Abstract
When we now discuss the two historical key experiments for Special Relativity, theMichelson experiment and the observation of the red \(H_{\alpha }\)-line in fast channel rays, we want to start from an empirical determination of the ratio of moving and stationary rulers and clocks, at first in the distinguished system \(\Sigma _o\). We remark again explicitly that Einstein’s universal constancy of the speed of light is not postulated in our procedure, but follows from the fully formulated theory, when we require for the definition of simultaneity in all other systems \(\Sigma '\) only the elementary relativity, cp. Sect. 4.
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Notes
- 1.
Maxwell had all of his life the opinion, that there exists a mechanical medium, a so-called aether, cp. Chap. 2, Sect. 1 and Chap. 8, Sect. 3, that can be used for the description of light propagation in a similar way as the propagation of sound waves through the air. A. Einstein believed probably until 1901 in such an aether.
- 2.
- 3.
One could come to the idea that this experiment could also be done with sound waves. As long as such a ‘sound clock’ is resting in system \(\Sigma _o\) as in Fig. 6, there is nothing wrong with this attempt. However, the sound clock might be running in a medium like air or water. For a moving sound clock, the transmitting medium must be moving with the clock. Different from the case with light in Fig. 7, we do not get the in \(\Sigma _o\) -observed velocity of sound waves without an additional hypothesis for the addition of the velocity v of the medium and the velocity of sound waves with respect to this medium.
- 4.
For the geometrically interested reader we refer to the presentation of SRT with all its phenomenena and paradoxa in space-time diagrams by Liebscher (2005).
- 5.
For those readers, that still are in doubt whether we must admit the logical possibility of length changes of moving rulers, and period changes of moving clocks, the nature provides an extra phenomenon, a miniature version of the Special Relativity Theory in solid states. We will discuss these issues in Chap. 12, Sects. 1 and 2, cp. also Günther (1994, 2000, 2006).
- 6.
For the unit: If an elementary charge runs through a potential difference of one Volt, it takes up an energy of \(\mathrm{1\, eV = 1.602 \cdot e^{-19}}\, J\) .
- 7.
If the grid takes up the repulsion energy \(E_r\), the \(\gamma \) quant looses this amount of energy and can no longer be absorbed from the grid as it would require an energy \(E_r\) larger than \(E_o\).
- 8.
The condition (234) for application of the pure transversal Doppler effect is here fulfilled. In our case we use in Eq. (234) \(\Omega R/c \ll R\,\nu /c\) , hence \(\Omega \ll \nu \). \(\Omega \) has an order of magnitude of about \(1000\,\mathrm{Hz}\), while \(14.4\,\,\mathrm{keV \, \gamma }\) quanta correspond to a frequency of \(3.5\,\cdot \, 10^{18}\,\mathrm{Hz}\). This follows from \(h\,\nu = 14.4\,\,\mathrm{keV}\) with \(h = 4.14\,\cdot \, 10^{-15}\,\mathrm{eV\, s}\).
- 9.
It should be observed that the linearity of space-time in the coordinates x and t, agreed upon in Chap. 1, Sect. 4, has nothing to do with the linearisation in v/c here discussed.
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Günther, H., Müller, V. (2019). Elementary Structure of Relativistic Space-Time. In: The Special Theory of Relativity. Springer, Singapore. https://doi.org/10.1007/978-981-13-7783-9_4
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DOI: https://doi.org/10.1007/978-981-13-7783-9_4
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