Related papers: Has the Goldstone theorem been revisited?
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
The existence of cosmological compact objects with very strong gravity is a prediction of General Relativity and an exact solution of the Einstein equations. These objects are called black holes and recently we had the first observations of…
Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this paper,…
Motivated by ideas from quantum gravity, Lorentz invariance has undergone many stringent tests over the past decade and passed every one. Since there is no conclusive reason from quantum gravity that the symmetry \textit{must} be violated…
Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance…
Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…
We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also…
The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are…
Bell's theorem proves only that hidden variables evolving in true physical time can't exist; still the theorem's meaning is usually interpreted intolerably wide. The concept of hidden time (and, in general, hidden space-time) is introduced.…
The claim that at the so-called Planck scale our current physics breaks down and a new theory of quantum gravity is required is ubiquitous, but the evidence is shakier than the confidence of those assertions warrants. In this paper, I…
We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions $d$ and the dynamical scaling $z$. Then, the answer to the question in the title is…
A currently discussed interpretation of quantum theory, Time-Symmetrized Quantum Theory, makes certain claims about the properties of systems between pre- and post- selection measurements. These claims are based on a counterfactual usage of…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
The confrontation between General Relativity and experimental results, notably binary pulsar data, is summarized and its significance discussed. The agreement between experiment and theory is numerically very impressive. However, some…
We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…
No-go theorems assert that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory. We examine two species of such theorems, value no-go theorems and expectation no-go theorems. The…
The famous hoop conjecture by Thorne has been claimed to be\ violated in curved spacetimes coupled to linear electrodynamics. Hod \cite{Hod:2018} has recently refuted this claim by clarifying the status and validity of the conjecture…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
The mathematical model of orthodox quantum mechanics has been critically examined and some deficiencies have been summarized. The model based on the extended Hilbert space and free of these shortages has been proposed; parameters being…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…