Does the EPR experiment imply QM is incomplete?

[DrChinese]

The correlation is 100% at 90°.
I think you are mixing up correlation with identity. In other word cos(delta) with 1/2 + (cos(delta))^2

True, I use match % and not proper correlation %. However, on that basis, the proper correlation at 90 degree is -1. At 45 degrees it is 0. At theta=0 degrees, it is 1. You don't produce those either with your simulation.

 

[PeterDonis]

The wave function picks up new information after the preparation and before measurement ?

No. The wave function for a system of multiple particles is a function of the position of all the particles (if we are working in the position basis), not just the position of the particle you are interested in. So the wave function for the probability of a particular measurement result for the particle you are interested in does not depend only on quantities associated with the particle you are interested in.

Have you ever heard of "hidden variable", "non-locality", "entanglement" and "correlation" ?

Of course. And what you are saying indicates to me that you do not understand how all of these things actually function in the proof of Bell's Theorem or in discussions of the EPR experiment. In fact, per my comment above, it's not even clear to me that you understand what a wave function is for a system containing more than one particle.

I strongly advise you to take a step back at this point and carefully consider all the responses you have already received before posting further. You are getting very close to a thread ban, since you are not the OP of this thread and the things you are bringing up don't seem to me to be making any positive contribution to discussion of the question the OP asked.

 

[kurt101]

Further, entanglement can exist between particles that have never existed in a common light cone.

Does anyone have doubts that the collapse algorithm would model this kind of entanglement correctly? I have not tried simulating it, but just reading through the experiment (the one with photons) it seems like it would.

 

[kurt101]

That's incorrect. There is no local hidden variable. And that's the whole point of Bell.
There is a set(of one element) of hidden variable that can easily reproduce QM prediction. But those variable must be non-local.
That's not my diagram. My diagram is ##A{\rightarrow}V{\leftarrow}B##. A cannot reach B in any way.

I strongly suspect you are agreeing on substance, but somehow disagreeing on language. I also have trouble when you say "A cannot reach B in any way". I think this is just a difference in what we want to call it. Because I would rather say A gives B its state when it interacts with the polarizer. I believe it is the same algorithm as what you are saying, but you would rather just make another variable called V that is shared between A and B until right after A interacts with its polarizer and then A no longer is associated with V, but B still uses V until it interacts.

Hopefully were just saying the same thing.

 

[kurt101]

No. The wave function for a system of multiple particles is a function of the position of all the particles (if we are working in the position basis), not just the position of the particle you are interested in. So the wave function for the probability of a particular measurement result for the particle you are interested in does not depend only on quantities associated with the particle you are interested in.

For calculating the probability of an outcome you square the sum of the probability amplitudes. What is interesting to me about this math as it relates to the collapse algorithm is that the QM math result only gives you terms that include 2 outcomes. For example if you have outcomes with probability amplitudes a, b, c; then you would get a probability of aa + ab + ac + bb + ba + bc + cc + ca + cb. You don't ever see a term like abc or aab for example. Does this imply that you really only have a superposition of 2 outcomes when you make a single measurement? (Even when you have the possibility for many outcomes) And bringing this back to the collapse algorithm, the algorithm only considers entanglement for exactly 2 particles at a time, until the interaction takes place and then presumably the entanglement is between a different set of 2 particles.

 

[DrChinese]

I strongly suspect you are agreeing on substance, but somehow disagreeing on language. I also have trouble when you say "A cannot reach B in any way". I think this is just a difference in what we want to call it. Because I would rather say A gives B its state when it interacts with the polarizer. I believe it is the same algorithm as what you are saying, but you would rather just make another variable called V that is shared between A and B until right after A interacts with its polarizer and then A no longer is associated with V, but B still uses V until it interacts.

I don't know about agreeing on substance or not. The issue is whether a non-local influence is occurring. Clearly, that is a viable possibility per Bell. And, for example, Bohmian Mechanics postulates a manner in which that can occur. However, there is mutual influence between A and B in that model.

So that is different than what Boing was saying. And his simulation did not feature mutual influence, it was based on either A influencing B or vice versa. But he was also denying that influence, which kinda misses the "out" that a non-local influence provides.

