) dL} = 1, so
|E(a,b) - E(a,d)| + |E(c,b) + E(c,d)| <= 2.
Stephen
s...@compbio.caltech.edu
You can always tell a pioneer by the arrows in his back.
Printed using 100% recycled electrons.
--------------------------------------------------------
franz heymann
Frank Wappler <fw7...@csc.albany.edu> wrote in message
news:3968A104...@csc.albany.edu...
> <snip>
> That's not a prediction, but unambiguously implied
> through the measurement procedure (Malus' procedure)
What is Malus' procedure?
> <snip>
> How, if at all, did Aspect et. al. determine the orientation_angle
> of particular polarizer pairs in particular sets of trials
> in the first place,
> and its relation and their "settings" in those trials?
With functions varying as slowly as cos^2 theta I guess a sixpenny
protractor would do the job if properly used.
> <snip>
Frank continued:
> How, if at all, was the orientation_angle of particular
> polarizer pairs in particular sets of trials be determined
> in those experiments in the first place,
> and its relation and their "settings" in those trials?
With functions varying as slowly as cos^2 theta I guess a sixpenny
protractor would do the job if properly used.
> <snip>
Franz Heymann
Frank Wappler
> What is Malus' procedure?
A measurement procedure for determining a relation
(orientation_angle) of two two-valued coordinate systems
wrt. to each other; suggested by E.-L. Malus (1775-1812):
Given observations that are collected and counted in the two
two-valued coordinate systems "{ Ah, Aj }" and "{ Bu, Bv }",
with admissable values "{ (Ah = 1, Aj = 0) }"
and "{ (Bu = 1, Bv = 0) or (Bu = 0, Bv = 1) }"
in a set of trials { k } (where the trial index has been
calibrated between the two observer systems A and B),
the relation "orientation_angle" is the measure
1/2 arccos( Sum_{ k }_( Ah_k Bu_k - Ah_k Bv_k ) /
Sum_{ k }_( Ah_k Bu_k + Ah_k Bv_k ) ) =
1/2 arccos( (2 Sum_{ k }_( Ah_k Bu_k ) /
Sum_{ k }_( Ah_k Bu_k + Ah_k Bv_k )) - 1 ) =
arccos( sqrt( Sum_{ k }_( Ah_k Bu_k ) /
Sum_{ k }_( Ah_k Bu_k + Ah_k Bv_k ) ) ) =
arccos( sqrt( Sum_{ k }_( Ah_k Bu_k ) /
Sum_{ k }_( 1 ) ) ).
The number
sqrt( Sum_{ k }_( Ah_k Bu_k ) / Sum_{ k }_( 1 ) ) )
is called "(average) intensity" of A and B wrt. each other,
in the set of trials { k }.
In generalization to trials with admissable values
{ (Ah = 1, Aj = 0) or (Ah = 0, Aj = 1) }" one defines
orientation_angle( A, B, { k } ) ==
1/2 arccos(
Sum_{ k }_( Ah_k Bu_k + Aj_k Bv_k - Ah_k Bv_k - Aj_k Bu_k ) /
Sum_{ k }_( Ah_k Bu_k + Aj_k Bv_k + Ah_k Bv_k + Aj_k Bu_k ) ) =
arccos(
sqrt( Sum_{ k }_( Ah_k Bu_k + Aj_k Bv_k ) /
Sum_{ k }_( Ah_k Bu_k + Aj_k Bv_k + Ah_k Bv_k + Aj_k Bu_k ) ) ).
arccos(
sqrt( Sum_{ k }_( Ah_k Bu_k + Aj_k Bv_k ) / Sum_{ k }_( 1 ) ) ).
There's a related definition of orientation_angle of two
one-valued coordinate systems wrt. each other:
Given observations that are collected and counted in the two
one-valued coordinate systems "{ Ah }" and "{ Bu }",
with admissable values "{ Ah = 1 or Ah = 0 }"
and "{ Bu = 1 or Bu = 0 }" in a set of trials { k }
(where the trial index has been calibrated between the
two observers A and B), one defines
orientation_angle( A, B, { k } ) ==
arccos( Sum_{ k }_( Ah_k Bu_k ) / Sum_{ k }_( 1 ) ).
> Frank Wappler wrote:
> > How, if at all, did Aspect et. al. determine the orientation_angle
> > of particular polarizer pairs in particular sets of trials
> > in the first place,
> > and its relation and their "settings" in those trials?
> [...] I guess a sixpenny protractor would do the job
> if properly used.
I suppose that "a sixpenny protractor, if properly used"
(perhaps along with a general survey) is a cheap way
to determine coordinates of various constituents of the setup,
wrt. each other.
Coordinates of which particular constituents should be surveyed?
If "coordinates of marks on the polarizers", then how should be
determined which marks pairwise correspond to each other;
how were the marks initially identified and labelled?
Also: how, if at all, did Aspect et. al. test and quantify
whether the surveyed experimental region contained
optically active media or fields, trial by trial?
Thanks again, Frank W ~@) R
Frank Wappler
> Frank Wappler wrote:
> > Stephen Speicher wrote:
> > > For a simple EPR-type thought experiment, quantum theory
> > > predicts a cos^2 dependence on the coincidence rate
> > > between angular settings of two differently oriented polarizers
> > > (actually, it is the difference angle between the polarizer
> > > settings which is important).
> > That's not a prediction, but unambiguously implied
> > through the measurement procedure (Malus' procedure)
> > by which the orientation_angle of a pair of polarizers
> > wrt. each other is being determined in the first place.
> The results of a mathematical analysis _predicts_ what
> experiments confirm.
No - the analysis you present below appears to be a _retro_diction.
> So, for instance, if one polarizer, A, is oriented at angle a,
... whatever you might mean by "orientation of one polarizer" ...
> its eigenstates are |psi_A_v> and |psi_A_h>
> (the notation should be clear -- polarizer A with vertical or
> horizontal)
The labels "vertical, v" and "horizontal, h" are two distinct labels
to denote two distinguishable states of A.
> and likewise for polarizer B, with primed directions,
> |psi_B_v'> and |psi_B_h'>.
Unless you wish to imply some particular a priori relation (which?)
between the two distinguishable states of A and
the two distinguishable states of B,
it might be clearer to drop the prime and choose fresh labels
for the states of B, let's say "B_p" and "B_q".
> The difference angle, b-a, is taken as the angle
> between the vertical axes of the polarizers.
Recall that "vertical, v" is a _label_ to denote a particular
state of A (alone).
Otherwise, please prescribe a reproducible measurement procedure
by which the parameter "b-a" can be unambiguously determined
for any particular appropriate setup, in any parituclar
trial (of sufficiently large set of trials).
> For simplicity, I'll just calculate one of the four eigenstates
> of the difference angle (b-a), and the other three,
> [psi__, psi-+, psi+-] follow in the same manner.
> [minor edits, for well-formedness. FW ...
> <psi'++|psi> = 1/sqrt(2) <psi_A_v|psi_B_v'|(|psi_A_L|psi_B_L> +
> +|psi_A_R|psi_B_R>)
> ]
I understand your Ansatz given the following conditions
on the states "A_L", "A_R", "B_L" and "B_R":
(A_L~A_R) = 0, and (A_L~A_L) + (A_R~A_R) = 1;
(B_L~B_R) = 0, and (B_L~B_L) + (B_R~B_R) = 1;
(B_L~A_R) = 0, (B_R~A_L) = 0, and (A_L~B_L) + (A_R~B_R) = 1.
I suppose that there may be very many different sets
{ "A_L", "A_R", "B_L" and "B_R" } that satisfy those conditions.
> = 1/sqrt(2) (<psi_A_v|psi_A_L> <psi_B_v'|psi_B_L> +
> +<psi_A_v|psi_A_R> <psi_B_v'|psi_B_R>)
> = 1/sqrt(2) [ 1 e^i(b-a) + 1 e^-i(b-a) ]
> ------- -------- ------- --------
> sqrt(2) sqrt(2) sqrt(2) sqrt(2)
IIUC, here you've also required
"(A_v~A_L) = e^(i -a)", and "(A_v~A_L) = e^(i a)";
"(B_p~B_L) = e^(i -b)", and "(B_p~B_R) = e^(i b)".
Even assuming that "a" and "b" were definite real numbers
(which I've already questioned above, but after all,
A and B might always be able to make up two real numbers) -
_why_ this particular requirement ??
Why this particular functional dependence on values of "a" and "b"?
Surely (given the constraints stated above), there exist
very many other { "A_L", "A_R", "B_L" and "B_R" }, too?
> = 1/sqrt(2) cos(b-a)
> P++(a,b) = |psi'++|psi|^2 = 1/2 cos^2(b-a)
> [...]
Using the particular requirement you've chosen above - sure.
> > How, if at all, did Aspect et. al. determine the orientation_angle
> > of particular polarizer pairs in particular sets of trials
> > in the first place,
> > and its relation and their "settings" in those trials?
> Read the literature.
> A. Aspect et al.,"Experimental Realization of
> Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation
> of Bell's Inequalities.", _Physical Review Letters_, V 49, Num 2,
> pp 91-94, 1982.
> A. Aspect et al.,"Experimental Test of Bell's Inequalities Using
> Time-Varying Analyzers", _Physical Review Letters_, V 49, Num 25,
> pp 1804-1807, 1982.
> [...]
> G. Weihs et al, "Violation of Bell's Inequality under Strict
> Einstein Locality Conditions", _Physical Review Letters_, V 81,
> Num 23, pp 5039-5042, 1998.
Having read the literature before I asked my question,
my question is not being addressed in that literature, AFAIU.
Read the literature.
> > > Normal coincidences should be <= 2
> > Please explain how one would arrive at such an expectation.
> Assume two polarizers, A and B, where A switches orientation
> between a and c, and B switches orientation between b and d, and
> a measurement distribution function p(L), normalized so that
> int{p(L)dL} = 1.
I'm particular interested in the most general cases of such
measurement distribution functions, for instance covering
the case where "L" is the trial index, and correspondingly
p( L ) == 1 / Sum_{ L }_( 1 ).
Note that the indices "a" and "c" refer to _distinct sets_
of trials conducted by A (with B), let's say the sets { P } and { Q },
respectively;
and "b" and "d" refer to _distinct sets_ of trials conducted
by B (with A), let's say the sets { L } and { M }.
{ P } and { Q } are disjoint, { L } and { M } are disjoint,
but { P } is not necessarily disjoint from { L } or { M },
and { Q } is not necessarily disjoint from { L } or { M }.
> The expectation value for photon A entering
> the polarizer with orientation a is denoted A(a,L)
I'd object to the notion of "a photon entering" and
would prefer to consider that
"detector A is observing a transition of the source
in the two-valued coordinates { v, h }, in some particular trial";
but that's just what would be denoted by "A( a, L )".
> and the expectation of photon B entering the polarizer
> with orientation b is denoted B(b,L). A +/- 1 corresponds
> to detection in the vertical or horizontal channels, respectively.
> Therefore,
> |A(a,L)| and |B(b,L)| <= 1. equ(1).
> For any joint measurement, say a and b, the expectation value is:
> E(a,b) = int{A(a,L) B(b,L) dL}
> Similarly,
> E(a,b) - E(a,d) = int{A(a,L) B(b,L) - A(a,L) B(d,L) p(L) dL}
This integral is over the _same_ set { L } for trials indexed
with "orientation b" _as well as_ for trials indexed with
"orientation d".
IOW, you may have assumed that { L } is
_not_ the set of trial indices, for instance.
Why should one make such an assumption?
Or else, you've selected a particular map { M } --> { L }
in order to introduce the values B( d, M ) and corresponding A( a, M )
into the integral over { L }, as B( d, L( M ) ), and A( a, L( M ) ).
How should one select such a map?
> = int{A(a,L)[B(b,L) - B(d,L)] p(L) dL}
Here's where you've required a particular map { M } --> { L }
explicitly in order to equate A( a, L ) and A( a, L( M ) ),
and factor out A( a, L ).
Having done so (again: how?), one arrives of course at
> [...]
> |E(a,b) - E(a,d)| + |E(c,b) + E(c,d)| <= 2.
Thanks again and best regards, Frank W ~@) R
Frank Wappler
Frank Wappler wrote:
> The number [...]
should of course be
Sum_{ k }_( Ah_k Bu_k ) / Sum_{ k }_( 1 ) )
> is called "(average) intensity" of A and B wrt. each other,
mediaglyphic
we have some reply's
i have to study them carefully, i still don't see why we can't say that the
reason we know what happens with photon b when we look at photon a is that
they are twins with the same mother? i believe that the answer is that b
didn't exist till a was observed, but what does this really mean? is there a
definition for "exist". i recently read sudarshan and rothman's book in
which they talk about probabilities greater than 100 and less than 0, i like
this interpretation, but years ago i read about the bootstratp
interpretation of a physicist named Chu, i liked that way of thinking, it
reminded me of Leibniz's Monads and also of the way real time concurrent
computer programs are written
(my bias as a former robotics engineer is that there must be some event
driven computer program somewhere with a random variable embedded, and that
this program runs the world, but of course i have not a smidgen of proof, or
even observation here!)
by the way my name is Paras, Mediaglyphic is an artifact from Neal
Stephenson's book Diamond Age.
"Hans Jud" <eh....@bluewin.ch> wrote in message
news:39679EE2...@bluewin.ch...
>
>
> Hy,
>
> its midnight here, but just a short replay. And when I ask questions, I
know,
> you cannot answer them, but maybe somebody else will be around.
>
> >
> > i believe that what you are stating when you say prob=130% is what is
> > implied by aspects experiment as applied to bell's inequality.
> >
> > in order to really understand this though i believe that i will really
have
> > to learn Quantum Physics from the bottom up.
> >
>
> This is what I just cannot believe, is there really no choice, but to
study the
> whole thing? ( I cannot make it a profession) That would mean, that QM
never
> would be understood by normal folks. Again, I don' t mean to understand
the
> whole thing, but there are so many authors that try to explain the
experiments,
> that it makes me think, that at least these should be understandable.
> I hope somebody is out there hearing our problems and despair
>
> Good night
>
>
> Hans Jud
>
mediaglyphic
"Ron House" <ho...@usq.edu.au> wrote in message
news:3968256C...@usq.edu.au...
> Hans Jud wrote:
> >
> > > in order to really understand this though i
> > > believe that i will really have
> > > to learn Quantum Physics from the bottom up.
> >
> > This is what I just cannot believe, is there really
> > no choice, but to study the whole thing? ( I cannot make
> > it a profession) That would mean, that QM never
> > would be understood by normal folks. Again, I don' t mean
> > to understand the whole thing, but there are so many authors
> > that try to explain the experiments, that it makes me think,
> > that at least these should be understandable.
>
> They are. Let me have a crack at it.
>
> You have two atomic particles that annihilate each other, resulting in
> two photons going in opposite directions. Now let's say that the wave
> function of this pair basically says "These two photons have the same
> polarisation". Note carefully, this particular wave fn doesn't tell us
> what the angle of polarisation is, just that, whatever it is, it is the
> same for both.
Why would a wave function only give the fact that the polarizations are the
same but not give the angle? if we know why this is so does it help later
on? i am suspicious that there is something implied by the polarizations
being the same but us not knowing the angles, this of course is how we can
know about B after measuring A!
>
> Now as you will be aware, if you are wearing polarised sunglasses (the
> polarisers oriented at 0 degrees, and polarised light reflects off the
> road with angle 90deg, then none of the light gets through. If you turn
> your glasses through 90deg, so that both the glasses and the oncoming
> light have polarisation angle 0deg, then all of the light gets through.
>
> What if the polarising filter is at some other angle to the plane of
> polarisation? It turns out that the intensity of polarised light passing
> through a filter is cos^2 theta (where theta is the angle between the
> plane of polarisation and the angle of the filter).
>
> OK, back to our two photons. Remember, the wave fn doesn't say what the
> polarisation angles are, only that they are the same. So let's place
> polarisers in the paths of our two photons. Say we put polariser A in
> the path of photon 1, at angle 45deg, and photon 1 passes through the
> filter. We now know that photon 1 is polarised at 45deg. Therefore so
> must photon 2 also be. So if we place polariser B in the path of photon
> 2, also at 45deg, 2 is guaranteed to pass through.
>
> So far so good.
>
> But what if we place polariser B at, say, 20deg? The probability that
> photon 2 goes through must be cos^2 ((45-20)*pi/180). That is greater
> than 1/2. How does photon 2 'know' that is should go through with
> greater than 1/2 probability? I mean, it doesn't know that I will place
> polariser A at 45deg, does it? If I had place polariser A at 65deg, the
> the angle between polariser A at 65deg and B at 20deg is 45deg, for
> which angle cos^2 theta is exactly 1/2.
I am not sure i understand what you mean that photon 2 knows that it must go
through with a certain probability. doesn't in fact Photon 2 go through with
a certain probability based on the fact that we know it has the same
polarization as Photon 1?
Snip
i am stuck here, and i get lost later on cause i keep coming back here!!!
sorry if i am being thick and thanks for your patience and kindness in
responding.
