Related papers: Has the Born rule been proven?
Remarks on mathematical proof and the practice of mathematics.
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure (POVM), is shown to be a consequence of the environment-assisted invariance (envariance) idea suggested by Zurek [Phys. Rev. Lett.…
In this paper the circulant Hadamard conjecture is proved.
Ogburn et al. (2019, arXiv:1910.05438) discuss "The Blessings of Multiple Causes" (Wang and Blei, 2018, arXiv:1805.06826). Many of their remarks are interesting. But they also claim that the paper has "foundational errors" and that its…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
It is shown that violation of the Born Rule leads to a breakdown of the correspondence between the quantum electromagnetic field and its classical counterpart. Specifically, the relationship of the quantum coherent state to the classical…
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…
The claims made for the Resonating Valence Bond ideas for the cuprates in a recent paper by Anderson et al. on the basis of a variational calculation are discussed.
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
The interpretation of an experimental realization of Wheeler's delayed-choice gedanken experiment is discussed and called into question.
We survey the classical results on the prime number theorem
The oft-repeated claim that life is written into the laws of nature are examined and criticized. Arguments are given in favour of life spreading between near-neighbour planets in rocky impact ejecta (transpermia), but against panspermia,…
I argue that most of the key experiments that have born semiconductor spintronics were done and published earlier than the papers cited in the Nature Physics, 4 S20 (2008) milestone article (http://www.nature.com/milestones/spin, milestone…
Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].