Recent content by PAllen

I guess it is worth pointing out that if you have two nuclei with equal and opposite momentum collide perfectly and fuse, the initial mass will be sum of the constituent rest masses plus sum of kinetic energy (treating energy in mass units). All of this kinetic energy will be carried off by the...

Maybe it would help to imagine two flash bulbs, one in motion relative to the other. They both flash when one just passes the other. In all frames, the light from the two flashes is different, even though the flash bulbs are each identical in behavior in their rest frames. And the difference is...

Let's stop right here. We will not get far by insisting that "we all must agree that 2 + 2 = 5". A given flash bulb (for example) has one world line, and at any point in its history, it is at rest in the origin of one family of frames connected by rotation. In all other frames, it is in motion...

I only have time for a quick reply now, just focusing on some issues with your first bullet: .. in the ship's inertial frame (assuming the ship moving inertially) No. Though each a circle in their respective frame, each circle represents a different set of events. This is fundamentally wrong...

Well, arbitrarily close any horizon, irrespective of how mild the tidal forces are near the horizon of a supermassive BH, the compressive forces are from holding an object stationary grow without bound, so any material would become a molecular monolayer, at some point. Of course, that’s assuming...

From the thesis I referenced earlier is a notion of what embeddings are 'hard' versus 'easy'. 'Hard' implies you are likely only to get a local smooth isometric embedding. 'Easy' implies that if there are no topological constraints, you are likely to get a global embedding. The determining...

A smooth embedding is possible. Just try to think about a 2-sphere embedded in Euclidean 3-space. There is no curvature anywhere in the Euclidean space, but the sphere embeds just fine. Even a small part of hyperbolic 2-space is smoothly embeddable in Euclidean 3-space. So just imagine the...

I found something right on point, but it is a thesis, so I don’t swear to its accuracy (I have not studied it in detail). Its results imply that a portion of a Euclidean plane can be smoothly isometrically embedded in any curved 3 space. It discusses use of the gauss-codazzi equations, as I...

I don’t see that as relevant to the example. It was just to point out that there can be balanced forces unrelated to, and in different directions, from proper acceleration of mass points. Therefore, that stress is not, in general, derivable from proper acceleration. And that if you supply the...

I assumed the beam was perpendicular to r, supported against gravity by external transverse force all along the bottom of the beam. Meanwhile, the rest of the structure presses the beam longitudinally, producing balanced longitudinal stresses. These exist without being reflected in proper...

But I think the claim is simply that you can’t deduce balance opposing forces from proper acceleration; that doesn’t mean they don’t exist, or the whole field of statics would vacuous.

You can start here to look for references: https://en.wikipedia.org/wiki/Nash_embedding_theorems Also look at the Whitney embedding theorem and also https://en.wikipedia.org/wiki/Embedding

Yes, since you are looking for a cause of changed pressure. The final state by itself has no memory of how it originated.

Of course I meant number density and coordinate values. I note you haven’t commented on the second part of that post, which, to me, proves a change in pressure due only to movement through changing curvature.

Ok, here I forgot to add 'preserving local density'.