More EPR Simulation Discussion

[FrediFizzx]

Copying this to a new thread here.

What makes it interesting is quantum mechanics would predict a straight line for constant setting difference over a range of absolute settings, so a model and its simulation would be required to provide the same.

This simulation produces exactly what quantum mechanics predicts in all conceivable physical scenarios. Your confusion arises because you have not understood what I have explained here: viewtopic.php?f=6&t=69#p3225.

I think I did understand what you were trying to say, and what you missed within. cos(a) and cos(-b) are poor representatives of cos(a-b) since they are each functions of a single variable.

Simple test for you to perform: in Joy's http://rpubs.com/jjc/16415, change beta for the first plot from 0 degrees to 30 degrees. If the model/simulation was true, the plot should be the -cos function with a 30 degree offset. It isn't because at the very least, the simulation is not true to expected results.

Incorrect. It is very easy to modify any simulation so that it stops working. Changing from 0 degrees to 30 degrees corresponds to a counterfactual change in the setting of Bob, which in turn means a different physical experiment altogether. Why should a different experiment produce the same result?

One has to produce only one correct simulation, like this one, to prove Bell wrong. You cannot prove Bell right by producing a simulation that does not work.

If you were actually demonstrating the proper function of two variables, it would be quite correct to do what I did. The second plot in your program does not change the initial conditions vector set u and does allow beta to breeze right through 30 degrees without any problems, so clearly it is not that for some strange reason beta can't be 30. Your simulation simply will not work without one of alpha or beta being 0. This is not a demonstration of -cos(alpha - beta). The rub is you can't do this without making the set u be a function of both Alice's and Bob's settings, which is precisely and very clearly evident in your x-y plot simulation within the following code snippet

Code: Select all

x <- runif(M, -1, 1)
t <- runif(M, 0, 2 * pi)
r <- sqrt(1 - x^2)
y <- r * cos(t)

u <- rbind(x, y)  ## 2 x M matrix; the M columns of u represent the
## x and y coordinates of M uniform random points on the sphere S^2

eta <- runif(M, 0, pi)  ##  My initial eta_o, or Michel Fodje's 't'

f <- -1 + (2/sqrt(1 + ((3 * eta)/pi)))  ## Pearle's 'r' is arc cosine of 'f'

for (i in 1:K) {
    alpha = angles[i]
    a = c(cos(alpha), sin(alpha))  ## Measurement direction 'a'

    for (j in 1:K) {
        beta = angles[j]
        b = c(cos(beta), sin(beta))  ## Measurement direction 'b'

        ua <- colSums(u * a)  ## Inner products of 'u' with 'a'
        ub <- colSums(u * b)  ## Inner products of 'u' with 'b'

        good <- abs(ua) > f & abs(ub) > f  ## Sets the topology to that of S^3

        p <- x[good]
        q <- y[good]
        N <- sum(good)

        v <- rbind(p, q)  ## N spin directions pre-selected at the source

        va <- colSums(v * a)  ## Inner products of 'v' with 'a'
        vb <- colSums(v * b)  ## Inner products of 'v' with 'b'

        corrs[i, j] <- sum(sign(va) * sign(-vb))/N

        ## corrs[j] <- sum(sign(vb))/N

        Ns[i] <- N
    }
}



Alice's measurements sign(va) and Bob's measurements sign(-vb) are both functions of v which in turn is a function of good, which in turn is a function of both a and b which are Alice's and Bob's chosen orientation angles respectively. You need to explain how this could possibly be valid.

This has been explained many many times already in this forum. I guess you missed all of them. I will try one more time; Joy may have something to add. The line,

good <- abs(ua) > f & abs(ub) > f ## Sets the topology to that of S^3,

is how you select the states that are possible in Nature. It is a simulation; you have to simulate what we think Nature is doing somehow. Please study this paper and tell us the first part that you don't understand for further explanation.

http://arxiv.org/abs/1405.2355

[Joy Christian]

Let me add a very basic point that seems to have been missed. It should not be surprising that the observations of Alice and Bob are "linked" or "connected" in the simulation. But of course they are linked. They have to be, otherwise there would be no correlation between their observations in the first place. The issue is not that the observations of Alice and Bob are linked or correlated, but that the correlation between them is explicable entirely locally, where the local explicability is understood precisely as it was understood by Einstein and quantified by Bell.

Also worth mentioning here is this series of simulations, distinguished only by the topological properties of R^3 and S^3.

