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In 1935 Einstein, Podolsky and Rosen (EPR) pointed out that Quantum Mechanics apparently implied some mysterious, instantaneous action at a distance. This paradox is supposed to be related to the probabilistic nature of the theory, but…
We prove a multidimensional ergodic theorem with weighted averages for the action of the group $\mathbb{Z}^d$ on a probability space. At level $n$ weights are of the form $n^{-d} \psi(j/n)$, $ j\in \mathbb{Z}^d$, for real functions $\psi$…
Hugh Everett III presented pure wave mechanics, sometimes referred to as the many-worlds interpretation, as a solution to the quantum measurement problem. While pure wave mechanics is an objectively deterministic physical theory with no…
Hartle and Srednicki have suggested that standard quantum theory does not favor our typicality. Here an alternative version is proposed in which typicality is likely, Eventual Quantum Mechanics. This version allows one to calculate…
One would not think that thought experiments could matter to nature, for they are a humble human device. Yet quantum mechanics very naturally frames thought experiments (as distinct from precisely defining what exists). They exemplify the…
It is argued that any operational measure of time is inseparably bound to the presence of a periodic process in some medium. Since, as first formulated by Einstein's (1905) equation for the energy, all "particles" (neutrons, electrons,…
When the semi-positive cosmological constant is dynamical, the naive Euclidean Einstein action is unbounded from below and the Hartle-Hawking wavefunction of the universe is not normalizable. With the inclusion of back-reaction (a crucial…
In accordance with the entropy principle of thermodynamics, under spontaneous evolutions, physical systems always evolve towards states with equal or greater randomness. But, where does this randomness originate? Renowned Birkhoff-von…
The formulation and some experimental implications of a general Lorentz-violating extension of the standard model are reviewed. The theory incorporates both CPT-preserving and CPT-breaking terms. It is otherwise a conventional quantum field…
Noether's theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time (PT)-symmetric…
Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…
Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
Non-local connections, i. e. long-range space-time correlations intrinsic to the observed subatomic dynamics of quantum systems is also exhibited by macro-scale dynamical systems as selfsimilar fractal space-time fluctuations and is…
This is partly a survey article for Constructive Approximation's Special Issue on Approximation and Statistical Physics. It reviews results of B. Shiffman-S.Zelditch, R. Berman. S. Boucksom, D. Witt-Nystrom, T. Bloom, O. Zeitouni and others…
It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
This paper defines, on the Galilean space-time, the group of asymptotically Euclidean transformations (AET), which are equivalent to Euclidean transformations at space-time infinity, and proposes a formulation of nonrelativistic quantum…
The ether concept -- abandoned for a long time but reinstated by Dirac in 1951-1953 -- has in recent years emerged into a fashionable subject in theoretical physics, now usually with the name of the Einstein-Dirac ether. It means that one…