Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/35



Further remarks on space and time, used as notes to the author's paper entitled "Space travel and future research into the structure of the universe."

In German.

Translated title: Relativistic rocket mechanics.

In this paper the mechanics of the special theory of relativity are extended to systems with timely changeable rest masses (rockets). The theorem of impulse and energy is examined as well as the law of the decrease of the mass of a rocket with an optional acceleration in a free space without outward power, that is, in the system of the resting ground observer and in the system of the astronaut, moved with the rocket. Two special cases are treated, namely, the movement of a rocket with constant self-acceleration and the movement of a rocket with constant amount of mass flow rate (thrust).

In French.

Translated title: The evolution of space and time.

Discussion, in detail, of the clock paradox.

The motion of the clocks as represented in a solution offered by C. Møller is studied in detail. It is found that in the non-inertial rest frame of the accelerated clock the free clock suffers discontinuities in velocity whenever the "gravitational field" in that frame abruptly changes. Although these discontinuities occur at points of discontinuity of the metric tensor, examination of a case in which the gravitational field is turned on smoothly reveals that the effect is a real one within the framework of the general theory of relativity. By the principle of equivalence, it follows that even in a real gravitational field when that field changes in time velocity, dependent terms in the acceleration of a particle exist.