Absolute spacetime: the twentieth century ether

TL;DR

This paper explores the concept of absolute spacetime as a fixed background in gauge theories, examining its structure, quantum implications, and historical gauge issues like Einstein's hole argument.

Contribution

It reviews the layered spacetime model, incorporates quantum logic considerations, and revisits fundamental gauge problems such as the hole argument in general relativity.

Findings

Spacetime's fine structure is empirically unobservable, especially with quantum mechanics.

Quantum logic influences the modeling of spacetime structures.

The hole argument highlights deep gauge issues in general relativity.

Abstract

All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something fixed,'' i.e., absolute. This model must provide at least the following sequence of structures: point set, topological space, smooth manifold, geometric manifold, base for various bundles. The ``fine structure'' of spacetime inherent in this sequence is of course empirically unobservable directly, certainly when quantum mechanics is taken into account. This issue is at the basis of the difficulties in quantizing general relativity and has been approached in many different ways. Here we review an approach taking into account the non-Boolean properties of quantum logic when forming a spacetime model. Finally, we recall how the fundamental gauge of diffeomorphisms (the issue of general covariance vs coordinate conditions) raised deep conceptual problems for Einstein in his early development of general relativity. This is clearly illustrated in the notorious ``hole'' argument. This scenario, which does not seem to be widely known to practicing relativists, is nevertheless still interesting in terms of its impact for fundamental gauge issues.