Vinaire's Blog

Reference: Einstein’s 1920 Book

Section XI (Part 1)
The Lorentz Transformation

Please see Section XI at the link above.

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Summary

Classical mechanics holds that space and time intervals between two events are independent of the condition of motion of the body of reference.

It is possible to derive a mathematical relationship for the distance and time characteristics of coordinate systems, such that, the velocity of light always has the same value despite their different motions.

Every event can be represented uniquely in each coordinate system. That coordinate system has a unique motion relative to other coordinate systems. The mathematical relationships among the coordinates of different systems is thus generated by the fact that the speed of light remains constant for all coordinate systems despite their different motions. This gives us the Lorentz transformations.

If we substitute an infinitely large value for the velocity of light c in the Lorentz transformation, we obtain the Galilean transformation.

We can readily see that, in accordance with the Lorentz transformation, the law of the transmission of light in vacuo is satisfied for coordinate systems moving with different velocities.

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Comments

The mathematical derivation of Lorentz transformation is based on the considerations expressed in Appendix I.

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Reference: Einstein’s 1920 Book

Section IX (Part 1)
The Relativity of Simultaneity

Please see Section IX at the link above.

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Summary

Events that are simultaneous with reference to a coordinate system at rest are not simultaneous with respect to a coordinate system in motion. Every coordinate system has its own particular time. Unless we are told the coordinate system to which the statement of time refers, there is no meaning in a statement of the time of an event.

Time has been considered to be independent of the state of motion of the coordinate system. But this is not so because of the velocity of light is not infinite. If we take the finiteness of the velocity of light into account, then the conflict between the law of the propagation of light in vacuo and the principle of relativity disappears.

The duration of a particular occurrence with respect to a coordinate system in motion must not be considered equal to the duration of the same occurrence as judged from the coordinate system at rest.

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Comments

The sense of time changes with the motion of a coordinate system.

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Reference: Einstein’s 1920 Book

Section VII (Part 1)
The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity

Please see Section VII at the link above.

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Summary

From all observation, the velocity of light depends neither on its color, nor on its direction, nor on the velocity of its source. We may consider it to be constant and absolute in nature.

But, if we apply the theorem of addition employed in classical mechanics, the velocity of light must change when observed from a moving system of reference.

The view based on classical mechanics contradicts the observed fact that the velocity of light is constant. If the speed of light is a universal constant and a natural law, then, according to the principle of relativity, it should be the same for all Galilean coordinate systems irrespective of their motion.

The theoretical investigations of H. A. Lorentz on the electrodynamical and optical phenomena connected with moving bodies show that the law of the constancy of the velocity of light in vacuo is a necessary consequence.

When we consider both the law of propagation of light, and the principle of relativity to be correct, we arrive at the special theory of relativity.

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Comments

The order of magnitude for the velocity of light is so different from the velocity of material bodies that the sum of the two velocities would not be appreciably different from the velocity of light.

One may also argue that the changes in the velocity of light due to differences in colors, directions and the velocity of its source could similarly be imperceptible.

The theoretical research in electrodynamics and optics simply relates the velocity of light to electrical constants related to space, and we do not understand the nature of space.

It is true that the special theory of relativity improves upon the law of addition of the classical theory, because it takes the finite velocity of light into account. But, it is not totally satisfactory because its assumptions are not completely explained.

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