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Register a new userMad-Dog Everettianism: Quantum Mechanics at Its Most Minimal
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To the best of our current understanding, quantum mechanics is part of the most fundamental picture of the universe. It is natural to ask how pure and minimal this fundamental quantum description can be. The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian. Typically one also relies on some classical structure, such as space and local configuration variables within it, which then gets promoted to an algebra of preferred observables. We argue that even such an algebra is unnecessary, and the most basic description of the world is given by the spectrum of the Hamiltonian (a list of energy eigenvalues) and the components of some particular vector in Hilbert space. Everything else - including space and fields propagating on it - is emergent from these minimal elements.
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We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the systems total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space), can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold, and provides a crucial first link for any theoretical model of quantum spacetime at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
We apply the ideas of effective field theory to nonrelativistic quantum mechanics. Utilizing an artificial boundary of ignorance as a calculational tool, we develop the effective theory using boundary conditions to encode short-ranged effects that are deliberately not modeled; thus, the boundary conditions play a role similar to the effective action in field theory. Unitarity is temporarily violated in this method, but is preserved on average. As a demonstration of this approach, we consider the Coulomb interaction and find that this effective quantum mechanics can predict the bound state energies to very high accuracy with a small number of fitting parameters. It is also shown to be equivalent to the theory of quantum defects, but derived here using an effective framework. The method respects electromagnetic gauge invariance and also can describe decays due to short-ranged interactions, such as those found in positronium. Effective quantum mechanics appears applicable for systems that admit analytic long-range descriptions, but whose short-ranged effects are not reliably or efficiently modeled. Potential applications of this approach include atomic and condensed matter systems, but it may also provide a useful perspective for the study of blackholes.
A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {it coordinate} system (X$^i$,$tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {it Euclidean time} variable ($tau$). Introducing a path (line or hypersurface) in this space (X$^i$,$tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {it mechanical} system. It is inspired by the {it extra dimensional model}, appearing in the unified theory of forces including gravity, using the bulk-boundary configuration. The system Hamiltonian appears as the {it area}. We show quantization is realized by the {it minimal area principle} in the present geometric approach. When we take a {it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {it hyper-surface} as the path, the system Hamiltonian is given by the {it area} of the {it hyper-surface} which is defined as a {it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. The two choices, (1) the {it line element} in the bulk ($X^i,tau $) and (2) the Hamiltonian(defined as the damping functional in the path-integral) specify the system dynamics. After explaining this new approach, we apply it to a topic in the 5 dimensional quantum gravity. We present a {it new standpoint} about the quantum gravity: (a) The metric (gravitational) field is treated as the background (fixed) one; (b) The space-time coordinates are not merely position-labels but are quantum (statistical) variables by themselves. We show the recently-proposed 5 dimensional Casimir energy is valid.
In a recent paper (arXiv:1701.04298 [quant-ph]) Torov{s}, Gro{ss}ardt and Bassi claim that the potential necessary to support a composite particle in a gravitational field must necessarily cancel the relativistic coupling between internal and external degrees of freedom. As such a coupling is responsible for the gravitational redshift measured in numerous experiments, the above statement is clearly incorrect. We identify the simple mistake in the paper responsible for the incorrect claim.
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