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Xeinstein

- 90

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Suppose we have a box at rest that is filled with a uniform gas. We denote the volume by V and the pressure by p. Suppose next that we apply a small force to the box and accelerate it until it has a speed v. Once it is at speed v, the gas in the box has acquired a kinetic energy, so one might think that the total energy that we had to add to the box in order to accelerate the gas in it would have been equal to its kinetic energy. But this is not the whole story, because the Lorentz contraction has shortened the length of the box and therefore changed its volume. Making a box smaller when it contains a gas with pressure requires one to do work on it, in other words to put some energy into the gas. This extra energy represents the extra inertia of the gas.

The key question is: Is it harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz contraction demands? In other words, the moving box will contract but the gas in it will resist the Lorentz-contraction of the box

The key question is: Is it harder to accelerate the gas because it takes work not only to accelerate the existing energy but also to compress the gas as the Lorentz contraction demands? In other words, the moving box will contract but the gas in it will resist the Lorentz-contraction of the box

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