EPR results equal the Fully Deterministic case

[Hans de Vries]

.

The entanglement case and the fully deterministic case produce
identical results (yes):

The entanglement dictates 100% correlation at equal detector
angles (a-b=0) as a result of the cos² Malus law. In multi
photon GHZ type experiments, with 3, 4 or more entangled
photons, this means that if you know the outcome of one
measurement then you know them all.

And that's of course the same for the fully deterministic case.



There is a difference though. To be more exact:
In an N photon experiment with equal detector settings there are:

- N random local processes in case of the Bell Inequality calculations.
- 1 random global process in case of N entangled photons.
- 0 random processes in the fully deterministic case.

The EPR tests do support both the entangled case and the fully
deterministic case. The fully deterministic case is proved if the A
photon is detected before the B photon is even emitted.
If the correlation is still 100% then this means that the results of
the B measurement is fully deterministic over the entire path from
PDC to detector.

All EPR experiments with PDC's test on the fully deterministic case
when viewed from the appropriate SR reference frame. The B photon
is emitted a long time (~5 ns) after the A photon in the PDC.
This means that there are always reference frames in which the
A photon is detected before the B photon is even emitted.

Special Relativity states that the laws of physics should be the same
in all reference frames.



It should not be that hard to device an experiment were the A photon
is detected before the emission of the B photon in all reference frames.
If B is emitted after any "collapse of the wave function" "projection"
"application of born's rule" or however you want to call it then this
would prove that the underlying physics of Quantum Mechanics could
be fully deterministic, at least for the spin type measurements.

The "hidden variables" would predetermine the outcome of the
measurement in the fully deterministic case. The stochastic nature
of QM would be due to a random spread in the HV's but not to
an a priory non-determinism of QM. No non-locality or FTL action
on a distance would be needed.

If the laws of physics are the same in all reference frames then
the current EPR experiments already support such a full determinism
for spin related experiments. That is, if there aren't any of these
loopholes anymore :^)



Regards, Hans.

 

[DrChinese]

You talk about the 100% correlated case. But the problem seeps in when you talk about the entire function across multiple angles, specifically comparing to [tex]cos^2\theta[/tex]. A lot harder to make those match.

Also, I am not sure we share the same definition of deterministic. Do you mean "pre-determined"? As in, cause precedes effect? If so, you come back to the idea that you could have measured the A particle at other angles (they are determined independent of measurement) - and this is "prohibited" by Bell's Theorem.

 

[Hans de Vries]

You talk about the 100% correlated case. But the problem seeps in when you talk about the entire function across multiple angles, specifically comparing to [tex]cos^2\theta[/tex]. A lot harder to make those match.

It's still 100% according to QM for entangled particles. If we set the
polarizers (Wollaston prisms) to an arbitrary but equal angle at both
A and B then there should be 100% correlation.

(I neglect here the inherent 90 degrees difference between the A and B
output from the PDC. it's just a fixed constant)

This means that if A is measured we know which way B will choose
through the Wollaston prism with 100% certainty. The A photon is
emitted a little bit earlier since the down conversion is a two step
process.

Also, I am not sure we share the same definition of deterministic. Do you mean "pre-determined"? As in, cause precedes effect? If so, you come back to the idea that you could have measured the A particle at other angles (they are determined independent of measurement) - and this is "prohibited" by Bell's Theorem.

(The text below has grown to what I understand to be the
whole EPR issue)

The polarization angle (contrary to the electron spin components) is
generally not considered to be a quantum mechanical parameter.
If you have a light beam with it's polarization lined up with the horizontal
axis of the Wollaston prism then all photons will choose the horizontal
output and non will leave the prism at the vertical output. The
polarization can be measured with 100% accuracy.

QM Randomness occurs at intermediate angles. Some will leave at one
side and some at the other. The wave function will go through both.
This randomness disappears in the case of two or more entangled particles
and polarizers at equal angles. The path through the Wollaston prism
becomes 100% predetermined.

The idea of entanglement was introduced to try to measure both
non-commuting parameters at the same time, but at two different
locations. The EPR paper talks about position/momentum and time/
energy relations. The Bell paper talks about electron spin components.
which are non-commuting.

The photon polarization used is by itself not non-commuting. What is
used instead is a superposition of a horizontal and vertical polarized
photon. This now replaces the non-commuting quantities. The idea is
that the A detector selects either the horizontal or the vertical state
and consequently the B detector must make the same choice as a
result of the entanglement.

In the actual experiment one can generally not tell which of the two
if chosen. The experiment is understood that the angle of the detector
of one measurement is transferred by teleportation to the other
photon.

