Mauro Lacy wrote:
> > I was thinking recently that it's not enough for gravity to be explained > merely as a consequence of a distortion of space. It's not a distortion of space, it's a distortion of spaceTIME, and the difference is extremely important. The metric in 4-dimensional spacetime is not fixed, it varies from one point to another. > There must be a flux, Can you define your term "flux"? > because a spatial distortion can explain at most the curvature in the > trajectory of _already_ moving bodies, Wrong. See, you've missed something here: *ALL* bodies are moving in spacetime. As I said, this is a distortion of spaceTIME, not SPACE, and that's extremely important, and it's apparently something you don't understand. One reason it's important is that in spaceTIME a body which you think of as just "sitting still" in space is still moving, at a rate of 1 second per second, directly down the time axis. This is *not* a trivial point -- in fact it's a vital point. The magnitude of your 4-momentum is your rest mass. That's true even if you are just "sitting still" -- because, of course, you're *never* just "sitting still", at rest in an inertial frame in 3-space you're already moving at 1 second per second in spacetime, and your 4-velocity looks like this (with speed of light set to 1): | 1 | | 0 | | 0 | | 0 | Your 4-momentum is the product of your 4-velocity and your rest mass, and it obviously has magnitude equal to your rest mass when you're sitting still in an inertial frame. When you are moving in 4-space, the magnitude of your 4-velocity is unaffected -- only its direction changes. Consequently the magnitude of the product of your 4-velocity and your rest mass, which is your 4-momentum, is always equal to your rest mass. The magnitude of your 4-velocity, by the way, is found by operating on your 4-momentum using the metric, which is a rank 2 tensor. As a rank 2 tensor, the metric is not affected by choice of coordinate system, nor equivalently by choice of reference frame. Consequently, since your apparent speed is just a function of the reference frame used to evaluate it, the magnitude of your 4-velocity and, in turn, your 4-momentum must be identical in all coordinate systems (or frames of reference). > i.e. inertial paths, but it's not > enough to explain 'force', that is, the acceleration of masses inside a > gravitational field. Certainly it is. You just take the covariant derivative of the 4-velocity of a body in free fall at that point and that tells you where a geodesic passing through that point goes, and any deviation from the geodesic shows up as requiring a 4-force. Gravity is *NOT* a force in GR theory, of course, and a body in free fall follows a geodesic. > Incidentally, that also shows why GR is so flawed: > the equivalence principle, between inertia and gravity, is complete > nonsense, because in inertia you have absence of forces, and in gravity, > presence of forces(flux). In short: GR replaces the gravitational > "force"(net flux towards the fourth dimension) Does "flux toward the fourth dimension" mean anything? Do you have any idea why gravity is not a force in GR theory? > with time > dilation/contraction, which is exactly the wrong thing to do. What you just said here is total nonsense. The equivalence principle is essentially exact, with the only apparent difference between uniform acceleration and a real gravitational field being that the Ricci tensor is nonzero in the latter case, which means there are tidal forces present. And in fact one can contrive situations in which the Ricci tensor is arbitrarily small in the presence of nonzero gravity, which of course is just an illustration of the fact that the gravitational field results from the connection, not directly from the metric -- i.e., gravity is *not* a tensor (in GR, and as born out by experiments done to date). In slightly less confusing terms, the gravity we perceive results from the first derivatives of the coefficients of the metric in our local coordinate system. Have you ever tried to learn anything about Riemannian geometry? Check out Horace's posts about gravimagnetics some time. If gravity is a force, then it is described with a rank 2 tensor, and when we change frames the transformation of that tensor should result in a new "force" appearing which is analogous to the magnetic force which appears when the E field is transformed. GR was founded, among other things, on the assumption that gravity affects all things equally in all frames, which, if true, means there's no gravimagnetic force, and that in turn means gravity is not a force. (Of course the assumption could be false, which is where Horace's notes on gravimagnetics come in.)