 

[PeterDonis]

For calculating the probability of an outcome you square the sum of the probability amplitudes.

The sum of the probability amplitudes for that outcome. You appear to be misunderstanding what that means.

Suppose there are three possible outcomes; call them A, B, and C. For outcome A, suppose there are two ways that can happen, with amplitudes ##a_1## and ##a_2##. For outcome B, suppose there are three ways it can happen, with amplitudes ##b_1##, ##b_2##, and ##b_3##. And for outcome C, suppose there is only one way it can happen, with amplitude ##c##.

Then the probabilities are: for A, ##\left( a_1 + a_2 \right)^2##; for B, ##\left( b_1 + b_2 + b_3 \right)^2##; and for C, ##c^2##. There are no "cross terms" between outcomes.

You should re-think things in the light of the above.

 

[Boing3000]

No one is arguing that non-local hidden variables won't work as an algorithm.

That's good, we are making progress.

The issue is that the measurement setting of either A or B... and the outcome at that setting... must be part of the algorithm.

It is. That has been explained over and over again.

You are in denial that must occur.

No, I am not. You are just enable to understand the sharing of a variable and the precise direction of the flow of information.There is no function that take A and B as input. There are two function that take A(thus V) and the other take B(thus V). This is the same V. Not only the same value, it is the same placeholder.
There is no way for function A to get any information about B. None. Yet the sharing of the variable allow for the correlation to hold

1. Assume A and B are randomly given a "+" or a "-" initial value (same for both). To be specific, it is "+".
2. A is measured first at 138 and yields value of "+", its initial value, and needs nothing else.
3. But B, which is also "+", needs to know about the 138. That value is transmitted to B via FTL means.
4. B can now give answers for any measurement setting simply by applying the Cos^2(theta) function.

All good. There is FTL communication in this model.

I have no idea why you, among all, would bring such trivial model. I have argue against it because step 3 is not possible. Not by virtue of the theory of relativity, nor even the lack of formula to be put in an algorithm (making it wishful thinking).
It is not possible because B may have transmitted a message to A, before B felt any need(??) to know anything. The absence of commutativity at every step makes it impossible.

Photons don't produce those statistics, my friend. It's COS^2(theta).

100% of the photon at one hand are strictly correlated (inverted) to those at the other end (at 90°). There is absolute correlation.
It is at 45° that the correlation is 0.5 (totally random)

If you're not sure, try taking a couple of polarized lenses and crossing them. 0% light transmitted.

Exactly, and I am happy you agree with that. But I am under the impression that you believe that Alice or Bob would get 0% light transmitted in a EPR experiment involving TWO entengled photon. That's not the case. They always get 50% light transmitted, whatever they try to do.

True, I use match % and not proper correlation %. However, on that basis, the proper correlation at 90 degree is -1. At 45 degrees it is 0. At theta=0 degrees, it is 1. You don't produce those either with your simulation.

I just dived the number of identical pair(fail) with the numbers of inverted pair(entangled) (making 0.5 the absolute lower value possible (random)). I will add another output of the correlation computation, if that help anybody.

 

[PeterDonis]

There is no function that take A and B as input. There are two function that take A(thus V) and the other take B(thus V). This is the same V.

You are missing the point: if you code the algorithm this way, it cannot reproduce the predictions of quantum mechanics. Your "V" is the equivalent of Bell's local hidden variables (he calls them ##\lambda##). So your algorithm will produce results that must obey the Bell inequalities; but the predictions of QM (and actual experimental results) violate the Bell inequalities. The only way to have an algorithm that reproduces the predictions of QM (and violates the Bell inequalities) is for the function in the algorithm to take the settings at both A and B as inputs.

100% of the photon at one hand are strictly correlated (inverted) to those at the other end (at 90°). There is absolute correlation.
It is at 45° that the correlation is 0.5 (totally random)

But your algorithm has to give the correct correlations at all angles, not just at one. Of course if you just have the 90 degree angle, it's easy to write an algorithm your way that gives perfect anti-correlation. But that won't work for all angles.

 

[Boing3000]

No.

I was also under this impression thus you contradicted you previous statement.

