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It is almost universally believed that in quantum theory the two following statements hold: 1) all transformations are achieved by a unitary interaction followed by a von Neumann measurement; 2) all mixed states are marginals of pure…

Quantum Physics · Physics 2020-12-04 Giacomo Mauro D'Ariano

We present a variation of Hurkens paradox, which can itself be seen as a variation of Reynolds result that there is no set theoretic model of polymorphism.

Logic in Computer Science · Computer Science 2023-09-01 Thierry Coquand

What if the paradoxical nature of quantum theory could find its source in some undecidability analog to that of G\"odel's incompleteness theorem ? This essay aims at arguing for such G\"odelian hunch via two case studies. Firstly, using a…

Quantum Physics · Physics 2023-08-25 Hippolyte Dourdent

Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…

Logic · Mathematics 2007-05-23 Gyorgy Sereny

There has been on-going philosophical debate on whether artificial life models, also known as digital organisms, are truly alive. The main difficulty appears to be finding an encompassing and definite definition of life. By examining…

Neural and Evolutionary Computing · Computer Science 2023-02-22 Yong Zher Koh , Maurice HT Ling

In this article we prove a reducibility result for the linear Schr\"odinger equation on the sphere $\mathbb{S}^{n}$ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of…

Analysis of PDEs · Mathematics 2019-05-29 Roberto Feola , Benoît Grébert

We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…

Logic · Mathematics 2010-11-24 Shira Kritchman , Ran Raz

We give some arguments to evaluate the "size" of Schrodinger cat for the flux qubit, which has really different results from ref.[1] Korsbakken et al. [1] J.Korsbakken,F.K.Wilhelm and K.B.Whaley,Physics Scripta T137,014022 (2009)

Quantum Physics · Physics 2016-03-15 Anthony J. Leggett

The marginalization paradox involves a disagreement between two Bayesians who use two different procedures for calculating a posterior in the presence of an improper prior. We show that the argument used to justify the procedure of one of…

Statistics Theory · Mathematics 2007-06-13 Timothy C. Wallstrom

Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to…

History and Overview · Mathematics 2026-01-29 Doeko Homan

The concept of a judgment as a logical action which introduces new information into a deductive system is examined. This leads to a way of mathematically representing implication which is distinct from the familiar material implication,…

Probability · Mathematics 2011-11-10 Ruadhan O'Flanagan

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

Quantum Physics · Physics 2007-05-23 Milos V. Lokajicek

In this article I aim to provide an intuitive and non-technical introduction to decoherence and quantum Darwinism. Together these theories explain how our classical reality emerges from an underlying quantum mechanical description. Here I…

Quantum Physics · Physics 2018-12-07 P. A. Knott

This paper aims to invalidate the hypothesis that consciousness is necessary for the quantum measurement process. To achieve this target, I propose a considerable modification of the Schroedinger cat and the Dead-Alive Physicist thought…

Quantum Physics · Physics 2022-05-04 Carlo Roselli

A classical analogue of the Adlam-Kent "Quantum paradox of choice" (arXiv:1509.04226) is presented.

Quantum Physics · Physics 2015-09-23 J. Finkelstein

Wigner's famous and influential claim that mathematics is "unreasonably effective" in physics is founded on unreasonable assumptions about the nature of mathematics and its independence of physics. Here I argue that what is surprising is…

History and Philosophy of Physics · Physics 2015-12-17 Derek K. Wise

We review both the Einstein, Podolsky, Rosen (EPR) paper about the completeness of quantum theory, and Schrodinger's responses to the EPR paper. We find that both the EPR paper and Schrodinger's responses, including the cat paradox, are not…

Quantum Physics · Physics 2007-05-23 Elias P. Gyftopoulos , Michael R. von Spakovsky

In this paper, we argue that while the concept of a set-theoretic paradox (or paradoxical set) can be relatively well-defined within a formal setting, the concept of a set-theoretic hypodox (or hypodoxical set) remains significantly less…

Logic · Mathematics 2025-01-31 Timotej Šujan

In this short report the first attempt of a new approach to the still mysterious phenomenon of the life, and its peak, the human being, is presented from the view point of the natural sciences, i.e. of the physics in the broad sense of the…

General Physics · Physics 2007-05-23 Boris Chirikov

Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with…

chao-dyn · Physics 2007-05-23 X. de Hemptinne