Stephen Speicher
> but years ago i read about the bootstratp interpretation of a
> physicist named Chu, i liked that way of thinking, it reminded
> me of Leibniz's Monads and also of the way real time concurrent
> computer programs are written
>
That is Chew, as in Geoffrey Chew. Chew wrote many papers on his
theory, and several books, including "The Analytic S Matrix: A
Basis for Nuclear Democracy." It was a short-lived theory, and
has hardly been heard from in the past two decades. Chew's
formulation was meant primarily for hadrons, and he thought it
unlikely that leptons could emerge from the theory.
Hans Jud
Thanks for the efforts of Frank Wapper, Stephen Speicher and Don House to bring me
closer to QM. I will study the postings an, sorry, come back with more (funny)
Questions.
Regards
Hans
Hans Jud
mediaglyphic schrieb:
> Hey Hans,
> we have some reply's
>
> i have to study them carefully, i still don't see why we can't say that the
> reason we know what happens with photon b when we look at photon a is that
> they are twins with the same mother? i believe that the answer is that b
> didn't exist till a was observed, but what does this really mean? is there a
> definition for "exist". i recently read sudarshan and rothman's book in
> which they talk about probabilities greater than 100 and less than 0, i like
> this interpretation, but years ago i read about the bootstratp
> interpretation of a physicist named Chu, i liked that way of thinking, it
> reminded me of Leibniz's Monads and also of the way real time concurrent
> computer programs are written
>
> (my bias as a former robotics engineer is that there must be some event
> driven computer program somewhere with a random variable embedded, and that
> this program runs the world, but of course i have not a smidgen of proof, or
> even observation here!)
>
> by the way my name is Paras, Mediaglyphic is an artifact from Neal
> Stephenson's book Diamond Age.
Hi Paras
Yes, finally there is something that a dummy like me can hang on. Thanks to the
first postings of F. Wapper, S. Speicher und Ron House.
My way to resolve problems is very simpel, but sometimes nerving other people.
Divide the Problem in as many elements as possible, put them in the right
order... thats all.... so I started to disect Ron's posting, it seems to be the
most basic answer. I think the solution of my personal knot (might be identical
to yours) can be found in there.
It will take me some time to work it out.
Have a nice week
Hans
Hans Jud
Hans Jud schrieb:
Sorry Frank, I meant Frank Wapp-l-er
Stephen Speicher
> Stephen Speicher wrote:
>
> > Frank Wappler wrote:
>
> > > Stephen Speicher wrote:
> > > > For a simple EPR-type thought experiment, quantum theory
> > > > predicts a cos^2 dependence on the coincidence rate
> > > > between angular settings of two differently oriented polarizers
> > > > (actually, it is the difference angle between the polarizer
> > > > settings which is important).
>
> > > That's not a prediction, but unambiguously implied
> > > through the measurement procedure (Malus' procedure)
> > > by which the orientation_angle of a pair of polarizers
> > > wrt. each other is being determined in the first place.
>
> > The results of a mathematical analysis _predicts_ what
> > experiments confirm.
>
> No - the analysis you present below appears to be a _retro_diction.
>
The results are a direct consequence of the mathematical
formalism of quantum mechanics. The particular form used has its
roots in Bohm's early work, Bell's analysis, and later in the
work of Clauser, long before Aspect's experiment. That there
exists an empirical representation does not negate the
mathematical formalism.
As to your comments about the two mathematical presentations:
they are standard formulations, and your concern about procedures
is best taken up with those who developed them. I have noted your
extreme concern with procedural development -- especially in
regard to relativistic formulations -- and I must say that, in
general, I do not share your passion.
> >
> > Read the literature.
> >
> > A. Aspect et al.,"Experimental Realization of
> > Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation
> > of Bell's Inequalities.", _Physical Review Letters_, V 49, Num 2,
> > pp 91-94, 1982.
> >
> > A. Aspect et al.,"Experimental Test of Bell's Inequalities Using
> > Time-Varying Analyzers", _Physical Review Letters_, V 49, Num 25,
> > pp 1804-1807, 1982.
> >
> > [...]
> > G. Weihs et al, "Violation of Bell's Inequality under Strict
> > Einstein Locality Conditions", _Physical Review Letters_, V 81,
> > Num 23, pp 5039-5042, 1998.
>
> Having read the literature before I asked my question,
> my question is not being addressed in that literature, AFAIU.
Then you best take it up with Aspect, and Zeilinger's group. For
your information, Zeilinger's group recently moved from Innsbruck
to Vienna, and all of their phone numbers and e-mail addresses
are available on the net. I'm sure they will be happy to address
your procedural concerns.
Frank Wappler
Stephen Speicher wrote:
> > > > > For a simple EPR-type thought experiment, quantum theory
> > > > > predicts a cos^2 dependence on the coincidence rate
> > > The results of a mathematical analysis _predicts_ what
> > > experiments confirm.
> Frank Wappler wrote:
> > No - the analysis you present below appears to be a _retro_diction.
> The results are a direct consequence of the mathematical
> formalism of quantum mechanics.
I've pointed out where the analysis you stated in the preceding post
was _not_ direct:
Having assumed quantum theory, which allows you to make
> > [your Ansatz ... the following conditions
> > on the states "A_L", "A_R", "B_L" and "B_R":
> > (A_L~A_R) = 0, and (A_L~A_L) + (A_R~A_R) = 1;
> > (B_L~B_R) = 0, and (B_L~B_L) + (B_R~B_R) = 1;
> > (B_L~A_R) = 0, (B_R~A_L) = 0, and (A_L~B_L) + (A_R~B_R) = 1
you seem to have irreprodicibly (to me, at least) concluded,
or additionally
> > required
> > "(A_v~A_L) = e^(i -a)", and ["(A_v~A_R) = e^(i a)"];
> > "(B_p~B_L) = e^(i -b)", and "(B_p~B_R) = e^(i b)".
for some arbitrary (in absence of any reproducible definition)
states "A_v" and "B_p", and (AFAIU) real numbers "a" and "b".
That's not only arbitrary/indirect, but even a contradiction:
Counterexample: Identify the arbitrary state "A_v" with "A_L".
Then by the initial conditions (A_v~A_R) == (A_L~A_R) = 0.
But OTOH there exists no real number "a" such that
0 = (A_L~A_R) == (A_v~A_R) =?= e^(i a),
i.e. such that the additional assumption were satisfiable as well.
Now, I assume that you wouldn't wittingly state or imply
contradictions. Therefore, if you believe that this, along
with the QM postulates
(u~u) >= 0, and (u~v) =/not_necessarily/= (v~u),
doesn't reproduce the assumptions you've made,
then please correct me by stating your assumptions and/or
your derivation reproducibly.
> about the two mathematical presentations:
> they are standard formulations, and your concern about procedures
> is best taken up with those who developed them.
I prefer to take up my concern already with those who refer to such
"standards" as if others were supposed to understand/reproduce them.
Otherwise - let them rest in peace.
(AFAIU, the following refers to my request
> > > > > Normal coincidences should be <= 2
> > > > Please explain how one would arrive at such an expectation.,
your response to that
> > > B switches orientation between b and d [...]
> > > a measurement distribution function p(L), normalized so that
> > > int{p(L)dL} = 1 [...]
> > > E(a,b) = int{A(a,L) B(b,L) dL} [...]
> > > E(a,b) - E(a,d) = int{A(a,L) B(b,L) - A(a,L) B(d,L) p(L) dL},
and my remaining questions:
> > general cases of such measurement distribution functions,
> > for instance covering the case where "L" is the trial index [...]
> > "b" and "d" refer to _distinct sets_ of trials conducted
> > by B (with A), let's say the sets { L } and { M } [...]
> > you've selected a particular map { M } --> { L }
> > in order to introduce the values B( d, M )
> > and corresponding A( a, M ) into the integral over { L },
> > as B( d, L( M ) ), and A( a, L( M ) ).
> > How should one select such a map? [...]
> The particular form used has its roots in Bohm's early work,
> Bell's analysis, and later in the work of Clauser,
> long before Aspect's experiment.
Sure.
But assumption of the form "E(a,b) = int{A(a,L) B(b,L) dL}"
doesn't lead to the expection that "Normal coincidences should be <= 2",
AFAIU and asked about, for instance
> > in the case where "L" is the trial index [and the labels] "b"
> > and "d" refer to _distinct sets_ of trials.
> That there exists an empirical representation does not negate the
> mathematical formalism.
I don't understand this statement (either). - Please explicate the
mathematical formalism in the special case where "L" is the trial index
and the labels "b" and "d" refer to distinct sets of trials;
or demonstrate how the mathematical formalism (or perhaps any
empirical considerations) rule this case out.
> > > > [How, if at all, did Aspect et. al. determine the
> > > > orientation_angle of particular polarizer pairs
> > > > in particular sets of trials in the first place,
> > > > and its relation and their "settings" in those trials?]
> > my question is not being addressed in that literature, AFAIU.
> Then you best take it up with Aspect, and Zeilinger's group [...]
> their phone numbers and e-mail addresses are available on the net.
No need to intrude in the privacy of people that may be too busy
even to participate in this public forum. My question was merely
a rhetorical tool, in order not to be too suggestive.
AFAIU, it is highly unlikely that they've made any such measurements:
Because if they had then
case (1), had they used Malus' procedure:
they would have written
"we define and measure orientation_angle in terms of the observed
intensity (of correlated counts) in each set of trials as
arccos( sqrt( Intensity ) ),
and we assign real numbers a and b to label the settings
of the two polarizers in this set of trials such that
a - b = orientation_angle ...",
i.e. equivalently
"our measurement procedures implies a cos^2 dependence ...",
and not
"quantum mechanics predicts a cos^2 dependence ...",
as they (equivalently) have;
or case (2), had they used any particular procedure that
derives values significantly different from those obtained
through Malus' procedure (while sticking to their notion
that "quantum mechanics predicts a cos^2 dependence ..."):
they would have titled their papers (equivalently)
"Experimental Determination of a Violation of Quantum Mechanics",
which they have not.
The third case (that they might have used some procedure
other than that of Malus, and still obtain values that were
not different enough to derive significant deviation
from "cos^2 dependence") is highly unlikely,
given their excellent statistics.
> I have noted your extreme concern with procedural development --
> especially in regard to relativistic formulations -- and I must say
> that, in general, I do not share your passion.
This was found written on Feynman's blackboard,
around the time of Feynman's death:
"What I cannot create I cannot understand".
IMHYPO, whoever wrote this was a physicist
and was greatly concerned about _the other_ physicists as well,
at least in principle.
Which also correctly - thank you - identifies my passion.
Best regards, Frank W ~@) R
franz heymann
I, and I suspect many others are heartily tired of the continued waffle in
this thread. Is there perhaps a philosophy newsgroup where this might be
discussed?
Franz Heymann
Stephen Speicher
>
> Stephen Speicher wrote:
> > I have noted your extreme concern with procedural development --
> > especially in regard to relativistic formulations -- and I must say
> > that, in general, I do not share your passion.
>
> This was found written on Feynman's blackboard,
> around the time of Feynman's death:
>
> "What I cannot create I cannot understand".
>
And just below that is:
"Know how to solve every problem that has been solved".
> IMHYPO, whoever wrote this was a physicist
> and was greatly concerned about _the other_ physicists as well,
> at least in principle.
>
However, there is more to physics than the specification of a
measurement procedure. I was being kind when I used the words
"extreme concern" above -- the seemingly endless responses of
"Please describe a reproducible measurement procedure..." are, to
my mind, an obsession, and one which disallows being able to see
the proverbial forest through the trees.
>
> Which also correctly - thank you - identifies my passion.
>
I greatly value a person's passion, but I find it hard to endure
forever hearing about trying to fit a square physics into a round
measurement procedure.
Frank Wappler
> [...]
I'm heartily tired of the continued waffle in this thread;
and AFAIU others are, too. Please (yourself, or anyone) address
the mathematically concise statements with which
I've responded to your analyses. In summary:
> Frank Wappler wrote:
> > [your Ansatz ... implies the following conditions
> > on the states "A_L", "A_R", "B_L" and "B_R":
> > (A_L~A_R) = 0, and (A_L~A_L) + (A_R~A_R) = 1;
> > (B_L~B_R) = 0, and (B_L~B_L) + (B_R~B_R) = 1;
> > (B_L~A_R) = 0, (B_R~A_L) = 0, and (A_L~B_L) + (A_R~B_R) = 1
> > you seem to have required
> > "(A_v~A_L) = e^(i -a)", and "(A_v~A_R) = e^(i a)";
> > "(B_p~B_L) = e^(i -b)", and "(B_p~B_R) = e^(i b)".
> > for some arbitrary states "A_v" and "B_p",
> > and real numbers "a" and "b".
> > Counterexample: Identify the arbitrary state "A_v" with "A_L".
> > There exists no real number "a" such that
> > 0 = (A_L~A_R) == (A_v~A_R) =?= e^(i a),
> > i.e. such that both the initial and additional assumption
> > were satisfiable]
And (restated, also to better correspond to your use of variables):
Given that there are three nonempty sets { L }, { M }, and { N },
with Union( { L } , { M } ) = { N } and Intersect( { L }, { M } ) = { },
(i.e. { L } and { M } are disjoint); and
given that there are four sets of numbers with elements
> > > [A( a, L ) = +/- 1],
and analogously A( a, M ) = +/- 1, B( b, L ) = +/- 1, B( d, M ) = +/- 1;
and given that for arguments from other sets there are no values B,
i.e. there are no values of "B( b, M )", nor "B( d, L )"; and given
> > > a measurement distribution function that satisfies
> > > int{p(L)dL} = 1;
and analogously int{p(M)dM} = 1; and finally
> > > [E(a,b) = int{A(a,L) B(b,L) p(L) dL}]
and analogously E(a,d) = int{A(a,M) B(d,M) p(M) dM},
then there exists maps { L } --> { M } and sets of values
A( a, L ), A( a, M ), B( b, L ) and B( d, M ), and
a measurement distribution function p: { N } --> real numbers
such that
> > > E(a,b) - E(a,d)
=/not_equal/=
> > > int{A(a,L) [B(b,L) - B(d,L)] p(L) dL},
where "B(d,L)" is set to the value of B(d,M( L ))
for a particular map { L } --> { M }.
For instance, with
A(a,L) = B(b,L) = 1, for all L in { L },
A(a,L) = -1, and B(b,M) = 1 for all M in { M },
{ L } --> { M } any injective function; therefore B(d,M( L )) = 1,
p(N) = 1/int{dL}, for all N in { L }, and
p(N) = 1/int{dM}, for all N in { M }:
E(a,b) - E(a,d) = 1 - (-1) = 2
=/not_equal/=
int{A(a,L) [B(b,L) - B(d,M( L ))] p(L) dL} =
int{ 1 [1 - 1] 1/int{dL} dL} = 0.
If you believe that I misrepresented or incorrectly guessed
any of the assumptions upon which your analyses were based,
then please state them explicitly and unambigously,
such that your analyses follow free of contradictions.
Thanks again, Frank W ~@) R
p.s.
Because:
The procedural/mathematical statements of your analyses are
what may be known and _understood_ by myself and everyone,
while your reports about your observations (if you were
detector A, for instance) may at most be _believed_.
> > This was found written on Feynman's blackboard,
> > around the time of Feynman's death:
> > "What I cannot create I cannot understand".
> And just below that is:
> "Know how to solve every problem that has been solved".
Clearly by attempting to recreate/reproduce/understand
what had been suggested as "solutions", as the remaining
blackboard writing indicated.
> [...] seemingly endless responses of
> "Please describe a reproducible measurement procedure..." are,
> to my mind, an obsession, and one which disallows being able
> to see the proverbial forest through the trees.
> [...] there is more to physics than the specification
> of a measurement procedure.
Of course: it remains
- to collect observations,
- to apply the selected specific reproduible measurement procedures
to those observations (or in turn to subsequent results),
- to report the results.
Assuming that specific reproducible measurement procedures
were given, do you consider any of those remaining three points
as requiring any further solution, at least in principle?
Frank Wappler
(in response to mathematical expression stated by Stephen Speicher):
> > > > [E(a,b) = int{A(a,L) B(b,L) p(L) dL}]
> and analogously E(a,d) = int{A(a,M) B(d,M) p(M) dM},
> [...] there exist maps { L } --> { M } and sets of values
> A( a, L ), A( a, M ), B( b, L ) and B( d, M ), and
> a measurement distribution function p: { N } --> real numbers
> such that
> > > > E(a,b) - E(a,d)
> =/not_equal/=
> > > > int{A(a,L) [B(b,L) - B(d,L)] p(L) dL},
> where "B(d,L)" is set to the value of B(d,M( L ))
> for a particular map { L } --> { M }.
> For instance, with
> A(a,L) = B(b,L) = 1, for all L in { L },
... correcting a distorting typo:
A(a,M) = -1, and B(b,M) = 1 for all M in { M } ...
Frank Wappler
> Given observations that are collected and counted in the two
> one-valued coordinate systems "{ Ah }" and "{ Bu }",
> with admissable values "{ Ah = 1 or Ah = 0 }"
> and "{ Bu = 1 or Bu = 0 }" in a set of trials { k }
> (where the trial index has been calibrated between the
> two observers A and B), one defines
... in correction to the previously stated expression:
orientation_angle( A, B, { k } ) ==
arccos( Sum_{ k }_( (1 - 2 Ah_k) (1 - 2 Bu_k) ) / Sum_{ k }_( 1 ) ).
How I identified that a correction was in order,
and selected a corrected expression:
The definitions are required to be commensurate
with a range for results of
2 Pi / least_number_of_coordinate_values_in_one_system,
and such that
orientation_angle( A, B, { k } ) = Pi/2
for uncorrelated/independed sets of values.
Stephen Speicher
> Stephen Speicher wrote:
> > [...]
>
> I'm heartily tired of the continued waffle in this thread;
Would you prefer pancakes?
> > [...] seemingly endless responses of
> > "Please describe a reproducible measurement procedure..." are,
> > to my mind, an obsession, and one which disallows being able
> > to see the proverbial forest through the trees.
>
> > [...] there is more to physics than the specification
> > of a measurement procedure.
>
> Of course: it remains
>
> - to collect observations,
> - to apply the selected specific reproduible measurement procedures
> to those observations (or in turn to subsequent results),
> - to report the results.
>
Oy vey!
Frank, thanks for the interchange. I've got work to do.
Frank Wappler
> Frank Wappler wrote:
> > [and AFAIU others are, too. Please (yourself, or anyone) address
> > the mathematically concise statements with which
> > I've responded ...]
Don't agonize over your omission - math is superbly nonperishable,
especially if archived.
> > > [...] there is more to physics than the specification
> > > of a measurement procedure.
> > Of course: it remains
> > - to collect observations,
> > - to apply the selected specific reproduible measurement procedures
> > to those observations (or in turn to subsequent results),
> > - to report the results.
> Oy vey!
> Frank, thanks for the interchange. I've got work to do.
You're welcome.
Hope that dreadfully hard bounce against step two's gonna break your
... insensibility towards contradictions.
Regards, Frank W ~@) R
Hans Jud
Ron House schrieb:
> You have two atomic particles that annihilate each other, resulting in
> two photons going in opposite directions. Now let's say that the wave
> function of this pair basically says "These two photons have the same
> polarisation". Note carefully, this particular wave fn doesn't tell us
> what the angle of polarisation is, just that, whatever it is, it is the
> same for both.
>
> Now as you will be aware, if you are wearing polarised sunglasses (the
> polarisers oriented at 0 degrees, and polarised light reflects off the
> road with angle 90deg, then none of the light gets through. If you turn
> your glasses through 90deg, so that both the glasses and the oncoming
> light have polarisation angle 0deg, then all of the light gets through.
>
Why is reflected light from the street polarized at 90deg? Is that just a
rule
that you set for the game?
> What if the polarising filter is at some other angle to the plane of
> polarisation? It turns out that the intensity of polarised light passing
> through a filter is cos^2 theta (where theta is the angle between the
> plane of polarisation and the angle of the filter).
>
> OK, back to our two photons. Remember, the wave fn doesn't say what the
> polarisation angles are, only that they are the same.
Are here x deg = x deg + 180 deg –the same-? Where do the properties UP and
DOWN fit into the game, they are not mentioned in these examples?
> So let's place
> polarisers in the paths of our two photons. Say we put polariser A in
> the path of photon 1, at angle 45deg, and photon 1 passes through the
> filter. We now know that photon 1 is polarised at 45deg. Therefore so
> must photon 2 also be. So if we place polariser B in the path of photon
> 2, also at 45deg, 2 is guaranteed to pass through.
>
> So far so good.
>
> But what if we place polariser B at, say, 20deg?
That means, the angle could also be 20deg + 180deg ? (question resulting
from missing -UP and DOWN-.
> The probability that
> photon 2 goes through must be cos^2 ((45-20)*pi/180). That is greater
> than 1/2. How does photon 2 'know' that is should go through with
> greater than 1/2 probability? I mean, it doesn't know that I will place
> polariser A at 45deg, does it?
Here is the point where I always got stuck. With your explanation, finally
it clicked, basically I understand now ......., well at least I hope though!
> If I had place polariser A at 65deg, the
> the angle between polariser A at 65deg and B at 20deg is 45deg, for
> which angle cos^2 theta is exactly 1/2.
>
> So the probability with which photon 2 goes through filter B at 20deg is
> 1/2 if I put filter A at 65deg,
.....and 1 / 2 for photon 1
> and more than 1/2 if I put filter A at 45deg.
.....and less than 1 /2 for Photon 1, right?
To the point: When I turn filter A, it affects results at filter B. I got
that one.
> Of course, for the photons that block at A, the probabilities for the
> photons at B are 1 minus the probability for the companions of those
> that pass at A (head spins, but it makes sense, as the total probability
> of a pass is always 1/2).
Which means, that, when I add both probabilities to pass, I get probability
50% of the produced photons that pass, right?.
Not sure, that I understand.
I try to rephrase your last sentence in 2 ways:
a)Of course, for the photons that block at A, the probabilities for the
photons to block at B are 1 minus the probability for the companions of
those
that block at A.
b)Of course, for the photons that block at A, the probabilities for the
photons to pass at B are 1 minus the probability for the companions of those
that pass at A
I'm confused, can you help me here?
> We don't notice anything odd at either A or B, because half the photons
> go through and half don't, no matter what the polarisation angles.
I try to figure out: does it mean, that the blocked photons in A plus the
blocked photons in B make 50% of the total of photons that were
produced?...... and 50% go through? ..Must be....., but why is the rate of
blocked photons always 50%, no matter how the angles of the filters are,
..... I have a confusion, wouldn' t that only be the case, when the to
filters are 90deg to each other?
> However, when we bring the two sets of records together and compare them
> photon by photon, we notice the strange dependence at B upon the angle
> of the filter at A. This is what is causing all the fuss.
I am glad to have it so far. I will try to understand the second part,
after getting answers to my questions above.
Thanks for your help
Hans
Hans Jud
see: Of course, for the photons that block at A.......
Which means, that, when I add both probabilities for passing, I get probability
50% FOR ALL PRODUCED PHOTONS, right?
.......
> Not sure, that I understand.
>
> I try to rephrase your last sentence in 2 ways:
>
regards
Hans
Ron House
>
> Why is reflected light from the street polarized at 90deg? Is that just a
> rule that you set for the game?
No. Light reflecting off a flat surface tends to be polarised parallel
to the surface. Depending on the angle, this can be partial or near
total. This is the reason polarised sunglasses cut down glare. The
important thing is, in this case the photons have a definite angle of
polarisation, but in the EPR experiment, they do not; they merely have a
fixed polarisation relative to each other.
> > What if the polarising filter is at some other angle to the plane of
> > polarisation? It turns out that the intensity of polarised light passing
> > through a filter is cos^2 theta (where theta is the angle between the
> > plane of polarisation and the angle of the filter).
> >
> > OK, back to our two photons. Remember, the wave fn doesn't say what the
> > polarisation angles are, only that they are the same.
>
> Are here x deg = x deg + 180 deg –the same-? Where do the properties UP and
> DOWN fit into the game, they are not mentioned in these examples?
A wave polarised at 180 deg would be in the same plane, but out of
phase. That wouldn't matter in the case of polarising filters. Up and
down are irrelevant because the photons don't have a definite
polarisation angle, only an angle relative to each other. Since
polarising filters don't measure phase, the difference between phases
plays no part. So even if I measure with filters vertical, I can't tell
the difference between phases. Also, as waves oscillate, there is no
permanent 'up' or 'down' anyway; it is not like the direction of spin of
a particle.
> > The probability that
> > photon 2 goes through must be cos^2 ((45-20)*pi/180). That is greater
> > than 1/2. How does photon 2 'know' that is should go through with
> > greater than 1/2 probability? I mean, it doesn't know that I will place
> > polariser A at 45deg, does it?
>
> Here is the point where I always got stuck. With your explanation, finally
> it clicked, basically I understand now ......., well at least I hope though!
It is counterintuitive. I find it helps to think of the wave fn as the
real thing and the 'photon' as a convenient description that works on
some occasions.
> > If I had place polariser A at 65deg, the
> > the angle between polariser A at 65deg and B at 20deg is 45deg, for
> > which angle cos^2 theta is exactly 1/2.
> >
> > So the probability with which photon 2 goes through filter B at 20deg is
> > 1/2 if I put filter A at 65deg,
>
> .....and 1 / 2 for photon 1
>
> > and more than 1/2 if I put filter A at 45deg.
>
> .....and less than 1 /2 for Photon 1, right?
If we assume photon 1 passed through A (that is, we only look at the
ones that pass), then we ask "what happened to photon 2 at B?" In other
words, in this setup I know that 1 went through A (probability 1,
because I am using the benefit of hindsight to only select the ones that
actually did go through).
The key (and very surprising) thing is that for these photons, the
probability that photon 2 goes through B depends on the angle between A
and B in such a way that seems to require that 2 knows the angle of
filter A. Thus one explanation could be that there is some kind of
instantaneous message passing. (And the experiments that get
backward-in-time effects extend that to requiring knowledge of the
future too.) I reject this idea because if, as I believe, the wave
function _is_ reality, then reality is inherently non-local. Secret
messages don't get passed around because reality inherently encompasses
all of the universe: there is only one wave function and it encompasses
all of the cosmos. (So when physicists do single particle calculations,
they are in fact making a huge simplification in order to carry out the
computation.)
> To the point: When I turn filter A, it affects results at filter B. I got
> that one.
Yes. Although remember, we can't repeat the experiment for the very same
photon pair because the first measurement we make modifies the wave
function. We have to do a 'run' with one setting and another run at
another setting and compare the results statistically. They have tested
whether they can randomly change the filter angles 'in flight' faster
than a light signal could get from A to B, and the effect still
persists.
> > Of course, for the photons that block at A, the probabilities for the
> > photons at B are 1 minus the probability for the companions of those
> > that pass at A (head spins, but it makes sense, as the total probability
> > of a pass is always 1/2).
>
> Which means, that, when I add both probabilities to pass, I get probability
> 50% of the produced photons that pass, right?.
Yes.
> Not sure, that I understand.
>
> I try to rephrase your last sentence in 2 ways:
>
> a)Of course, for the photons that block at A, the probabilities for the
> photons to block at B are 1 minus the probability for the companions of
> those
> that block at A.
>
> b)Of course, for the photons that block at A, the probabilities for the
> photons to pass at B are 1 minus the probability for the companions of those
> that pass at A
>
> I'm confused, can you help me here?
(b) is what I was saying. (I hope!)
> > We don't notice anything odd at either A or B, because half the photons
> > go through and half don't, no matter what the polarisation angles.
>
> I try to figure out: does it mean, that the blocked photons in A plus the
> blocked photons in B make 50% of the total of photons that were
No. At B, 1/2 pass and 1/2 block, period. But, _if we consider only
those photons at B that are companions of photons that passed at A (or
blocked at A, take your pick) then the percentage that pass need not be
50%, and this number can differ from 50% in extremely counterintuitive
ways.
> produced?...... and 50% go through? ..Must be....., but why is the rate of
> blocked photons always 50%, no matter how the angles of the filters are,
> ..... I have a confusion, wouldn' t that only be the case, when the to
> filters are 90deg to each other?
Think of it this way: a photon hits a polarising filter. Because the
filter is 'measuring' its polarisation, it has to decide what
polarisation angle it has (if it hasn't got a definite angle already for
some reason). On average, ALL ELSE BEING EQUAL, the photon might choose
any angle out of 360deg. My filter can be at any angle, so (as the cos^2
theta function averages 1/2), the photon will pass with probability 1/2.
So, if we count ALL photons (not just those whose companions passed at
the other filter) then we must get 1/2 pass at this filter.
BUT! _If_ we only count photons whose companions passed at the other
filter, _then_ the entanglement of the two photons in the wave function
means that all else is NOT equal; this photon must choose the same
polarisation angle as the other photon, so it hits my filter at a
definite angle rather than a random angle. Therefore I am not dealing
with the average value of cos^2 theta but with the specific value of
that function for the angle between filters A and B. That specific value
need not be 1/2.
> > However, when we bring the two sets of records together and compare them
> > photon by photon, we notice the strange dependence at B upon the angle
> > of the filter at A. This is what is causing all the fuss.
>
> I am glad to have it so far. I will try to understand the second part,
> after getting answers to my questions above.
>
> Thanks for your help
I hope the above straightens out some of the foggy wording in my earlier
attempt.
Ron House
>
> ...a corrction:
> see: Of course, for the photons that block at A.......
>
> Which means, that, when I add both probabilities for passing, I get probability
> 50% FOR ALL PRODUCED PHOTONS, right?
That's it. If we count only companions of photons that passed at A, we
need not get 50% (depending on the angle), but we do get 50% if we count
every photon that comes our way.
Hans Jud
Thanks for your explanations. I am exited. I have made a big step, at least in my
point of view. It will take some days to get your posting into my system (brain).
Just a short remark about my dreams: I believe, that things that seem to be
counterintuitive can be understood one time..... ( I am an architect)
Regards
Hans
Ron House
I have to agree with you there. IMHO, being scientific is not
incompatible with imagination and intuition.
mediaglyphic
Thanks for your explanation. I believe i am following along. I believe that
you have just explained the EPR thought experiment and why EPR thought that
the thought experiment posed difficulties. Are you also familiar with
Aspect's experiment and how it violated Bells inequality?
I am also a little suspicious that we are doing some funny things with
probabilities here. I read an interesting paper about 20 years ago by a guy
named dempster at Harvard about the nature of probability and how we really
don't know what we mean by the word probability, i read this paper as part
of a fuzzy sets course.
The paper mentioned that there were two kinds inference, modus tolens and
modus ponens (i might have these wrong as this is from memory), one is more
like an if and only if, the other is more like an if a then b is possible,
so we can infer things about a from knowing about b. I wonder if the kinds
of probability that we are talking about in this experiment are different
from each other.
the probability wave that a photon represents, is more like the first kind
about, where as the probabilty of detection at B after we have seen A is
more like a Baysian probability or the second kind above.
Sorry if i am being vague and non-specific above, wonder if this makes sense
or if physicsts have discussed what they mean by probability?
"Ron House" <ho...@usq.edu.au> wrote in message
news:397148F7...@usq.edu.au...
> Hans Jud wrote:
> >
> > Thanks for your explanations. I am exited. I have made a big step, at
least in my
> > point of view. It will take some days to get your posting into my system
(brain).
> >
> > Just a short remark about my dreams: I believe, that things that seem to
be
> > counterintuitive can be understood one time..... ( I am an architect)
>
> I have to agree with you there. IMHO, being scientific is not
> incompatible with imagination and intuition.
>
Ron House
>
> Ron,
> Thanks for your explanation. I believe i am following along. I believe that
> you have just explained the EPR thought experiment and why EPR thought that
> the thought experiment posed difficulties. Are you also familiar with
> Aspect's experiment and how it violated Bells inequality?
Aspect's experiment was a test of the EPR thought experiment. Bell's
inequality merely makes precise the idea I explained intuitively, giving
a limit to how much correlation the two photons can have. Aspect's
experiment (I don't recall the exact experimental setup) had to also
deal with the fact that in real experiments, a certain amount of data is
lost due to the experimental setup, etc., so analysing it was a bit
harder than in the case of the thought experiment. Nevertheless, the
idea is the same and Bell's inequality _was_ violated, which shows that
this effect is real. That doesn't mean that the precise theory known as
quantum mechanics is the correct one, but it means that QM _could_ be
the right theory, whereas no local 'realistic' theory can be. I put
"realistic" in scare quotes because people use that word as if only a
material, mechanist explanation can be 'realist', whereas I regard the
logical relation in the wave function as being every bit as real, only
not fitting a mechanical picture.
> I am also a little suspicious that we are doing some funny things with
> probabilities here. I read an interesting paper about 20 years ago by a guy
> named dempster at Harvard about the nature of probability and how we really
> don't know what we mean by the word probability, i read this paper as part
> of a fuzzy sets course.
There may be some deep problems in statistics that are too subtle for
me, but on the normal level of operations, I don't think anything shonky
is being done: the theorems are being applied correctly, etc. The only
thing I think needs to be remembered is that, though QM describes what
happens to specific pairs of photons, probabilities can only be tested
by running the experiment enough times to get a statistical
distribution. Although I don't think it is, something extremely subtle
might be hiding in there, such as maybe a really subtly different theory
is actually true, but it gives the same overall probabilities. (Such a
thing would not change the conclusions about the EPR experiment,
though.)
> The paper mentioned that there were two kinds inference, modus tolens and
> modus ponens (i might have these wrong as this is from memory), one is more
> like an if and only if, the other is more like an if a then b is possible,
> so we can infer things about a from knowing about b. I wonder if the kinds
> of probability that we are talking about in this experiment are different
> from each other.
