SciPhysicsForums.com

... well actually it was Mermin's experiment, first. But anyway... [correction; thanks to Joy: Peres]

Instead of doing Joy's experiment for real, why not do it by computer simulation? ("In silico", one might say). In that case we can even do it in zero gravity, at absolute temperature zero, and in a vacuum. (It will be *easier* to do it that way).

Here are some thoughts. We want to simulate spinning hemispheres. This is what computer graphics is all about. This is what your GPU (NVidia card) does. It even has quaternions "hard-wired" (geometric algebra!).

I found two R packages with support for quaternions:

http://cran.r-project.org/web/packages/onion/onion.pdf

http://cran.r-project.org/src/contrib/A ... aternions/

But this is of course about implementing them at a high level, not taking advantage of built-in hardware level (GPU instead of CPU) opportunities.

I saw a paper about tracking spinning ping-pong balls using quaternions.

http://dspace.mit.edu/bitstream/handle/ ... 13-005.pdf

I saw some stuff about GPU computing with R.

http://www.r-tutor.com/gpu-computing

We need to use "CUDA".

I suppose that one would access CUDA through intermediate level programs written in C++. There is a wonderful interface between R and C++ called Rcpp. So I think the way to go is through building transparent interfaces R - C++ - CUDA

We want to do the hard core supercomputing with the best tools (CUDA on one or more GPU's). A supercomputer on your desk. We want to do the more "front office" stuff (managing data, doing the statistics and graphics) with R.

Of course if Joy would agree on a computer simulation of his exploding colourful balls we could in principle do his experiment a whole lot more cheaply than what he has in mind (I guess he has contacts with some renegade scientist from Kazachstan or something...).

However once we enter the domain of computer simulation models, we also enter the domain where logical analysis, mathematics, including a bit of probability theory, can be used to predict the outcome of the experiment with near certainty. That would also make all the investment in supercomputers and programming superfluous too!

gill1109 wrote:... well actually it was Mermin's exoeriment, first. But anyway...

Not quite. Mermin had nothing to do with it. It is based on Bell's own local model, described in eqs. (8) to (10) of his famous 1964 paper. Bell's model was turned into a thought experiment involving a bomb by Peres, published in AJP, and later in his book (as cited in this 2008 paper of mine: http://arxiv.org/abs/0806.3078). Peres's description, however, is still just an abstract description. It takes a bit of a thought to turn his abstract description into a realizable experiment. My proposal of how to realize the experiment is still just a sketch; although according to the Nobel Laureate David Wineland it is "doable." If realized, it may not involve exploding balls.

gill1109 wrote:Of course if Joy would agree on a computer simulation of his exploding colourful balls we could in principle do his experiment a whole lot more cheaply than what he has in mind...

In principle I have no problem with a computer simulation of the experiment. The challenge would be to simulate the physical space S^3 in which the ball explodes.

gill1109 wrote:(I guess he has contacts with some renegade scientist from Kazachstan or something...)

As far as I know, David Wineland lives in Colorado, United States of America, not in Kazachstan or something.

Joy Christian wrote:

gill1109 wrote:... well actually it was Mermin's exoeriment, first. But anyway...

Not quite. Mermin had nothing to do with it. It is based on Bell's own local model, described in eqs. (8) to (10) of his famous 1964 paper. This model was turned into a thought experiment involving a bomb by Peres, published in AJP, and later in his book (as cited in this 2008 paper of mine: http://arxiv.org/abs/0806.3078). Peres's description, however, is still just an abstract description. It takes a bit of a thought to turn his abstract description into a realizable experiment. My proposal of how to realize the experiment is still just a sketch; although according to the Nobel Laureate David Wineland it is "doable." If realized, it may not involve exploding balls.

gill1109 wrote:Of course if Joy would agree on a computer simulation of his exploding colourful balls we could in principle do his experiment a whole lot more cheaply than what he has in mind...

In principle I have no problem with a computer simulation of the experiment. The challenge would be to simulate the physical space S^3 in which the ball explodes.

gill1109 wrote:(I guess he has contacts with some renegade scientist from Kazachstan or something...)

