Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

@article{Hehl2019PhysicalDA,
  title={Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity},
  author={Friedrich W. Hehl and Claus L{\"a}mmerzahl},
  journal={Annalen der Physik},
  year={2019},
  volume={531}
}
The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action h , electric charge q, and magnetic flux ϕ. Also, q×ϕ=action and q/ϕ=1/resistance are known. These results of classical… 
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References

SHOWING 1-10 OF 114 REFERENCES
Dimensions and units in electrodynamics
We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated
Relativity: Special, General, and Cosmological
Wolfgang Rindler is known as a writer of exceptional clarity. This quality is evident in this book as it explores in depth first special relativity, then general relativity, and finally relativistic
Equivalence Principles, Spacetime Structure and the Cosmic Connection
After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the
History and progress on accurate measurements of the Planck constant.
  • R. Steiner
  • Physics
    Reports on progress in physics. Physical Society
  • 2013
TLDR
A brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant and a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued.
On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this
The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram
1 Introduction.- Part I Analysis of variables and equations.- 2 Terminology revisited.- 3 Space and time elements and their orientation.- 4 Cell complexes.- 5 Analysis of physical variables.- 6
Premetric equivalent of general relativity: Teleparallelism
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric
Relativity
TLDR
The Theory of Special Relativity is an axiomatic theory, derived from two main axioms: the laws of physics are the same in all inertial frames (the principle of relativity) and the speed of light is determined by the Laws of physics.
Intrinsic measurement errors for the speed of light in vacuum
The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to c=299792458 m s−1. Advanced theories predict possible deviations from this
Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram
Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base
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