[Mikko]

Let me add a very basic point that seems to have been missed. It should not be surprising that the observations of Alice and Bob are "linked" or "connected" in the simulation. But of course they are linked. They have to be, otherwise there would be no correlation between their observations in the first place. The issue is not that the observations of Alice and Bob are linked or correlated, but that the correlation between them is explicable entirely locally, where the local explicability is understood precisely as it was understood by Einstein and quantified by Bell.

The important point is that for any causal connection between Alice and Bob, both measurements are at the effect end of the connection and not on the cause end. Otherwise we have non-local causality.

[Rick Lockyer]

In the thread the original post was copied from

You are ducking.

I am ducking nothing. I am simply trying to point out to you---as politely as I possibly can---that you do not know what you are talking about.

Are Alice's observations to be independent of Bob's settings? Yes or no. If yes, why are they not in your simulation?

Alice's observations are independent of Bob's settings in my simulation, as anyone knowledgeable can see for themselves: http://rpubs.com/jjc/16415.

Joy, your statement here is both incorrect and condescending. Maybe Fred could explain why he did not remove it? As I have clearly stated several times, and I fully believe you completely understand, in the referenced simulation Alice has a free choice of directions yielding correct correlations only if Bob chooses a direction of 0, as I demonstrated in the suggestion to Fred to try beta = 30 degrees. So Alice's choice IS dependent on Bob's choice in your simulation and your statement above is clearly untrue. Perhaps you and/or Fred could explain to me where you stopped understanding what I said. Be happy to try explaining it in terms you might better understand.

Moreover, I stated in my post Fred inserted within the first post above that the x-y plot was successful because what Joy claimed in the quote just above was not the case either. Really simple to prove. All one has to do is fix Alice's direction "a" at some value, use Joy's program steps within the x-y "for loops" to determine Alice's observations for two separate Bob directions "b", then compare the two sets of Alice observations. They are going to be different. So once again Joy's statement about one's observations being independent of the other's settings in his simulations is clearly false. Fred perhaps you could do the program and report the results, being the unbiased moderator you clearly have demonstrated so many times.

Now for http://arxiv.org/abs/1405.2355

So Fred, you want me to let you know the first part I did not understand. I find this assumption offensive, rude and condescending. But it does put you on record as agreeing to the article content. So I do not have to assume anything about your abilities, and can point out where both you and Joy have fallen short of the mark without any assumptions.

For P and Q members of the domain S^n, P+Q is assured not to be a member of S^n. That nukes Joy's derivation out of the gate, since the Triangle Inequality is not relevant to S^n. Also, the equality only holds when the domain admits zero vectors, clearly never the case for S^n. Beyond that, I think Joy pulled equation 16 out of thin air maintaining decorum of course. Think about an earlier arxiv derivation when the state of his simulations was less refined?? Triangle Inequality approach with a different equation 16 both stated as being topologically required. One could not be faulted to think he is backing into the desired results.

Prove me wrong Joy, explain the validity of using the Triangle Inequality, put up an explicit derivation of both choices for eq. 16 and explain why both are valid or withdraw the first.

[Joy Christian]

The derivations and content of this paper http://arxiv.org/abs/1405.2355 are impeccable, including equation (16). The very fact that Rick Lockyer is demanding a "derivation" of the complete or initial state (16) speaks volumes (cf. the elementary introductory discussion in the famous paper of Bell). Beyond this, I decline to engage with Rick Lockyer's comments. Let the community be the judge of the merits of my work---especially of this paper: http://arxiv.org/abs/1405.2355.

[Yablon]

Joy,

I will assume for the sake of discussion that your theory correctly explains local correlations between the observations of Alice and Bob for two parts of a singlet systems which as laid out by EPR "we permit to interact from time t=0 to t=T, after which time we suppose there is no longer any interaction between the two parts," and which are then separately and independently observed at any time t>T.

On that basis, let me ask a two very simple question sets:

In general, irrespective of your theory, do you see a way in which the double slit can be understood in the EPR sense as also involving states which a) interact, b) cease interaction and then c) are separately observed?

In specific, can your theory also be used to explain the double slit results? If so, in what manner?

Thanks,

Jay

[Joy Christian]

Hi Jay,

I can provide a formal argument. The detailed analysis of the problem is another matter.

Formally the double slit experiment is no different from any other experiment. In the quantum mechanical description we begin with an initial state such as

,

where 1 and 2 label the two slits. Next we look for a self-adjoint operator, say , representing the observable quantities. The expectation value of this operator in the above state, , then provides the predictions of what will be observed on the screen beyond the slits.

