System of Co-ordinates

ReferenceA Logical Approach to Theoretical Physics

We always observe the trajectory of a moving body from a viewpoint. Einstein identifies that viewpoint with a material body, such as, a platform or a train. In other words, we can observe the trajectory of a moving body either from the platform or from the train.

This identification of viewpoint with a material body gives us a co-ordinate system. Space is then defined as an extension of this reference body. It expands and contracts just like the reference body. The reference coordinate system is as rigid as the reference body. In other words, it endures in time at the same rate as the reference body. Therefore, the space and time are unique to the reference co-ordinate system.

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The Principle of Relativity

Einstein states his principle of relativity (in the restricted sense) as follows:

“If, relative to K, K’ is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K’ according to exactly the same general laws as with respect to K.”

The theory of special relativity (SR) looks at the uniform motion of K’ with respect to K. The magnitude of this uniform motion may vary.  Since there is no external force causing different uniform motions, these motions must be a characteristic of the co-ordinate system. According to The Logic of Motion these uniform motions are an expression of inertia (mass concentration) associated with the co-ordinate system.

This logic generalizes the classical laws, incorporated in the co-ordinate system, to also include the phenomena of optics and electrodynamics.

This logic, however, was not considered by Einstein. In its place Einstein proposed the principle of relativity. See The Principle of Relativity (In the Restricted Sense).

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Co-ordinate System at Rest

According to The Logic of Motion, a co-ordinate system of infinite inertia may be regarded as being absolutely at rest. We may call it K0 and choose it as our body of reference. All motion relative to K0 will then be absolute.

Einstein argues that since earth is in motion, it is obviously not K0. Therefore, its motion should play a part in the general laws of nature. But the motion of earth has revealed no physical non-equivalence of different directions. Einstein, therefore, concludes that there is no co-ordinate system that can be absolutely at rest.

The weakness of this argument is that the relative motion of earth is being confused with its absolute motion. The high mass concentration of earth shows its absolute motion is close to zero. It is 4 times denser than the sun. Denser than earth would be a neutron star or a black hole. Their absolute motion shall be still closer to zero.

Einstein’s conclusion that there is no co-ordinate system at absolute rest may be in error.

The higher is the mass concentration, the closer is the co-ordinate system to being at rest.

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