Stephen A. Lawrence wrote: > 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. >
Hi Stephen, You are exactly right. As I've said previously: "GR replaces the gravitational "force"(net flux towards the fourth dimension) with time dilation/contraction". "Which is exactly the wrong thing to do". And I'll tell you why(BTW, I've already done it, some months ago): Time is not a physical entity. So, you cannot mess with time if you want to make a physically sound theory. Time will result as a consequence of your theory, when all the physical entities are correctly modeled. Time is a consequence of movement in space. If you correctly model space and movement(which are physical realities), a correct time will result as a consequence. > The metric in 4-dimensional spacetime is not fixed, it varies from one > point to another. > Exactly. That's precisely the point: instead of measure physical reality with a fixed rule (as a good physicist will do), you're changing your ruler to coincide with physical reality. That's a very bad way of proceeding. Everything can be made to measure 1 meter, or to last for one second, that way. > >> There must be a flux, >> > > Can you define your term "flux"? > Mmmm, probably some of you are better equipped than me to find the right physical entity or entities. I can try to explain it to you with an image, and a little story. First, the little story: I still remember an afternoon, many years ago at a country house, when I got out for a walk after lunch. This was a friend of a friend's house, that was in a beautiful place near a small creek. I walked upstream the creek, and got a nice surprise when found out a pond, due to an artificial dam in the creek. The water was perfectly flat, and translucent. The interesting thing was that in one side of the pond, there was a little drainage, that formed a whirlpool. The whirlpool gently curved under the water(the drainage was in one of the sides), to appear at the surface. So, from my vantage point, and due to the translucent water, I could clearly see both aspects of the whirlpool; its underwater part, and the figure it formed at the surface. I spent many long minutes observing that whirlpool, having at the same moment the clear intuition that I was observing something very significative, although at that moment didn't know why it was so. Only years later, reading about the fourth dimension, the image of that day came to me again, this time in its full significance. What I'm saying is that gravity is the fourth dimensional equivalent of some aspects of a whirlpool of that kind. If you make a kind of piercing of the tridimensional fabric of space, and because around the neighborhood of the piercing, everything is pressing (trying to escape tridimensionality), a whirlpool will form, due to _something_ escaping through the small hyper-dimensional hole. Returning to the example of the tridimensional water whirlpool: imagine you are a bidimensional dweller living on the surface of the pool. When the whirlpool forms, you'll start to notice you're being attracted to the vortex. And you initially probably wouldn't notice that the surface of the water, where you live has curved on the z dimension, in the surroundings of the vortex. Because you dwell only on the x and y dimensions. After a while you'll start talking, (if you have some physics inclinations, and are able to make some measurements and comparisons on the surroundings) about time dimensions, space-time constructs, and the sudden relativity of all your previous assumptions about your previous (euclidean) space and time. All this simply because you cannot imagine a third spatial dimension, and the depths of water you're floating on. > > >> 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. > Yes, I know. I've intentionally talked about the distortion of space alone. Just to make clear that the distortion of time is no more than the equivalent of a hyper-dimensional spatial distortion. > 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 know what you're talking about, but (to return you the gentleness), that's complete nonsense to me. Better said: all that lacks physical soundness and reality to me. In my opinion, you're talking with good knowledge about a model that lacks physical reality. The fact that in GR measurements coincide don't represent the last word about a theory. As I've said before: if you change your ruler, everything can be made to measure what you want. > > >> 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? > Yes! A radial inward flux, which is equivalent to (can be understood as) a distortion of space. Do you remember (or can visualize) the little shape formed on the surface of the water, in the tridimensional whirlpool? Gravity is the fourth dimensional equivalent to that shape, geometrically speaking. > Do you have any idea why gravity is not a force in GR theory? > I think so: because all you said previously about spacetime; which sounds like total nonsense to me. Best regards, Mauro > > >> 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.) > > >
