Finding Einstein’s Hidden Variable

[RandallB]

I personally like to think there is a Einstien local multiple hidden variable solution to the Bell inequality type experiments but unfortunately this does not appear to be it.

I appreciate the effort, but allow me to correct a couple points. Although your analysis is a bit short on detail, I can see enough to point out your errors with a couple specific measurements.

First – In reference to a “local multiple hidden variable solution”; what I’ve described in post # 7 is a two variable solution. Using a previously unknown (but still hidden from direct & complete measurement) variable by revising the polarization description of an individual Photon and Photon pairs in the case of Type II PDC. The key is EPR-Bell must use TWO variables, the well known Mauls description of light polarization, plus my fixed width description of photons. As I’ve said the Logic of the Bell Theorem can only deny the possibility of a single variable.

Now to your Analysis:

For the “Sunglasses” multi filter Vert. Hrzt. Vs. Vert. Diag. Hrzt paradox.

Analysis:
Light passing through 1 polarizing filter = 1/2 Pass
Light passing through 2 polarizing filters at 45 degrees to each other = 1/4 Pass
Light passing through 2 polarizing filters at 90 degrees to each other = 0 Pass
Light passiing through 3 polarizing filters at +45 degress in succession = 1/8 Pass
So far, so good.

By “so far so good”, your are saying that you agree: Instead of using a non-local probability at a second filter to decided if an individual photon shall pass that filter; my locally defined value established at the prior filter has preset within the photon if it will pass any given future polar measurement. A successful “Einstein-Local” solution to the Sunglasses paradox.

Now for using my Hidden Variable PDC test using four test areas A1 & A2 with there paired photons in B1 & B2.

PDC Bell type test. Alice and Bob's polarizing filters aligned with each other.

Number of photons detected at the same time by Alice and Bob = 0. Fail.
Number of photons detected by Alice but not by Bob =1. Fail.
Number of photons detected by Bob but not by Alice =1. Fail.

The graph from 0 to 90 degrees would appear to be a straight line in the opposite direction to the basic single hidden variable graph.

This is way off, what you are describing here MATCHS not fails to match the QM predictions. If Alice and Bob both measure at the same angle such as 0° or Vertical; Alice will only see V photons paired with H photons on Bob side and with Bob’s measurements in the same vertical alignment he can never see those H photons. i.e. detected at the same time as ALL expect QM included. That is the definition of Type II PDC and QM agrees with that. Your comment about “opposite direction” tells me you are getting confused by the unfortunate practice of allowing Bob to define Horizontal as 0° instead of 90° when collecting his results. That means 0° by Alice vs. 0° by Bob giving 100% correlations is in fact a 90° measurement separation as I describe.

Much better to insist that Bob use the same “compass” measurements as Alice, so you do not get confused like that. I makes it easier to track the locations of paired photons e.g. if Alice makes a set of measurements at 22° with a sample that expects 100 V photons and 100 H photons to come by her test area(s) she would see 86 V’s and 14 H’s half the total of 200. We know at any angle she will always see one half of the total 200 photons, detecting a normal beam of polarized light at that angle and not detecting the other half. Now Bob by QM definition expects to find 100% correlation with those at 112° (or 22° if Bob resets 0° to horizontal) a 90° separation of measurement. At that angle Bob will find 14 V’s in B2 paired with 14 H’s Alice saw. Bob also finds 86 H’s in the B1 test area paired with the 86 V’s Alice saw. These are the only 100 photons Bob will see of the 200 passing his test area(s). And when you copy over the polarization shape of each of those 100 photons based on my local hidden variable for photons defined in Post #7, a normal looking beam of polarized light this time aligned at 112° is defined. And against just this group of photons if Bob had measured at any other angle the count of detections would follow Malus. Therefore even though Bob will always count 100 photons at any angle, he will only correlate with Alice’s detections based on Malus’ Law at other angles. Including + or - 90° from 112° for Zero correlations when Bob measures at the same angle that Alice did 22° or 202°.

In other words it successfully predicts the violation of the Bell inequities, all based a two sets of Local Variables. One already known variable defining Light polarization by Malus and my definition of fixed photon polarization no probabilities required. The only probabilities needed are the locally defined ones in Malus.

PDC Bell type test. Alice and Bob's polarizing filters at 120 degrees to each other.
-Number of photons detected at the same time by Alice and Bob =2/3. Fail.
The proportion should be 1/4 to agree with QM.