And that is false: the wave function "computes" what happens at event A using input from other events as well as event A.

Because:

The wave function for a system of multiple particles is a function of the position of all the particles (if we are working in the position basis), not just the position of the particle you are interested in. So the wave function for the probability of a particular measurement result for the particle you are interested in does not depend only on quantities associated with the particle you are interested in.

And that exactly similar to V. After the preparation the wave function is non-local and consul-table by every event in the laboratory to get they (probability) value. Note that any individual event only need to specify its local-position to the wave function to get get the probability, nothing else.
That's identical to how the hidden variable work in the simulation.

 

[PeterDonis]

And that exactly similar to V.

Okay, at this point you're either trolling, shifting your ground, or waving your hands about the properties of an algorithm that you haven't actually constructed. Please give an explicit definition of V and your algorithm.

 

[PeterDonis]

Note that any individual event only need to specify its local-position to the wave function to get get the probability, nothing else.

If you think this is possible while still reproducing the predictions of QM, you need to think again. As I've already said before: the wave function of a two-particle system is a function of both particles' positions, not just one.

 

[Boing3000]

Your "V" is the equivalent of Bell's local hidden variables (he calls them ##\lambda##).

No, it is not. My V can be local (two copy of the same Value), or non-local (a sharing of a variable)

So your algorithm will produce results that must obey the Bell inequalities; but the predictions of QM (and actual experimental results) violate the Bell inequalities.

It does both.

The only way to have an algorithm that reproduces the predictions of QM (and violates the Bell inequalities) is for the function in the algorithm to take the settings at both A and B as inputs.

This is false. And the way you propose is not possible, for reason explained previously.
It is not even sensible because one function cannot decide BOTH apparatus angle then pilot A and B at once (it is superdeterminism which is kind of lame)
Only a simulation, using a wavefunction (which does NOT use A and B as input for a result, but only A local position as input for the result (and only A & B as preparation/initial WF value/state).
Or another type of non-local Value/state

But your algorithm has to give the correct correlations at all angles, not just at one. Of course if you just have the 90 degree angle, it's easy to write an algorithm your way that gives perfect anti-correlation. But that won't work for all angles.

Of course

 

[PeterDonis]

Of course

In other words: you agree that your algorithm only reproduces the correct QM correlations for one angle--90 degrees--not all angles?

 

[PeterDonis]

My V can be local (two copy of the same Value), or non-local (a sharing of a variable)

What's the difference? You're saying there's this variable V that can be taken as an input by the "function" that gives you the measurement result for either A or B. What does it matter how the variable is stored?

If you would explicitly write out your algorithm, showing how V is calculated and how the measurement results at A and B are calculated, it would be a lot easier to understand what you are saying. Right now, as I said, it looks like you are either trolling, shifting your ground, or waving your hands about the properties of an algorithm that you haven't actually constructed.

one function cannot decide BOTH apparatus angle then pilot A and B at once

The function doesn't have to "decide" both measurement angles. It has to take them as inputs. It also doesn't have to output both A's and B's results; it just has to output either A's or B's--you can have one function for each.

 

[Boing3000]

Okay, at this point you're either trolling, shifting your ground, or waving your hands about the properties of an algorithm that you haven't actually constructed. Please give an explicit definition of V and your algorithm.

Have you ever consider that there is another possibility ? That you simply never tried to understand what I say instead of trolling me and threatening me ?
The explicit definition is at line 13 and both locality (or not) done at lie 14 here

If you think this is possible while still reproducing the predictions of QM, you need to think again. As I've already said before: the wave function of a two-particle system is a function of both particles' positions, not just one.

A OK. I though it was only the case in BM. So Alice or Bod cannot compute anything from the WF.

 

[Boing3000]

In other words: you agree that your algorithm only reproduces the correct QM correlations for one angle--90 degrees--not all angles?

Why don't you test it, to check...

 

[Boing3000]

What does it matter how the variable is stored?

Non-locality makes all the difference. Once you understand what Bell is actually proving, you know how to conserve correlation, without allowing any possibility for A to "influence" B (or the contrary)

Right now, as I said, it looks like you are either trolling, shifting your ground, or waving your hands about the properties of an algorithm that you haven't actually constructed.

