Some remarks on clock rates in special relativity

Abstract

In part I a simple gedanken experiment is discussed that clearly develops a connection between the rates of accelerated clocks in special relativity theory and the rates of clocks at different points in a uniform gravitational field in any theory which incorporates the equivalence principle, such as general relativity theory. In part II it is shown that the time dilation effect observed when the rate of a moving clock is compared with that of a clock at rest can be derived by observing the Doppler shift, not only of light waves emitted by the moving clock, but of any periodic wave, e.g., sound.

Relativistic twins or sextuplets?

“…Although Boughn [56], as well as Sears [61] and Gruber and Price [73], showed that acceleration was not essential for the resolution of the 'paradox' it nevertheless has been previously featured [17,37,46,51] in other flight scenarios. Flights in the presence of gravitational fields have also been extensively analysed [29,30,34,39,45,51]. Special mention might be made of the recent paper by Dolby and Gull [79], who applied the concept of radar time to define hypersurfaces of simultaneity for a class of travelling twins, from the 'immediate turn-around' case, through the 'gradual turn-around' case and finally to the 'uniformly accelerating' case.…”

The Principle of Equivalence and the Twin Paradox

“…By classical or Galilean world we mean a kinematical world endowed with a preferred frame (of ether) S with 4 In terms of ordinary acceleration g = dv/dt, measured with respect to S the formula comes out to be Z = (gγx 0 /c 2 )(1 − v 2 γ 2 /c 2 ) which for small velocities can also be written as Z = gx 0 /c 2 . 5 The connection between gravity with this temporal offset through EP was first pointed out by Barron and Mazur [22], who derived the approximate formula for the "clock rate difference" mentioned in the previous foot-note. respect to which the speed of light c is isotropic and moving rods and clocks do not show any length contraction and time dilation effects.…”