There's a description of these at
http://www.kcmetro.cc.mo.us/longview/ctac/corenotes.htm
Modus Ponens-
1. If A then B,
2. A
3. B (conclusion)
Modus Tolens-
1. if A then B,
2. Not B
3. Not A
I don't believe that any problem lurks here for QM. The theory doesn't,
as it stands, require anything that differs from classical logic.
> the probability wave that a photon represents, is more like the first kind
> about, where as the probabilty of detection at B after we have seen A is
> more like a Baysian probability or the second kind above.
It really isn't this difficult a problem. If certain assumptions (no
communication between photons, photons have a definite polarisation)
hold, then certain rates of correlation are impossible; yet they happen,
proving at least one of the assumptions wrong. A implies B, but not B,
therefore not A.
> Sorry if i am being vague and non-specific above,
> wonder if this makes sense or if physicsts have
> discussed what they mean by probability?
That is a fair enough question. I think there is a wide perception that
something at the extreme edge of our usual logical understanding is
going on in QM. I deny this. Surprises happen, for sure, such as some
oddities caused by the genuine indistinguishability of identical
particles. However, the 'surprises' in the EPR experiment only come
because the result violates our usual assumptions about physical
reality, not because it obeys some extremely subtle logic.
Ilja Schmelzer
> this effect is real. That doesn't mean that the precise theory known as
> quantum mechanics is the correct one, but it means that QM _could_ be
> the right theory, whereas no local 'realistic' theory can be. I put
> "realistic" in scare quotes because people use that word as if only a
> material, mechanist explanation can be 'realist', whereas I regard the
> logical relation in the wave function as being every bit as real, only
> not fitting a mechanical picture.
That's not the point. The EPR criterion of reality is not of this
type of "realist" which requires a material, mechanist explanation.
If you take the wave function as real, no problem - it would fit the
definition of realism. It fits it in Bohmian mechanics, which is
certainly a realistic theory.
So, if you decide to throw away realism, you throw away much, much
more than material, mechanist explanation. Realism does not even
require the existence of spacetime.
And there is a simple alternative to throwing away realism. It is
accepting realism and the violation of Einstein causality.
If you decide to throw away realism, you win nothing but loose a lot.
In a world without reality, you have only observations. Therefore,
only observable effects may be Einstein-causal. But if you accept
realism, you don't loose this property: observable effects remain
Einstein-causal, the violations of Einstein causality remain hidden.
Thus, you throw away realism for nothing.
> However, the 'surprises' in the EPR experiment only come because the
> result violates our usual assumptions about physical reality, not
> because it obeys some extremely subtle logic.
It does not violate any usual assumption about reality.
Except you are a relativity orthodox who requires what reality has to
be Lorentz-covariant, and if it doesn't, than its worse for reality.
Ilja
--
I. Schmelzer, <il...@ilja-schmelzer.net>, http://ilja-schmelzer.net
Jon J Thaler
>
> The EPR criterion of reality is not of this
> type of "realist" which requires a material, mechanist explanation.
> If you take the wave function as real, no problem - it would fit the
> definition of realism. It fits it in Bohmian mechanics, which is
> certainly a realistic theory.
Bohm's theory requires superluminal motion of the pilot wave.
Every theory that satisfies Bell's theorem must violate either
realism or locality (or other, even more cherished, ideals).
> But if you accept realism, you don't loose this property:
> observable effects remain Einstein-causal, the violations of
> Einstein causality remain hidden.
Right. Bohm's theory has an unobservable reality. So, which
is more objectionable? This is, at its core, an aesthetic
decision. No observable consequences.
[...this snippet is out of order...]
> In a world without reality, you have only observations.
These debates were beaten to death 300 years ago.
mediaglyphic
thanks again for the explanations.
back to EPR for a second.
1) after the electron annihilates and turns into 2 photons with the same
polarization, I assume that this is a result of the fact that they came from
the same electron so they must have the same polarization. or are we
choosing only photons with the same polarization?
2) Are the polarizations exactly defined at the moment the photons are born,
or are do we only know them as probability functions?
3) If we know them only as probability functions do we mean that they are in
precisely one state at any moment in time or do we mean that they are in
many states at once. If it is the latter then perhaps we are not really
talking about probabilities but something else?
wrote in message news:3973D5F8...@usq.edu.au...
> mediaglyphic wrote:
> >
> > Ron,
> > Thanks for your explanation. I believe i am following along. I believe
that
> > you have just explained the EPR thought experiment and why EPR thought
that
> > the thought experiment posed difficulties. Are you also familiar with
> > Aspect's experiment and how it violated Bells inequality?
>
> Aspect's experiment was a test of the EPR thought experiment. Bell's
> inequality merely makes precise the idea I explained intuitively, giving
> a limit to how much correlation the two photons can have. Aspect's
> experiment (I don't recall the exact experimental setup) had to also
> deal with the fact that in real experiments, a certain amount of data is
> lost due to the experimental setup, etc., so analysing it was a bit
> harder than in the case of the thought experiment. Nevertheless, the
> idea is the same and Bell's inequality _was_ violated, which shows that
> this effect is real. That doesn't mean that the precise theory known as
> quantum mechanics is the correct one, but it means that QM _could_ be
> the right theory, whereas no local 'realistic' theory can be. I put
> "realistic" in scare quotes because people use that word as if only a
> material, mechanist explanation can be 'realist', whereas I regard the
> logical relation in the wave function as being every bit as real, only
> not fitting a mechanical picture.
>
> particles. However, the 'surprises' in the EPR experiment only come
> because the result violates our usual assumptions about physical
> reality, not because it obeys some extremely subtle logic.
>
Stephen Speicher
> Ron House <ho...@usq.edu.au> writes:
> > this effect is real. That doesn't mean that the precise theory known as
> > quantum mechanics is the correct one, but it means that QM _could_ be
> > the right theory, whereas no local 'realistic' theory can be. I put
> > "realistic" in scare quotes because people use that word as if only a
> > material, mechanist explanation can be 'realist', whereas I regard the
> > logical relation in the wave function as being every bit as real, only
> > not fitting a mechanical picture.
>
> That's not the point. The EPR criterion of reality is not of this
> type of "realist" which requires a material, mechanist explanation.
> If you take the wave function as real, no problem - it would fit the
> definition of realism. It fits it in Bohmian mechanics, which is
> certainly a realistic theory.
>
I would hardly call Bohm's theory[ies] realist in nature. For
instance, Bohm's quantum potential is explicitly nonlocal. There
is no question that Bohm's attempt at acknowledging real
particles and real waves can be considered 'realist' in some
sense, but nonlocal action certainly cannot be so considered. (I
assume you were referring to Bohm's quantum potential, for if you
had meant his later work, such as 'Wholeness and the Implicate
Order', then the issue is even more clear.)
Frank Wappler
> Bell's inequality merely makes precise the idea [...], giving
> a limit to how much correlation the two photons can have.
> Bell's inequality _was_ [experimentally found] violated, which [...]
> means that QM _could_ be the right theory, whereas no local
> 'realistic' theory can be.
Please sketch or reference the assumptions and a proof
of Bell's inequality.
Do the assumptions reproduce what you mean by "realistic theory",
or are they stronger?
Thanks, Frank W ~@) R
Frank Wappler
Ilja Schmelzer
>> The EPR criterion of reality is not of this
>> type of "realist" which requires a material, mechanist explanation.
>> If you take the wave function as real, no problem - it would fit the
>> definition of realism. It fits it in Bohmian mechanics, which is
>> certainly a realistic theory.
>
> Every theory that satisfies Bell's theorem must violate either
> realism or locality (or other, even more cherished, ideals).
Exactly.
> Right. Bohm's theory has an unobservable reality. So, which
> is more objectionable? This is, at its core, an aesthetic
> decision. No observable consequences.
Hm, is the decision between realism and solipcism an aesthetic one
too? If yes, I agree.
>> In a world without reality, you have only observations.
>
> These debates were beaten to death 300 years ago.
300 years ago people have after such debates, AFAIU, preferred
realism. Why not today?
Ilja Schmelzer
>> That's not the point. The EPR criterion of reality is not of this
>> type of "realist" which requires a material, mechanist explanation.
>> If you take the wave function as real, no problem - it would fit the
>> definition of realism. It fits it in Bohmian mechanics, which is
>> certainly a realistic theory.
> I would hardly call Bohm's theory[ies] realist in nature.
It meets the EPR criterion of reality. It has a clear ontology.
> For instance, Bohm's quantum potential is explicitly nonlocal.
> There is no question that Bohm's attempt at acknowledging real
> particles and real waves can be considered 'realist' in some sense,
> but nonlocal action certainly cannot be so considered.
??? Was Newton's (also nonlocal) theory of gravity nonrealistic?
> (I assume you were referring to Bohm's quantum potential,
Yep.
Stephen Speicher
> Stephen Speicher <s...@compbio.caltech.edu> writes:
> >> That's not the point. The EPR criterion of reality is not of this
> >> type of "realist" which requires a material, mechanist explanation.
> >> If you take the wave function as real, no problem - it would fit the
> >> definition of realism. It fits it in Bohmian mechanics, which is
> >> certainly a realistic theory.
>
> > I would hardly call Bohm's theory[ies] realist in nature.
>
> It meets the EPR criterion of reality. It has a clear ontology.
>
No. It meets the criteria known as 'Einstein separability (the
particles separate into real independent physical entities), but
not the condition known as 'local reality' (not being described
by a single wavefunction at the time of measurement). Bohm
reinterpreted the wavefunction as an objectively real field,
where the quantum potential is, in effect, the medium through
which are transmitted influences between separated correlated
particles. A measurement of a property of one particle has an
instaneous change in quantum potential of the other correlated
particle. This is a nonlocal action connected by a reinterpreted
wavefunction called a quantum potential, and as such does not
represent 'local reality.'
> > For instance, Bohm's quantum potential is explicitly nonlocal.
> > There is no question that Bohm's attempt at acknowledging real
> > particles and real waves can be considered 'realist' in some sense,
> > but nonlocal action certainly cannot be so considered.
>
> ??? Was Newton's (also nonlocal) theory of gravity nonrealistic?
>
Absolutely. To the degree that Newton's (brilliant) system
represents acausal behavior -- and instantaneous effects -- to
that degree it is not a realist system.
Jim Heckman
"mediaglyphic" <pa...@deezel.com> wrote:
> Ron,
> thanks again for the explanations.
>
> back to EPR for a second.
>
> 1) after the electron annihilates and turns into 2 photons with the
> same polarization, I assume that this is a result of the fact that
> they came from the same electron so they must have the same
> polarization. or are we choosing only photons with the same
polarization?
I came in late to this thread, but permit me to butt in.
I'm not sure what electron you're talking about, but the correlation of
the photon spins is due simply to conservation of angular momentum.
Before the annihilation, the system had the property that measuring its
a.m. would give certain values with certain amplitudes -- conservation
dictates that the values and amplitudes remain unchanged afterwards.
> 2) Are the polarizations exactly defined at the moment the photons
> are born,
No, not in the 'traditional' interpretation of QM. That's the whole
point of Bell's Theorem. All that's known for sure is the a.m.
amplitudes for the whole system, to which the polarizations contribute.
More precisely, what Bell's Inequality shows is that QM predicts
correlations between measurements of the photons' spins that *cannot*
be explained by assuming that: (1) each photon has a well-defined spin
when it's created; (2) the photons cannot 'communicate' with each other
over arbitrary distances in arbitrarily short times.
Aspect's experiment, and others confirming Bell's Inequality,
demonstrate that the 'correct' description of nature cannot have both
the (1) and (2) properties.
> or are do we only know them as probability functions?
That's one way to say it.
> 3) If we know them only as probability functions do we mean that they
> are in precisely one state at any moment in time or do we mean that
> they are in many states at once.
Closer to the latter.
> If it is the latter then perhaps we are not really talking about
> probabilities but something else?
We know the state of the entire system, i.e., of both photons considered
together. According to QM, this state *cannot* be expressed in terms of
knowing the states of both photons individually, i.e., they're
"entangled". In fact, it doesn't even *make sense* to talk about the
states of the individual photons -- only their amplitudes for being in
certain states. (Technically, the state of the whole system is not a
tensor product of states of its 'parts'.)
--
~~ Jim Heckman ~~
-- "As I understand it, your actions have ensured that you will never
see Daniel again." -- Larissa, a witch-woman of the Lowlands.
-- "*Everything* is mutable." -- Destruction of the Endless
Sent via Deja.com http://www.deja.com/
Before you buy.
Wayne Throop
:: objectionable? This is, at its core, an aesthetic decision.
:: No observable consequences.
: Ilja Schmelzer <schm...@wias-berlin.de>
: Hm, is the decision between realism and solipcism an aesthetic one
: too? If yes, I agree.
Heh! Interesting!
But the comparison is both a bit unfair, and has some illustrative
juxtapositions that Ilja probably didn't intend, but which are
nonetheless instructive for all that.
Unfair, because solipsism is often thought of as a rejection of
objective reality existing at all, while the weakened form of
materialism where corelation isn't taken to imply causation is still
predicated on an objective, external reality.
But instructive, because one can think of solipsism as the ultimate
"prefered frame" theory. The solipscist says that, despite there being
no way to demonstrate it (not in the domain of experiment), that there
is only one prefered viewpoint in the universe, only one mind, the
others are mere appearance, smoke and mirrors. Ilja says that, despite
there being no way to demonstrate it, that there is only one prefered
time relationship in the universe, and the others that are loretz
transforms of it are mere appearance, smoke and mirrors.
So. The interesting point here is, the difference between Ilja's
position and solipscism is actually SMALLER than the difference
between what we might call "weakened realism" and solipscism.
So, bottom line, yes, in the context of observational equivalence, the
decision between realism and solipscism is an aesthetic one. And the
person who chooses solipsism must choose one of the solipscistic models
that "just happens" to match objective models, because the solipscist
still has to deal with the fact that that mirage sure *seems* to be
talking to me, and sure *seems* to be getting irritated that I'm
ignoring him because he's a mirage, and it will sure *seem* to hurt when
he seems to get angry enough to seem to punch the solipscist in the
nose.
Similarly, the prefered-framer is limited to those models where the
erstatz frames are just as good, and hence any utility of the model is
severely blunted, and any stock one puts in the model is, indeed, purely
aesthetic, just like the solipscist. Those clocks sure *seem* to
satisfy all the requirements of timekeeping, etc, etc.
When it's a more reliable practical guide to suppose that the erstaz
frames are every bit as good as the prefered frame than anything you can
deduce from the prefered frame without that extra assumption ... well.
I find that very interesting.
Wayne Throop thr...@sheol.org http://sheol.org/throopw
mediaglyphic
thanks for "butting" in, i need all the help i can get in grasping at EPR
and QM!
also as far as i can see all of your assumptions are correct.
1) Does conservation of angular momentum mean that if i do something to
photon A then the opposite has to happen to photon "B". If so i am not sure
why it would. because by acting on photon A i have interacted with the
system and so the previous state of homogenity is gone. similarly when i
measure the polarization of a photon am i not interacting with it and hence
nullifying the conservation of angular momentum?
2) Can you explain in more or less plain english, why Bell's inequality says
that QM and SR are in conflict?
3) In what sense is the photon's state a probability? it sounds like we
don't really know anything about each photon's individual state, only the
state of the combined system.
"Jim Heckman" <jhec...@my-deja.com> wrote in message
news:8l5ml3$n71$1...@nnrp1.deja.com...
> In article <Wq5d5.133426$HK2.2...@news20.bellglobal.com>,
> "mediaglyphic" <pa...@deezel.com> wrote:
>
> > Ron,
> > thanks again for the explanations.
> >
> > back to EPR for a second.
> >
> > 1) after the electron annihilates and turns into 2 photons with the
> > same polarization, I assume that this is a result of the fact that
> > they came from the same electron so they must have the same
> > polarization. or are we choosing only photons with the same
> polarization?
>
> I came in late to this thread, but permit me to butt in.
>
> I'm not sure what electron you're talking about, but the correlation of
> the photon spins is due simply to conservation of angular momentum.
> Before the annihilation, the system had the property that measuring its
> a.m. would give certain values with certain amplitudes -- conservation
> dictates that the values and amplitudes remain unchanged afterwards.
>
> > 2) Are the polarizations exactly defined at the moment the photons
> > are born,
>
> No, not in the 'traditional' interpretation of QM. That's the whole
> point of Bell's Theorem. All that's known for sure is the a.m.
> amplitudes for the whole system, to which the polarizations contribute.
>
> More precisely, what Bell's Inequality shows is that QM predicts
> correlations between measurements of the photons' spins that *cannot*
> be explained by assuming that: (1) each photon has a well-defined spin
> when it's created; (2) the photons cannot 'communicate' with each other
> over arbitrary distances in arbitrarily short times.
>
> Aspect's experiment, and others confirming Bell's Inequality,
> demonstrate that the 'correct' description of nature cannot have both
> the (1) and (2) properties.
>
> > or are do we only know them as probability functions?
>
> That's one way to say it.
