Abstract
Accelerated observers are discussed in detail, first on the specific case of a uniformly accelerated observer, leading to the concept of Rindler horizon. The difference between local rest spaces and simultaneity hypersurfaces, which coincide for non-accelerated observers, is computed in terms of the four-acceleration. Next, some aspects of physics in an accelerated frame are considered: the problem of clock synchronization, the behaviour of a rigid ruler, the motion of free particles and the redshift of spectral lines. Finally Thomas precession is investigated and applied to the motion of a gyroscope carried by an accelerated observer.
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Notes
- 1.
Let us recall that a has the dimension of the inverse of a length and that, \(\overrightarrow{\boldsymbol{a}}\) being a spacelike vector, \(\left \|\overrightarrow{\boldsymbol{a}}\right \|_{\boldsymbol{g}} = \sqrt{\overrightarrow{\boldsymbol{a} } \cdot \overrightarrow{\boldsymbol{a}}}\) [cf. Eq. (1.19)].
- 2.
Let us recall that O(t) stands for the position of \(\mathcal{O}\) at the proper time t.
- 3.
- 4.
Gerald J. Whitrow (1912–2000): British cosmologist and historian of science.
- 5.
In view of the result (12.44), we may omit the qualifier local in the denomination of \(\mathcal{E}_{\boldsymbol{u}}(t)\).
- 6.
In the previous sections, we have denoted by x 0 the x-coordinate of observer \(\mathcal{O}^{\prime}\); here we rather use x em, which recalls that he is an emitter.
- 7.
- 8.
The inertial observer \(\mathcal{O}_{{\ast}}\) in our language.
- 9.
Underlined by us.
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Gourgoulhon, É. (2013). Accelerated Observers. In: Special Relativity in General Frames. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37276-6_12
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