Originally, Einstein Podolsky and Rosen hoped to be able to extract
all information (eg. position and momentum) exact in a more classical
deterministic way. Today we are looking at a parameter (polarization)
which is not even considered a non commuting quantity.

The confusion started with Bell. Instead of using the presumption
that A and B are identical to be able to extract all information exact
he changed the EPR gedanken experiment in a test of entanglement.

The Bell inequalities have now became (in the current EPR tests) the
prediction of QM for two or more independent photons without
entanglement while the "QM" result predicts the correlation for
two or more photons which behave dependent as a result of
entanglement.


So while Einstein Podolsky and Rosen hoped to get rid of Quantum
Randomness, by inventing a trick to measure both non-commuting
parameters exact, we are now left with Bell Inequalities which
exhibit even more Quantum Randomness (less correlation) then
the entangled case which is supposed to save Heisenberg's Uncertainty
Principle.

Exact measurement of any hidden variables gets rid of Quantum
randomness. Bell Inequalities introduce more Quantum randomness.
Oddly enough, we can quote major teleportation proponents saying
that teleportation circumvents Heisenberg's Uncertainty Principle
by transferring the exact and complete quantum state from one
place to another.

The EPR paper was written with the primary intention to attack the
Uncertainty Principle by finding a way to circumvent it ...

-----------------------------------------------------------

What I wanted to show with this thread is that there are fully
deterministic explanations of the current EPR results and that
there are also simple test with current equipment possible to
test these assumptions.


Regards, Hans

 

[DrChinese]

Your description is not correct in important ways. Sure, you can align the prisms to get 100% correlation (ideal case of course) but that does not make anything predetermined. (There is always randomness and I assume you meant correlation in that respect.)

You can see that by Bell's Theorem. The whole point of that is that hidden variables theories can mimic the results of QM at some angles but not at others. It is the exercise of making a deterministic theory agree with QM at every setting which is absolutely impossible.

All of the Bell tests relate to entangled photons; some folks simply deny that entanglement is an actual phenomenon. As to quantum teleportation, I don't think I know of anyone asserting it violates HUP as that is ultimately what this is all about anyway.

 

[Hans de Vries]

Your description is not correct in important ways. Sure, you can align the prisms to get 100% correlation (ideal case of course) but that does not make anything predetermined. (There is always randomness and I assume you meant correlation in that respect.)

It is 100% under equal angles! That's the whole point of entanglement.
the results must be the same under identical conditions because it's
supposed to be a single wave function. The Local Realist value is 75% for
equal angles (a-b=0 degrees)

See for instance Aspect's paper: http://www.drchinese.com/David/Aspect.pdf
fig. 4 (It says relative orientation of the polarizers)

Or fig 3 in Caroline's paper. which has both the QM and LR curves.
http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066.pdf

(both figures are for the A+B+ cases, you'll need to add the A-,B- case)

You can see that by Bell's Theorem. The whole point of that is that hidden variables theories can mimic the results of QM at some angles but not at others. It is the exercise of making a deterministic theory agree with QM at every setting which is absolutely impossible.

They mimic only at 45% in the photon case.

All of the Bell tests relate to entangled photons; some folks simply deny that entanglement is an actual phenomenon. As to quantum teleportation, I don't think I know of anyone asserting it violates HUP as that is ultimately what this is all about anyway.

See for instance Anton Zeilinger in "Circumventing Heisenberg":
http://www.quantum.univie.ac.at/links/sci_am/teleportation.pdf
page 36 and 32.

Or Gregor Weihs who's experiments you referred to several times
here: http://www.quantum.univie.ac.at/research/photonentangle/entanglementswapping.pdf
on page 7: "Quantum State Teleportation Classically impossible due to
Heisenberg Uncertainty"


Regards, Hans

 

[DrChinese]

It is 100% under equal angles! That's the whole point of entanglement.
the results must be the same under identical conditions because it's
supposed to be a single wave function. The Local Realist value is 75% for
equal angles (a-b=0 degrees)

Yes, it is true that the LR value is 75% but that is simply for one incarnation. It is possible to have other postulated functions depending on the particular LR model. The "75%" model, while "reasonable", is far from experimental results. There are models, and Caroline has some of those plotted too, in which the LR prediction sits at the edge of the Bell Inequality.

And you are correct that most LR models match QM at 45 degrees, it wouldn't make much sense otherwise. The real issue is that every single LR model must necessarily deviate from QM if it is going to respect Bell.