>
> > 3) If we know them only as probability functions do we mean that they
> > are in precisely one state at any moment in time or do we mean that
> > they are in many states at once.
>
> Closer to the latter.
>
> > If it is the latter then perhaps we are not really talking about
> > probabilities but something else?
>
Ilja Schmelzer
>>> Bohm's theory has an unobservable reality. So, which is more
>>> objectionable? This is, at its core, an aesthetic decision.
>>> No observable consequences.
>
>> too? If yes, I agree.
> Heh! Interesting! But the comparison is both a bit unfair,
There is nothing unfair. It is possible to understand "realism",
"solipcism" and "aesthetic decision" so that the answer is positive.
In this understanding of "aesthetic decision" it would be foolish to
question the original statement.
If the answer is "no", I want to continue to ask why in one case
(BM/QM) the answer is "yes", and in the other case (realism/solipcism)
"no".
> Unfair, because solipsism is often thought of as a rejection of
> objective reality existing at all, while the weakened form of
> materialism where corelation isn't taken to imply causation is still
> predicated on an objective, external reality.
All what we observe are correlations, and what we describe in
realistic theories are causations. If a correlation is not explained
by some causation in the realistic theory, the theory has a problem
(is falsified).
If you reject this classical scheme, what is the purpose to name the
theory realistic? (I see only one - to hide the problem.)
> But instructive, because one can think of solipsism as the ultimate
> "prefered frame" theory. The solipscist says that, despite there being
> no way to demonstrate it (not in the domain of experiment), that there
> is only one prefered viewpoint in the universe, only one mind, the
> others are mere appearance, smoke and mirrors. Ilja says that, despite
> there being no way to demonstrate it, that there is only one prefered
> time relationship in the universe, and the others that are loretz
> transforms of it are mere appearance, smoke and mirrors.
> So. The interesting point here is, the difference between Ilja's
> position and solipscism is actually SMALLER than the difference
> between what we might call "weakened realism" and solipscism.
That's really funny ;-).
But, essentially, only a word game. First, based on the confusing
notion of "frame" and "preferred frame". They are not objects of
reality, but ways to describe this reality in our theory. In GET
reality there is absolute space and time, but we have no observational
possibilities to distinguish some really very different states.
The comparison fails too, because, if I'm solipsist, I have an obvious
way to decide who is the only real person - its me.
> So, bottom line, yes, in the context of observational equivalence, the
> decision between realism and solipscism is an aesthetic one.
So why we usually prefer realism? It seems, even if it is only an
aesthetic question, it may be answered in a more or less unique way?
I prefer to think about solipcism what it is simply a mind-game,
developed with the intend to prove that realism cannot be proven.
Once solipcism does not have internal contradictions, is logically
possible, we cannot prove that realism is true.
Nonetheless, we (mostly) prefer realism. We need no proofs for this.
> Similarly, the prefered-framer is limited to those models where the
> ersatz frames are just as good, and hence any utility of the model is
> severely blunted,
Why blunted? If some other coordinates work nice, fine. Of course,
any physical theory works in all coordinates.
> Those clocks sure *seem* to satisfy all the requirements of
> timekeeping, etc, etc.
No, all clocks are trash. A clock which shows different time if moved
is trash, it does not satisfy the requirements for really good clocks.
Having nothing better, we use them nonetheless.
Ilja Schmelzer
>>> I would hardly call Bohm's theory[ies] realist in nature.
>>
>> It meets the EPR criterion of reality. It has a clear ontology.
>
> No. It meets the criteria known as 'Einstein separability (the
> particles separate into real independent physical entities), but
> not the condition known as 'local reality' (not being described
> by a single wavefunction at the time of measurement).
BM is not local, but realistic. Therefore, meets criteria for
reality, not for locality.
> Bohm reinterpreted the wavefunction as an objectively real field,
> where the quantum potential is, in effect, the medium through which
> are transmitted influences between separated correlated particles. A
> measurement of a property of one particle has an instaneous change
> in quantum potential of the other correlated particle. This is a
> nonlocal action connected by a reinterpreted wavefunction called a
> quantum potential, and as such does not represent 'local reality.'
Nobody has claimed that BM is local realistic.
>> ??? Was Newton's (also nonlocal) theory of gravity nonrealistic?
>
> Absolutely. To the degree that Newton's (brilliant) system
> represents acausal behavior -- and instantaneous effects -- to
> that degree it is not a realist system.
So you have simply a different notion of realism. That's all.
What's the purpose of this new notion of realism, which includes
locality? Of course, feel free to use whatever name you want for a
given concept. But we have already a nice, much less confusing, name
for this concept - locality or local realism.
In the usual notion of realism Newton's theory is realistic. It is
also EPR-realistic and realistic in the sense of Bell's/my
understanding.
Ilja Schmelzer
> 2) Can you explain in more or less plain english, why Bell's inequality says
> that QM and SR are in conflict?
Hans Jud
break.
Ciao
Hans Jud
Ron House schrieb:
> Hans Jud wrote:
> >
> > Thanks for your explanations. I am exited. I have made a big step, at least in my
> > point of view. It will take some days to get your posting into my system (brain).
> >
> > Just a short remark about my dreams: I believe, that things that seem to be
> > counterintuitive can be understood one time..... ( I am an architect)
>
> I have to agree with you there. IMHO, being scientific is not
> incompatible with imagination and intuition.
>
Ron House
You'll find a simple description at:
http://www2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
Essentially, it is a simple logical property, with no dependence on
advanced (or any) physics.
Ron House
>
> Ron House <ho...@usq.edu.au> writes:
> > this effect is real. That doesn't mean that the precise theory known as
> > quantum mechanics is the correct one, but it means that QM _could_ be
> > the right theory, whereas no local 'realistic' theory can be. I put
> > "realistic" in scare quotes because people use that word as if only a
> > material, mechanist explanation can be 'realist', whereas I regard the
> > logical relation in the wave function as being every bit as real, only
> > not fitting a mechanical picture.
>
> type of "realist" which requires a material, mechanist explanation.
> If you take the wave function as real, no problem - it would fit the
> definition of realism. It fits it in Bohmian mechanics, which is
> certainly a realistic theory.
>
> more than material, mechanist explanation. Realism does not even
> require the existence of spacetime.
Exactly. As you will have seen, I state emphatically that I am a
realist.
> And there is a simple alternative to throwing away realism. It is
> accepting realism and the violation of Einstein causality.
>
> If you decide to throw away realism, you win nothing but loose a lot.
> In a world without reality, you have only observations. Therefore,
> only observable effects may be Einstein-causal. But if you accept
> realism, you don't loose this property: observable effects remain
> Einstein-causal, the violations of Einstein causality remain hidden.
> Thus, you throw away realism for nothing.
>
> > However, the 'surprises' in the EPR experiment only come because the
> > result violates our usual assumptions about physical reality, not
> > because it obeys some extremely subtle logic.
>
> It does not violate any usual assumption about reality.
People usually assume that the photons have some definite state. The
very fact that they do not puzzles numerous people. It doesn't violate
REALITY, but it most certainly does violate common ASSUMPTIONS about
reality. If it didn't, there wouldn't be so many people confused about
it.
Ron House
>
> Ron,
> thanks again for the explanations.
>
> back to EPR for a second.
>
> 1) after the electron annihilates and turns into 2 photons with the same
> polarization, I assume that this is a result of the fact that they came from
> the same electron so they must have the same polarization. or are we
> choosing only photons with the same polarization?
Just a quibble: Actually it's an electron and a positron annihilating,
not just one electron. The wave function says that the two photons have
the same polarisation as each other. (Actually, it's 90deg, not 0deg,
but I slide over that as a complication that doesn't affect the question
at hand.)
> 2) Are the polarizations exactly defined at the moment the photons are born,
> or are do we only know them as probability functions?
Neither. This is what causes the kafuffle. The wave fn says they have
the same polarisation, but NOT what the value of that polarisatoin is.
In fact, it doesn't exist until it is measured. This is why the
experiment gives the seemingly puzzling results I described earlier.
> 3) If we know them only as probability functions do we mean that they are in
> precisely one state at any moment in time or do we mean that they are in
> many states at once. If it is the latter then perhaps we are not really
> talking about probabilities but something else?
They are in the state of having the same value but no particular value.
The first photon only gets a value when we measure it. This is why
people attached to thinking of the little fuzzy photon critters as real
have such a difficult time here. It's the wave function that is real,
the photons are just a convenient description of some of its properties;
but like many convenient approximations, it breaks down in some cases.
mediaglyphic
you said (snipped above)
> They are in the state of having the same value but no particular value.
> The first photon only gets a value when we measure it.This is why
> people attached to thinking of the little fuzzy photon critters as real
> have such a difficult time here
.
i wonder what you mean by real when you say that
"It's the wave function that is real,"
> the photons are just a convenient description of some of its properties;
> but like many convenient approximations, it breaks down in some cases.
it sounds to me like you are saying that photons exist as soon as we see
them and not before or after. So, in my layman's terms, the photon is the
description of the interaction between the measurer and the wave function.
are these waves probability waves? if so what do we mean by probability
here?
sorry to beat the probability horse to death here, but it bugs me!!!
Stephen Speicher
You are using the term 'realism' (or 'realist') in the colloquial
sense, whereas in the philosophy of science it has a more precise
meaning. The concept of epistemic realism incorporates causal
mechanisms as a necessary element in its formulation. See, for
instance, Bas C. van Fraassen's essay "The Charybdis of Realism:
Epistemological Implications of Bell's Inequality", in
_Philosophical Consequences of Quantum Theory_, University of
Notre Dame Press, 1989. (Incidentally, this is a wonderful
volume containing a fine assortment of papers originally
presented at a 1987 conference, attended by a superb group of
philosophers and physicists interested in the philosophical
underpinnings of quantum mechanics. As the editors of the book
point out, though the conference had not intended to focus on
Bell's theorem, most all took Bell's work as a starting point.)
I think we agree on the facts, but we disagree about terminology.
No big deal, and hardly worth fussing about.
Jim Heckman
"mediaglyphic" <pa...@deezel.com> wrote:
> Jim,
> thanks for "butting" in, i need all the help i can get in grasping at
> EPR and QM! also as far as i can see all of your assumptions are
> correct.
First, let me say that's it very hard to explain all this without going
into the mathematics. You really ought to find yourself a good
introductory *textbook* on QM. (I believe one or two have been
written. :-)
> 1) Does conservation of angular momentum mean that if i do something
> to photon A then the opposite has to happen to photon "B".
"Do something" is a very tricky concept. Here, what it means is that
if you "measure" (as defined by the postulates of QM) the spins of A
and B along definite (and possibly different) axes, there will indeed
be correlations between the results of the two measurements.
> If so i am not sure why it would.
Because angular momentum is conserved. :-) This is an observed fact of
the Universe we live in. Any useful theory of 'How Things Work' must be
constrained by this observation. Most current theories make a 'deep'
connection between the conservation of a.m. and the belief that space
is "isotropic", i.e., has no underlying preferred direction. (I am
specifically excluding General Relativity here, which is whole 'nother
can of worms.)
> because by acting on photon A i have interacted with the system and
> so the previous state of homogenity is gone.
What do you mean by "homogeneity"? Why is it "gone"? But yes, in
general "interacting" with (some part of) the system will change its
state, as will "measuring" some "observable". (Again, you need to study
the rigorous meanings of these words, as used by physicists.)
> similarly when i measure the polarization of a photon am i not
> interacting with it
Well, there's a difference between the technical terms "measure" and
"interact", as they're usually used. But either one will, in general,
cause a change in the system's state...
> and hence nullifying the conservation of angular momentum?
Why would you think that? :-) Seriously, the a.m of the *whole system*,
which now includes *you*, will still be conserved.
> 2) Can you explain in more or less plain english, why Bell's
> inequality says that QM and SR are in conflict?
^_^ In the opinions of many physicists, it *doesn't* say that, and they
*aren't* in conflict. In fact, Quantum Field Theory (QFT) is a theory
incorporating both 'classical' QM (which is a good approximation of QFT
in the limit of negligible relative velocities and negligible
gravitation) and 'classical' SR (which is a good approximation of QFT
when 'quantum' effects can be ignored).
> 3) In what sense is the photon's state a probability?
In the technical sense that each individual photon is described by a
"density matrix", not a "state".
> it sounds like we don't really know anything about each photon's
> individual state, only the state of the combined system.
Again, each individual photon doesn't even *have* a "state" (again, in
the technical sense of that term) when they're "entangled". This
doesn't mean that we can't make accurate predictions about what values
we'll find, with what probabilities, if we "measure" specific
"observables" of each photon.
I can try to answer more detailed questions if you're interested, but I
don't know how well I can make you 'understand' all this unless you
study the basic mathematics of Hilbert spaces, and the Postulates of
QM.
Matthew Nobes
> In article <PVtd5.139350$HK2.2...@news20.bellglobal.com>,
> "mediaglyphic" <pa...@deezel.com> wrote:
>
> > Jim,
> > thanks for "butting" in, i need all the help i can get in grasping at
> > EPR and QM! also as far as i can see all of your assumptions are
> > correct.
>
> First, let me say that's it very hard to explain all this without going
> into the mathematics. You really ought to find yourself a good
> introductory *textbook* on QM. (I believe one or two have been
> written. :-)
Let me just chime in here with a recomendation of "The Odd Quantum" by Sam
Treiman. This a "semi-popular" book, it's not at the level of an
introductory textbook, but it is higher than an average pop-sci treatment
(he assumes you've seen some one variable calculus). I have'nt read the
whole thing in detail, but it looked quite good from the skimming I gave
it. IIRC he discusses EPR type stuff.
----------------------------------------------------------------
"Neutral Kaons are even more |Matthew Nobes
crazy than silly putty." |c/o Physics Dept.
|Simon Fraser University
Gerard 't Hooft |8888 University Drive
|Burnaby, B.C.
|Canada
http://hapiland.phys.sfu.ca
mediaglyphic
difficult. i skimmed through one of the volumes and it seemed like it did a
good job of explaining things but i wonder how the later chapters are?
"Matthew Nobes" <man...@fraser.sfu.ca> wrote in message
news:Pine.GSO.4.21.000721...@fraser.sfu.ca...
Frank Wappler
> Frank Wappler wrote:
> > Ron House wrote:
> > > Bell's inequality _was_ [experimentally found] violated,
> > > which [...] means that QM _could_ be the right theory,
> > > whereas no local 'realistic' theory can be.
> > Please sketch or reference the assumptions and a proof
> > of Bell's inequality.
> > Do the assumptions reproduce what you mean by
> > "[local] realistic theory", or are they stronger?
> You'll find a simple description at:
> http://www2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
There is derived
. the famous Bell's Inequality
(which however bears little resemblance to Bell's or
Clauser-Horne-Shimony-Holt's inequalities in forms I know)
for a very peculiar case of assumed "physical properties"
of electrons:
namely that each electron not only has the property to "liked,
knew and imposed" the outcome that _has_ been measured, in a
particular trial (e.g. that in this trial:
. detector A, in orientation A1, flashed green)
and that each electron has property to "liked, knew and
imposed" outcomes that _were not_ being measured, in a particular
trial, but that were only potential (e.g. that in this trial:
detector A, if it _had been_ in orientation A2, it had flashed red);
but it is also assumed that
. the electrons come out of the source with the _same_ properties;
i.e. those properties that had been found actually, _as well as_
those that remained only potential
(e.g. in this trial, properties of the one electron:
- A in orientation A1, flashed green,
- if A had been in orientation A2, then A had flashed red,
- if A had been in orientation A3, then A had flashed green,
and corresponding same properties of the other electron:
- if B had been in orientation B1, then B had flashed green,
- B in orientation B2, flashed red,
- if B had been in orientation B3, then B had flashed green).
Note that this is only an _assumption_. The claim that
. having set same orientations [...] we find that the result
. is always the same
refers only to selected trials in which the individual
"orientations" of detectors A and B were found _set up_.
The correspondence of { A1, A2, A3 } to { B1, B2, B3 } must be
(and apparently had been implicitly) derived in the first place,
by correlating actually measured outcomes,
which however don't reveal any potential properties.
Do the descriptions and assumptions given at the referenced site
correspond to and really entirely include your notion of
"[local] realistic theories"?
Certainly not AFAIU - I'd call a description and assumption
still "local and realistic" in which the individual electrons
"liked, knew and imposed" _only the actual_ outcomes,
in any particular trial.
Can you derive Bell's inequality (or an equivalent) for those
(weaker) assumptions of a "local and realistic theory", too?
> Essentially, [Bell's inequality] is a simple logical property,
> with no dependence on advanced (or any) physics.
But its derivation is still subject to specific assumptions,
about which I'm asking.
Best regards, Frank W ~@) R
p.s.
The referenced site states in Appendix III:
. [...] if an electron is pointing in a particular direction,
. and you measure its spin in another direction which is
. some angle q away from the first one, then the probability
. of finding it pointing in that direction is (cos( q ))^2.
