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Therefore, they tick at the same rate.

2. Let clock B be located inside a ship.

As long as the ship doesn't turn on its engines clock B will remain at rest with respect to clock A, but if the ship turns on its engines then clock B is being accelerated by an outside force, and is no longer in an inertial reference frame.

Let us now suppose that the ship is uniformly accelerating, thus the speed of clock B relative to clock A is getting faster and faster.

Clock A is in an inertial reference frame, and can use the time dilation formula to conclude that clock B ticks slower and slower, and if the relative speed reaches c then clock B stops ticking (else the time dilation formula leads to division by zero error).

However, if time inside the ship stopped passing, then there would be no motion inside the ship, which would mean that the ship's temperature reached absolute zero degrees kelvin, which is thermodynamically impossible. Thus, clock B cannot be accelerated from rest to the speed of light (by thermodynamics).

In conlusion, as clock B moves faster and faster, its temperature gets closer and closer to absolute zero, and can be made arbitrarily close to zero, as the relative speed v gets arbitrarily close to c, but never reach absolute zero (and never reach speed c).

Therefore, SR is overthrown.

Why?

Well, let us suppose that after some amount of time, the ship stops uniformly accelerating, and coasts along at some constant final speed V which is necessarily less than c. (V is the final relative speed of the clocks to one another)

After the ship stops accelerating, clock B is again in an inertial reference frame. Hence, the time dilation formula can be used in clock B's frame, and the conclusion is that clock A is now ticking slower than clock B.

Likewise, by the same formula, clock A concludes that clock B is ticking slower than clock A.

Thus, one theory leads to two conclusions:

After the ship stops accelerating:

1. Clock A is ticking slower than clock B

2. Clock B is ticking slower than clock A

From which we can extrapolate the explicit contradiction that:

Clock B is and isn't ticking slower than clock A.

Thus, thermodynamics overthrows SR.

Yet, the rate of clock B slowed during its acceleration, and went back to its normal rest rate as soon as the uniform acceleration was over.

At that point, clock B now ticks at its rest rate, which is the same as the rest rate of clock A. And clock A's rate never changed. Hence, at the end of the event, clock B does and doesn't tick at the same rate as clock A, which is impossible.

Therefore, the time dilation effect isn't relative.