PeterDonis's latest activity
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Zero or negligible, it's still pointless. You're making it negligible by making the beam itself negligible. Which means we can just... -
PeterDonis replied to the thread I Euclidean geometry and gravity.If you build the object in curved spacetime, hovering against gravity, you can't make the stresses in it negligible, because it's under...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Meaning, you build the object in an accelerating spaceship or something like it in flat spacetime, and then bring it into curved...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.A beam of "negligible mass" might as well not be there; you're only getting the result that the stress in it is zero by saying it has no...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.The OP specified a piece of paper, not a truss structure. Also, your claims, if they are correct, should apply to any object, not just...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Really? You can externally apply a force to an atom in the center of the object? You can't apply an external force to a part of an...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Btw, for the particular special case under discussion in this thread, we don't even need the Riemann tensor, because we know that the...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.I strongly suggest that you do the math. If you do, you will find that your statement here is false. First, the "spatial curvature" you...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Yes, that's true, but... Yes, which is why the stationary congruence does not fall into the first type of congruence that the H-N...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.While the theorem was originally proved before GR was even discovered, AFAIK it does not actually require flat spacetime. The two types...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.This is also correct. I don't know if we discussed this particular case in previous threads some time back on the Herglotz-Noether...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.Yes, this is correct. Since the worldlines in the congruence are integral curves of a timelike KVF, you can derive the result...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.The kinematic decomposition is useful, yes, but to obtain it, you have to already know the worldlines. But you need to know the material...
-
PeterDonis replied to the thread I Euclidean geometry and gravity.No, that's not correct. Knowing the spacetime curvature does not tell you the deformation, because spacetime curvature only tells you...
-
PeterDonis replied to the thread I Are primordial fluctuations the source of all structure?.No, they didn't. That's because the theory does not, and is not intended to, account for structure on human scales. More generally...