As far as I know, David Wineland lives in Colorado, United States of America, not in Kazachstan or something.

OK! David Wineland would be splendid!

A simulation: we just need to find a competent person who will program Joy's S^3 model to his satisfaction. How about asking Chantal Roth? You need to do this. Initially, we think of three separate computer programs. One to simulate the flights of the hemispheres. One to observe the spin of one of them in any externally chosen direction. And one more for the other. But in fact, it can be just one program, which is used twice, with the pseudo random seed reset the second time to exactly what it was the first time.

The single program allows either Alice or Bob to "interrogate" one hemisphere, at the end of the simulated flight of both.

I'm sure our board of adjudicators will be equally happy to adjudicate on the results of a computer simulation experiment, as on a real experiment with all the messy details that that entails. In fact, the protocol of the experiment could be identical to that of my proposed bet with Luigi Accardi many years ago.

Metal ingots contain a complex collection of matter, especially including quarks and gluons. Would not a simulation of such an experiment need to use S7? Even using S7, a simulation could not reproduce the microscopic complexity of the immense number of quarks in an ingot. Would the simulation need to treat an ingot as if it were a single electron using S3? In which case it would not be a good simulation of a macroscopic event.

Do available 3D software modules use rotations with a 2π period rather than a 4π period? For gaming purposes, which may be the main use (?), it would be unnecessary to use anything other than a 2π periodicity of rotation. So won't the outcome inevitably be stacked against hidden variables if existing software modules are used? And, likewise, making one's own module with a 4π periodicity could be stacking the result in favour of hidden variables.

One advantage of a macroscopic experiment is that pairs of ingots are generated (for flatlanders and 3spherers alike), whereas in a simulation the generated data are not necessarily particles
(according to 3spherers). I suspect that in an S3 simulation of the macrosopic events, treating the ingot like a pseudo electron with (somehow) added volume, some of the generated data will be seen as non-particles by the 3spherers.

If the ingot is treated as if it were an S3 point electron with added volume, then it seems to me that electron spin would be being treated like the ingot's angular rotation. I am an amateur,
but is not the electron spin always denied to be equivalent to an angular rotation of a body? Moreover, if the electron spin represents another dimension available on the microscopic scale to
the electron, then the 4π rotational periodicity of the electron could be caused by that extra dimension anchoring the electron to it as the electron rotates (cf Dirac's belt analogy). But attributing an
added volume to a pseudo electron in a simulation, and equating the angular rotation to electron spin seems wrong somehow. If the simulation coding gave an ingot a 4π periodicity, then we would be left wondering if a positive result for Joy had been caused by unrealistic software coding.

My comments are probably only showing my lack of ability to see any simulation as a good enough representation of the experiment.

Ben6993 wrote:My comments are probably only showing my lack of ability to see any simulation as a good enough representation of the experiment.

Ben, you are being modest.

A simulation is merely a crude implementation of whatever is being simulated. If simulations were good enough, we would all be simulating our travels than flying.

Joy Christian wrote:

Ben6993 wrote:My comments are probably only showing my lack of ability to see any simulation as a good enough representation of the experiment.

Ben, you are being modest.

A simulation is merely a crude implementation of whatever is being simulated. If simulations were good enough, we would all be simulating our travels than flying.

If Joy can explain his mathematics clearly enough then a competent computer programmer can program it. No problem with computer implementation of algebra in S^7 or S^3 or whatever. We are talking about two halves of a ping-pong ball which fly apart due to the detonation of a small explosive device inside them, there are small weights attached inside the shells as well. They are brightly coloured and they will be filmed by a battery of video cameras from a whole of different angles. After the experiment, we will use standard image reconstruction software to determine whether each hemisphere is spinning up or down with respect to directions specified by the experimenters, at particular time moments determined I suppose by the experimenters too.

This seems is a classical mechanics problem. It's like modelling the toss of a coin or a dice.

