Einstein's Special Theory of Relativity SR concern aspects of relativity in comparison of observations made by different observers moving with respect to each other.
More generally, relativity is always related to comparison and observation of difference in one form of the other and so may be viewed to be a fundamental aspect of a liberal democratic society allowing differences to coexist and so open to comparison, as a opposed to a fully socialistic paradise with everybody being equal and so closed to comparison.
A basic question concerning relativity as comparison, is if an observed difference expresses illusion or reality. Consider the following situations:
- Two persons of equal height view each other at distance and both get the impression that the other is smaller. Illusion or reality?
- People viewing other people to be more successful (or stupid) than themselves. Illusion reality?
- A person viewing a clock moving away with constant velocity getting the impression that it runs slow as compared to his/her own clock = time dilation of SR. Illusion or reality?
You would probably say that 1. is only an illusion: Viewing a person at distance does not really shorten the height of the person. You would also probably say that 2. can be both illusion and reality depending on the situation.
What about SR? Illusion or reality?. Comparing with the height of a person as not changing with distance, we expect the same with a moving clock: There is no sufficient reason that the functioning of a clock whether atomic or mechanical will change under motion with constant velocity, and so its rate will not change under motion, at least not according to Leibniz' Principle of Sufficient Reason PSR. If the person viewing the moving clock gets the impression that it runs slow, it must be an illusion, right?
At least this is what Leibniz would say. In case 1. the two persons can be brought together and it can be checked if they are equally tall. But in case 3. this is not possible, since the clock moving away cannot be brought back without changing velocity and so upset conditions. It means that it is impossible to decide between illusion and reality. This means that it is not possible to say that Leibniz was wrong by direct comparison of clock rates at the same place, and so by PSR time dilation can only be illusion. QED
Or is it possible that a perceived difference can be upheld if actual comparison cannot be made? What can prevent you from viewing yourself to be smarter than other people if comparison cannot be made? Isn't that a form of reality that can help you go forward with confidence? What prevents you from believing that that a clock moving away from you runs slow if there is no way to prove that you are wrong?
If it is impossible to show that you are are wrong, does it mean that you are right?
Recall Gödel's famous self-reference construction:
- "This statement cannot be proved to be true" is true but impossible to prove so.
with the following variant:
- "This statement can be proved to be false" is false but impossible to prove so.
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