That's wrong in two ways:
First of all, the relative orientation angle in any particular
set of trials is only defined and _measured through_ the
outcomes concerning the "pointing of the electron",
as found in those trials;
secondly, the definition/measurement procedure (due to E.-l.Malus)
is such that
q == 2 arccos(
sqrt( Sum_{ trials with the electron pointing right } /
Sum_{ all trials } ) ),
q == 2 arccos( sqrt( probability ) ),
or IOW:
q == arccos( (Sum_{ trials with the electron pointing right } -
Sum_{ trials with the electron pointing wrong }) /
Sum_{ all trials } );
and
probability = (cos( q/2 ))^2.
Jim Heckman
"mediaglyphic" <pa...@deezel.com> wrote:
> do the feynman lectures do a good job of explaining or are they
> relatively difficult. i skimmed through one of the volumes and it
> seemed like it did a good job of explaining things but i wonder how
> the later chapters are?
In my experience, people's reaction to the Feynman Lectures is very
much a matter of personal taste. Myself, I would read them and feel
like I 'understood' things, but then have no idea how to actually go
out and make concrete predictions about what would happen in the real
world. :-(
I actually took a course from Dr. Feynman once (introductory General
Relativity), but dropped out soon into it, because he and I simply
didn't *think* alike, and I couldn't follow him -- which is why he was
a Nobel Laureate, and I won't be. :-)
Frank Wappler
> Every theory that satisfies Bell's theorem must violate either
> realism or locality (or other, even more cherished, ideals).
Please sketch or reference the assumptions and a proof
of Bell's theorem.
(Assuming that the ability to do that is among the cherished ideals.)
Do the assumptions reproduce what you mean by "realism"
(and "locality"), or are they stronger?
Matthew Nobes
> In article <tY3e5.7039$Z43....@news20.bellglobal.com>,
> "mediaglyphic" <pa...@deezel.com> wrote:
>
> > do the feynman lectures do a good job of explaining or are they
> > relatively difficult. i skimmed through one of the volumes and it
> > seemed like it did a good job of explaining things but i wonder how
> > the later chapters are?
>
> In my experience, people's reaction to the Feynman Lectures is very
> much a matter of personal taste. Myself, I would read them and feel
> like I 'understood' things, but then have no idea how to actually go
> out and make concrete predictions about what would happen in the real
> world. :-(
I think Feynamn's lectures are very good _after_ you've seen another
presentation of the same material. I could be baised since that's how cam
to them. As an introduction they might not be the best. Another example
of this is the Landau and Lifshitz series. After seeing the materialin
their classical mechanics textbook elsewhere coming to L&L was
excellent. But to actually try to *learn* CM from their book would not be
a good idea.
> I actually took a course from Dr. Feynman once (introductory General
> Relativity), but dropped out soon into it, because he and I simply
> didn't *think* alike, and I couldn't follow him -- which is why he was
> a Nobel Laureate, and I won't be. :-)
There is a "genius classification scheme" I've heard of. I can't remember
wether i is due to Fermi, Pauli or somebody else. The basic idea is that
there are two kinds of geniuses. The first is simple "smarter then me by
a large factor". I.e. if you took your intellegence dial and turned it
way up you'd get there. I've heard Steven Weinberg cited as this type of
genius. Then there's the "magical" type of genius. Feynman is there.
BTW when was that GR course? Was it the one written up as the "Feynman
Lectures on Gravtiation"?
Jim Heckman
Matthew Nobes <man...@fraser.sfu.ca> wrote:
> On Sat, 22 Jul 2000, Jim Heckman wrote:
>
> [...]
>
> > I actually took a course from Dr. Feynman once (introductory General
> > Relativity), but dropped out soon into it, because he and I simply
> > didn't *think* alike, and I couldn't follow him -- which is why he
> > was a Nobel Laureate, and I won't be. :-)
>
> [...]
>
> BTW when was that GR course?
1981 +/- ~2 yrs
> Was it the one written up as the "Feynman Lectures on Gravtiation"?
Don't know -- haven't read it.
Ron House
>
> Thanks again Ron,
>
> you said (snipped above)
> > They are in the state of having the same value but no particular value.
> > people attached to thinking of the little fuzzy photon critters as real
> > have such a difficult time here
> .
> i wonder what you mean by real when you say that
That's a hard one to answer precisely, because I use words to get across
my meaning, rather than set up the words a priori and speak within a
consistent system. The latter might be preferable, but no one has ever
succeeded in doing it, especially for the hard cases. So I can only
answer with examples:
pi: real (absolutely), because any thinker in any conceivable existence
could discover pi.
My self: real, because I have direct knowledge of it. (More subtle than
it seems; this point is related to the old question of empiricism in a
deep way.)
Santa Claus: not real, because nothing has the properties of Santa
Claus.
The myth of Santa Claus: real, because there is such a pattern of belief
in some human societies.
a cricket ball: real, because the pattern of behaviour of certain actual
round objects fulfils the expectations in the concept "cricket ball".
This remains so even when we admit that the material in the ball is
itself just an epiphenomenon.
an electron: not real (at least not to a 'common sense' thinker),
because at least one part of the common sense concept of an electron
(travels from A to B by continuous increments, is in one place at a
time, etc.) is not obeyed by any existing entity.
an 'electron' (used as a convenient label for certain observable
patterns): real, because these patterns do arise from the behaviour of
the wave fn.
What is missing from the above examples is any kind of assertion that
there is any actual 'stuff' of which material things are composed. I
don't believe in 'stuff'. All reality is ultimately logical/mental.
> "It's the wave function that is real,"
> > the photons are just a convenient description of some of its properties;
> > but like many convenient approximations, it breaks down in some cases.
>
> it sounds to me like you are saying that photons exist as soon as we see
> them and not before or after. So, in my layman's terms, the photon is the
> description of the interaction between the measurer and the wave function.
At times the wave fn allows us to talk about the unseen location of the
'electron', but at others, not. A scientist makes perfect sense in some
experimental setups to say "The electron's path was curved by the
magnetic field" (or whatever), even though we never looked at it. The
concept applies in many places where we don't make observations, but it
doesn't apply _everywhere_, and it is this small leftover residue that
causes all the ruckus.
> are these waves probability waves? if so what do we mean by probability
> here?
I have a fairly simpleminded idea here: merely the degree of reliance
that I can put on a prediction, or, in other words, the strength of my
knowledge. A probability of 1 means I can rely absolutely on the
prediction; probability 1/2 means it could as equally happen as not, and
prob. 0 means I know it will not happen. The wave fn times its conjugate
is a probability density. So for informal purposes it is sufficient to
call it a probability wave.
> sorry to beat the probability horse to death here, but it bugs me!!!
A lot of our modern insecurity about probability comes from the various
deductivist theories of knowledge, such as Poppers, to which we have
been subjected. These theories are unsupportable, so a reasonably simple
mental picture seems to suffice to capture reality, provided we don't
look for it in the wrong places.
Ron House
> Ron House wrote:
> > Essentially, [Bell's inequality] is a simple logical property,
> > with no dependence on advanced (or any) physics.
>
> But its derivation is still subject to specific assumptions,
> about which I'm asking.
I think the following is not far from the mark. Imagine two computers
communicating at time A. They are then separated and their communication
severed permanently. At time B, one of the computers is asked a question
(not knowing what it will be in advance). At time C, the other computer
is asked a question, not knowing what question was asked of the first
computer (nor does the first know the question to be asked of the
second, btw).
Now: given that we can ask questions about specific angles around a
circle (we can ask anything), and given that the computers can use their
common assumptions (agreed to at time A) as well as any algorithms they
please to decide how to answer the questions, we may ask: how much
agreement is logically possible between the answers of these two
computers for various chosen angles? (We imagine repeating this many
times to build up a statistical profile: just put the program in a
loop.)
The above scenario clearly incorporates every conceivable physical
theory that postulates independent behaviour of the photons after
separation, because I permit the computers to use _any algorithm_ to
decide their answers. And any algorithm clearly includes using the
equations of any given theory of physics.
I get the feeling you are looking for a great subtlety, but I don't
believe this is a stratospheric problem in philosophy. It is a very
basic thing, easily visualised by any sensible person. If you don't
believe Bell's theorem, try actually programming two computers as
described above, and see if you can 'beat the system'.
Ilja Schmelzer
>> So you have simply a different notion of realism. That's all.
>>
>> What's the purpose of this new notion of realism, which includes
>> locality? Of course, feel free to use whatever name you want for a
>> given concept. But we have already a nice, much less confusing, name
>> for this concept - locality or local realism.
>>
>> In the usual notion of realism Newton's theory is realistic. It is
>> also EPR-realistic and realistic in the sense of Bell's/my
>> understanding.
>
> You are using the term 'realism' (or 'realist') in the colloquial
> sense, whereas in the philosophy of science it has a more precise
> meaning. The concept of epistemic realism incorporates causal
> mechanisms as a necessary element in its formulation.
That's fine, and EPR's, Bell's and my definition includes causality
too.
But not locality. Locality appears only if we combine realistic
causality with SR to obtain Einstein causality (which is Einstein
locality).
> See, for instance, Bas C. van Fraassen's essay "The Charybdis of
> Realism: Epistemological Implications of Bell's Inequality", in
> _Philosophical Consequences of Quantum Theory_, University of Notre
> Dame Press, 1989.
Thanks, will be part of my future reading list.
Ilja Schmelzer
>> That's not the point. The EPR criterion of reality is not of this
>> type of "realist" which requires a material, mechanist explanation.
>> If you take the wave function as real, no problem - it would fit the
>> definition of realism. It fits it in Bohmian mechanics, which is
>> certainly a realistic theory.
>>
>> So, if you decide to throw away realism, you throw away much, much
>> more than material, mechanist explanation. Realism does not even
>> require the existence of spacetime.
>
> Exactly. As you will have seen, I state emphatically that I am a
> realist.
But "realist" in the meaning of EPR/Bell?
Note that this requires to accept the reality of causal FTL in
Aspect's experiment.
>>> However, the 'surprises' in the EPR experiment only come because
>>> the result violates our usual assumptions about physical reality,
>>> not because it obeys some extremely subtle logic.
>> It does not violate any usual assumption about reality.
> People usually assume that the photons have some definite state.
That's not the point. QM metaphysics is not the point at all.
It violates the combination of
a) usual assumption about reality and causality
b) Einstein causality
> It doesn't violate REALITY, but it most certainly does violate
> common ASSUMPTIONS about reality.
If "reality" is a meaningful scientific concept, it makes assumptions.
The notion of (classical) proposed by EPR/Bell makes assumptions.
Frank Wappler
(AFAIU, in reference to
> > > http://www2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html)
> Imagine two computers communicating at time A. They are
> then separated and their communication severed permanently.
> At time B, one of the computers is asked a question
> (not knowing what it will be in advance).
> At time C, the other computer is asked a question,
> not knowing what question was asked of the first computer
> (nor does the first know the question to be asked of the second, btw).
Allright - though I'd rather had used the indices "A" and "B"
to label these two computers, instead their or someone else's
states/clock_readings/proper_times.
> Now: given that we can ask questions about specific angles
> around a circle (we can ask anything), and given that the
> computers can use their common assumptions (agreed to at time A)
> as well as any algorithms they please to decide how to answer
> the questions, we may ask: how much agreement is logically
> possible between the answers of these two computers
> for various chosen angles? (We imagine repeating this many times
> to build up a statistical profile: just put the program in a loop.)
> The above scenario clearly incorporates every conceivable physical
> theory that postulates independent behaviour of the photons after
> separation, because I permit the computers to use _any algorithm_
> to decide their answers. And any algorithm clearly includes using
> the equations of any given theory of physics.
> [...] If you don't believe Bell's theorem
Well - I'm unable to follow the derivation of Bell's inequality
(or certain equivalent inequalities) as stated in
J. S. Bell, "Speakable and unspeakable in quantum mechanics", p. 37,
or references therein.
> try actually programming two computers as described above
Allright - let the one computer alternate answers "0" and "1",
in successive trials, and let the other computer alternate
answers "0", "0", "1" and "1" in successive trials.
(I'd assume that the trial numbers are calibrated;
at least that both are asked an equal number of questions.)
The strings of their answers (ordered by trial number, of course)
are thereby "0101010101010101 ..." and "0011001100110011 ..." .
I suppose that the following questions would be asked
(one per trial, regardless of order):
x (or not x): "This way - or the other way?"; or
y (or not y): "In this direction - or in the opposit direction?"; or
z (or not z): "This side - or that side?".
Now it would have to be determined in which of the conducted trials
the experiment had been "set up". Following the prescription about
values of "orientation_angles" as given at the referenced site,
trials are discarded (as "not set up") in which the same question
was put to the two computers, and they gave different answers.
Further, trials would have to be discarded one by one
(as "not set up") until
arccos(
Sum_{ remaining trials k }_( del_x_y_k (2 x_k y_k - 1) / ) /
Sum_{ remaining trials k }_( del_x_y_k ) ) = 2/3 Pi,
arccos(
Sum_{ remaining trials k }_( del_x_z_k (2 x_k z_k - 1) / ) /
Sum_{ remaining trials k }_( del_x_z_k ) ) = 2/3 Pi,
arccos(
Sum_{ remaining trials k }_( del_y_z_k (2 y_k z_k - 1) / ) /
Sum_{ remaining trials k }_( del_y_z_k ) ) = 2/3 Pi;
where del_x_y_k == 1 if in trial k one detector was asked
question x, and the other detector was asked question y
(with the corresponding answer values x_k and y_k),
and del_x_y_k == 0 otherwise.
(Analogous definitions for del_x_z_k and del_y_z_k.)
(Since "we imagine" to conduct many trials, there'll be sufficiently
many trials for the above conditions to be satisfied without
the Sum_{ remaining trials k }_( del_x_y_k ) becoming zero.)
> I get the feeling you are looking for a great subtlety, but
> I don't believe this is a stratospheric problem in philosophy.
> It is a very basic thing, easily visualised by any sensible person.
I'm emphasizing the procedures by which to decide whether or not
some particular experiment had been "set up", in any particular
trial, or set of trials.
That's very basic, and naturally considered by any experimenter.
(About the philosophical consequences of such considerations
I could only speculate anyways.)
The setup as hereby selected guarantees that the "angles between"
the three pairs of detector responses to the three distinct
questions are (+/-) 2/3 Pi each; and the "angles between"
same questions to both detectors is zero.
However, in order to follow the derivation of
"the famous Bell's Inequality" as suggested at the referenced site,
one would have to make additional assumptions:
In each trial in which one detector was asked question x,
and the other detector was asked question y,
and the corresponding answers were different, e.g.
"0" and "1", respectively (such trial were necessarily selected),
then one would have to _assume_ that if the questions had been
interchanged (the one detector had been asked question y, while
the other detector had been asked question y) then their answers
had been interchanged, too (to "1" and "0", respectively).
(And similar assumptions would have to be made for
the question pairs (x, z), and (y, z).)
Would your notion of "realism" imply and require to make
such assumptions?
(Apparently, they'd not be satisfied by the computer answers
that I specified above.)
Else, could you suggest other (presumably "more realistic",
and/or "local") assumptions based on which one might expect
that the described setup would have to satisfy
"the famous Bell's Inequality"?
Or else, if you wouldn't conduct the suggested selection of
trials as "set up" at all, would you assume that this (or any)
experiment were "set up" a priori, in all trials?
Thanks again, Frank W ~@) R
Daryl McCullough
>> try actually programming two computers as described above
>
>Allright - let the one computer alternate answers "0" and "1",
>in successive trials, and let the other computer alternate
>answers "0", "0", "1" and "1" in successive trials.
>(I'd assume that the trial numbers are calibrated;
>at least that both are asked an equal number of questions.)
>
>The strings of their answers (ordered by trial number, of course)
>are thereby "0101010101010101 ..." and "0011001100110011 ..." .
Let me be a little bit more explicit about Ron's request.
One "trial" consists of the following steps:
1. Allow the computers to exchange information to decide
on their strategy for answering questions.
2. Sever the communication lines and move the computers
into different rooms.
3. In each room, a user types in one of three possible
angles: 0 degrees, 120 degrees, or 240 degrees.
4. Each computer outputs either 0 or 1 (computed using
whatever information is available---but no communicating
with the other computer).
As these trials are repeated again and again, the following
statistical correlations hold:
A. For each computer, whatever the input, the output
is 0 half the time and 1 half the time.
B. If the inputs to each computer are the same during
one trial, then the outputs are always different.
C. If the inputs are different, then the outputs
are the same 3/4 of the time, and different 1/4
of the time.
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
Ron House
Then your computers fail Bell's inequality. Let's say I set detector A
to 0deg., and detector B to 10deg. Cos^2 theta, without resorting to a
calculator, will be a number very close to 1, yet your result string
will give agreement only 50% of the time. Before you doctor it to fix
that problem, remember that next time I might pick some other angle.
> I suppose that the following questions would be asked
> (one per trial, regardless of order):
>
> x (or not x): "This way - or the other way?"; or
> y (or not y): "In this direction - or in the opposit direction?"; or
> z (or not z): "This side - or that side?".
