Pressure and Newtonian potential energy

[PeterDonis]

If a support breaks, causing the pressure to drop, it IS still at rest initially.

No, it isn't. Some parts of it are at rest, and other parts are not. You can't treat the support as a single object. You have to treat it as a continuous substance whose 4-velocity can vary from point to point.

I'll say it once more: your argument is based on intuitive hand-waving, but intuitive hand-waving doesn't count when it goes against an exact mathematical theorem. The exact mathematical theorem says that the change in internal pressure is balanced by something else to keep the external field the same (in the idealized case where the external field is the same). The fact that we have not yet figured out in this thread what that something else is does not mean the exact mathematical theorem is wrong. So if you are claiming that the exact mathematical theorem is wrong, but all you have to back that up is intuitive hand-waving, we will just have to close this thread as it will go nowhere.

 

[Jonathan Scott]

No, it isn't. Some parts of it are at rest, and other parts are not. You can't treat the support as a single object. You have to treat it as a continuous substance whose 4-velocity can vary from point to point.

You're going down to a microscopic level which is completely unnecessary. I was just using classical mechanics, as that's all that's necessary here.

It's true that suddenly releasing the support could for example cause a brief "ping" of oscillation. However, as I just said, the energy stored in the compression of the support, which would be the only source of any instant overall change of momentum or position, is related to the pressure integral in a similar proportion to the way that the length by which the support is compressed is related to the total length of the support, and it depends on the rigidity of the support, so it is independent of the pressure integral. So there is no way that anything the support can do could make up for the missing "source" term caused by the pressure dropping to around zero.

 

[PeterDonis]

You're going down to a microscopic level which is completely unnecessary.

Well, you are getting an answer that seems clearly wrong (that the source of gravity is not conserved) by not going down to a microscopic level.

I was just using classical mechanics, as that's all that's necessary here.

Not if you're going to claim that there is a paradox in GR. You can't do that based on an analysis that uses Newtonian mechanics.

there is no way that anything the support can do could make up for the missing "source" term caused by the pressure dropping to around zero

You don't know that, because you aren't doing the math; you're just waving your hands and claiming something that appears to contradict an exact mathematical theorem. I've already explained why that's not going to work.

At this point I am closing the thread since we are just repeating our positions and the discussion is going nowhere.