But apart from that the challenge from Sascha (however sarcastically stated) is the same as in this blog: if a LHV model is possible, it can be demonstrated and proved by an open source program.

The reference application for these simulations, based on the work of DeRaedt, has now been completely rewritten. The classes that implements a simulation have been separated. Adding a new type of simulation can be done easily by copying a folder with classes from another simulationtype and change their implementation.

The classes mostly represents the real objects that are involved in a typical EPR experiment. A special feature in this release is the availability of a libary with classes for Geometric Algebra, as they are generated for C-sharp by Gaigen. As always, the program can be downloaded at sourceforge

Hello Albert Jan,

ReplyDeleteWith great respect for you personally and great admiration for your underappreciated work, I beg to differ with your main premise here. A computer simulation is an implementation of a model, not an experiment that can either prove or disprove a model. I have produced impeccable analytical arguments to demonstrate that Bell’s theorem is not only wrong, but his premises are unphysical and naive. Moreover, I have produced impeccable and explicit analytical models to explain the correlations observed in the actual optical experiments performed at both Orsay and Innsbruck (cf. arXiv:1106.0748). To be sure, it would be wonderful if a numerical simulation can also be produced to support my analytical demonstrations. But demanding such a simulation of my topologically non-trivial model is like demanding a flight-simulation from the Wright brothers when they have just produced an actual, real-life flying machine. If reality can always be so simply simulated then there would be no need for the staggeringly expensive actual experiments. Reality is far richer and profound than some of us mathematically challenged are able to fathom, let alone a computer.

Nevertheless, you have my full support for your hard and well informed work.

Joy Christian

Hi Joy,

ReplyDeleteThank you for your constructive remark. Perhaps I should have used 'confirm' instead of 'prove'. The thing with the Bell premise I think is a little different from other type of disputes. A numeric simulation cannot prove whether a model represents the physical reality. But in the Bell case it can show beyond doubt that results of EPR type experiments can be mimicked without having used the opposite polarizer angle in the calculations. So it bypasses all discussions about wrong or hidden assumptions that can be raised in formal proof.

But I agree that finding a correct implementation of such a simulation is probably not trivial, otherwise it would already have been found by now.

Summarizing: The ‘prove’ used in the text above was mend to be about the disprove of the Bell no-go theorem and not so much about the model itself.

Albert Jan

DearAlbert Jan,

ReplyDeleteThanks for your thoughtful reply on the Vongehr challenge. He does not have much that is why he is in need of noise.

Concerning the computer simulation requirement I would like to add the following. Where is the proof (logical or mathematical even philosophical) that a simulation is superior over a mathematical argument such as in ASTP 4(20) 495 (2010) and e.g. Joy's work?

The fact that a crackpot challenge was opened by Vongehr means absolutely nothing. So where is the proof?

Yours

Han

Hi Han,

ReplyDeleteI don’t have any knowledge of theories weighting both types of proof, maybe somebody else can comment on that. But although many may be able to understand a mathematical argument, I think few are able to completely judge its validity (flaws are possible on both ‘sides’). On the contrary the boundaries for a computer- or macro-scale simulation yielding Bell-type results are well defined and can be easily checked. So in my opinion it is really helpful to present such models.

Albert Jan

Dear Albert Jan,

ReplyDeleteThe 'we want a computer simulation'argument is based on confidence in Bell's theorem. His mathematics did not lead to a theorem at all. In ASTP 4(20), 495-499 (2010) I showed with straightforward means that Bell's mathematics is incomplete. In fact I am the one that may ask a for a proof of the generality of Bell's inequality. Please note that for CHSH the same argument applies. There is no escaping and the other way around is sheer empty rethorics.

Now what is wrong with Bell's proof?

He allows functions A and B to project in {-1,1}. Those functions belong to the generalized function domain. Hence, I may question whether or not the use of the absolute signs are justified as they are in elementary mathematics. Moreover I may ask if there is ambiguity in Bell's definition.

If those questions are answered with 'we want a computer simulation' it is the world upside down in logical reasoning. This way of reasning squarly ignores an important mathematical result beacuse of alleged flaws. There are no flaws. The mathematics of my ASTP is equivalent to Bell's mathematical methodology. There is no escaping. Asking for additional proof is ignoring already existing proof and that is rethorics dear friend.

