Originally Posted by **AndrewS** I will begin with a standard opening.
When two observers, A and B, move inertially in relation to each other, SR predicts they will each see each other’s clock has slowed down. Suppose the speed of A’s clock is x and the speed of B’s is y. A will know that x>y and B will know that x<y. If a mathematical proposition gave rise to this result it would obviously be considered to be false. So it is with SR. A quantity cannot simultaneously be both larger and smaller than something else. SR leads to logically inconsistent predictions and so it must be false.
Any comments so far? |

SR is based on two postulates:

1) The laws of nature are the same in all inertial frames of reference.

2) The speed of light has the same value in all inertial frames of reference.

Given those two postulates all of SR follows. The predictions of SR have been tested to great precision.

Consider the following thought experiment: In A's inertial frame there is a baseball moving at 100 m/s, as measured by observer A, towards the inertial observer B who is moving away from observer A at 100 m/s.

According to A the baseball is moving at 100 m/s. According to B the baseball is at rest.

Do these facts also bother you?

It's rather simply to show the relative rate that clocks tick. See the derivation on my website at:

Time Dilation
There is absolutely

*no* paradox here and there is also nothing a mathematician could or would object to.

By the way: if a < b and b < a then that's a contradiction and does not imply that a = b.

That could only be true if and only if a <= b and b <= a

where "<=" means "is less than or equal to"

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