Special Relativity for Physicists by G. Stephenson & C. W. Kilmister

Author:G. Stephenson & C. W. Kilmister
Language: eng
Format: epub
Publisher: Courier Publishing
Published: 2019-03-10T16:00:00+00:00

3 . Equations of Motion

The Lorentz transformation was found in Chapter 1 as a transformation leaving Newton’s first law invariant. This was a first step towards a satisfactory formulation of dynamics. We must now consider the second law of Newtonian mechanics, which we regard here as a definition of how force is to be measured. It is clear that in the form

the law is not invariant under the Lorentz transformation. (For example, it has been shown in Chapter 2, § 7, that F = c is not an invariant condition for constant acceleration.) Equation (3.1), therefore, will not be a useful definition of how to measure force in relativistic mechanics. The situation is saved, however, in the same way as in Chapter 2, § 7, by the existence of one coordinate-system—the rest-frame—in which we may define the force by equation (3.1). This ensures that the relativistic form of our mechanics will agree with the Newtonian form for velocities small compared with that of light. The force can then be defined in any other inertial frame, in which the particle is moving, by performing a Lorentz transformation. Accordingly, we postulate the equation

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