I have no idea how you came up with “=2/3 Fail” the correct answer using my HV is 3/4. And QM does not expect 25%, it instead matches my prediction with 75%. A 120° advance by Bob beyond Alice’s measurement at 22° would be 142° or 60° separation from Alice’s test at 22° (aka 202°). For Bob his 142° test is only 30° away from 112° where he would measure the max 100% correlations. Both QM and my approach expect Malus (Cos 30)^2 to apply giving 75% not 1/4.

I am sure when you redo your analyses carefully you will find this is an affective Einstein Local solution to the EPR-Bell paradox just as you found it to be so for the “Sunglasses Paradox”.

Randall B

 

[yuiop]

.. my locally defined value established at the prior filter has preset within the photon if it will pass any given future polar measurement. A successful “Einstein-Local” solution to the Sunglasses paradox.
Randall B

The Sunglasses paradox was only tested at 0, 45 and 90 degrees. These are the exact and only 3 points on the linear single HV graph that happen to coincide the Malus' law graph so the tests do not establish that the new model follows the Malus' law any better than a single variable HV model.

Much better to insist that Bob use the same “compass” measurements as Alice, so you do not get confused like that. I makes it easier to track the locations of paired photons e.g. if Alice makes a set of measurements at 22° with a sample that expects 100 V photons and 100 H photons to come by her test area(s) she would see 86 V’s and 14 H’s half the total of 200.
Randall B

I will accept your correction on the “compass” bearings but this does not change the straight line relationship as far as I can tell. You have not really explained how you obtained the numbers 86 and 14, but it looks like you have simply assumed and applied Malus’ law as follows:

V photons= 100*cos(22°)2 = 86
H photons = 100*cos(90° -22°)2 = 14


My interpretation of the model is that photons with a detectable polarization zone within 45 degrees of the polarizing filter pass axis are allowed to pass. On this basis I calculate:

V component = 100*((90° -22°)/90°) = 76
H component = 100*(22°/90°) = 24

This also adds up to 100 out of every 200 photons, but unfortunately it has the same linear relationship as a basic single variable HV model. I am not sure where your second variable is.

Maybe I am still misunderstanding something about your model. To only get 14 photons at Alice’s horizontal detector A2 I assume you are talking about the experiment with “pre-polarizers” at the source to ensure only horizontally polarized photons go to detectors A2 and B1. If that is the case then the example is not really representative of a typical Bell EPR type test so it is difficult to compare it to one. Without the “pre-polarizers” the model would appear to predict that detectors A1,A2, B1 and B2 would all record 50% of the photons arriving at those locations no matter what the orientation of filters at those locations are. You have also not really made it clear how the photon paths are split between the detectors in each region. It might help if you produced a diagram of a practical experiment using optical fibre connections between the various mirrors, splitters and filters to make it easier for us to understand the light paths you are assuming.
This link showing diagrams of various real Alain Aspect Bell type experiments that include vertically and horizontally aligned polarizing filters at both ends of the source might be of interest. http://chaos.swarthmore.edu/courses/phys6_2004/QM/17_EPR_Bell_Details.pdf

(You will have to scroll quite a long way down the article to see the relevant diagrams)

 

[RandallB]

The Sunglasses paradox was only tested at 0, 45 and 90 degrees. These are the exact and only 3 points on the linear single HV graph that happen to coincide the Malus' law graph so the tests do not establish that the new model follows the Malus' law any better than a single variable HV model.

Why are you complaining about the test angles you selected, go ahead select other angles. However do not impose your own restriction of a linear relationship onto a two dimensional drawing of a three dimensional reality. Polarizer measurements have already been Classically defined as distributed non-linearly by Malus around 1809, a classical description NOT unique to QM.

The issue of “better” is not a matter of more accurate; it is Einstein Local vs. Non-Local as required by QM. QM requires that the decision to pass the second filter is based on a single problematic “roll of the dice” made at the second filter, non-local to the creation of the photon at the prior polarization filter. A single variable that cannot be known as a realistic thing. But a mathematical formalism of a QM “state” defining a part of the photon. Based on using the Malus probability distribution from 100% to 0% for measurements from 0° to 90° (or 0° to -90°).