>
> Now it would have to be determined in which of the conducted trials
> the experiment had been "set up". Following the prescription about
> values of "orientation_angles" as given at the referenced site,
> trials are discarded (as "not set up") in which the same question
> was put to the two computers, and they gave different answers.
You'll have to explaint that one better; I can find no sensible
interpretation for your remark. In physics we don't get to reject the
observable results because they don't fit our theory (or at least, we
shouldn't do). If the experiment is correctly set up, we have to accept
whatever results it gives us.
>...
> I'm emphasizing the procedures by which to decide whether or not
> some particular experiment had been "set up", in any particular
> trial, or set of trials.
> That's very basic, and naturally considered by any experimenter.
> (About the philosophical consequences of such considerations
> I could only speculate anyways.)
But it is not determined by the _results_! It is determined by
questions, suitable to the experiment, about the fairness of the
apparatus, whether it is operating correctly, etc. As I understand your
comment above, you want to reject results simply because they don't fit
a theoretically predicted pattern. That can never be valid, that's just
fudging results.
>...
Furthermore, in the abstract scenario I have described, the question of
experimental setup does not arise. We are discussing whether any
algorithm can violate Bell's inequality. Therefore we use an abstract
setup (two computers) to which questions of correctly working apparatus
cannot arise. I correctly 'measure' _every_ result from your computers,
simply by looking at your printout.
Ron House
>
> Frank says...
>
> >> try actually programming two computers as described above
> >
> >Allright - let the one computer alternate answers "0" and "1",
> >in successive trials, and let the other computer alternate
> >answers "0", "0", "1" and "1" in successive trials.
> >(I'd assume that the trial numbers are calibrated;
> >at least that both are asked an equal number of questions.)
> >
> >The strings of their answers (ordered by trial number, of course)
> >are thereby "0101010101010101 ..." and "0011001100110011 ..." .
>
>
> One "trial" consists of the following steps:
>
> 1. Allow the computers to exchange information to decide
> on their strategy for answering questions.
>
> 2. Sever the communication lines and move the computers
> into different rooms.
>
> 3. In each room, a user types in one of three possible
> angles: 0 degrees, 120 degrees, or 240 degrees.
>
> 4. Each computer outputs either 0 or 1 (computed using
> whatever information is available---but no communicating
> with the other computer).
>
> As these trials are repeated again and again, the following
> statistical correlations hold:
>
> A. For each computer, whatever the input, the output
> is 0 half the time and 1 half the time.
>
> B. If the inputs to each computer are the same during
> one trial, then the outputs are always different.
>
> C. If the inputs are different, then the outputs
> are the same 3/4 of the time, and different 1/4
> of the time.
>
> Daryl McCullough
> CoGenTex, Inc.
> Ithaca, NY
That's a nice simplification of my challenge. In fact, any angle would
do (with the appropriate frequencies computed), but your choices bring
the problem into nice focus.
Ron House
>
> Ron House <ho...@usq.edu.au> writes:
> >> That's not the point. The EPR criterion of reality is not of this
> >> type of "realist" which requires a material, mechanist explanation.
> >> If you take the wave function as real, no problem - it would fit the
> >> definition of realism. It fits it in Bohmian mechanics, which is
> >> certainly a realistic theory.
> >>
> >> So, if you decide to throw away realism, you throw away much, much
> >> more than material, mechanist explanation. Realism does not even
> >> require the existence of spacetime.
> >
> > Exactly. As you will have seen, I state emphatically that I am a
> > realist.
>
> But "realist" in the meaning of EPR/Bell?
>
> Note that this requires to accept the reality of causal FTL in
> Aspect's experiment.
If I choose to use the convenient summary of certain facts about the
wave function as are contained in the phrase "two photons", then I am
forced to also summarise some other information in the wave function
with a remark like "they communicated faster than light". But if (as I
indeed do) I regard the one and only universal wave function as the only
reality, then what it tells me about my measurements (i.e. probabilities
of certain outcomes) does not require me to assert anything about
communication FTL, as in that case I am not speaking with regard to the
simplifying phrase. Indeed, I can consistently regard this as a case in
which the phrase "two photons" does not describe reality.
> >>> However, the 'surprises' in the EPR experiment only come because
> >>> the result violates our usual assumptions about physical reality,
> >>> not because it obeys some extremely subtle logic.
>
> >> It does not violate any usual assumption about reality.
>
> > People usually assume that the photons have some definite state.
>
> That's not the point. QM metaphysics is not the point at all.
>
> It violates the combination of
>
> a) usual assumption about reality and causality
> b) Einstein causality
Given the way of speaking I describe earlier, yes, we have this choice
of which one we reject. As both of these correspond to what I think are
most people's usual assumptions about reality, you seem to be saying you
agree with me, but that I have missed the point. Why?
> > It doesn't violate REALITY, but it most certainly does violate
> > common ASSUMPTIONS about reality.
>
> If "reality" is a meaningful scientific concept, it makes assumptions.
> The notion of (classical) proposed by EPR/Bell makes assumptions.
This is not a comment impinging on my previous statement. "Reality" is
what is actually out there (whatever it is, whatever surprises it has in
store for us). "Assumptions about reality" are beliefs in minds. I can
consistently assert that something violates one but not the other.
Ilja Schmelzer
>>> Exactly. As you will have seen, I state emphatically that I am a
>>> realist.
>>
>> But "realist" in the meaning of EPR/Bell?
>>
>> Note that this requires to accept the reality of causal FTL in
>> Aspect's experiment.
>
> If I choose to use the convenient summary of certain facts about the
> wave function as are contained in the phrase "two photons", then I am
> forced to also summarise some other information in the wave function
> with a remark like "they communicated faster than light". But if (as I
> indeed do) I regard the one and only universal wave function as the only
> reality, then what it tells me about my measurements (i.e. probabilities
> of certain outcomes) does not require me to assert anything about
> communication FTL, as in that case I am not speaking with regard to the
> simplifying phrase. Indeed, I can consistently regard this as a case in
> which the phrase "two photons" does not describe reality.
That's certainly not the point.
Assume one experimenter located on Earth, the other on Mars. The
experimenters, their decisions what to measure, are clearly local.
The results of their observations too.
If you are EPR realist, you have to accept that the information about
the decision what to measure on Mars was used to define the
measurement result on Earth, or reverse.
It doesn't matter at all what you think about photons. It matters
what you think about the decisions of the experimenters, the observed
results, and the causal influences between them.
>> That's not the point. QM metaphysics is not the point at all.
>>
>> It violates the combination of
>>
>> a) usual assumption about reality and causality
>> b) Einstein causality
>
> Given the way of speaking I describe earlier, yes, we have this choice
> of which one we reject. As both of these correspond to what I think are
> most people's usual assumptions about reality, you seem to be saying you
> agree with me, but that I have missed the point. Why?
Sorry, Einstein causality is a particular physical theory, not a
general, fundamental assumption like realism. Scientists have been
realists in Newtons time, without believing into Einstein causality.
>>> It doesn't violate REALITY, but it most certainly does violate
>>> common ASSUMPTIONS about reality.
>> If "reality" is a meaningful scientific concept, it makes assumptions.
>> The notion of (classical) proposed by EPR/Bell makes assumptions.
> This is not a comment impinging on my previous statement. "Reality"
> is what is actually out there (whatever it is, whatever surprises it
> has in store for us).
In this case, you use "reality" as a name for the stuff outside,
that's all. Its not a scientific concept, but a convention. The
solipsist may name some part of his own thoughts "reality" too.
I use "realism" as a scientific concept. You can be realist or can
reject realism. If you are a realist, you prefer realistic theories
in comparison with purely phenomenological theories and believe that
something like a realistic theory of everything is at least in
principle possible.
Ilja Schmelzer
>> [...] If you don't believe Bell's theorem
>
> Well - I'm unable to follow the derivation of Bell's inequality
> (or certain equivalent inequalities) as stated in
> J. S. Bell, "Speakable and unspeakable in quantum mechanics", p. 37,
> or references therein.
Its really simple.
You need the "EPR part": if there is no communication between two
rooms, and if measuring the same direction gives always the reverse
result, the values are predefined before the experiments happen. This
is the part where we have to discuss realism and so on. But once we
have accepted (or decided to accept as an assumption of the theorem)
the remaining part is really simple
You have three cards, l,m,r, each red or black. I tell you three
claims: l != m, m != r, l != r. Obviously, at least one of them must
be wrong. You can test one of them opening two cards. Once one of
them must be wrong, and your choice is free, independent, you have a
1/3 chance to detect a wrong one. In reality, you have only a 1/4
chance. Wonder.
Daryl McCullough
>
>Daryl McCullough wrote:
>> As these trials are repeated again and again, the following
>> statistical correlations hold:
>>
>> A. For each computer, whatever the input, the output
>> is 0 half the time and 1 half the time.
>>
>> B. If the inputs to each computer are the same during
>> one trial, then the outputs are always different.
>>
>> C. If the inputs are different, then the outputs
>> are the same 3/4 of the time, and different 1/4
>> of the time.
>
>That's a nice simplification of my challenge. In fact, any angle would
>do (with the appropriate frequencies computed), but your choices bring
>the problem into nice focus.
Actually, my challenge has a simple solution: The state
of one computer is represented by a triple (x,y,z), where
x,y, and z are either 0 or 1. The state of the other computer
is the complement: (1-x,1-y,1-z). If the input is 0, output
x, if the input is 120 output y, if the input is 240 output z.
Now, all the computer has to do is to choose states
according to the following probabilities:
State Probability
(0,0,1) 3/16
(0,1,0) 3/16
(0,1,1) 3/16
(1,0,0) 3/16
(1,0,1) 3/16
(1,1,0) 3/16
(0,0,0) -1/16
(1,1,1) -1/16
Those negative probabilities might be a little tricky to
implement, though.
mediaglyphic
the past and that there "states" were determined then?
"Ilja Schmelzer" <schm...@wias-berlin.de> wrote in message
news:i3g1z0i...@wias-berlin.de...
Ron House
>
> Ron says...
> >
> >That's a nice simplification of my challenge. In fact, any angle would
> >do (with the appropriate frequencies computed), but your choices bring
> >the problem into nice focus.
>
> Actually, my challenge has a simple solution: The state
> of one computer is represented by a triple (x,y,z), where
> x,y, and z are either 0 or 1. The state of the other computer
> is the complement: (1-x,1-y,1-z). If the input is 0, output
> x, if the input is 120 output y, if the input is 240 output z.
>
> Now, all the computer has to do is to choose states
> according to the following probabilities:
>
> State Probability
> (0,0,1) 3/16
> (0,1,0) 3/16
> (0,1,1) 3/16
> (1,0,0) 3/16
> (1,0,1) 3/16
> (1,1,0) 3/16
> (0,0,0) -1/16
> (1,1,1) -1/16
>
> Those negative probabilities might be a little tricky to
> implement, though.
That's beautiful! Is a development of that solution on the net anywhere?
Ron House
>
> Ron House <ho...@usq.edu.au> writes:
> >>> Exactly. As you will have seen, I state emphatically that I am a
> >>> realist.
> >>
> >> But "realist" in the meaning of EPR/Bell?
> >>
> >> Note that this requires to accept the reality of causal FTL in
> >> Aspect's experiment.
> >
> > If I choose to use the convenient summary of certain facts about the
> > wave function as are contained in the phrase "two photons", then I am
> > forced to also summarise some other information in the wave function
> > with a remark like "they communicated faster than light". But if (as I
> > indeed do) I regard the one and only universal wave function as the only
> > reality, then what it tells me about my measurements (i.e. probabilities
> > of certain outcomes) does not require me to assert anything about
> > communication FTL, as in that case I am not speaking with regard to the
> > simplifying phrase. Indeed, I can consistently regard this as a case in
> > which the phrase "two photons" does not describe reality.
>
> That's certainly not the point.
If I can do it (which I can) it certainly is the point. You are
insisting in believing in objects located in places, whereas that is
just a convenient simplification of a more general theory. I choose to
use the more general theory whilst you choose to use the simplification
in a case where it has deficiencies.
> Assume one experimenter located on Earth, the other on Mars. The
> experimenters, their decisions what to measure, are clearly local.
> The results of their observations too.
>
> If you are EPR realist, you have to accept that the information about
> the decision what to measure on Mars was used to define the
> measurement result on Earth, or reverse.
>
> It doesn't matter at all what you think about photons. It matters
> what you think about the decisions of the experimenters, the observed
> results, and the causal influences between them.
I perfectly well see your point. Now you have to see my point that these
consequences only follow from making an inadequate simplification. To
make it clearer: you are talking about "causal influences" between two
entities. In the universal wave function there are no such entities. If
you think there are, then answer this one: I can schedule my
measurements on A and B so close in time that another observer moviing
at speed will see the time order of these observations reversed. So did
the "influence" go from A to B or B to A?
> Sorry, Einstein causality is a particular physical theory, not a
> general, fundamental assumption like realism. Scientists have been
> realists in Newtons time, without believing into Einstein causality.
When I meantioned the "usual assumptions" I was speaking informally, as
any reasonable reader would have seen, and by the "usual assumptions" I
meant those we make today. This remark is as pointless as if, when a
person mentions the usual items sold in a food store, someone objects
that in Julius Caesar's Rome, these things weren't usual at all.
> >>> It doesn't violate REALITY, but it most certainly does violate
> >>> common ASSUMPTIONS about reality.
>
> >> If "reality" is a meaningful scientific concept, it makes assumptions.
> >> The notion of (classical) proposed by EPR/Bell makes assumptions.
>
> > This is not a comment impinging on my previous statement. "Reality"
> > is what is actually out there (whatever it is, whatever surprises it
> > has in store for us).
>
> In this case, you use "reality" as a name for the stuff outside,
> that's all. Its not a scientific concept, but a convention. The
> solipsist may name some part of his own thoughts "reality" too.
Reality is not a concept at all. The word "reality" is a concept (maybe
may different ones for different people) but we do not get a choice in
what reality actually is. It is what it is.
> I use "realism" as a scientific concept. You can be realist or can
> reject realism. If you are a realist, you prefer realistic theories
> in comparison with purely phenomenological theories and believe that
> something like a realistic theory of everything is at least in
> principle possible.
I have a realistic theory: "The wave function is real." There you go.
Robert Little
quantum entangled particles synchronized? Without even knowing the
equations, the fact that the synch is occurring at speeds greater than the
speed of light must mean that some of the variables will undoubtedly be
infinite. Is this correct?
--
Robert C. Little
robert...@earthlink.net
"Unless it eventuates in compassion, wisdom is worthless."
From "The Religions of Man", Huston Smith, p. 136
{In his once sentence summarization of Mahayana Buddhism he inadvertently
answered our universal question of "Why are we here?"}
"Ron House" <ho...@usq.edu.au> wrote in message
news:397BD1D0...@usq.edu.au...
Gordon D. Pusch
> Has anyone calculated the minimum amount of energy required to keep two
> quantum entangled particles synchronized?
Zero. According to Quantum Theory, there is no ``force'' _keeping_ the
particles ``in synch;'' they are merely always _OBSERVED_ to be ``in synch.''
However, no ``causal mechanism'' is thought to be involved in this correlation.
The entanglement-correlations are what so-called ``Philosophers of Science''
sometimes refer to as a ``fact-like'' rather than a ``law-like'' property of
nature: nothing ``makes'' it happen, there is no ``communication'' involved ---
it merely _is_.
> Without even knowing the equations, the fact that the synch is occurring
> at speeds greater than the speed of light must mean that some of the
> variables will undoubtedly be infinite. Is this correct?
No --- According to Quantum Theory, this is NOT correct.
You are suffering from what the standard ``Copenhagen Interpretation'' of
Quantum Theory considers to be a serious misconception: that there is some
_causal mechanism_ ``forcing'' the correlations into being. According to
Orthodox Quantum Theory, NO SUCH CAUSAL MECHANISM IS SUPPOSED TO EXIST ---
the correlations of ``entanglement'' are merely the consequences of the
conservation of linear and angular momentum, as reinterpreted according
to Quantum Measurement-Theory.
(I make no claim to understand how this can be --- and in fact many claim
that =NO= human being can =EVER= understand how this can be, because of the
mental blinders imposed by our existence as macroscopic beings; Nils Bohr
liked to say that ``If you think you understand Quantum Theory, then you
_DON'T_ understand Quantum Theory...'' :-/ Personally, I'd _prefer_ a
``local realistic'' theory over Quantum Mechanics --- but unfortunately,
they don't appear to describe the Universe we live in... :-(
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
mediaglyphic
what is the evidence that the two particles don't receive their polarization
at birth?
wouldn't that explain the results here?
"Gordon D. Pusch" <gdp...@NO.xnet.SPAM.com> wrote in message
news:m17la8h...@pusch.integratedgenomics.com...
mediaglyphic
other change also? or are the particles out of synch after such an event?
Ron House
>
> ok another silly question,
>
> what is the evidence that the two particles
> don't receive their polarization at birth?
> wouldn't that explain the results here?
