Universal quantum mechanics

Abstract

If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the "standard" postulates of quantum mechanics, in particular those involving time and measurement. This paper proposes a framework that appears sufficiently general to incorporate some expected features of quantum gravity. These include the statement that space and time may only emerge approximately and relationally. One perspective on such a framework is as a sort of generalization of the S-matrix approach to dynamics. Within this framework, more dynamical structure is required to fully specify a theory; this structure is expected to lack some of the elements of local quantum field theory. Some aspects of this structure are discussed, both in the context of scattering of perturbations about a flat background, and in the context of cosmology. *

Gravitational dressing, soft charges, and perturbative gravitational splitting

“…Viewed from a "quantum-first" perspective [41] [16,34], beginning with the postulates of quantum mechanics, a key question for quantum gravity is what mathematical structure on Hilbert space is necessary to describe the foundations of the theory. Since any such structure should presumably have a perturbative version, at least for certain states of the theory, this suggests that important clues should be found in the perturbative structure of the theory.…”

Black holes in the quantum universe

“…To address these problems, one can try to develop a principled approach, based on the assumption that the fundamental description of the theory should be quantum-mechanical. This is what I call the "quantum-first" approach to gravity [16][17][18][19][20][21][22][23]: instead of trying to quantize geometry, we should ask what kind of quantum structure can approximately describe gravity.…”

“…Attempts to modify quantum mechanics 4 have typically led to disaster; quantum mechanics is a remarkably rigid framework. Because of this "quantum rigidity," and for other reasons such as its many experimental tests, I will therefore make the (radically conservative) assumption that the Universe is governed by quantum-mechanical principles (suitably generally formulated to incorporate gravity [16]). This means we should look for a different error of principles.…”

Quantum-First Gravity

“…Such a "quantum-first" approach to gravity has been advocated in [1][2][3], and also recently by Carroll and collaborators [4][5][6], and will be elaborated further here. 1 In contrast, previous approaches have started with a classical theory, such as general relativity (GR), and attempted to apply a set of rules to quantize the theory. These approaches have encountered vexing problems: at first that of non-renormalizability, but perhaps more profoundly, also the problem of respecting the basic quantum principle of unitarity, when one accounts for black hole formation and decay.…”

“…[9][10][11][12] proposed a "generalized quantum mechanics," but this is still too closely tied to the notion of quantizing a classical theory and is not sufficiently general. This motivated a proposal [1] for the essential postulates of quantum mechanics -those of "universal quantum mechanics" (UQM). In brief, as outlined in [1], these are the existence of a linear space of states with an inner product ("Hilbert space"), and the existence of linear hermitian operators that are interpreted as providing quantum observables; the postulates include unitarity, e.g.…”