I’m saying TWO Classically defined variables are established at the time the photon is created at first polarization. Making them locally determinate (not the same as determinism) variables that establish if the photon will pass the next filter based only on those two variables and the setting of the next measurement, no HUP at the second filter. The first variable is the distribution of photon polarization center points naturally based on Classical Malus Law from - 45° to 45° of the Light beam polar alignment. Plus as I’ve defined in post #7 the second “hidden” variable of fixed photon polarization width as the “unknown” variable Einstein was searching for, at least as it relates to Polarization Measurements & EPR-Bell testing.

The point is this produces the exacta same accurate result as non-local QM in a local way that translates correctly to EPR-Bell tests as well, thus falsifying the previous conclusions that a Einstein Local or Bell Local solution was not possible.

I assume you are talking about the experiment with “pre-polarizers” at the source to ensure only horizontally polarized photons go to detectors A2 and B1. If that is the case then the example is not really representative of a typical Bell EPR type test so it is difficult to compare it to one.

Incorrect, you are not understanding the experiment. Look at the diagram included with Post #2; A2 & B1 are horizontally polarized because they come from the BBO PDC ring of light that only gives horizontal “H” photons. The only purpose of the “pre-polarizers” (better described as “re-polarizers”) was to retain the existing polarization but remove any “Entanglement” or Hidden Variables to define what a Local Realist currently knows in classical terms. The question is what was removed by those “re-polarizers”; “Entanglement” or LOCAL Hidden Variable information.
The experiment duplicates typical Bell EPR type test by combining A1 & A2 to stand in for observations made at the A side intersection and combining B1 & B2 to stand in for B side intersection area observations that includes photons from both rings of light.

You have also not really made it clear how the photon paths are split between the detectors in each region.

You are allowing yourself to be confused by entirely different experiment. EPR-Bell is not about Paths or interference patterns, just selecting the test areas from the rings of light coming off a BBO PDC crystal as described in the diagram in Post #2, we are not dealing with the paradox of photon paths to interference fringes here. Labs are well versed at picking out the two small areas of intersection shown in that diagram for an EPR-Bell test. Duplication that test with four areas of known polarization should actually be even easier to perform.

 

[yuiop]

.. do not impose your own restriction of a linear relationship onto a two dimensional drawing of a three dimensional reality. Polarizer measurements have already been Classically defined as distributed non-linearly by Malus around 1809, a classical description NOT unique to QM.

I am trying to be constructive but you are making very difficult. If you have a 3 dimensional model of a photon in your head then perhaps you should illustrate what you have in mind with 3 dimensional sketch. Considering you have a whole book on the subject you are being frugal with details. As others have said, you have provided no formulas or calculations making it very difficult to be objective. If your drawings are a 2D representation of a 3D reality then perhaps you should indicate the axes the drawing to make it clear. I am assuming we are looking at both the horizontal and vertical photons from along the travel path (call that the z axis) and from that point of view both we are looking at the both the horizontal and vertical photons in the x, y plane. If there is something important about the 3D shape can you show a sketch from one of the other axes, eg from “above”?

I’m saying TWO Classically defined variables are established at the time the photon is created at first polarization. Making them locally determinate (not the same as determinism) variables that establish if the photon will pass the next filter based only on those two variables and the setting of the next measurement, no HUP at the second filter. The first variable is the distribution of photon polarization center points naturally based on Classical Malus Law from - 45° to 45° of the Light beam polar alignment. Plus as I’ve defined in post #7 the second “hidden” variable of fixed photon polarization width as the “unknown” variable Einstein was searching for, at least as it relates to Polarization Measurements & EPR-Bell testing.

I can see that it might be possible to create a distribution of polarization angles at the source that pre-codes the behaviour of the photons at a future polarization filter in a way that would satisfy the Bell tests, but there are several provisos.

First, it would seem that there would have to be a preferred reference angle. This preferred reference angle would have to be encoded not just into the first pair of entangled photons, but into all subsequent entangled pairs. In other words we would not just have entangled pairs, but a completely "entangled system" of photons. The preferred reference angle would have to be determined either by the source or relative to some hypothetical absolute rotational space.

