A thought experiment with clocks in static gravity

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a forma...

A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using as reference a clock bound to a free falling reference system (FFRS). Derivations along these lines have already been proposed, but generally introducing some shortcut in order to make the presentation elementary. The treatment is here exac...

We consider gravitational time dilation between stationary observers and present examples, which contradict the statement that "time slows down as gravity increases". We show furthermore that this statement cannot be true in general, if strength of gravity is defined in an observer independent manner. We provide also a pedagogical introduction to gravitational time dilation, and discuss aspects of this phenomenon, which are often omitted in textbooks on general relativity.

A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using as reference a clock bound to a free falling reference system (FFRS). Derivations along these lines have already been proposed, but generally introducing some shortcut in order to make the presentation elementary. The treatment is here exac...

While adhering to the formalism of Special and General Relativity, this paper considers the interpretation of clock rates and the rating of clocks in detail. We also pay particular attention to the crucial requirement of reciprocity between inertial frames. Our overriding concern is to bring out a distinction between clocks which run slow (slowly) in the everyday sense and those which record a smaller time interval between specific event pairs - while running at the standard ...

This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If inertial frames are explicitly identified by motion with respect to the large scale structure of the universe, it makes it possible to consider the relative inertiality of different frames.

Students at Colorado College and cadets at the US Air Force Academy have conducted an experimental test of gravitational time dilation. This relativistic effect, highlighted in the movie Interstellar, causes clocks to tick more slowly near massive objects. A measurement of gravitational time dilation was made by comparing signals generated by a GPS frequency standard, which is based on sea-level time, to a cesium-beam frequency standard located at three different elevations a...

The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: on the one hand the phenomenon is explained through the behaviour of clocks which run the faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency...

In this paper we show how the student can be led to an understanding of the connection between special relativity and general relativity by considering the time dilation effect of clocks placed on the surface of the Earth. This paper is written as a Socratic dialog between a lecturer Sam and a student Kim.

As a consequence of gravitomagnetism, which is a fundamental weak-field prediction of general relativity and ubiquitous in gravitational phenomena, clocks show a difference in their proper periods when moving along identical orbits in opposite directions about a spinning mass. This time shift is induced by the rotation of the source and may be used to verify the existence of the terrestrial gravitomagnetic field by means of orbiting clocks. A possible mission scenario is outl...