Quantum Gravity: A Heretical Vision

Abstract

The goal of this work is to contribute to the development of a background-independent, non-perturbative approach to quantization of the gravitational field based on the conformal and projective structures of space-time. But first I attempt to dissipate some mystifications about the meaning of quantization, and foster an ecumenical, non-competitive approach to the problem of quantum gravity (QG), stressing the search for relations between different approaches in any overlapping regions of validity. Then I discuss some problems raised by the approach we call unimodular conformal and projective relativity (UCPR). Only TheoriesPerhaps it will be helpful if I recall a tripartite classification of theories that I proposed many years ago. The three categories are: 1) Perfectly perfect theories: The range of these theories includes the entire universe:There is nothing In the world that these theories do not purport to explain, and they correctly explain all these phenomena. Today we call such theories TOEs-Theories of Everything. 2) Perfect theories: These are more modest. They correctly explain all phenomena within their range of application, but there are phenomena that they do not purport to explain. 3) Then there are just plain Theories: There are phenomena that they do not purport to explain, and there are phenomena that they do purport to explain, but do not explain correctly.Both the history of science and my own experience have taught me that all we have now, ever have had in the past, or can hpe to have in the future are just plain theories. This tale had two morals:1) Every theory has its range of validity and its limits; to understand a theory better we must find its limits. In this sense, we understand Newtonian gravity better than general relativity (GR).2) There will be theories with over-lapping ranges of validity; to understand each of these theories better we must explore the relations between them in the overlap regions. Some examples will be given in the next Section. What is quantum theory? What quantization is and is notA certain mystique surrounds the words "quantum theory." The very words conjure up visions of probing the depths of reality, exploring the paradoxical properties of the exotic building blocks of the universe: fundamental particles, dark matter, dark energy-dark thoughts.But the scope of the quantum mechanical formalism is by no means limited to such (presumed) fundamental particles. There is no restriction of principle on its application to 2 any physical system. One could apply the formalism to sewing machines if there were any reason to do so! (Stachel 1986).Then what is quantization? Quantization is just a way accounting for the effects of the existence of h, the quantum of action, on any process undergone by some system--or rather on some theoretical model of such a system. This is the case whether the system to be quantized is assumed to be "fundamental" or "composite." That is, whether the model describes some (presumed) fundamental entities, or whether it describes the...

Quantum gravity: Meaning and measurement

“…Everything depends on the utility of the results in explaining some physical processes. (Stachel, 2012) There are many such examples of different approaches to quantization of the same physical process, each successful within its range of applicability (Stachel, 2012). Rather than leading to a contradiction, this leads to a new and interesting question: what is the relation between such two approaches?…”