Space-time exchange invariance: Special relativity as a symmetry principle

A.

Einstein

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H.

Minkowski

, , ().

H.

Minkowski

, The group property of the LT and its equivalence to a rotation in four-dimensional space-time had previously been pointed out by Poincaré in “The Dynamics of the Electron,” , –, 166–175 ().

W.

v Ignatowsky

, , ();

W.

v Ignatowsky

, , ();

W.

v Ignatowsky

, , ();

W.

v Ignatowsky

, , ().

P.

Frank

and

H.

Rothe

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P.

Frank

and

H.

Rothe

, , ().

See, for example, Ref. 18 of

V.

Berzi

and

V.

Gorini

, “,” , – ().

More recent references may be found in Ref. 6, and in J. R. Lucas and P. E. Hodgson, Space Time and Electromagnetism (Oxford U.P., Oxford, 1990).

J. H.

Field

, “,” , – ().

That is, all laws applying to physical systems where the curvature of space-time may be neglected, so that general relativistic effects are unimportant, and may be neglected.

See, for example, A. Einstein, Relativity, the Special and General Theory (Routledge, London, 1994).

N. D.

Mermin

, “,” , – ();

S.

Singh

, “,” , – ();

A.

Sen

, “,” , – ().

In

J. A.

Wheeler

and

R. P.

Feynman

, “,” , – (), this quantity is called “co-time.”

L. J.

Eisenberg

, “,” , ().

Y. P. Terletskii, Paradoxes in the Theory of Relativity (Plenum, New York, 1968), p. 17.

J. M.

Lévy-Leblond

, “,” , – ().

The positive sign for γ is taken in solving Eq. (2.12). Evidently $γ→1$ as $β→0.$

A.

Einstein

, , ().

J. H.

Field

, “,” , – ().

See, for example, I. J. R. Aitchison and A. J. G. Hey Gauge Theories in Particle Physics (Hilger, London, 1982), Appendix C.

See, for example, S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), p. 36.

See, for example, Eq. (2.36) of Ref. 6.

For a recent discussion of the physical meaning of the three-vector magnetic potential see

M. D.

Semon

and

J. R.

Taylor

, “,” , – ().

It is often stated in the literature that the potentials φ, $A⃗$ are introduced only for “reasons of mathematical simplicity” and “have no physical meaning.” See, for example: F. Röhrlich, Classical Charged Particles (Addison-Wesley, Reading, MA, 1990), pp. 65–66. Actually, the underlying space-time symmetries of Maxwell’s equations can only be expressed by using the four-vector character of $Aμ.$ Also the minimal electromagnetic interaction in the covariant formulation of relativistic quantum mechanics, which is the dynamical basis of quantum electrodynamics, requires the introduction of a quantum field for the photon that has the same four-vector nature as the electromagnetic potential.