Abstract
The measuring process in mechanics and the description of the motion of bodies in space and time cannot be separated.
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Notes
- 1.
The metre was originally understood as the 40-millionth part of the circumference of the Earth.
A definition of the metre with the help of the speed of light is avoided in the beginning for avoiding confusion with the logic of our exposition.
- 2.
Soon after establishing his Special Relativity Theory, Einstein (1955) has shown, that the universal mass attraction, the gravitation requires a substantial extension of the theoretical framework of space and time. The understanding of Special Relativity, a logically closed theory, will become more difficult by the inclusion of gravitational effects. Therefore, in this book, all gravitational effects are excluded besides in the last Chap. 13, where the fundamentals of this extension called General Relativity Theory are introduced.
- 3.
Well known is Foucault’s pendulum, a long, well-suspended pendulum on the roof of high room of building, that shows a continuous change of its oscillation plane without any force impact. The room does not represent an inertial system, the Earth is in rotation with respect to the inertial system \(\Sigma _o\) . Considered from this system \(\Sigma _o\), the oscillation plane does not move at all. The property of our rotating Earth, not to represent an exact inertial system, will become especially significant in precision experiments to the relativistic time dilatation, s. Problem 4.
- 4.
Thereby, we suppose that the sum of inner angles in a triangle measures \(180^\circ \) or \(\pi \) in arc scale. For the three-space holds the Euclidean geometry. This basic assumption will only be modified in Einstein’s General Relativity Theory.
- 5.
For a deeper discussion of the time definition we refer to Barbour (1999, 2001).
- 6.
If one replaces the photons by bodies K, that are given identical velocities v by some precision machine, then from practical points of view we will never get the same precision as with light. Furthermore, there we will not have the independence of the velocity according to statement (5).
- 7.
The meaning of the symbol ‘\(:=\) ’ is ‘equal by definition’.
- 8.
The notion ‘special’ is used in this sense for ‘special Lorentz transformations’ . In the destination ‘Special Relativity Theory’ it has another meaning. There we distinguish it from the ‘General Relativity Theory’, the theory of space, time and gravitation, s Chap. 13.
- 9.
As complement to Eq. (18), we also add
\(f_1(x_o \,{+}\, v\,t, t_o \,{+}\, t, v)\,{=}\, f(x_o \,{+}\, v\,t - v(t_o + t), v)\,{=}\,f(x_o \,{+}\, v\,t - v\,t_o \,{-}\, v\,t), v) = f(x_o - v t_o,v) = f(x_o, \, t_o, v).\)
- 10.
Indeed, there exists an additional effect: The period of a clock depends on the strength of the gravitational field at its place. However, here we neglect all gravitational effects.
- 11.
The standard proof for the linearity of coordinate transformations is shown in Chap. 9, Sect. 1, cp. e.g. also Rindler (1977), Fock (1964), Weyl (1952). It follows from Einstein’s relativity principle, s. Chap. 2, Sect. 1. With the postulate of a universal constancy of the speed of light Einstein introduced also a definition of simultaneity, and indeed with a linear synchronisation recipe with the prescription of Eq. (20) for the function \(\theta \) in Eq. (103) as will be shown in Chap. 4, Sect. 4.
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Günther, H., Müller, V. (2019). Space, Time and Motion. In: The Special Theory of Relativity. Springer, Singapore. https://doi.org/10.1007/978-981-13-7783-9_1
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DOI: https://doi.org/10.1007/978-981-13-7783-9_1
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