Abstract
Using the Lorentz transformation we can deduce all effects of the special theory of relativity. In this chapter, we will first revisit already familiar results, such as the relativity of simultaneity and composition of velocities. Then, we will derive new effects, relatedal to the order of events and length measurements.
Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
H. Minkowski, “Space and Time”.
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Notes
- 1.
Strictly speaking, electromagnetic is the part of so called electroweak interaction, but this is not very important here.
- 2.
See Appendix A.1.
- 3.
Max Born, Einstein’s Theory of Relativity, Dover, 1965, pp. 253–255.
- 4.
FitzGerald, The Ether and the Earth’s Atmosphere, Science 17 May 1889, Vol. 13, Issue 328, pp. 390.
- 5.
H. A. Lorentz, The Relative Motion of the Earth and the Aether, 1892.
- 6.
G. S. Viereck What Life Means to Einstein, The Saturday Evening Post, October 26, 1929.
- 7.
Or anything else traveling at the speed of light.
- 8.
To rigorously prove this, we must know how accelerated motion affects time measurements. This is the domain of general theory of relativity. Alternatively, we could break a smooth curve into “inertial” pieces and use the ideas of infinite sums from calculus.
- 9.
Recall that k = (1 + v)γ and, therefore, 1 ≤ γ ≤ k.
References
Minkowski, H. (1952). Space and time. In The Principle of Relativity. New York: Dover.
Born, M. (1965). Einstein’s Theory of Relativity (pp. 253–255). New York: Dover
FitzGerald, G. F. (1889). The Ether and the Earth’s Atmosphere. Science 17, 13(328), 390.
Lorentz, H. A. (1892). The Relative Motion of the Earth and the Aether. Amsterdam: Zittingsverslag Akad. v. Wet.
Viereck, G. S. (1929). What Life Means to Einstein, the Saturday Evening Post.
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Deshko, Y. (2022). Special Relativity B. In: Special Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-91142-3_6
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