Let me now generalize this prescription to any physical system, in any initial state, for any observable, as follows.

Suppose we consider an arbitrary quantum state and the corresponding self-adjoint operator in some Hilbert space , parameterized by an arbitrary number of local parameters etc. Note that I am imposing no restrictions on the state , or on the size of the Hilbert space . In particular, can be as entangled or un-entangled as one may like, and can be as large or small as one may like (in the case of the double slit there is no entanglement, for example). The quantum mechanical expectation value of the operator in the state would then be

,

where is a statistical operator of unit trace representing the state. Now I have shown that the quantum correlation predicted by this expectation value can always be reproduced as local and realistic correlation among a set of points of a parallelized 7-sphere, by following a procedure very similar to the one discussed above for the 3-sphere. In fact, I have proved the following theorem:

Every quantum mechanical correlation can be understood as a deterministic, local-realistic correlation among a set of points of a parallelized 7-sphere, specified by maps of the form

.

The proof of this theorem can be found in this paper.

Admittedly, this is quite a formal argument. But it is now possible to fill in the details for the case of the double slit experiment.

Joy

[FrediFizzx]

In specific, can your theory also be used to explain to double slit results? If so, in what manner?

Joy's model / theory says that space has unique spinor properties so I think one would have to go from that for an explanation of double slit scenarios. It probably would be worthwhile to work it out more formally but I can see some interpretations may be necessary. You allude to the same thing on page 123 of your paper where you say, "..., there is an underlying fermion structure to spacetime that lay hidden in a set..." when talking about Dirac's discovery. So I think there is some agreement here. Now to just work out more details.

There is also to consider what Michel said in his thread about double slits, viewtopic.php?f=6&t=51

[Yablon]

Hi Jay,

I can provide a formal argument. The detailed analysis of the problem is another matter.

. . . formal argument. . .

Admittedly, this is quite a formal argument. But it is now possible to fill in the details for the case of the double slit experiment.

Joy

Hi Joy,

It is the details I am after. For example, http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html has an excellent simulation of quantum-by-quantum accumulation in the double slit experiment for electron, photons, protons, neutron and mesons. Can you show directly and visually how it is that the field quanta of any given type and energy, and with any given slit configuration, "know" the probability with which they are supposed to strike at any given position on the detector, and end up striking the detector in this way? Can you do a simulation which reproduces http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html? And if so, how does one think, physically, about what these field quanta encounter in the vacuum along the way that makes them strike this way?

I am OK if you start with your:



then show the explicit wavefunctions and operators and results which yield the http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html probability density patterns along the detector which are of the general form:



as graphed in my Figure 24 at http://jayryablon.files.wordpress.com/2 ... mplete.pdf.

Jay

[Joy Christian]

It is the details I am after. For example, http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html has an excellent simulation of quantum-by-quantum accumulation in the double slit experiment for electron, photons, protons, neutron and mesons. Can you show directly and visually how it is that the field quanta of any given type and energy, and with any given slit configuration, "know" the probability with which they are supposed to strike at any given position on the detector, and end up striking the detector in this way? Can you do a simulation which reproduces http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html? And if so, how does one think, physically, about what these field quanta encounter in the vacuum along the way that makes them strike this way?

Good questions, Jay. I am sure all of these things can be worked out with sufficient time and effort. I am not motivated enough or inspired enough to work it all out, however. Perhaps because double slit, uncertainty principle, wave-particle duality etc. aren't the deepest issues to someone like me who works in the foundations of quantum mechanics. The deepest issue for me is the so-called quantum entanglement, and that immediately leads us back to the EPR argument and Bell's theorem. You can put this down to "cultural differences" between particle physics and quantum foundations.

[Yablon]

It is the details I am after. For example, http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html has an excellent simulation of quantum-by-quantum accumulation in the double slit experiment for electron, photons, protons, neutron and mesons. Can you show directly and visually how it is that the field quanta of any given type and energy, and with any given slit configuration, "know" the probability with which they are supposed to strike at any given position on the detector, and end up striking the detector in this way? Can you do a simulation which reproduces http://phys.educ.ksu.edu/vqm/html/doubleslit/index.html? And if so, how does one think, physically, about what these field quanta encounter in the vacuum along the way that makes them strike this way?

