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I have been doing some research on gravity, and I am having a very hard time with the following example I found in a book entitled Gravity From the Ground Up by Bernard Schutz. It sounds like a 3rd grader explaining Lorentz-Fitzgerald contractions...

"The inertia of pressure can be traced to the Lorentz-Fitzgerald contraction. In Investigation 15.4 on the next page we show how to calculate the extra inertia, but even without much algebra it is not hard to see why the effect is there. Consider what happens when we accelerate a box filled with gas. We have to expend a certain amount of energy to accelerate the box, to create and maintain the force of acceleration. In Newtonian mechanics, this energy goes into the kinetic energy of the box; as its speed increases so does its kinetic energy. This happens in relativity too, of course, but in addition we have to spend some extra energy because the box contracts.

The Lorentz-Fitzgerald contraction is inevitable; the faster the box goes, the shorter it gets. But this shortening does not come for free. The box is filled with gas, and if we shorten the box we reduce the volume occupied by the gas. This compression is resisted by pressure, and the energy required to compress the gas has to come from somewhere. It can only come from the energy exerted by the applied force. This means the force has to be larger (for the same increase in speed) than it would be in Newtonian mechanics, and this in turn means that the box has a higher inertia, by an amount proportional to the pressure in the box."

I just really am not sure what to make of this statement. What the hell is so special about the box that the gas doesn't also have? I had assumed the contractions were either a dimensional change in space-time, or at the very least Lorentz's idea that it was a reduction between atoms. I have also found where the author states that the units of the cosmological constant is 1/sec^2, which the consensus elsewhere is that it is 1/length^2.

This guy knows more about cosmology than I ever will, so this logic really throws me.

Any thoughts on this, cited examples would help greatly.

On second thought...maybe his example is just very poor wording. He is trying to link this pressure increase into how neutron stars work, but I think he would have been better off stating that the pressure within the walls of the box as well as the gaseous pressure increase. Thoughts still welcome on this.

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# Lorentzian contraction of a box increases the pressure inside?

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