... KINEMATICS[*]
With hearty felicitations to Jacob Bekenstein, the father of black hole entropy.
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...[*]
To appear in ``Thirty Years of Black Hole Entropy'', a special issue of Foundations of Physics.
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... source[*]
This difficulty might not be of much bother to the physicist who can find sources which are subject to extreme acceleration but which cease to exist well before they reach him.
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...[*]
As far as can be ascertained, the four acceleration-induced sectors $I,F,II,P$ and their respective coordinates were first introduced by Bondi in Trautman et al. (1965) and independently by Rindler in Rindler (1966)
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...[*]
As far as can be ascertained, the four acceleration-induced sectors $I,F,II,P$ and their respective coordinates were first introduced by Bondi in Trautman et al. (1965) and independently by Rindler in Rindler (1966)
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... equations[*]
Reference Gerlach (2001), ``Radiation from violently accelerated bodies'', dealt with the dynamics of the Maxwell field equations, to which the present paper is a sequel.
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... radar[*]
This has been done in a highly original way by Bondi in Trautman et al. (1965)
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... Rand[*]
``Cognition and Measurement'', Ch. 1 in Binswanger and Peikoff (1990)
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... Peikoff[*]
``Concept-Formation as a Mathematical Process'', p.81 ff in Peikoff (1993)
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... length[*]
Geometrical clocks with with cavity ends at relative rest ($k_{AB}=1$) where first used by R.F. Marzke and J.A. Wheeler Chiu and Hoffman (1963) and advocated by them as a standard of length.
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... properties[*]
These three properties, reflexivity, symmetry, and transitivity, make this relation what in mathematics is called an equivalence relation. It divides the set of clocks into mutually exclusive equivalence classes. In our context these classes are the various boost-invariant sectors, whose clocks can be synchronized in each sector. This synchronization is highlighted in Sections V+.1667emB and V+.1667emC.
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... event[*]
See, for example, chapter 7 in Einstein (1961) for ``a clear explanation that anyone can understand''.
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... cases[*]
If $n_2\pm n_1$ is odd, then this simply means that there does not happen to exist a clock tick at B simultaneous with event $(m,n)$. This is, of course, due to the fact that the clock does not furnish half-integer ticks.
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... next[*]
For a cavity with ends at relative rest, this is, in fact, what happens in a Ti-doped sapphire laser. When turned on, usually only one or two modes are excited. Consequently, it starts its operation in in a continuous wave mode. However, by shining light pulses into this laser, the lasing action starts in other cavity modes. Since Ti-doped sapphire is a broadband amplifying medium, it is capable of sustaining this lasing action. The superposition of these lasing modes constitutes a light pulse bouncing back and forth inside the cavity. This bouncing is in perfect synchrony with the external light pulses that have been shined into the laser.
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... definition[*]
The Doppler shift between two bodies A and B is given by

\begin{displaymath}
k_{AB}=\sqrt{\frac{1+v}{1-v}}~.
\end{displaymath}

Here $v$ is their relative velocity, which in terms of the coordinates of spacetime sector $F$ is given by

\begin{displaymath}
v=\frac{\sinh(\tau_B-\tau_A)}{\cosh(\tau_B-\tau_A)}~.
\end{displaymath}

This yields

\begin{displaymath}
k_{AB}=e^{(\tau_B-\tau_A)}~.
\end{displaymath}

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... frequencies[*]
For accelerated cavities one talks about temporal frequencies, while for inertially expanding cavities one talks about spatial frequencies, but frequencies nevertheless.
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... meaning''[*]
Remark by E. Wigner on page 285 in the discussion following papers by S.S. Chern and T. Regge in Wolf (1980)
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... computations].''[*]
Page 20 in Schroedinger (1956)
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... fallacies[*]
One of them, the fallacy of the ``stolen concept'', deserves special mention because of its ubiquity, even among physicists. It is exemplified in statements such as (i) ``coordinates are unphysical'', (ii) ``before $t=0$ the universe did not exist'' (iii) ``the beginning of the universe'', (iv) ``the creation of the universe'', (v) ``the birth of the universe'', (vi) ``Why does the universe exist?'', etc.
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