On Earth, the experiment would be disturbed by air, gravity, temperature. In silica, all of these factors can be excluded! On earth, we have the problem of doing all the image analysis to make our measurements. In silico there is no problem - at each time instant each hemisphere has a definite position and orientation! And is instantaneously turning about one particular axis!

gill1109 wrote:If Joy can explain his mathematics clearly enough then a competent computer programmer can program it. No problem with computer implementation of algebra in S^7 or S^3 or whatever.

I have explained the physics and mathematics of the problem quite clearly and in great detail: http://arxiv.org/abs/1211.0784.

The challenge would be to implement the true geometry and topology of the physical space in the simulation from the beginning.

In other words, the challenge would be to simulate the physical space as S^3, not as R^3. The bombs are exploding in S^3, not in R^3.

I asked Chantal Roth, but she said she does not know how to simulate S^3 without having to discard some "events" "a posteriori", as in Michel Fodje's simulation.

Of course, no states are being discarded in Michel Fodje's simulation. One cannot discard that which is not there in the first place.

Joy Christian wrote:The challenge would be to implement the true geometry and topology of the physical space in the simulation from the beginning.
In other words, the challenge would be to simulate the physical space as S^3, not as R^3. The bombs are exploding in S^3, not in R^3.
I asked Chantal Roth, but she said she does not know how to simulate S^3 without having to discard some "events" "a posteriori", as in Michel Fodje's simulation.

So you have to explain to her (or someone like her) how to simulate the motion of, e.g., a small hemispherical object in S^3. Apparently your description of the the physics and mathematics of the problem at http://arxiv.org/abs/1211.0784 does not have quite enough clarity and/or detail. You could start with explaining the motion of a single small coloured sphere, to make things more simple.

A detailed description of the mathematics/physics should be enough to enable a competent programmer to lay out the main lines of a simulation program. If any further details turn out to be necessary, you can elaborate on them as necessary. Or suggest a provisional fix.

gill1109 wrote:So you have to explain to her (or someone like her) how to simulate the motion of hemispherical objects in S^3.

Hemispheres are irrelevant. My description of the experiment is just a sketch. One can "explode", for example, a chemical bond into two perfectly round fragments.

The fragments would have to be prepared in a singlet state, and they would be flying off from the bond with different spins, which must be represented by bivectors.

What is the singlet state of two half ping-pong balls? When is the spin of a half ping-ball a bivector? You've got to explain to your experimentalist friend what this entails, in operational terms.

I think you might find it easier to explain the mathematics to a programmer. But we haven't seen a programmable mathematics yet.

gill1109 wrote:What is the singlet state of two half ping-pong balls? When is the spin of a half ping-ball a bivector?

It means that the initial spin is zero. This requires that the initial body is a boson. If it is uncharged (which seems reasonable) it must contain an even number of neutrons. This might be hard to arrange in a real experiment but should be no problem in simulation.

Mikko wrote:

gill1109 wrote:What is the singlet state of two half ping-pong balls? When is the spin of a half ping-ball a bivector?

It means that the initial spin is zero. This requires that the initial body is a boson. If it is uncharged (which seems reasonable) it must contain an even number of neutrons. This might be hard to arrange in a real experiment but should be no problem in simulation.

Mikko, there is no difficulty at all in doing a quantum mechanical simulation. But there is some difficulty in doing a simulation of a quantum mechanics Bell-CHSH experiment while at the same time imposing locality. In fact, according to Bell's theorem it is impossible.

Anyway, Joy claims that classical physical systems can violate Bell's theorem. He thinks that what we call quantum entanglement is nothing to do with quantum mechanics. Nothing to do with quantum superposition. Only to do with physical space being S^3, not R^3.

gill1109 wrote:Mikko, there is no difficulty at all in doing a quantum mechanical simulation.

There is if the system is too complicated (like some 10^24 degrees of freedom). Anyway, the topic was not a quantum mechanical simulation but a classical one.

Mikko wrote:

gill1109 wrote:Mikko, there is no difficulty at all in doing a quantum mechanical simulation.

