# Tag Info

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Wolfram's early work on cellular automata (CAs) has been useful in some didactical ways. The 1D CAs defined by Wolfram can be seen as minimalistic models for systems with many degrees of freedom and a thermodynamic limit. Insofar these CAs are based on a mixing discrete local dynamics, deterministic chaos results. Apart from these didactical achievements, ...

16

Oh crud, this! I read this paper a month ago. What Joy Christian does is to write out the Bell inequalities, and then effectively identifies quantum states with the variables in the terms of the inequality. This is silly, for the whole point is to erect the inequalities and then demonstrate how quantum states violate them. Joy identifies the quantum ...

16

Bell's theorems indeed rule out simple theories where hidden variables obey local equations. However, no matter how you reason, it's always at some point where you need another assumption. In its simplest form, it is the assumption that two observers, Bob an Alice, have the "free will" to choose along which axis they will measure the spin of a particle (...

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Shortly after NKS came out, I wrote a review in which I tried to explain why the answer to your excellent question is yes. A deterministic model like Wolfram's can't possibly reproduce the Bell inequality violations, for fundamental reasons, without violating Wolfram's own rule of "causal invariance" (which basically means that the evolution of a CA shouldn'...

11

I'm assuming you're talking about plane-polarized photons, where a photon that passes a 0º analyzer is horizontally polarized, a photon that passes a 90º analyzer is vertically polarized, and there's an orthogonal polarization basis at ±45º. Here's the trouble: Now whoever is at A measures A first at 0°, then (if it goes through), at 40°. Like a river,...

9

Here are some facts: As others have said, the evolution of a quantum state, including entanglement, can be simulated arbitrarily well classically with sufficient resources. Actually, modelling the evolution of a quantum system is not even (believed to be) NP hard- if it was, a quantum computer could solve NP problems! That said, it does generally require ...

8

What you are looking for is an experiment violating a Bell inequality, like the CHSH inequality. From the redaction of your question, I infer that you've already looked at it but weren't convinced (Tell me if I'm wrong.) Maybe the Memin-GHZ game will convince you. Motivation It is a game where 3 parties (A,B,C) play together against a referee (R). The ...

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The general point of experiments is checking how nature actually behaves. Bell demonstrated that local hidden variable assumptions do in fact produce restrictions on the possible predictions of theories based on such assumptions, and that these restrictions leave some of the results of quantum mechanics out of the reach of LHV theories. This draws an ...

7

My reading of Joy's paper —just as it is, without having carefully read the arXiv paper I cited, nor all of Joy's responses to critics that I also mentioned— is, so far: the left and right hand sides of eq(1) and eq(2), without the central interpolations, state that $A(\mathbf{a},\lambda)=\lambda$ and $B(\mathbf{b},\lambda)=-\lambda$, where $\... 7 It's not completely clear what you're asking, but I can make one thing clear: quantum mechanics was not developed with the specific aim of correctly describing the precise amounts to which CHSH inequalities can be violated. Quantum mechanics was developed in the 1920s and early 30s. Bell published his first paper on Bell inequalities in 1964. The first ... 6 Helder, A lot of comments surround this question and we are awaiting some further responses from the Author of the papers. However this is my understanding of the conclusion of these papers: Every theory - even classical physics - violates the Bell Inequalities So in a sense there is no dispute with the Bell calculation as a demonstrable result of Quantum ... 5 I'm not sure it makes sense to ask if Nature is "imitating" Quantum Mechanics. Quantum mechanics is a mathematical model that gives predictions that are in excellent, well so far perfect, agreement with what we actually see. I guess the question is whether QM is just a good approximation to the real world or whether it's an exact description of the real ... 5 Most of these automata models are deterministic in the same sense as pseudorandom number generators are. For example in the lattice gas models the deterministic rules end up generating noise and large scale fluctuations in accord to the Navier-Stokes equations (including turbulence, although this is computationally impractical because of the large lattice ... 5 This is a truly excellent question in my opinion. It is still being worked on. Here are some professional references that will somewhat clarify the issue, or perhaps even confuse you further: http://arxiv.org/abs/1102.4467 http://arxiv.org/abs/1007.5518 http://arxiv.org/abs/1006.3680 Michael J.W. Hall http://arxiv.org/abs/0808.2178 Travis Norsen http://... 5 I completely agree with Scott that this particular "Grassmannization" isn't equivalent to what supersymmetry is doing in physics. Supersymmetry is a constraint that picks a subset of theories – ordinary theories with ordinary bosonic and fermionic fields that are just arranged (and whose interactions are arranged) so that there is an extra Grassmann-odd ... 5 This is a very specific question. Bell's theorem rules nothing out or in. Bell made the assumption that hidden variables existed, and using simple statistical arguments he derived a set of inequalities. If hidden variables existed they should make a measurable contribution to the correlatiions of spins. Therefore, if the measured correlations satisfied ... 5 Wouldn't the first measurement at time one destroy the entanglement? I would think that for particle two, whatever result you got from the SG apparatus at time 3 would be the same as the result for particle two at time 1.... Here is a rather helpful and insightful blog post by Chad Orzel that may clear up some points about entanglement: Entanglement is not ... 5 Let's assume for the sake of argument that the experimentalists here did a good job, didn't make any obvious mistakes, and will be confirmed by future experiments of this type**. My understanding is that other Bell tests that close these loopholes are currently being performed or are even completed and being analyzed, so in the unlikely event that this isn't ... 4 The$S$in this inequality is defined as $$S = E(a b) − E(a b') + E(a' b) + E(a' b')$$ where$E(M)$is the "expectation value of$M\$" which means the average value calculated from many repetitions of the same experiment (empirically) or from the probability distributions (theoretically). All the expectation values are taken from the products of two ...

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Try Theorem 12 in (the arXiv version) of http://arxiv.org/abs/quant-ph/0411098. What I call "lattice states" there should exactly be the class of states you are interested in.

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In mathematics a super lie algebra is defined as a graded algebra with commutators and anti-commutators satisfying a generalised Jacobi identity. No Grassman variables are needed in the defintion. The osp used for super qubits is a basic example of such an algrebra. This particular supersymmetry algebra cannot be used for SUSY theories in physics because ...

4

Jherico, I see that you are keen in finding answers to your questions, or putting your views across for a debate, and this is really good. This is what science is all about. I think your questions deserve attention and proper debate. Here is an effort from my side to help dilute some of the misunderstanding through the comments section of this forum. (1)...

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In the original EPR gedanken experiment, they assumed two particles that have perfect correlations in position, i.e., they are described by a delta function. That does not pose a problem for a thought experiment but cannot be performed in a lab because such a state cannot be normalized and is therefore unphysical. However, in quantum optics, many ...

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I agree with much of what you write in your question. Whether quantum mechanics is considered to be deterministic is a matter of interpretation, summarised in this wiki comparison of interpretations. The wiki definition of determinism is this context, which I think is entirely satisfactory, is Determinism is a property characterizing state changes due ...

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Bell's theorem shows that standard QM is inconsistent with local realism. Local realism is a very general principle that was not originally thought to make any testable physical predictions. A major part of Bell's achievement was showing that Bell's inequality is implied by local realism, while standard QM predictions violate it. Experiments like Aspect's ...

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For now I will only give you an overview of the ideas involved and show you how you should interpret the idea of a "local realistic theory" that cannot exist at the microscopic scale. Once you've read it, and if you feel you need more mathematical rigor to be convinced, then I will draw you step by step the proof of Bell's inequality (it is not the only one ...

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