I have posted it maybe a year ago in another thread.

The function doesn't have to "decide" both measurement angles. It has to take them as inputs. It also doesn't have to output both A's and B's results; it just has to output either A's or B's--you can have one function for each.

If I have one function for each, then each of those functions will only use one input. But that is right, you may create two local functions from one(non-local) which is globally aware of the two. That is the closest thing you have written that resemble the even more simply algorithm that I use.

 

[PeterDonis]

The explicit definition is at line 13 and both locality (or not) done at lie 14

I can read Javascript, but you can hardly expect everyone here to do so. When I asked for an explicit description I meant a description in words or math, something that everyone here could be expected to understand.

 

[PeterDonis]

When I asked for an explicit description I meant a description in words or math, something that everyone here could be expected to understand.

Actually, rather than wait for @Boing3000 to do this, I'm going to give such a description of a straightforward algorithm using the QM math. Here, schematically, is such a description:

The algorithm assumes a number of "trials", each of which consists of making a polarization measurement on each of a pair of entangled photons. Each pair of photons is assumed to be prepared identically in the "PP" state (i.e., their polarizations are 100% correlated if measured at the same angle, and 100% anti-correlated if measured at angles 90 degrees apart). The photons in each pair are labeled A and B, corresponding to the locations of the polarizers that measure them. (Strictly speaking, each polarizer either passes its photon or not, and a photon detector after the polarizer either detects the photon or doesn't.)

The algorithm provides two functions, ##f_A## and ##f_B##, each of which takes defined inputs (given below) and outputs a measurement result for its corresponding photon for that trial. All of the information about the preparation procedure (identical for each trial) is encoded in these functions. So the only variables for each trial are the measurement settings (polarizer angles) at A and B; everything else is known in advance. Each measurement result is a boolean value: "1" means the photon was detected (i.e., passed the polarizer), "0" means the photon was not detected (did not pass the polarizer).

The inputs provided to the algorithm are the measurement settings (A, B) for each trial. These can be determined by any means desired, but they are external to the algorithm; the algorithm does not compute them, it just takes them as inputs. The input also, implicitly, determines the number of trials (by the number of pairs of settings that are provided).

According to Bell's Theorem, in order to properly reproduce the QM predictions (and the actual experimental results), each function, ##f_A## and ##f_B##, must take as inputs the measurement settings for that trial at both A and B. It is impossible to have ##f_A## only take as input the settings for A, and ##f_B## only take as input the settings for B, and still reproduce the QM predictions.

I'll hold off on saying what the functions ##f_A## and ##f_B## actually are, for the case under discussion, since the above might already be enough to clarify what, exactly, the algorithm in question needs to compute and what inputs it takes.

 

[PeterDonis]

Alice or Bod cannot compute anything from the WF.

If they only know their own measurement setting, that's true. They need to know both measurement settings in order to compute probabilities from the WF.

 

[PeterDonis]

They need to know both measurement settings in order to compute probabilities from the WF.

Actually, I need to clarify this. If, for example, all Alice wants to know is the probability of a single photon passing her polarizer, if she knows the photons are all prepared in the PP state, then she already knows the answer to that question: 50%.

However, as I described in post #55, the algorithm we have been talking about has to produce an actual sequence of measurement results, not just the probability of a single photon passing the polarizer. The sequence of measurement results has to satisfy all of the predictions of QM, not just its prediction for what fraction of Alice's photons pass her polarizer. Those predictions include the correlation between Alice's and Bob's results; and producing results that satisfy the QM predicted correlations is what the algorithm cannot do unless the functions it uses to output Alice's and Bob's results at each trial take as input both Alice's and Bob's measurement settings for that trial.

 

[PeterDonis]

Why don't you test it, to check...

I have. Its results seem obviously wrong; for example, it's giving 100% correlation with Alice's angle at 0 and Bob's angle at 90.

 

[Mentz114]

Non-locality makes all the difference. Once you understand what Bell is actually proving, you know how to conserve correlation, without allowing any possibility for A to "influence" B (or the contrary) I have posted it maybe a year ago in another thread.If I have one function for each, then each of those functions will only use one input. But that is right, you may create two local functions from one(non-local) which is globally aware of the two. That is the closest thing you have written that resemble the even more simply algorithm that I use.

