Abstract
Much of our presentation here will be an abbreviation of the treatment provided in the text The Classical Theory of Fields [[45], pp. 273–306]. Because of the importance that must be attached to an understanding of the basis of special relativity, which Einstein called der Schritt (the step) [[89], p. 163], we have elected not to simply summarize the results.
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- 1.
The terminology Einstein used was clock. We have used timepiece because the clock with hands is becoming less common.
- 2.
If this time of transit were not the same synchronization would not be possible and time would lose its meaning for points that are not in our immediate neighborhood.
- 3.
From the German Gedankenexperiment. In a thought experiment it must be possible to construct the required apparatus and to perform all the measurements. A thought experiment is not fanciful.
- 4.
The standard term is “observer” for the German Beobachter. The use of person seems less awkward here.
With modern timepieces a single person can gather the data.
- 5.
Hermann Minkowski was a German mathematician of Lithuanian Jewish descent. He was one of Einstein’s professors at the Eidgenössische Polytechnikum in Zürich.
- 6.
The designation 4-vector is that used by Jackson. We choose it here as well.
- 7.
Separate inertial frames must contain (material) measuring instruments, i.e. rods and timepieces.
- 8.
The geometrical definition of a cone includes both \(x^{\text {0}}>0\) and \(x^{ \text {0}}<0\).
- 9.
Here, as in our discussion of electrodynamics, we use Q rather than the traditional q to designate electrical charge. In this text q is reserved for the generalized coordinates.
- 10.
The terms in (8.68) are all simply numbers and commute.
- 11.
We note that CM designates center of mass in nonrelativistic (Newtonian) mechanics. The designation here as center of momentum is standard.
- 12.
In Newtonian, 3 dimensional space this would mean perpendicular.
- 13.
Of course this was already clear from the fact that a non-electromagnetic force must hold the nucleus together.
- 14.
We can verify this result by partial differentiation.
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Helrich, C.S. (2017). Special Relativity. In: Analytical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-44491-8_8
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DOI: https://doi.org/10.1007/978-3-319-44491-8_8
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