 

[Hans de Vries]

Yes, it is true that the LR value is 75% but that is simply for one incarnation. It is possible to have other postulated functions depending on the particular LR model. The "75%" model, while "reasonable", is far from experimental results. There are models, and Caroline has some of those plotted too, in which the LR prediction sits at the edge of the Bell Inequality.

Caroline's LR model gives the correlation for the QM model in case of non-
entangled particles. Real experiments with non-entangled particles should
indeed produce these results. Particles are generally not entangled
(This even though Caroline isn't really a "QM proponent", I guess here
objection to QM is more the entanglement aspect of it)

The ideal case has many presumptions like rotational invariance and other
issues. Rotational Invariance is a bit broken in most experiments. See for
instance here on page 15:

http://www.quantum.univie.ac.at/research/photonentangle/entanglementswapping.pdf

There are 3 different measurements with a relative angle of 67.5 degrees.
Each at another absolute angle. The systematic differences are significantly
larger than the precision of the experiment.

angle: 67.5^o ( 0, 22.5) ==> 18.595% (-0.6281)
angle: 67.5^o (45, 22.5) ==> 21.260% (-0.5748)
angle: 67.5^o (45, 67.5) ==> 22.965% (-0.5407)

And the ideal values for QM and LR are:

angle: 67.5^o (QM ideal) ==> 14.644% (-0.7071)
angle: 67.5^o (LR ideal) ==> 32.322% (-0.3536)


(red angles are excluding the 90 degrees inherent photon polarization difference)
(green values are the expectation values between +1 and -1, divide by 2
and add one half to get percentages between 0 and 100%)

And you are correct that most LR models match QM at 45 degrees, it wouldn't make much sense otherwise. The real issue is that every single LR model must necessarily deviate from QM if it is going to respect Bell.

The reason behind this is that these LR models tend to follow QM
locally without the extra correlation brought in by entanglement.
It's the entanglement that reduces Quantum Randomness and
increases the correlation.

Any local theory that starts with local Quantum Randomness.
(The chance that the photon is detected at the + or the - detector
can never explain the reduction in randomness (increase in correlation)
as seen in the EPR tests.


Regards, Hans

 

[DrChinese]

Any local theory that starts with local Quantum Randomness. (The chance that the photon is detected at the + or the - detector can never explain the reduction in randomness (increase in correlation) as seen in the EPR tests.

Regards, Hans

It is pretty hard to explain how there is MORE correlation than expected!

If you were playing craps at a casino, how many 7s in a row would it take to convince you that the dice were loaded?

 

[Hans de Vries]

It is pretty hard to explain how there is MORE correlation than expected!

If you were playing craps at a casino, how many 7s in a row would it take to convince you that the dice were loaded?

I wouldn't get involved in any casino game except if I was the owner

A little bit more serious:

There is no randomness in rolling dice, loaded or not loaded.
The perceived randomness is the prove of our own shortcomings.


Regards, Hans


P.S. You can't expect somebody to be convinced before experiments are
known in all details. I myself am not convinced at all that I have enough
information to draw the fundamental conclusions that the experimenters
require from the reader. Some of the papers unfortunately give hardly any
measurement data or even what exactly they have measured except for
a single number as a conclusion.

Experiments must be separable from the opinion of the experimenter.

It seems that this will keep me busy for a while.

 

[DrChinese]

Experiments must be separable from the opinion of the experimenter.

That is sort of a strange comment. Scientists are professionals. They are trained to make the experiment the focus of their work, and subjugate their opinions - which everyone has.

The essence of science is the repeatability of the experiment. Although the published paper represents the tip of the iceberg of raw data, it is made available to other professionals in a variety of ways as appropriate. Because most important papers are published in peer reviewed journals, there is a process which is intended to insure the highest integrity.

If you are implying that EPR experimenters, out of all scientists everywhere, are a shady lot with questionable practices... you will be alienating a lot of folks around here. Myself at the top of that list. I will assume that your comment is innocent.

 

[Hans de Vries]

That is sort of a strange comment. Scientists are professionals. They are trained to make the experiment the focus of their work, and subjugate their opinions - which everyone has.

The essence of science is the repeatability of the experiment. Although the published paper represents the tip of the iceberg of raw data, it is made available to other professionals in a variety of ways as appropriate. Because most important papers are published in peer reviewed journals, there is a process which is intended to insure the highest integrity.

If you are implying that EPR experimenters, out of all scientists everywhere, are a shady lot with questionable practices... you will be alienating a lot of folks around here. Myself at the top of that list. I will assume that your comment is innocent.

That's indeed not what I'm implying. To use your words: I'm just looking for
the iceberg, not just the tip of it.


Regards, Hans.