If the source is the key to the preferred reference angle then a measurable change in the coincidences between Alice and Bob's count rates would be seen when the source is rotated. I am not sure that is what would be seen in real experiment. I am also not entirely convinced your assertion that type II PDCs naturally only send vertical photons in one direction and only horizontal photons in the other direction, is entirely accurate. Can you post some links to support that claim? I am under the impression they send horizontal and vertical photons randomly in either direction, while maintaining an orthogonal polarization angle between the two paired photons of each entangled pair. I also get he impression that practical experiments put a quarter wave plate in one arm of the experiment to maintain coherence of the entangled pairs. If you are referring to some sort of hypothetical absolute space coordinate then there would be a lot of resistance to that concept as relativity dismissed the notion of an absolute space coordinates. However it could be argued that special relativity can not rule out an absolute rotational effect. The action of gyroscopes and the Sagnac effect give great support to the concept of “absolute rotational coordinates”.

The other hurdle is accounting for quantum erasure type experiments. That might be a bit more difficult.

Incorrect, you are not understanding the experiment. Look at the diagram included with Post #2; A2 & B1 are horizontally polarized because they come from the BBO PDC ring of light that only gives horizontal “H” photons.

As I mentioned earlier I would like to see “proof” that a PDC ONLY gives horizontal photons in a given direction, in the form of a link to an authorative document.

You are allowing yourself to be confused by entirely different experiment. EPR-Bell is not about Paths or interference patterns, just selecting the test areas from the rings of light coming off a BBO PDC crystal as described in the diagram in Post #2, we are not dealing with the paradox of photon paths to interference fringes here.

I am well aware we are not discussing interference type effects or experiments. I am just saying that your diagram is a bit vague and easily leads to misunderstandings.

Just to check I am understanding you correctly, you are saying the average distribution of 100 vertical entangled photon pairs leaving the source would be something like this:

0 to 7.5 degrees either side of vertical = 25.9 photons
7.5 to 15 degrees either side of vertical = 24.1 photons
15 to 22.5 degrees either side of vertical = 20.7 photons
22.5 to 30 degrees either side of vertical = 15.9 photons
30 to 37.5 degrees either side of vertical= 10 photons
37.5 to 45 degrees either side of vertical = 3.4 photons

whereas a purely random distribution of polarised orientations would expect:

0 to 7.5 degrees either side of vertical = 16.7 photons
7.5 to 15 degrees either side of vertical = 16.7 photons
15 to 22.5 degrees either side of vertical = 16.7 photons
22.5 to 30 degrees either side of vertical = 16.7 photons
30 to 37.5 degrees either side of vertical= 16.7 photons
37.5 to 45 degrees either side of vertical = 16.7 photons

If the sample of 100 photons meet a polarization filter at 22.5 degrees clockwise to the reference axis then we would expect the clockwise half of the source photons orientated between 22.5 and 45 degrees not to pass through the filter. From the first table, half the number of photons between 22.5 and 45 degrees is
(15.9+10+3.4)/2 = 14.7
The number that pass would then be 100-14.7= 85.3 which would be in agreement with Malus’ law. On that basis the theory works provided that a preferred reference angle can be proved.

One other thing to consider. In an earlier post you mentioned that when a random selection of polarized photons pass through a polarization filter, the photons that pass through are randomly re-orientated to within + or – 45 degrees of the polarization filter pass axis. You might have to rethink that. The conventional interpretation (as I understand it) is that all the photons are exactly aligned with polarization axis of the filter. (i.e. the polarization is quantisized) The difference between the two interpretations might make a difference to how light would be expected to behave when first passed through a polarizing filter and then passed through a quarter wave plate (QWP) or a half wave plate (HWP). Your theory would have to be consistent with the known behaviour of linear polarizing filter and HWP/QWP combinations as observed in experiments to be a valid theory.

P.S. Try to be less confrontational. Ueit's offer to drop BM from the discussion and his request to see a scan of the relevant pages in the book, do not seem entirely unreasonable to me. However, your desire to discuss a book that only you are allowed to know the detailed contents of, does seem unreasonable. Might that be why everyone else has dropped out the discussion?

 

[yuiop]

In my last post I stated "The conventional interpretation (as I understand it) is that all the photons are exactly aligned with polarization axis of the filter. (i.e. the polarization is quantisized) ". I am not sure where I read that but after some further research I can not find any support for that interpretation, so your statement that photons are randomly realigned + or - 45 degrees from the polarization axis seems reasonable.

I finally managed to track down the book ( ISBN 9781420888263 ) on the internet and noticed in the free preview that the book does address the issue of half and quarter wave plates. Could you tell us more about that?