It is necessary and sufficient to model entanglement to assume that the entangled pair always have the same value for the entangled property.
Writing ##P(xy|\alpha\beta) = \tfrac{1}{2}(P(x|\alpha)P(y|\alpha\beta) + P(y|\beta)P(x|\alpha\beta)## to reflect the fact that whichever projection happens first, the setting is known by the other wing. ##\alpha## and ##\beta## are the binary variables representing the polarizer settings on the two wings, and 'xy' is the four possible outcomes (00,01,10,11).

From Malus law ## P(x|\alpha) = \cos(\theta_0-\alpha)^2## so we can write
##P(11|\alpha\beta)=\tfrac{1}{2}\cos(\alpha-\beta)^2\left[ \cos(\theta_0-\alpha)^2+\cos(\theta_0-\beta)^2 \right]##
##P(00|\alpha\beta)=\tfrac{1}{2}\sin(\alpha-\beta+\pi/2)^2\left[ \sin(\theta_0-\alpha)^2+\sin(\theta_0-\beta)^2 \right]##
and so
##P(11\ or\ 00) = \cos(\alpha-\beta)^2##
The only assumptions are that whichever photon is projected first is irrelevant and that the photons always have the same polarization. It also shows that that only the probability of a coincidence ( or anticoincidence) is estimable.

 

[PeterDonis]

only the probability of a coincidence ( or anticoincidence) is estimable

I don't think this is correct; QM also predicts, for the entangled state in question, that, for each wing taken by itself, the probability of a photon passing its polarizer is 50%.

 

[Mentz114]

I don't think this is correct; QM also predicts, for the entangled state in question, that, for each wing taken by itself, the probability of a photon passing its polarizer is 50%.

Right. And that is also the result predicted by ##P(01|\alpha\beta)+P(00|\alpha\beta)=P(10|\alpha\beta)+P(11|\alpha\beta)=1/2## and the other marginals work out the same.

I have it written out explicitly but it would be a long post.

 

[Boing3000]

I can read Javascript, but you can hardly expect everyone here to do so. When I asked for an explicit description I meant a description in words or math, something that everyone here could be expected to understand.

I have done that at post 13# and give more details at post #20. The problem is that you don't realize that the "algorithm" IS the EPR experiment. There is a one to one relationship between each step of the EPR setup within the algorithm. It is a straightforward implementation. There is no fuss, no weirdness added, no information added. The trouble is that some people here wants to add things (like speed/FLT) or "signal" (B(or A) can detect a change), when there is factually no such things anywhere to be found. For the last time I will repeat those steps. I expect again disappointment on you part, because you'll pretend then things are missing (like a function that take A and B as input). There is no such thing.

As a side note, I have taken a great deal of time to additionally explain that wanting to ADD more functionality in the algorithm, is not even possible, it would break its ability to reproduce QM correlation. So here is again those steps, with "uneeded" comment centered (but needed by DrChinese or you). Again those comments have nothing to do with explaining the algorithm result. But just explaining how they relate to incorrect interpretation.
On the right I will restate some general comment on how some step can be related to physical phenomena. (but it is just comments)
Things that are not written don't have to be added.

1. A pair of photon (A & B) is prepared in an entangled state.
   That state in the algoritm is ##A{\rightarrow}V{\leftarrow}B## representing a unique shared hidden variable V. V in this setup is the hidden polarization angle chosen randomly.
   
   
   It is trivial that at this point any function using A as input will always give the same answer with B as input, because all the information is in V, which is identical to both A and B. The key point is unique-shared that implement non-locality
   

   
   If V was not hidden, Alice(or Bod) could guess before hand, with more than 0.5 chance. She could arrange the polarizer angle to anything but V+-45°. But then this has nothing to do with entanglement. Just with previous knowledge, like in any simple polarization test
   ​
2. Each photon are separated (to arbitrary long distance) to Alice and Bod who are going to process to a measurement that will use inputs that only exist locally at Alice and Bod. Those input (two polarizer angle) are decided randomly and locally. Nor Alice nor Bod have any idea on how the other is choosing its angle. The result is "pass" or "don't pass". The result(and angle) are stored locally (but not reused) before later comparison.
   
