Existence of Minkowski space
Serge Wagner

TL;DR
This paper argues that Minkowski space's existence can be rigorously established through coordinate-free methods, challenging traditional reliance on coordinate transformations and suggesting possible need for its generalization or abandonment.
Contribution
It provides a formal, coordinate-free proof of Minkowski space's existence and questions its fundamental necessity in physical theory.
Findings
Coordinate-free transformation confirms Minkowski space exists.
Traditional coordinate-based methods are cumbersome and less fundamental.
Suggests potential for generalizing or abandoning Minkowski space concept.
Abstract
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have provided a reasonable rationale for this mathematical construct. In physics, such a rationale should show lower-level statements that determine where the proposed mathematical structure is applicable and yield formal premises for proving its existence. The above failure has apparently been due to the features of the adopted formalism based on the unjustifiably exclusive use of coordinates in the theoretical analysis of physical phenomena, which ignores the necessity of having physical grounds for mathematical concepts. In particular, the use of a coordinate transformation between two inertial reference frames makes the consideration so cumbersome…
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Taxonomy
TopicsRelativity and Gravitational Theory · Quantum Mechanics and Applications · Cosmology and Gravitation Theories