Good questions, Jay. I am sure all of these things can be worked out with sufficient time and effort. I am not motivated enough or inspired enough to work it all out, however. Perhaps because double slit, uncertainty principle, wave-particle duality etc. aren't the deepest issues to someone like me who works in the foundations of quantum mechanics. The deepest issue for me is the so-called quantum entanglement, and that immediately leads us back to the EPR argument and Bell's theorem. You can put this down to "cultural differences" between particle physics and quantum foundations.

Fair enough Joy. But I have seen you argue for years with skeptics of your theory. Don't you think that if you were able to work this out and show it, that you would gain a lot more traction convincing people of your theory? I say this as a friend who is following a parallel path to you insofar as having a body of theoretical work which a number of people think is interesting, but which has not (yet) acquired mainstream acceptance. I would go an extra mile, or dare I say, an extra ten miles, to do something that would get me across that threshold.

Jay

[FrediFizzx]

Hi Jay,

I think you are actually in a better position to work this out from a particle physics perspective. I am sure that Joy would help out with any particular questions. Now considering what Michel said about double slits after reviewing it once again, this may not even be a mystery that needs to be solved.

Well since you are impatient to know the answer, let me give you the brief version. You will have to ask specific questions to get detailed explanations.

1) quanta/particles can transfer momentum to the walls if the slits.
2) The amount of momentum transferred, determines the angle of deflection of the particle.
3) Transfered momentum is quantized. Therefore the particles are deflected into discrete directions.
4) The allowed directions are determined by the relationship between the normal modes if the slit system and the frequency of the quanta/particle.
5) Since different slit systems have different normal modes, the diffraction patterns are different.
6) The pattern produced, and the slit system producing it have a dual relationship. They can be expressed as Fourier transforms of each other.

So if there is a mystery to be solved, then Michel must be wrong about one or more of the above. What do you think it might be? Or... can you actually work out the details of the scattering from the slits above?

[Joy Christian]

Fair enough Joy. But I have seen you argue for years with skeptics of your theory. Don't you think that if you were able to work this out and show it, that you would gain a lot more traction convincing people of your theory? I say this as a friend who is following a parallel path to you insofar as having a body of theoretical work which a number of people think is interesting, but which has not (yet) acquired mainstream acceptance. I would go an extra mile, or dare I say, an extra ten miles, to do something that would get me across that threshold.

You may have a point, Jay. However I have already accumulated a large number of results in 15 papers and a book. Most people who are interested in the foundations haven't even bothered to look beyond the EPRB correlation in my work. I have worked out much more complicated states than the EPRB state in great detail, but there seems to be no curiosity among the "experts" about how have I been able to reproduce all these complicated correlations local-realistically (see, for example, the results in this paper: http://arxiv.org/abs/0904.4259). So it seems to me that if, in addition, I worked out the double slit problem (which is not even an entangled state), then that is unlikely to impress anyone in the quantum foundations culture. They would be impressed already if they just looked at my already existing results.

[Yablon]

Hi Jay,

I think you are actually in a better position to work this out from a particle physics perspective. I am sure that Joy would help out with any particular questions. Now considering what Michel said about double slits after reviewing it once again, this may not even be a mystery that needs to be solved.

Well since you are impatient to know the answer, let me give you the brief version. You will have to ask specific questions to get detailed explanations.

1) quanta/particles can transfer momentum to the walls of the slits.
2) The amount of momentum transferred, determines the angle of deflection of the particle.
3) Transfered momentum is quantized. Therefore the particles are deflected into discrete directions.
4) The allowed directions are determined by the relationship between the normal modes if the slit system and the frequency of the quanta/particle.
5) Since different slit systems have different normal modes, the diffraction patterns are different.
6) The pattern produced, and the slit system producing it have a dual relationship. They can be expressed as Fourier transforms of each other.

So if there is a mystery to be solved, then Michel must be wrong about one or more of the above. What do you think it might be? Or... can you actually work out the details of the scattering from the slits above?

Hi Fred,

1 and 2) I agree. But that is the beginning of the trip to the detector. There may be other factors in the vacuum (like the potential) which determine where a particle ends up striking.
3) Let's be clear when we use the word quantized. We are now talking about a single particle going through the slit. The fact that we have a single particle says all we need to say about quantization. The energy of that single particle E=hf, and its momentum p=hf/c=h/lambda. If the particle can enter the slit near the edge or away from the edge over a continuous spatial domain, then I do not see why there has to be a discrete deflection direction.
4&5) I'd like to know better what that means. Maybe it is is meaningful, maybe not. Probably my own lack of understanding what Mike means.
6) That is very interesting and a correct mathematical observation. The envelope functions for both the single an double slit experiments are sinc^2 functions, and indeed for sinc(x) the Fourier transform is rect(p) and for sinc^2(x) it is tri(p). But it would be good to really understand the physics of why that is so.