To give more power to my point let me state the following. Bell uses A and B in {-1,1}. This can be modeled with sgn(x) type of functions. Now I am perfectly allowed to employ the definition: sgn(x) = 2H(x) - 1. The Heaviside function H(x) is defined as: H(x)=1, for x>0 and H(x)=0 for x<0. Now there are people that claim that H(x) is properly defined in x=0. They are wrong. If we use the Gaussian expression for the Dirac delta function, then H(x) in x=0 equals 1/2. But let us take H(x) as the limit, N->inf, of exp[-(1/N)exp(-xN)]. Then for x=0 we see that the Heaviside H(0)=1.

Let us define sgn(x)=2H(x)-1 based on N->inf, of exp[-(1/N)exp(-xN)]. Ok, now take a look at sgn(x-y). We may write sgn(x-y)=(x-y)/|x-y|. Note please that the RH of this equation is defined in x=y in the definition of the sgn generalized function provided previously. This is so because, |x-y| = (x-y)sgn(x-y) and sgn(x-y) in {-1,1} unequal to zero. The latter can be demanded too from the functions that Bell uses because we do not have spin 0 in his case. In addition, we also have d {sgn(x-y)}/dx = 2delta(x-y). The delta(x-y) is the Dirac delta in x-y. No flaws, read Lighthil, read Gel'fand and Shilov's first book on generalized functions.

Now we are also allowed, in the definition provided, to write |x-y| = (x-y)sgn(x-y). Hence, d|x-y|/dx = sgn(x-y) + 2 (x-y) delta(x-y). Do not strike the second term. We are allowed to insist to keep that term.

If, we then take d/dx of (x-y)/|x-y|, then, we see: d{(x-y)/|x-y|}/dx = {|x-y| - (x-y){sgn(x-y)+ 2 (x-y) delta(x-y)}/{|x-y|.|x-y|}. After some arithmetic one sees

d{(x-y)/|x-y|}/dx = -2delta(x-y).

Hence, an ambiguity in the evaluation of Bell's integrals when partial integration is employed to evaluate the correlation. Hence, the correlation has an ambiguity burried inside its framwork. Hence, another -no flaw- argument agianst the theorem status of BT.

When will people start showing *me* a proof of their convictions ?

Please do note *it is absolutely unacceptable* in any other quarter of science to escape from this -not flawed- criticism on the derivation of a theorem with demanding *yet another* type of proof because all the previous one's are considered 'flawed'. Sorry this is science not a kids game or highschool boys that may write a contest.

Han

In addition to the previous. How would a computer program be possible without mathematical flaw in Bell's own derivation of the inequality and the CHSH leading to B T?

ReplyDeleteHence, the LHV opposition, when they ignore e.g. my ASTP mathematical criticism on BT, are pretty sure about the validity of BT. They are really in no way inclined to give up their pet interpretation. So simply stalling the problem of accepting mathematical flaws in their own argument and replacing it with a 'mission impossible'-type of requirement.

But please do note that if there are mathematical flaws in BT, that this fact or possibility does *not at all* imply by necessity that a classical computer program is necessary. The computer is a discrete arithmetic machine. In classical probability there is a difference between discrete and continuous stochastics. There are other ways to show that classical Kolmogorovian probability does not fail in the restrictive application the opposition want to force it.

Again, if 'Bell has not derived a theorem at all' claim is ignored without showing real flaws in this claim, when there is a forced move for classical Kolmogorovian probability to a computer simulation domain without actual prove of it superiority over mathematical claims and disprove and the only thing the opposition can come with is.... hey your argument *may* be flawed, then I think the opposition's argument is deeply biased and flawed beyond understanding. It is expected that after a computer simulation another rethoric trick will be discovered to keep the LHVs are wrong experiments going. I think physicists no longer have any reason to claim their research to be free of values outside the field that is studied. The laughable attack on Joy Christian with only white noise type arguments is a perfect example and socials science proof of the downfall of reasoning and fairness in this field.