T. Lawrence, General Relativity - its beauty, its curves, its rough edges . . . and its lessons for gauge fields (click on title to read the paper)
**Abstract:**
This essay argues that the most elegant aspects of General Relativity (GR) are those which are reasoned from first principles. It looks at how the conceptual structure of GR could be extended to incorporate non-gravitational interactions. It ends with a broad-brush discussion about aspects of the spaces inhabited by spinor fields.

Starting with Minkowski's spacetime, we set up the mathematical machinery to describe non-inertial frames in this spacetime. Describing gravity as curvature then follows naturally and inevitably. In taking this step, Einstein revealed a fundamental truth about the universe we inhabit.

This degree of uniqueness is not shared by the field equation or corresponding action. I suggest that for any truly unified fundamental theory of physics, the whole theory - including its field equations - should be reasoned from first principles. To develop such a theory, the core principle of GR, that curved spacetime is manifested as a force, is a good place to start.

Kaluza-Klein theories and theories of spontaneous compactification use this principle to interpret non-gravitational interactions. Many such theories extend GR by the inclusion of additional dimensions forming a compact manifold, on which a unitary gauge symmetry is considered to act *directly* - despite the fact that the carrier space for a unitary group is *complex*. If, instead, spacetime is extended in the most natural way, * orthogonal* gauge symmetries result. These represent the action of the 'internal' symmetries on * vectorial matter.* * Unitary* groups act on their * spinors.*

Complex spaces are needed to describe spinors, which have their own geometry.

Quote as: T. Lawrence, "General Relativity - its beauty, its curves, its rough edges . . . and its lessons for gauge fields," *Minkowski Institute Physics Journal*, 23 June 2024

V. Petkov, Relativistic Mass is an Experimental Fact (click on title to read the paper)

**Abstract:** Since mass is defined as the measure of the (experimentally established) resistance a particle offers to its acceleration and as it is also an experimental fact that a particle's resistance to its acceleration increases when its velocity increases, it follows that, like mass, the concept of relativistic mass also reflects an experimental fact. This means that the rejection of the relativistic velocity dependence of mass amounts to both rejection of the experimental evidence and refusing to face and deal with one of the deepest open questions in fundamental physics - the origin and nature of the inertial resistance of a particle to its acceleration, i.e., the origin and nature of its inertial mass.

Quote as: V. Petkov, "Relativistic Mass is an Experimental Fact," *Minkowski Institute Physics Journal*, 10 January 2023

V. Petkov, Note on inertial forces, inertial energy and the origin of inertia (click on title to read the paper)

**Abstract:** As a result of the open question of inertia the status of inertial forces has been a difficult subject in physics with
implications for the proper understanding of the force of weight in general relativity where gravity is not a force, but a
manifestation of the spacetime curvature. The purpose of this note is fourfold. First, to state explicitly when the
inertial forces are fictitious and when real. Second, to provide a virtually self-evident derivation, which demonstrates
that kinetic energy is in fact inertial energy - the energy equal to the work done by inertial forces. Third, to stress
that weight, which has been traditionally regarded as a gravitational force, is an inertial force in general relativity.
Fourth, to outline what spacetime physics implies about the origin of inertia.

Quote as: V. Petkov, "Note on inertial forces, inertial energy and the origin of inertia," *Minkowski Institute Physics Journal*, 30 October 2020

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