- #1
Frank Wappler
- 4
- 1
- TL;DR Summary
- É. Gourgoulhon "Spec. Rel. in General Frames", sect. 2.3.2 defines "ideal clock(s)", introducing a "proportionality factor K", for short: "between duration and number of elapsed ticks"; cmp. eq. (2.11). Question: Is K the inverse of ticking rate?
In sect. 2.3.2 "Ideal Clock", p. 33, of É. Gourgoulhon's text book on "Special Relativity in General Frames"
$$ \tau_C [ \, \text{tick}_{j}, \text{tick}_{(j + N)} \, ] = K_C \, N. $$
(equation (2.11); notation adapted.)
The only other reference to this "constant K" is on the following page 34, as
On this "constant proportionality factor K" I have a few closely related questions:
(1) Is it correct to understand "constant K" as being specific to each ideal clock;
e.g. constant KC of ideal clock C, constant KQ of ideal clock Q, etc. ?
(2) Is it then correct that those specific constants, such as KC of ideal clock C, and KQ of ideal clock Q,
are not outright and necessarily presumed equal; but may be found equal, or not equal, by measurement ?
(3) Is it correct to identify KC as the inverse of the ticking rate of ideal clock C ?
(4) In case that KC is not zero, is it then correct to identify the value 1 / KC as value of the ticking rate of ideal clock C ?
[... a]n ideal clock is [...] defined as a clock [C] for which [C's duration] between two [not necessarily consecutive of its] ticks [...] is equal to a constant K times the number N of elapsed ticks:
$$ \tau_C [ \, \text{tick}_{j}, \text{tick}_{(j + N)} \, ] = K_C \, N. $$
(equation (2.11); notation adapted.)
The only other reference to this "constant K" is on the following page 34, as
proportionality factor K
On this "constant proportionality factor K" I have a few closely related questions:
(1) Is it correct to understand "constant K" as being specific to each ideal clock;
e.g. constant KC of ideal clock C, constant KQ of ideal clock Q, etc. ?
(2) Is it then correct that those specific constants, such as KC of ideal clock C, and KQ of ideal clock Q,
are not outright and necessarily presumed equal; but may be found equal, or not equal, by measurement ?
(3) Is it correct to identify KC as the inverse of the ticking rate of ideal clock C ?
(4) In case that KC is not zero, is it then correct to identify the value 1 / KC as value of the ticking rate of ideal clock C ?
Last edited: