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Reference: Einstein’s 1920 Book

Section XII (Part 1)
The Behaviour of Measuring-Rods and Clocks in Motion

Please see Section XII at the link above.

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Summary

The rigid unit of rod of the “other” coordinate system will always appear to shrink in its direction of motion. The more quickly it is moving, the shorter is the rod. But since the length of the rod cannot disappear or turn imaginary, the velocity c plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body.

Similarly, the clock of the “other” coordinate system will always appear to run slow. The more quickly it is moving, the slower is the clock. Here also the velocity c plays the part of an unattainable limiting velocity.

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Comments

The above conclusions from the theory of special relativity are often misunderstood, because they are very limited in their validity. Unfortunately, they have been very much exaggerated in general literature leading to very irrational ideas.

First of all, the special theory of relativity predicts the space will always shrink and time will always dilate with motion. This is similar to what you feel when you are sitting in the carriage of a train and the train next to you starts to move slowly. It is not always true that you are always at rest and the other train is always in motion. There is an illusion involved because one is not looking at some other pertinent factors.

Based on Michelson-Morley’s experiment; the measurement of the speed of light of 3 x 10⁸ meters/second was not affected by the velocity of the earth, which is 3 x 10⁴ meters/second relative to the sun. This velocity of the earth is 1/10,000 of the speed of light. Therefore, the Lorentz transformation is good for v/c ratios of the order of 1/10,000. The “v/c ratios” of most material bodies in the universe are of this order. The special theory of relativity is not valid for v/c ratios that are greater in order than 1/10,000. For Lorentz transformation to be applicable in practice, c must be extremely large compared to v. So, way before v approaches c this transformation stops being applicable in practice.

It is inconsistent to have the space always shrink and time always dilate. This inconsistency is resolved at the level of the general theory of relativity.

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Reference: Einstein’s 1920 Book

Section X (Part 1)
On the Relativity of the Conception of Distance

Please see Section X at the link above.

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Summary

We determine the same two points on the train and on the embankment using the concept of simultaneity. Then we measure the distance between those two points on the train, and on the embankment. We cannot be certain that the two measurements shall be the same.

To get some idea of the logic involved, please click on the link “Continue reading” below.

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Comments

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

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Reference: Einstein’s 1920 Book

Section VIII (Part 1)
On the Idea of Time in Physics

Please see Section VIII at the link above.

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Summary

To define time properly, we require a definition of simultaneity such that this definition supplies us with the method by means of which two events can actually be observed to occur at the same time. This stipulation must be satisfied regardless of any other condition for two events to be considered simultaneous.

We place identical clocks at the position of the events. These clocks tick at the same rate, so their pointers are going to move simultaneously. By reading the position of the pointer when the event occurs, we can assign a time value to that event.

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Comments

The time value shall be read differently from different distances because of the finite velocity of light.

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