No it would not, and this has been verified by experiment. Explaining
why this is so was the point of my post last week. To briefly
recapitulate, no matter what _predetermined_ answers to measurements the
particles cooked up at birth, they could never simulate the statistical
values measured in actual experiments. It is impossible.
mediaglyphic
thanks again for your patience and kindness in responding. sorry if i am
rehasing the same things again and again.
but here is my understanding
both photons have the same polarization at birth but we don;t know what the
polarizations are until we measure them. if eons afterwards when the two
photons are galaxies apart we measure one, the results show that
statistically the value of the second depends on the how we measure the
first. of course we can never duplicate this experiment with the same
photons twice measuring them differently to "prove" that this is so.
so how do we know that the photons pair didn't have a preordained
polarization value at birth? if you have explained this in detail before i
didn't get it (sorry).
i just finished reading a non quant book that deals with this subject
(rothman and sudarshan's "Doubt and Certainty") and it seems to say that the
values found in aspect's experiment indicate that the above couldn't be
true, or if it is true it implies a negative probability. I believe these
folks, and everyone in this newsgroup, i just don't understand why!!
perhaps i need to understand hilbert spaces et al (which being an engineer
and mathmetician i should be able to get upon study, it will take some time
though, nothing important comes easy i guess(
"Ron House" <ho...@usq.edu.au> wrote in message
news:397F9992...@usq.edu.au...
Frank Wappler
> One "trial" consists of the following steps:
> 1. Allow the computers to exchange information to decide
> on their strategy for answering questions.
> 2. Sever the communication lines and move the computers
> into different rooms.
> 3. In each room, a user types in one of three possible
> angles: 0 degrees, 120 degrees, or 240 degrees.
That's typing in one of three distinct (strings of) ASCII characters.
> 4. Each computer outputs either 0 or 1 (computed using
> whatever information is available---but no communicating
> with the other computer).
That's putting out one of two distinct ASCII characters.
> As these trials are repeated again and again, the following
> statistical correlations hold:
> A. For each computer, whatever the input, the output
> is 0 half the time and 1 half the time.
Therefore, if there has been collected some set of trials
in which the outputs were observed in different ratios
(and/or an odd number of trials had been observed),
then, as setup procedure, individual trials would be discarded
(in some particular order) until the remaining set of
selected trials satisfies your specification.
Given sufficiently many trials and a suitable distribution
of outputs, the remaining set is not empty.
> B. If the inputs to each computer are the same during
> one trial, then the outputs are always different.
Therefore, if the values in the set of trials that has been
selected/set_up in step A did not satisfy this correlation
(and they rarely would, a priori),
then, as further setup procedure, individual trials would be
discarded (in some particular order) until the remaining set
of selected trials satisfies your specification.
Given sufficiently many trials and a suitable distribution
of outputs, the remaining set is not empty.
> C. If the inputs are different, then the outputs
> are the same 3/4 of the time, and different 1/4
> of the time.
Therefore, if the values in the set of trials that has been
selected/set_up in steps A and B did not satisfy this correlation
(and they rarely would, a priori),
then, as further setup procedure, individual trials would be
discarded (in some particular order) until the remaining set
of selected trials satisfies your specification.
Given sufficiently many trials and a suitable distribution
of outputs, the remaining set is not empty.
Note that your setup prescriptions are such that it cannot
be determined whether any particular set of trials had been
set up _before_ the inputs and outputs are all available
to conduct the setup procedure on them.
A set of trials that would have satisfied your setup prescription
is for example:
trial a: input "0 degrees", output A: "0", output B: "1",
trial b: input "0 degrees", output A: "1", output B: "0",
trial c: input "120 degrees", output A: "0", output B: "0",
trial d: input "120 degrees", output A: "0", output B: "1",
trial e: input "120 degrees", output A: "0", output B: "1",
trial f: input "120 degrees", output A: "1", output B: "0",
trial g: input "240 degrees", output A: "1", output B: "1",
trial h: input "240 degrees", output A: "1", output B: "0",
trial j: input "240 degrees", output A: "1", output B: "0",
trial k: input "240 degrees", output A: "0", output B: "1".
The trial indices "a", "b" etc. correlate input and output
values in each particular trial, but do not necessarily prescribe
the order in which those trials were observed.
Of course this set would in general have been selected
by the described setup procedure, from some larger set
which might have also observed for instance
trial r: input "0 degrees", output A: "0", output B: "0".
Note that in selecting the trials that had been set up according
to your prescription, the input and outputs in those trials
(as correlated through the trial index) had to be given together.
Now, please explicitly state the further assumptions (if any)
that would allow you to derive "the famous Bell's inequality"
as suggested by
[
. Ron House wrote:
. .
http://www2.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html)
]
(or some eqivalent), and show or reference the derivation.
Frank Wappler
> Frank Wappler wrote:
> > I suppose that the following questions would be asked
> > (one per trial, regardless of order):
> > x (or not x): "This way - or the other way?"; or
> > y (or not y): "In this direction - or in the opposit direction?"; or
> > z (or not z): "This side - or that side?".
> > Now it would have to be determined in which of the conducted trials
> > the experiment had been "set up".
> In physics we don't get to reject the observable results because
> they don't fit our theory (or at least, we shouldn't do).
> If the experiment is correctly set up, we have to accept
> whatever results it gives us.
Certainly. However, if the setup has a reproducible and nontrivial
description, then it is not known a priori _whether_ the experiment
had been set up correctly/in compliance with that description,
in any particular trial. If the trial _has been_ determined to be
correct, then the experimental procedure proceeds to be applied
to the observations collected in that trial, and results of this
trial may be derived accordingly.
If the trial _has been_ determined to be incorrect, then this trial
is discarded and no further result obtained by the particular
experimental procedure under consideration
(thought the trial may still satisfy some other setup prescriptions
and may remain useful under different experimental procedures).
> > Allright - let the one computer alternate answers "0" and "1",
> > in successive trials, and let the other computer alternate
> > answers "0", "0", "1" and "1" in successive trials.
> > (I'd assume that the trial numbers are calibrated;
> > at least that both are asked an equal number of questions.)
> > The strings of their answers (ordered by trial number, of course)
> > are thereby "0101010101010101 ..." and "0011001100110011 ..." .
> Then your computers fail Bell's inequality.
That's my point: I don't understand that all "local realistic"
descriptions of the EPR/Aspect/Gisin experiment would have to
imply that their results satisfy Bell's inequality.
> Let's say I set detector A to 0deg.
Wrt. what? Measured how?
> and detector B to 10deg.
Wrt. what? Measured how?
Perhaps you prescribe to "set up" two particular two-valued axes of
detectors A and B wrt. each other at an orientation_angle of 10deg,
e.g. the axes/coordinate systems { x, not x }_A, and
{ y, not y }_B. In order to set up this particular experiment,
I'd use Malus' definition of orientation_angle and consider and
keep any nonempty set of trials { k } for which
> > arccos(
> > Sum_{ remaining trials k }_( del_x_y_k (2 x_k y_k - 1) ) /
> > Sum_{ remaining trials k }_( del_x_y_k ) )
= 2 * 10deg,
IOW
arccos( sqrt(
Sum_{ remaining trials k }_( del_x_y_k x_k y_k ) /
Sum_{ remaining trials k }_( del_x_y_k ) ) )
= 10deg
> > where del_x_y_k == 1 if in trial k one detector [A] was asked
> > question x, and the other detector [B] was asked question y
> > (with the corresponding answer values x_k and y_k),
> > and del_x_y_k == 0 otherwise.
Any remaining trials are discarded as "not set up properly",
according to your prescription.
> will be a number very close to 1
If 10deg == Pi/18, sure.
> yet your result string will give agreement only 50% of the time
That's in _all_ trials, before having selected/set_up any more
specific setup (as you described and I'd measure by pairwise
oriantation_angle).
> Before you doctor it to fix that problem
> remember that next time I might pick some other angle.
There's no problem whatsoever, unless you insist that
any particular of your picks for a setup description
were ("somehow, magically") satisfied a priori.
They rarely are (as any experimentalist can attest) -
instead, the corresponding correct trials have to be
identified/selected/set_up.
> you want to reject results simply because they don't fit
> a theoretically predicted pattern.
Not at all - I'd merely like to select the setup that you prescribed.
If you like to define and measure "detector B set to 10deg" not by
Malus' procedure (wrt. detector A) but by some other procedure
(as long as it is an unambiguous reproducible measurement procedure)
then please state your suggestion so that everyone can consider
the corresponding thought experiment, and even analyze
experimental observations through that procedure.
> Furthermore, in the abstract scenario I have described,
> the question of experimental setup does not arise.
I agree that the abstract scenario you described in the preceding
post itself doesn't specify or mention that critical aspect of
the experimental setup yet.
However, you haven't derived any Bell inequality corresponding
to (some specific instances of) your scenario, nor given any
QM descriptions for comparison. If you get to those considerations
I expect that the question of experimental setup _will_ arise
(and I'll be happy to try and point out where. Having been asked
> > > try actually programming two computers as described above
I considered particular instances already with emphasis on that
question; as quoted above, and also (perhaps more basically):
> > trials are discarded (as "not set up") in which the same question
> > was put to the two computers, and they gave different answers.
> We are discussing whether any algorithm can violate Bell's
> inequality. Therefore we use an abstract setup (two computers)
> to which questions of correctly working apparatus cannot arise.
Would you not object if the two detectors gave unequal answers
to "the same" question (at least in some trials)?
Could you derive Bell's inequality under such conditions?
Best regards, Frank W ~@) R
Frank Wappler
> Frank Wappler wrote:
> > Well - I'm unable to follow the derivation of Bell's inequality
> > (or certain equivalent inequalities) as stated in
> > J. S. Bell, "Speakable and unspeakable in quantum mechanics",
> > p. 37, or references therein.
> It's really simple.
> You need the "EPR part": if there is no communication between
> two rooms, and if measuring the same direction gives always
> the reverse result,
How would be determined whether "the same direction"
had been measured, in any particular trial or set of trials?
> the values are predefined before the experiments happen.
Surely one may define how to measure and select "direction"
from specific observed values before the experiments happen.
Surely the specific individual values in any one experimental trial
are _not_ known before that experimental trial happens.
> This is the part where we have to discuss realism and so on.
Apparently.
> But once we have accepted (or decided to accept as an
> assumption of the theorem) the remaining part is really simple
Please identify that assumption and clarify the remaining part
in the context of derivation of Bell's inequality
(or certain equivalent inequalities) as stated in J. S. Bell,
"Speakable and unspeakable in quantum mechanics", p. 37,
or references therein.
Thanks again, Frank W ~@) R
p.s.
> You have three cards, l,m,r, each red or black.
> I tell you three claims: l != m, m != r, l != r.
> Obviously, at least one of them must be wrong.
> You can test one of them opening two cards. Once one of
> them must be wrong, and your choice is free, independent,
> you have a 1/3 chance to detect a wrong one. In reality,
> you have only a 1/4 chance. Wonder.
Wonder indeed. Depending on the distribution from which
the cards are drawn, I'd figure my average/chance to
open an equal pair at 1/3 or better.
This seems to be a part where we'd have to discuss
realism and so on, too.
Ken H. Seto
wrote:
>Ron,
>
>thanks again for your patience and kindness in responding. sorry if i am
>rehasing the same things again and again.
>
>but here is my understanding
>
>both photons have the same polarization at birth but we don;t know what the
>polarizations are until we measure them. if eons afterwards when the two
>photons are galaxies apart we measure one, the results show that
>statistically the value of the second depends on the how we measure the
>first. of course we can never duplicate this experiment with the same
>photons twice measuring them differently to "prove" that this is so.
>
>so how do we know that the photons pair didn't have a preordained
>polarization value at birth? if you have explained this in detail before i
>didn't get it (sorry).
>
>i just finished reading a non quant book that deals with this subject
>(rothman and sudarshan's "Doubt and Certainty") and it seems to say that the
>values found in aspect's experiment indicate that the above couldn't be
>true, or if it is true it implies a negative probability. I believe these
>folks, and everyone in this newsgroup, i just don't understand why!!
There is absolutely no FTL correlation between the photons. The extra
correlation observed by Aspect's experiment was due completely to the
the switching between the horizontal and vertical polarizers at a rate
of 200 million time per second. The switching chopped some photons
into pieces and thus gave the observed higher correlation. This can be
tested by determining the correlation rates at the various swtitching
rates. If I am right the correlation rates will increase as the
switching rates are increased.
Ken Seto
Daryl McCullough
>A set of trials that would have satisfied your setup prescription
>is for example:
>
>trial a: input "0 degrees", output A: "0", output B: "1",
No. Each trial consists of *two* inputs---one to each computer.
Daryl McCullough
>
>Daryl McCullough wrote:
>
>> One "trial" consists of the following steps:
>
>> 1. Allow the computers to exchange information to decide
>> on their strategy for answering questions.
>
>> 2. Sever the communication lines and move the computers
>> into different rooms.
>
>> 3. In each room, a user types in one of three possible
>> angles: 0 degrees, 120 degrees, or 240 degrees.
>
>That's typing in one of three distinct (strings of) ASCII characters.
Yes, it is.
>> 4. Each computer outputs either 0 or 1 (computed using
>> whatever information is available---but no communicating
>> with the other computer).
>
>That's putting out one of two distinct ASCII characters.
Yes, it is.
>> As these trials are repeated again and again, the following
>> statistical correlations hold:
>
>> A. For each computer, whatever the input, the output
>> is 0 half the time and 1 half the time.
>
>Therefore, if there has been collected some set of trials
>in which the outputs were observed in different ratios
>(and/or an odd number of trials had been observed),
>then, as setup procedure, individual trials would be discarded
>(in some particular order) until the remaining set of
>selected trials satisfies your specification.
What???? What are you talking about? You aren't allowed
to do that. I specified the procedure---you program your
computers, let them exchange initial information, then
separate them to allow isolated users to type in their
inputs. Then you take whatever output the computer produces.
You repeat this procedure many times to get statistics
on the correlations among the two inputs and two outputs.
You aren't allowed to throw away *any* trials.
mediaglyphic
"Ken H. Seto" <ken...@erinet.com> wrote in message
news:3980a4de$0$62225$53a6...@news.erinet.com...
Jim Heckman
"mediaglyphic" <pa...@deezel.com> wrote:
> Ron,
>
> thanks again for your patience and kindness in responding. sorry if i
> am rehasing the same things again and again.
Yes, you are. :-/ You *really* need to study the math behind this
stuff, which you should be capable of understanding if you truly are an
engineer and mathematician. Bell's Inequality is *not* that hard to
grok, mathematically. (Philosophically, obviously, is another matter.)
> but here is my understanding
>
> both photons have the same polarization at birth but we don;t know
> what the polarizations are until we measure them.
You keep throwing out words here that can be interpreted in different
ways. You really need to study the rigorous meanings behind what you
seem to think of as "same", "birth", "measure", ...
> if eons afterwards when the two photons are galaxies apart we measure
> one, the results show that statistically the value of the second
> depends on the how we measure the first.
Yes! You've summed it up nicely! But don't get overly misled by "first"
and "second", although that's indeed the point that many people seem to
get hung up on (IMHO). I prefer to think of them as "one" and the
"other" -- remember that if the measurements are separated by a
space-like interval, different observers will disagree on which is
"first" and which is "second"...
> of course we can never duplicate this experiment with the same
> photons twice measuring them differently to "prove" that this is so.
No, but we can perform lots of experiments with different pairs of
photons and compare the results.
> so how do we know that the photons pair didn't have a preordained
> polarization value at birth? if you have explained this in detail
> before i didn't get it (sorry).
Here's where you need to look at the math behind Bell's Inequality. I
don't know how to say it any more plainly than that, under very general
assumptions of "determinacy", "locality" (technical terms again), and
the ability of experimenters to make non-predetermined choices of what
observables to measure (which some people equate with 'free will'),
Bell showed that *no* assignment of "preordained polarization value at
birth" could be made *mathematically* consistent with the results
predicted by QM -- results that were subsequently demonstrated by
Aspect-type experiments.
> i just finished reading a non quant book that deals with this subject
> (rothman and sudarshan's "Doubt and Certainty") and it seems to say
> that the values found in aspect's experiment indicate that the above
> couldn't be true, or if it is true it implies a negative
> probability. I believe these folks, and everyone in this newsgroup, i
> just don't understand why!!
>
> perhaps i need to understand hilbert spaces et al (which being an
> engineer and mathmetician i should be able to get upon study, it will
> take some time though, nothing important comes easy i guess(
Actually, you don't need to know anything about Hilbert spaces et al to
grasp the basic point behind Bell's Inequality. However, such spaces,
together with the Postulates of QM, will give you a specific model of
physics in which you can make definite predictions about the results of
actual experiments, which will violate Bell's Inequality. This is
important, because when you see how general Bell's assumptions are,
it's not immediately apparent (at least it wasn't to me) that it's even
*possible* to formulate such models and have them be mathematically
consistent.
--
~~ Jim Heckman ~~
-- "As I understand it, your actions have ensured that you will never
see Daniel again." -- Larissa, a witch-woman of the Lowlands.
-- "*Everything* is mutable." -- Destruction of the Endless
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