Abstract
It is well known that at the beginning of the 20th century, a deep fracture was detected between classical mechanics and electrodynamics. It was evident that if classical mechanics is accepted without modification, then electrodynamics is valid only in a frame of reference: the ether frame. All the attempts to localize this frame of reference failed. Einstein with the special theory of relativity overcame all the difficulties accepting electrodynamics and modifying mechanics. In this chapter, adopting Einstein’s original approach, we analyze the foundations of this theory together with some applications. Then, we discuss the four-dimensional formulation of the special relativity proposed by Minkowski and write the physical laws in tensor form.
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Notes
- 1.
See, for instance, [37].
- 2.
For the topics of this chapter see [15, 22, 27, 36, 38, 39, 41, 42, 47, 48, 56].
- 3.
A simple proof is shown at the end of this section.
- 4.
For the difficult topic of electromagnetism in matter, see, for instance, [27, 39, 44].
- 5.
If moving charge are present, then, instead of (26.117), we have
$$\begin{aligned} \frac{\partial {F}^{\star \alpha \beta }}{\partial {x}^{\beta }} = J^{\alpha }. \end{aligned}$$(26.120)
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Romano, A., Marasco, A. (2018). An Introduction to Special Relativity. In: Classical Mechanics with Mathematica®. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77595-1_26
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DOI: https://doi.org/10.1007/978-3-319-77595-1_26
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