There is if the system is too complicated (like some 10^24 degrees of freedom). Anyway, the topic was not a quantum mechanical simulation but a classical one.

If we are talking about spin measurements of two qubits in an entangled state, we just have to write down a 2x2 table of joint probabilities of the joint outcomes, given the joint settings. No difficulty in simulating this.

...
I suggest that a real experiment be done using macroscopic bunches of photons as I outlined here. Most quantum labs are already setup somewhat to try to accomplish an experiment of this type. And... I suspect it will easily show the paralllelized 3-sphere character of space. Now, if it were possible to fully simulate S^3, then this should be able to be simulated on a computer also.

FrediFizzx wrote:...
I suggest that a real experiment be done using macroscopic bunches of photons as I outlined here. Most quantum labs are already setup somewhat to try to accomplish an experiment of this type. And... I suspect it will easily show the paralllelized 3-sphere character of space. Now, if it were possible to fully simulate S^3, then this should be able to be simulated on a computer also.

It is possible to fully simulate S^3 (or S^7 for that matter). The problem is not S^3 or S^7. The problem is Joy's "model": Joy has given no instructions which anyone could make much sense of, yet.

Joy proposed an experiment with definitely classical physical objects. Exploding colourful hemispherical balls. That's the experiment we want to see (either performed or simulated). The definitive quantum experiment with pairs of photons is due to take place in about five years. It will be many years more before that can be done with entangled pairs of bunches of photons.

I guess you didn't read what I was proposing at the link. I do believe it is possible to produce macroscopic bunches of "entangled" photons right now. You just have to filter them a different way. Instead of trying to just pass single photon pairs, you have to filter to pass in-phase bunches of photons after the parametric downconverter. Experimenters are very clever. I would imagine they could figure out how to do it.

gill1109 wrote:Joy proposed an experiment with definitely classical physical objects. Exploding colourful hemispherical balls. That's the experiment we want to see (either performed or simulated).

I think it is a good idea (in this case and in general) to simulate an experiment before performing it, and to simulate several variants of the experiment. The simulations are helpful in the design of the experiment. In addition, a simulation can demostrate that the predictions of a theory differ from the predictions of another theory or of naive common sense, and consequently that the experiment would be scientifically interesting.

FrediFizzx wrote:I guess you didn't read what I was proposing at the link. I do believe it is possible to produce macroscopic bunches of "entangled" photons right now. You just have to filter them a different way. Instead of trying to just pass single photon pairs, you have to filter to pass in-phase bunches of photons after the parametric downconverter. Experimenters are very clever. I would imagine they could figure out how to do it.

I am not denying this. They are extremely clever. They are only five years away from a definitive experiment with photon pairs. It took 50 years to get so far. My guess is that will take them another 10 or 20 years before they can do it with bunches of photons.

Mikko wrote:

gill1109 wrote:Joy proposed an experiment with definitely classical physical objects. Exploding colourful hemispherical balls. That's the experiment we want to see (either performed or simulated).

I think it is a good idea (in this case and in general) to simulate an experiment before performing it, and to simulate several variants of the experiment. The simulations are helpful in the design of the experiment. In addition, a simulation can demostrate that the predictions of a theory differ from the predictions of another theory or of naive common sense, and consequently that the experiment would be scientifically interesting.

Exactly. And so far there are no simulation instructions lying on the table. And Joy's own description of the data-gathering part of his experiment would lead to an experiment which will, with very large probability, fail.

Joy's original description of the experiment contain the instructions that the spins of the two hemispheres, say u and v, as two directions in real 3-D space, will be determined by computer image processing of the results of a battery of video cameras ... so that the sign of the inner products a^T u and b^T v are simultaneously determined for all a and for all b in S^2? If we restrict attention to the two pairs of CHSH directions for a and for b, and do N runs, we obtain the Nx4 spreadsheet which was discussed seriously by several persons in another thread, though others exhibited strange rowdy behaviour reminiscent of the lower house of the British parliament.