   The algorithm don't care about space like separation. There is no position, nor distance anywhere.
   

   
   To stress this point further, the algorithm can execute Alice test before Bod or after, Bod or randomly before or after
   ​
3. Two interaction/measure happens at random angle ##\alpha## and ##\beta##.
   In the algorithm a unique and identical function is used to represent this interaction. This function don't have any internal special knowledge except a random generator. This function is local because it uses two local input ##(Site photon, Site polarization angle)##
   This function is atomic, meaning is cannot "run in parallel" in algorithmic jargon.
   This function return "pass" or "not pass" and can modify anything that is accessible to it ##A{\rightarrow}V## in the case of Alice, ##B{\rightarrow}V## in the case of Bob.
   
   
   It is trivial to understand how correlation is conserved at any angle, because the function can "drop" any value in V that can be reused later by any other input also referencing the same V. But again, there is no possibility for Alice to know if she get's to V before or after Bob. Nor does Bod. FAPP V is always a random hidden value with no "A" smell nor "B" smell. There is no link between A & B.
   

   
   The algorithm local measure function will sever the local link form the photon to its "old" hidden variable, and replace it by a new identical new one. The reason have nothing to do with the EPR results. It has to do with avoiding Alice to retest A shortly after, in the hope to guess if Bod (or Jon or whatnot) have modified it "in between". This implement "destructive measurement"/dis-entanglement
   ​
   The "test" is random() < Cos^2((Site photon->V)-Site polarization angle). This test is the classical proportion of light that goes trough a filter.
   if (true) -> set V to polarization angle and return "pass"
   if (false) -> set V to (polarization angle + 90°) and return "don't pass"
   
4. After running a (big) number of those experiments, all the results are compared again but with what the "actual" angle between Alice and Bod was in each case.
   The correlation is given by "number of pair that matched", versus "number of pair that don't"

 

[Mentz114]

I have done that at post 13# and give more details at post #20. The problem is that you don't realize that the "algorithm" IS the EPR experiment. There is a one to one relationship between each step of the EPR setup within the algorithm. It is a straightforward implementation. There is no fuss, no weirdness added, no information added.
[..]

1. The algorithm don't care about space like separation. There is no position, nor distance anywhere.
   

   
   To stress this point further, the algorithm can execute Alice test before Bod or after, Bod or randomly before or after​

It sounds as if you have caught some of the essentials - the randomness of the 'before/after'.
My own simulation based on the equations I gave generates data sets that are indistinguishable from actual 2-channel EPR experiments.
Like yours nothing it is added except the shared state. I don't know why you think there's anything special about it. It is standard programming.

Could you let me have some simulated data for analysis ?

 

[DrChinese]

Have you ever consider that there is another possibility ? That you simply never tried to understand what I say instead of trolling me and threatening me ?
.

You have things backwards. You are flirting with forum rules by putting forth your own (often incorrect) ideas. Meanwhile, PeterDonis is being patient and giving you latitude.

BTW, did you ever fix your simulation?

 

[DrChinese]

The correlation is given by "number of pair that matched", versus "number of pair that don't"

Assuming you are making proper correlation be Matches - Non-matches: the results will vary from 1 to -1 as theta changes. The correlation is 0 at 45 degrees, 1 at 0 degrees, -1 at 90 degrees. At 60 degrees, it should yield -.5 (.25-.75).

 

[kurt101]

The sum of the probability amplitudes for that outcome. You appear to be misunderstanding what that means.
Suppose there are three possible outcomes; call them A, B, and C. For outcome A, suppose there are two ways that can happen, with amplitudes ##a_1## and ##a_2##. For outcome B, suppose there are three ways it can happen, with amplitudes ##b_1##, ##b_2##, and ##b_3##. And for outcome C, suppose there is only one way it can happen, with amplitude ##c##.
Then the probabilities are: for A, ##\left( a_1 + a_2 \right)^2##; for B, ##\left( b_1 + b_2 + b_3 \right)^2##; and for C, ##c^2##. There are no "cross terms" between outcomes.
You should re-think things in the light of the above.

