Abstract
Galileo stated the Principle of Relativity using a series of thought experiments to be performed inside a ship. This was revolutionary in a time dominated by Aristotelian misconceptions, when the common wisdom was that there is an absolute rest system and a force is needed to keep objects moving (However, the times were ripe and some of the works by Giordano Bruno (1548–1600) imply correct ideas about the relativity of motion). The worst difficulty was that the 2000-years-old teaching of Aristotle was upheld by the Church.
Everyone is entitled to use their own measurements to describe physical reality, and the descriptions of observers who are in different inertial frames are related by simple transformation laws. This was well understood by Galileo, but the finite speed of light required Einstein to fit electromagnetism into the scheme, with paradoxical and astounding consequences.
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- 1.
However, the times were ripe and some of the works by Giordano Bruno (1548–1600) imply correct ideas about the relativity of motion.
- 2.
Albert Einstein (Ulm 1879 - Princeton 1955) is so famous that it is hardly necessary to mention his merits. Definitely, the most important physicist since the time of Newton, besides inventing and developing Special and General Relativity he gave a formidable contribution to Quantum Mechanics as well. Being of Jewish origin, he was forced to flee from Germany already in 1933. He spent the rest of his life in Princeton (USA).
- 3.
If the astronaut is unaware of Relativity, he will find a still stronger disagreement. He notes that the clocks in the Earth system go slow by a factor of \(\frac{1}{\gamma }\); so, if he keeps the length \(\frac{L}{\gamma }\) that he measures as the true length, then he expects that on the Earth, the elapsed time should be \(\frac{L}{u\gamma ^{2}}\), while in reality it is \(\frac{L}{u}\), as we know.
- 4.
About half of the authors define it as \( s^{2}=-r^{2}+c^{2}t^{2}\).
- 5.
At first sight, it may seem odd that the components \({x_{\alpha }}\) measured in the system of the observer are differentiated with respect to the time measured in the reference of the moving body, but actually, \({c d\tau =ds}\) is an interval and does not depend on the reference system.
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The infinite set of matrices so obtained are called a representation of the Lorentz Group.
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In general, one can form tensors that belong to irreducible representations of the Group of permutations of the indices; such a property is invariant.
- 8.
Here u is the speed of the train; more usually the law is written in terms of the speed \(-u\) of the source relative to the observer.
- 9.
For the experimental confirmation of the transverse Doppler effect, see Hay et al., Phys. Rev. Letters 4, 165 (1960).
- 10.
Using \({1 \over \sqrt{1-x^{2}}} \approx 1 +{x^{2} \over 2} + {3 x^{4} \over 8}\).
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Cini, M. (2018). Special Relativity. In: Elements of Classical and Quantum Physics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-71330-4_6
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DOI: https://doi.org/10.1007/978-3-319-71330-4_6
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