The Nature of Physical Theory: A Study in Theory of Knowledge

By Victor F. Lenzen | Go to book overview

CHAPTER XII
THE GEOMETRICAL CONCEPTION OF NATURE
B. THE THEORY OF GRAVITATION

1. ACCELERATED FRAMES OF REFERENCE

THE geometrical conception of nature is the outcome of the endeavor to reconstruct physical theory so that it will satisfy a general principle of relativity.

Classical dynamics presupposes a set of priviliged systems of reference. A privileged frame which is employed in practice is one whose origin is at the center of mass of the solar system and whose axes are oriented with respect to the fixed stars. The equations of dynamics also hold with respect to frames in uniform rectilinear motion with respect to the foregoing privileged frame. The special theory of relativity presupposes the same privileged frames as does the classical dynamics. The proposition that the laws of physics have the same form with respect to a set of privileged frames is called the special principle of relativity.

Classical dynamics and the special theory of relativity did not admit the use of accelerated frames of reference. This may be illustrated by the following example from dynamics. Suppose that a car is moving with constant velocity relative to the surface of the earth; then mechanical phenomena within the car are described with respect to the car approximately by classical dynamics. For example, suppose that a body of negligible size is attached to the lower end of a spring balance which is attached to the roof of the car. The body will be in equilibrium in a position directly below the point of support of the spring. Now the condition for the equilibrium of a particle is that the resultant force be zero. Neglecting the resistance of the air, the only forces acting on the body are its weight

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