Related papers: A general comparison theorem
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely…
Hardy (quant-ph/0101012) conjectures in his Axiom 2 that K=K(N), and that in classical probability K=N, while in quantum mechanics K=N^2. We offer an example in classical probability for which K=NV, V the number of independent complete…
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…
In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
In the Hilbert space formulation of classical mechanics (CM), pioneered by Koopman and von Neumann (KvN), there are potentially more observables that in the standard approach to CM. In this paper we show that actually many of those extra…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
In this paper we generalize the comparison theorem of Hecht and Taylor to arbitrary parabolic subalgebras of a complex reductive Lie algebra and then apply our generalized comparison theorem to obtain results about the geometric realization…
The equivalence principle postulates a frame. This implies globally special and locally general relativity. It is proposed here that spacetime emerges from the gauge potential of translations, whilst the Lorenz symmetry is gauged into the…
We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant…
We give a mathematical uniqueness theorem which in particular shows that symmetric tensors in general relativity are uniquely determined by their monomial functions on the light cone. Thus, for an observer to observe a tensor at an event in…
It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So…
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…
An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of…
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit…
Let Riemannian metrics $g$ and $\bar g$ on a connected manifold $M^n$ have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the…
We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the "timelessness" of the hypothetical…
We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some ``position'' variables of this formulation…