As I said earlier to Joy, for the double slit, the probability density observed at the detector is:



But for the single slit is it:

.

If this was a linear problem, then we would just have the latter sinc^2 superimposed upon itself, that is, we would have two of these sinc^2 patterns superimposed with a separation equal to the slit separation. But that is not what we see. We see a cos^2 which sits inside the sinc^2 envelope. That means this is a non-linear problem, because "experiment with slits A and B together" is not equal to "experiment with slit A alone plus experiment with slit B alone."

I'd like to see how Mike gets that sinc^2 x cos^2 result from his 1 through 6 above. Maybe the Fourier transform does something that makes "A plus B" not equal to "A union B." But if that is so, we still need to understand the physics which makes that so, and not just the cute mathematics.

And on second thought, that cannot be so, because Fourier transforms are linear. So if I start with, say tri(x) + tri(x-a) to represent two slits with centers separated by a along the x axis, the Fourier transform of this whole function will be the sum of the two separate Fourier transforms. So the non-linearity has to arise in some other way.

Jay

[FrediFizzx]

Hi Jay, just a quick note; it is Michel not Mike for minkwe's name.

[Joy Christian]

Hi Jay,

This paper may be the answer you are looking for: http://philsci-archive.pitt.edu/3205/1/DSlit.pdf.

Joy

[Yablon]

Hi Jay,

This paper may be the answer you are looking for: http://philsci-archive.pitt.edu/3205/1/DSlit.pdf.

Joy

Thanks Joy:

I completely agree with the following statements by the author about the double slit outcomes:

"There are four questions concerning these outcomes that need to be explained:
A. Why are particles that have been prepared in a like manner detected at different spots on Σ_2?
B. How does the interference pattern emerge as the accumulated effect of many single particle events?
C. How can a single particle pass through both slits and subsequently interfere with itself?
D. Why are only individual particles detected on Σ_2?"

I do not agree with the way in which he answers these questions, because the author relies on abstract mathematical spaces and numbers which may not be ontologically real, while as a physicist I believe we need an explanation that uses the real, physical spaces and numbers of our natural experience, as well as principles of least action / geodesic evolution. But again, he certainly does a very good job articulating the problem to be explained.

I will be preparing my own explanation for these questions, based on the isomorphism between probability density and Bohmian guiding potential developed in my paper at http://jayryablon.files.wordpress.com/2 ... mplete.pdf, as is under discussion in a related thread. I already wrote and posted PART I at viewtopic.php?f=6&t=75&start=30#p3405. I just need to find a good six to eight hours to pull the rest of this together.

Jay

[minkwe]

1 and 2) I agree. But that is the beginning of the trip to the detector. There may be other factors in the vacuum (like the potential) which determine where a particle ends up striking.

You expect a particle to change direction without transfer of momentum? What happens to conservation then. If you do not expect the particle to change direction without transfer of momentum, then it should take a direct straight path to the detector, then what need do you have for the potential? If you agree that the only opportunity for momentum transfer is at the slits then you don't need any spooky vacuum or "potential" to change the trajectory of the particle. Then the only remaining question is why momentum transfer is nonlinear at the slits.

3) Let's be clear when we use the word quantized. We are now talking about a single particle going through the slit. The fact that we have a single particle says all we need to say about quantization.

There are two parties to every interaction. Don't forget the slits, they are not passive. They too are made of atoms and electrons that can take part in momentum transfer. And what is the most important variable in momentum transfer, when force is constant? -- Distance. The relevant distances at the point of scattering in the direction of deviations (ie,pendicular to the direction of photon impingement) are the distances between slits, and within slits. This dynamics is non-linear, and determines the amount of momentum transferable.

[florence]

...and what about when the slits are not made of atoms and electrons, but standing waves of light? like, e.g here:
http://www.univie.ac.at/qfp/research/ma ... twave.html
(though i strongly suspect that a light grating would not be first choice if the incoming beam was photons!)

[minkwe]

...and what about when the slits are not made of atoms and electrons, but standing waves of light? like, e.g here:

What about it?