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The Born Representation Theorem and the Unistochastic Theorem
Jacob A. Barandes
This paper presents self-contained, constructive proofs of two new theorems about stochastic matrices, with direct relevance to quantum theory. The first theorem, herein called the…
Against Many Worlds
Emily Adlam, Jacob A. Barandes
Any viable interpretation of quantum theory needs to account for the Born rule, from which the theory gets its probabilistic empirical predictions. In this paper, we give an overvi…
Pilot-Wave Theories as Hidden Markov Models
Jacob A. Barandes
The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology…
The Trouble with Weak Values
Jacob A. Barandes
In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose d…
The ABL Rule and the Perils of Post-Selection
Jacob A. Barandes
In 1964, Aharonov, Bergmann, and Lebowitz introduced their well-known ABL rule with the intention of providing a time-symmetric formalism for computing novel kinds of conditional p…
A Deflationary Account of Quantum Theory and its Implications for the Complex Numbers
Jacob A. Barandes
Why does quantum theory need the complex numbers? With a view toward answering this question, I argue that the usual Hilbert-space formalism is a special case of the general method…