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Comments on ‘‘Assumptions implying the Schrödinger equation,’’ by Thomas F. Jordan [Am. J. Phys. 59, 606–608 (1991)]

Nicolas Gisin

American Journal of PhysicsJan 1, 199310 citations

Piron's foundation of quantum mechanics (Comment on his paper)

W. Balzer

ErkenntnisNov 1, 19813 citations

A note on misunderstandings of Piron's axioms for quantum mechanics

David J. Foulis, Charles H. Randall

Foundations of PhysicsJan 1, 198420 citations

The Free Will Theorem and the Flash Ontology implicitly assume the Before-Before Experiment and thereby imply free will. Comment on a note by Nicolas Gisin in arXiv:1002.1392v1

Antoine Suárez

It is argued that both the "Free Will Theorem" (FWT) and the "relativistic GRW model with Flash Ontology" (rGRWf) hiddenly assume the result of the before-before experiment, and for this reason both FWT and rGRWf imply free will in the world outside free experimenters.

arXiv:1002.2697Feb 13, 20102 citations

Assumptions implying the Schrödinger equation

Thomas F. Jordan

A program of proofs is outlined to show how the linear structure of quantum mechanics can be derived from basic principles. For the dynamics part, three alternatives are reviewed briefly. They include the Kadison theorem for evolution of density matrices and the Segal–Simon theorem for evolution of observables in the Heisenberg picture. The focus is on Wigner’s theorem that gives linear operators for evolution of state vectors. New insights are described that motivate the key assumption about probabilities in that theorem. One is that it is implied by the second law of thermodynamics. Another is that it follows from assumptions that evolution in time preserves mixtures of states and preserves probabilities for what is in the mixture.A program of proofs is outlined to show how the linear structure of quantum mechanics can be derived from basic principles. For the dynamics part, three alternatives are reviewed briefly. They include the Kadison theorem for evolution of density matrices and the Segal–Simon theorem for evolution of observables in the Heisenberg picture. The focus is on Wigner’s theorem that gives linear operators for evolution of state vectors. New insights are described that motivate the key assumption about probabilities in that theorem. One is that it is implied by the second law of thermodynamics. Another is that it follows from assumptions that evolution in time preserves mixtures of states and preserves probabilities for what is in the mixture.

American Journal of PhysicsJul 1, 199120 citations

Why Non-Linear Source Geometry Does Not Imply Superluminal Signaling: A TCGS-SEQUENTION Response to Gisin-Polchinski

Henry Arellano-Peña

The Gisin-Polchinski (GP) no-go theorem (1990–1991) is widely cited as proof that non-linear modifications to quantum mechanics necessarily permit superluminal signaling, thereby violating special relativity. This note demonstrates that the GP argument relies on ontological assumptions that do not hold within the Timeless Counterspace & Shadow Gravity (TCGS) framework. Specifically, GP assumes: (i) time is ontically fundamental, (ii) Alice’s measurement “causes” a change in Bob’s state, and (iii) the density matrix is the complete description of physical reality. In TCGS, where observable 3D reality is a projection of a static 4D counterspace, the apparent “signaling” dissolves as a foliation artifact. Non-linearity at the source level is fully compatible with operational no-signaling at the shadow level.The Gisin-Polchinski (GP) no-go theorem (1990–1991) is widely cited as proof that non-linear modifications to quantum mechanics necessarily permit superluminal signaling, thereby violating special relativity. This note demonstrates that the GP argument relies on ontological assumptions that do not hold within the Timeless Counterspace & Shadow Gravity (TCGS) framework. Specifically, GP assumes: (i) time is ontically fundamental, (ii) Alice’s measurement “causes” a change in Bob’s state, and (iii) the density matrix is the complete description of physical reality. In TCGS, where observable 3D reality is a projection of a static 4D counterspace, the apparent “signaling” dissolves as a foliation artifact. Non-linearity at the source level is fully compatible with operational no-signaling at the shadow level.

Dec 26, 20250 citations

Using the theorem of Emch and Piron: A response to N. Gisin’s ‘‘Comment on ‘Assumptions implying the Schrödinger equation’’’

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