aqora

The Nature of Quantum Paradoxes

Van der Merwe, Alwyn, Gino Tarozzi

Springer eBooksJan 1, 19889 citations

Banach-Tarski Paradoxes in Quantum Mechanics

Abhishek Mehta

We show that Quantum Mechanical Hilbert space can be paradoxical under some group action and explore its physical consequences. (1) Is there a more natural way of resolving the paradox of Wigner’s friend without invoking the Heisenberg’s cut?; (2) We notice the qualitative similarities between the paradox and paradoxical sets and use it as a motivation to rigorously prove that the Hilbert space H of the harmonic oscillator is paradoxical under the group action induced by SO(2, 1); (3) This paradoxical nature of the Hilbert space H provides the natural resolution for the paradox by using the Axiom of Choice instead of the Heisenberg’s cut; (4) Finally, we show that due to the very same paradoxical nature of H, certain class of quantum gravities naturally emerge from Quantum Mechanics that mediates a self-decoherence of the system.We show that Quantum Mechanical Hilbert space can be paradoxical under some group action and explore its physical consequences. (1) Is there a more natural way of resolving the paradox of Wigner’s friend without invoking the Heisenberg’s cut?; (2) We notice the qualitative similarities between the paradox and paradoxical sets and use it as a motivation to rigorously prove that the Hilbert space H of the harmonic oscillator is paradoxical under the group action induced by SO(2, 1); (3) This paradoxical nature of the Hilbert space H provides the natural resolution for the paradox by using the Axiom of Choice instead of the Heisenberg’s cut; (4) Finally, we show that due to the very same paradoxical nature of H, certain class of quantum gravities naturally emerge from Quantum Mechanics that mediates a self-decoherence of the system.

Feb 18, 20260 citations

Quantum Paradoxes

Shahen Hacyan

The frontiers collectionJan 1, 20230 citations

Banach-Tarski Paradoxes in Quantum Mechanics

Abhishek Mehta

We show that Quantum Mechanical Hilbert space can be paradoxical under some group action and explore its physical consequences. (1) Is there a more natural way of resolving the paradox of Wigner’s friend without invoking the Heisenberg’s cut?; (2) We notice the qualitative similarities between the paradox and paradoxical sets and use it as a motivation to rigorously prove that the Hilbert space H of the harmonic oscillator is paradoxical under the group action U ≤ U(H) × U(1); (3) This paradoxical nature of the Hilbert space H provides the natural resolution for the paradox by using the Axiom of Choice instead of the Heisenberg’s cut; (4) Finally, we show that due to the very same paradoxical nature of H, certain class of quantum gravities naturally emerge from Quantum Mechanics that mediates a self-decoherence of the system.We show that Quantum Mechanical Hilbert space can be paradoxical under some group action and explore its physical consequences. (1) Is there a more natural way of resolving the paradox of Wigner’s friend without invoking the Heisenberg’s cut?; (2) We notice the qualitative similarities between the paradox and paradoxical sets and use it as a motivation to rigorously prove that the Hilbert space H of the harmonic oscillator is paradoxical under the group action U ≤ U(H) × U(1); (3) This paradoxical nature of the Hilbert space H provides the natural resolution for the paradox by using the Axiom of Choice instead of the Heisenberg’s cut; (4) Finally, we show that due to the very same paradoxical nature of H, certain class of quantum gravities naturally emerge from Quantum Mechanics that mediates a self-decoherence of the system.

Feb 11, 20260 citations

Quantum Mechanics as Projection: Paradox Without Paradox

Yulia Avetisova

The Schrödinger’s cat paradox points not to the nature of the cat, but to the nature of our description. This work shows that superposition arises from a mismatch in reaction density (p_R) between quantum process and observer, deriving the Schrödinger equation as a projection limit. This bilingual publication (English/Russian) is presented as a single integrated document, containing the complete text in both languages.

Jan 1, 20260 citations

Quantum Paradoxes

Yakir Aharonov, Daniel Rohrlich

Wiley eBooksFeb 17, 2005436 citations

The Nature of Quantum Paradoxes.

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