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2 - The formalism of special relativity

Published online by Cambridge University Press:  05 April 2013

Hans C. Ohanian  and
Remo Ruffini
Hans C. Ohanian
Affiliation:
University of Vermont
Remo Ruffini
Affiliation:
Università degli Studi di Roma 'La Sapienza', Italy
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Summary

Raffiniert ist der herrgott,

Aber boshaft ist er nicht.

[God is cunning, but not malicious.]

Albert Einstein

Throughout this book we are concerned with fields – that is, functions of space and time, such as gravitational fields, electromagnetic fields, and velocity fields – and density distributions that describe masses and charges. Spacetime is the arena in which these fields perform their joint evolutions. It is therefore clear that we must first get to know the structure and geometry of spacetime. Unfortunately, because the velocity of light is so large, everyday experience leads us to acquire various misconceptions about the geometry of spacetime. This set of misconceptions goes under the name of Newtonian, or Galilean, spacetime. The true (or more true) geometry of spacetime was discovered through the development of Einstein’s theory of special relativity, starting in 1905. The keystone of this theory is the principle of relativity, according to which the laws of physics are the same in all inertial reference frames. Einstein was led to this principle by his investigation of Maxwell’s equations. As he wrote in his autobiographical notes,

After ten years of reflection such a principle (the principle of special relativity) resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam as an electromagnetic field constant in time, periodic in space. However, there seems to exist no such thing, neither on the basis of experience, nor according to Maxwell’s equations.

(Einstein, 1951)
Type
Chapter
Information
Gravitation and Spacetime , pp. 47 - 94
Publisher: Cambridge University Press
Print publication year: 2013

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References

Einstein, A. (1951). Autobiographical Notes. In Albert Einstein: Philosopher-Scientist, ed. Schilpp, P. A.. New York: Tudor Publishing Co., p. 53.Google Scholar
Marzke, R. F., and Wheeler, J. A. (1964). In Gravitation and Relativity, ed. Chiu, H.-Y. and Hoffmann, W. F.. New York: Benjamin, pp. 48–60.Google Scholar
Minkowski, H. (1908). In Lorentz, H. A., et al., The Principle of Relativity. London: Methuen (1923), p. 75.Google Scholar
Ohanian, H. C. (1988). Classical Electrodynamics, 2nd ed. New York: Jones and Bartlett Learning.Google Scholar
Ohanian, H. C. (2004). Am. J. Phys. 72, 141.CrossRef
Pauli, W. (1958). Theory of Relativity. London: Pergamon Press, pp. 61, 87, 125.Google Scholar
Schwartz, M. (1972). Principles of Electrodynamics. New York: McGraw-Hill.Google Scholar
Synge, J. L. (1956). Relativity: The Special Theory. Amsterdam: North-Holland, pp. 24–26.Google Scholar
Wheeler, J. A. (1968). Einstein's Vision. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Wigner, E. P. (1939). Ann. Math. 40, 39.CrossRef

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