The Two-Measure Theory and an Overview of Some of its Manifestations

TL;DR

The paper reviews the Two-Measure Theory (TMT), highlighting its development since 1998, its ability to replicate general relativity under classical tests, and its foundational mathematical justification, emphasizing its relevance to physical laws.

Contribution

It provides a comprehensive overview of TMT's mathematical basis and summarizes key results achieved over 25 years, clarifying its potential as a viable alternative to traditional models.

Findings

TMT can reproduce Einstein's general relativity in classical tests.

It offers a mathematically consistent framework for gravity and matter fields.

The theory has yielded significant results over 25 years of development.

Abstract

The Two-Measure theory (TMT) has been developing since 1998 and has yielded a number of highly interesting results, including those not realized in traditional field theory models. The most important advantage of TMT as an alternative theory is that, under the conditions under which all classical tests of general relativity are performed, TMT models are able to accurately reproduce Einstein's general relativity. Despite this, TMT is still often perceived as something too exotic to be relevant to reality. In fact, the fundamental idea underlying TMT seems undeniable: if we truly believe in the effectiveness of mathematics in studying nature, we must agree that there must be a correspondence between the fundamental laws of nature and the structure of the mathematical apparatus necessary to adequately describe them. It then turns out that there is no reason to ignore the volume measure existing on the differentiable manifold on which the theory of gravity and matter fields is built. This idea has far-reaching implications. The goals of this paper are: 1) to provide a clear mathematical and conceptual justification for TMT; 2) to collect in a single article some of the main results of TMT obtained over the past 25 years.