On Adler's "Conway-Kochen Twin Argument"
英文摘要:
We respond to Stephen Adler's comments on our paper "The Free Will Theorem",and add some further observations.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
John Conway, Simon Kochen
We respond to Stephen Adler's comments on our paper "The Free Will Theorem",and add some further observations.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
Recently Cator & Landsman made a comparison between Bell's Theorem and Conway & Kochen's Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway-Kochen Theorem has been performed thus far, and, secondly, because the Conway-Kochen Theorem is strongly connected to the Kochen-Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In this paper I show that the finite precision loophole does not apply to the Conw…
A physicists' explanation of why thou shalt not clone one bit gives a stronger version of Conway and Kochen's theorem.
This is a revision of my original posting, in which I raised objections to part of the Conway-Kochen argument. I now agree with them that their recent reply answers my original concerns. In the first part of these notes (identical to the original), I give a reformulation of the part of the Conway-Kochen result that closes the contextuality loophole in the original Kochen-Specker (KS) theorem. In the second part (modified in this revision) I review my concerns connected with the finite time needed to make a measurement, and briefly indicate how Conway and Kochen have reponded to them.
In a recent paper, Conway and Kochen proposed what is now known as the "Free Will theorem" which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we discuss why the theorem of Conway and Kochen does not affect the progr…
Bell's Theorem from 1964 and the (Strong) Free Will Theorem of Conway and Kochen from 2009 both exclude deterministic hidden variable theories (or, in modern parlance, `ontological models') that are compatible with some small fragment of quantum mechanics, admit `free' settings of the archetypal Alice & Bob experiment, and satisfy a locality condition called Parameter Independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their differences. Our reformulation imposes determinism in what we see as the only con…
In a recent paper [quant-ph/0604079], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper [quant-ph/0406094] and by Dowker and Henson [J. Statist. Phys. 115: 1327 (2004), quant-ph/0209051]. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.
We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).
It is discussed, why classical simulators of quantum computers escape from some no-go claims like Kochen-Specker, Bell, or recent Conway-Kochen "Free Will" theorems.
Modal quantum theory (MQT) is a simplified cousin of ordinary Hilbert space quantum theory. We show that two important theorems of actual quantum theory, the Kochen-Specker theorem excluding non-contextual hidden variables and the Conway-Kochen "free will theorem" about entangled systems, have direct analogues in MQT. The proofs of these analogue theorems are similar to, but much simpler than, the originals. We also show that the structure of possible measurement results for an entangled system in MQT cannot be represented by probability assignments satisfying the no-signaling principle, such …
The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here, via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits, of randomness, communication, and/or correlation, that they require. For example, measuremen…
It is argued that the Strong Free Will Theorem (Conway-Kochen) does not prove nonlocal determinism wrong. This is done by the before-before (Suarez-Scarani) experiment, which is used here to prove the following General Free Will Theorem: If humans have a certain amount of free will, there are other free beings outside space-time producing nonlocal effects in our world, which are both random and lawful.
Conway and Kochen's Free Will Theory is examined as an important foundational element in a new area of activity in computer science - developing protocols for quantum computing
We give a purely logical proof of the J. Conway and S. Kochen Free Will theorem concerning undeterminacy in Quantum Mechanics (Notices of the AMS, February 2009, Vol. 56/2, p. 226). The logical method seems to be very powerful.
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable models; models that allow a realist interpretation. In this thesis some of these proofs are discussed, like von Neumann's Theorem, the Kochen-Specker Theorem and the Bell-inequalities. Some more recent developments are also investigated, like Meyer's nullification of the Kochen-Specker Theorem, the MKC-models and Conway and Kochen's Free Will Theorem. This la…
Conway and Kochen have presented a "free will theorem" (Notices of the AMS 56, pgs. 226-232 (2009)) which they claim shows that "if indeed we humans have free will, then [so do] elementary particles." In a more precise fashion, they claim it shows that for certain quantum experiments in which the experimenters can choose between several options, no deterministic or stochastic model can account for the observed outcomes without violating a condition "MIN" motivated by relativistic symmetry. We point out that for stochastic models this conclusion is not correct, while for deterministic models it…
In a recent series of papers and lectures, John Conway and Simon Kochen presented The Free Will Theorem. "It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity." Perhaps the primary motivation of their papers was to place stringent constraints on quantum mechanical hidden variable theories, which they indeed do. Nevertheless, the notion of free will is crucial to the proof and they even speculate that the free will afforded to elementary particles is the ultimate explanation of our own free will. I …
We review the argument that latent image formation is a measurement in which the state vector collapses, requiring an enhanced noise parameter in objective reduction models. Tentative observation of a residual noise at this level, plus several experimental bounds, imply that the noise must be colored (i.e., non-white), and hence frame dependent and non-relativistic. Thus a relativistic objective reduction model, even if achievable in principle, would be incompatible with experiment, the best one can do is the non-relativistic CSL model. This negative conclusion has a positive aspect, in that t…
The concept of 'super-indeterminism' captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, "universal indeterminism"). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter "freedom", "free will", or "free choice", is redundant in relation to …
The title refers to the Free Will Theorem by Conway and Kochen whose flashy formulation is: if experimenters possess free will, then so do particles. In more modest terms, the theorem says that individual pairs of spacelike separated particles cannot be described by deterministic systems provided their mixture is the same for all choices of measurement settings. We reformulate and generalize the Free Will Theorem theorem in terms of systems of random variables, and show that the proof is based on two observations: (1) some compound systems are contextual (non-local), and (2) any deterministic …
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。