Three Attempts at Two Axioms for Quantum Mechanics

Rohrlich, Daniel

doi:10.1007/978-3-642-21329-8_12

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…We return now to the GHZ correlations of Equation ( 3 ) and show that they permit jamming [ 16 ]. Suppose Alice, Bob and Jim share an ensemble of particle triplets in the GHZ state.…”

Section: Retrocausality In Pr-box and Ghz Correlationsmentioning

confidence: 99%

GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality

Rohrlich

Hetzroni

2018

Entropy

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We review an argument that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does-i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit-then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical limit.) However, we find that the argument does not extend to GHZ correlations. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not.

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“…We return now to the GHZ correlations of Equation ( 3 ) and show that they permit jamming [ 16 ]. Suppose Alice, Bob and Jim share an ensemble of particle triplets in the GHZ state.…”

Section: Retrocausality In Pr-box and Ghz Correlationsmentioning

confidence: 99%

GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality

Rohrlich

Hetzroni

2018

Entropy

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Schrödinger’s Equation as a Consequence of the Central Limit Theorem Without Assuming Prior Physical Laws

Grinwald¹

2022

Found Phys

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The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex–valued Gaussian, looking for relevance to quantum mechanics. Here we show that the Gaussian, with all terms fully complex, acting as a propagator, leads to Schrödinger’s non-relativistic equation including scalar and vector potentials, assuming only that the norm is conserved. No physical laws need to be postulated a priori. It thereby presents as a process of irregular motion analogous to the real random walk but executed under the rules of the complex number system. There is a standard view that Schrödinger’s equation is deterministic, whereas wavefunction “collapse” is probabilistic (by Born’s rule)—we have now a demonstrated linkage to the central limit theorem, indicating a stochastic picture at the foundation of Schrödinger’s equation itself. It may be an example of Wheeler’s “It from bit” with “No underlying law”. Reasons for the primary role of $$\mathbf {C}$$ C are open to discussion. The present derivation is compared with recent reconstructions of the quantum formalism, which have the aim of rationalizing its obscurities.

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A Reasonable Thing That Just Might Work

Rohrlich¹

2016

Quantum Nonlocality and Reality

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In 1964, John Bell proved that quantum mechanics is "unreasonable" (to use Einstein's term):there are nonlocal bipartite quantum correlations. But they are not the most nonlocal bipartite correlations consistent with relativistic causality ("no superluminal signalling"): also maximally nonlocal "superquantum" (or "PR-box") correlations are consistent with relativistic causality. Ishow that-unlike quantum correlations-these correlations do not have a classical limit consistent with relativistic causality. The generalization of this result to all stronger-than-quantum nonlocal correlations is a derivation of Tsirelson's bound-a theorem of quantum mechanics-from the three axioms of relativistic causality, nonlocality, and the existence of a classical limit. But is it reasonable to derive (a part of) quantum mechanics from the unreasonable axiom of nonlocality?!

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Three Attempts at Two Axioms for Quantum Mechanics

Cited by 4 publications

References 25 publications

GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality

GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality

Schrödinger’s Equation as a Consequence of the Central Limit Theorem Without Assuming Prior Physical Laws

A Reasonable Thing That Just Might Work

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