相关论文: Quantum Evoluton and Space-time Structure

In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…

In this paper we consider generalization of classical and quantum mechanics that directly follows from the causality principle and topology of a system state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the…

General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…

Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…

The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial…

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules…

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…

We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…

Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…

Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time…

A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…

It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…

The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…