First of all I agree with the just of your post that there are no "cross terms" between outcomes. I made a superposition of the word "outcome" in my previous post on this thread. First to mean outcome in the way you use it and second to mean as the path it took (in a way my brain thinks of the path as an outcome). That being said I think I did use it correctly in the thread you closed. Sorry for the confusion, but my underlying point is still valid (at least in my mind). If I am still mixed up, I appreciate your effort in correcting me!
So let me rephrase with your example. For outcome B there are 3 ways that it can happen. This gives a probability of b₁b₁ + b₁b₂ + b₁b₃ + b₂b₁ + b₂b₂ + b₂b₃ + b₃b₁ + b₃b₂ + b₃₃.
You are multiplying all of the ways the path b₁ can interfere with plus all of the ways path b₂ can interfere with plus all of the ways path b₃ can interfere with.
Again my point is that only 2 paths can interfere at a time to give you a definite state.

And maybe I don't really understand the definition of superposition, but either way, I don't see any evidence that there is really a mixture of states other than in then in a probabilistic sense. And the math suggests that there is only ever a mixture of 2 paths for any given instance. This seems similar, if not equivalent to the entanglement collapse algorithm that myself, Boing3000, Mentz114 and maybe others have posted on this forum; where there is only ever a mixture of 2. Maybe that should not be surprising, given that the collapse algorithm does give the same result as QM.

 

[PeterDonis]

For outcome B there are 3 ways that it can happen. This gives a probability of b1b1 + b1b2 + b1b3 + b2b1 + b2b2 + b2b3 + b3b1 + b3b2 + b33.

No, it doesn't. As I said in my previous post, it give a probability of ##\left( b_1 + b_2 + b_3 \right)^2##. But since these are complex numbers, and the probability is a real number, you actually need to take the squared modulus, i.e., the probability is actually ##\vert \left( b_1 + b_2 + b_3 \right) \vert^2##. Or, to write it another way: ##\left( b_1 + b_2 + b_3 \right) \left( b_1 + b_2 + b_3\right)^*##, where the asterisk denotes the complex conjugate. None of these things are the same as what you wrote; none of them are the same as just multiplying out the two factors of ##\left( b_1 + b_2 + b_3 \right)##. The only correct way to describe the process in words is that you add together all of the amplitudes for the different ways a particular outcome can happen, and then take the squared modulus of the result.

my point is that only 2 paths can interfere at a time to give you a definite state.

And this is not correct. You are mistaken about how the probability is computed from the amplitude. There is nothing in that process that corresponds to "only 2 paths can interfere at a time". See above.

The rest of your post just compounds this error.

 

[PeterDonis]

I have done that at post 13# and give more details at post #20.

If those posts made sense we would not still be having this discussion.

There is a one to one relationship between each step of the EPR setup within the algorithm.

Do you mean the EPR setup with local hidden variables, as described in Bell's paper? (Apparently you do--see below.) If so, that setup must satisfy the Bell inequalities, so it cannot reproduce the QM predictions. I thought you were claiming that your algorithm reproduced the correct QM predictions.

That state in the algoritm is ##A{\rightarrow}V{\leftarrow}B## representing a unique shared hidden variable V. V in this setup is the hidden polarization angle chosen randomly.

There is no "hidden polarization angle" in the correct QM model. This V is a local hidden variable, in Bell's terminology, and it means your algorithm (if it is correct in all other respects) will produce results that satisfy the Bell inequalities, not results that match the correct QM predictions.

I don't see the point of trying to make sense of the rest of your description since the above shows that you already have the most important point wrong.

 

[PeterDonis]

My own simulation based on the equations I gave generates data sets that are indistinguishable from actual 2-channel EPR experiments.

Are the code and generated data sets available somewhere?

 

[Mentz114]

Are the code and generated data sets available somewhere?

I can do one or more of the following
a) let you have datasets as csv text files
b) Let you have the simulation if you have a windows machine so you can make datasets
c) the code is Delphi and the source is available

The simulation does exactly what is described by the probabilities I worked out.