farsight. if i was face to face with you, i would put down 50K$[which is just one months salary for me] that you could not do a simple y intercept.

Thanks for the laugh. It sounds like you think I care what anyone here, thinks about me. Did you want links to definitions and the words used in a couple of Goggle searches? You are yourself hilarious!

and yet, here you are. responding with a manipulative backpedaling post. sound like you care to me. i find your nonsense just as hilarious. all you do is just click on links and reiterate them towards others. this is just as much as a joke.

Einstein and many others would accept all of what most have been saying here, and its certainly an agenda and evil the way Farsight and other anti science nuts here have. It appears we are really an easy mark for these goons.

Sorry Billy. I'll try again: Yes. Or at least it ought to be, because "the time" is merely a measure of local motion. And d is distance: motion traverses a distance. Like Quarkhead conceded the other day, there's no motion in spacetime. It's an abstract "arena", a block-universe that is absolutely static. You can draw worldlines in it, and you can use it to work out spacetime intervals and other things. But we do not live in spacetime, the map is not the territory. Ours is a world of space and motion. Whether that motion is through space, or within the thing we call a clock.

Space exists...It evolved from the BB. Time exists...It likewise evolved from the BB. Henceforth these are known as spacetime. "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. – Hermann Minkowski, 1908" Motion occurs in spacetime...spacetime does not occur in motion. "Experiments continue to show that there is no 'space' that stands apart from space-time itself...no arena in which matter, energy and gravity operate which is not affected by matter, energy and gravity. General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field. This is not speculation, but sound observation." https://einstein.stanford.edu/content/relativity/a11332.html

OK, so can you show us, using your map with distance and no time, how to do a physics problem? Because otherwise you have no map at all. Or is this another physics question you will dodge?

No. What does "flat-but-titled" mean? If you respond, as I expect you to, that it refers to a Minkowski space with the diag{1. 1, 1, -1} metric, where the light cone "rotates" as it follows a spacetime geodesic, then you immediately find a contradiction. Surely even you can see this? According to your god, according to me, according to any sane mathematician/physicist there exist 2 and only 2 options. Spacetime is globally flat (\(R_{jk} =0\)) or it is not. As I and PhysBang have wasted too much time trying to explain to you, that locally flat (in this context) does NOT imply "globally flat". It is elementary differential geometry

There's no contradiction if you remember that a light cone is an abstract thing that doesn't actually exist. See this Stanford article for a mention of the tilted light cones, but better still take a look at a depiction of Riemann curvature: Please Register or Log in to view the hidden image! Imagine you placed light-clocks throughout an equatorial slice of space, then plotted the clock rates. The curvature you can see on the plot depicts spacetime curvature which relates to tidal force. But the force of gravity at any location depends on the gradient at that location. The spacetime "tilt". The first derivative of potential, not the second. There's no problem with that. Look at the plot again, or better still look at a bigger "rubber sheet" depiction like this one. Look at the bottom centre. There's a small region in the middle where spacetime is flat and level. If there was no curvature, the entire plot would stay that way. You need the curvature to get off the flat and level. But light doesn't curve because "the spacetime in the room you're in is curved". It curves because "the spacetime in the room you're in is tilted". PhysBang is a troll. And you're still having trouble understanding gravity, because you confuse mathematical abstraction for physics reality. You now know that there is no motion in spacetime. You now know that light doesn't move through spacetime. So you now know that the real reason light curves is because space is inhomogeneous, just like Einstein said. Such that the speed of light is spatially variable. Have you got that yet?

Hypothetically, if space could exist apart from time and therefore exist apart from space-time, one could move across a region of space-time in zero time. Don't quantum jumps works this way?

OK, we are getting an admission out of Farsight that "tilted spacetime" is just "curved spacetime", so at least that's progress. Not all spacetime curvature relates to "tidal force" and the difference in gravity across a finite region (i.e, tidal difference) is not the cause of gravitational time dilation, it's the absolute effect of gravity. Notice here that Farsight is using specific mathematical terms, even though he refuses to learn or use mathematics. If anyone doubts that, merely ask Farsight to show the mathematics that represent his idea and, eventually, you will see him write about the evils of mathematics. Note that this is an imaginary plot that nobody can look at. Farsight wants us to ignore how actual plots might look (NB: if we did the plot as he suggests, we wouldn't see a difference in the plots) and he is simply going to substitute his own ideas for any observational evidence. This is because Farsight hates observational evidence and would rather substitute his own "understanding" in place of physics that can produce results. He says this, but never produces influence. Farsight is great at insulting people when he can't answer their questions. If you want Farsight to insult you, simply ask him a simple question about the mathematics behind his ideas. Or ask him to show you how his ideas on photons making everything can reproduce the spin that he talks about so much. See, there you go: Farsight hates math, even though he makes mathematical claims all over the place. People likely haven't got this because Farsight, despite being asked for years, has never been able to show how to do the simplest gravity application with inhomogeneous space. Not one. You would think that a "physics expert" could do even a little physics, even that of his own choice. But, no.

OK, big boy, try this In flat spacetime, all geodesics are what, in ordinary parlance, we would call "straight lines", Otherwise they are "curves" Every geodesic is entitled to a tangent vector at every point. So if you "tilt" the light-cone as you "move" it along a straight-line geodesic you ru the risk of converting space-like vector into a time-like vector. Not good. Conversely, if you wish to avoid the same thing happening on a curved geodesic, you are obliged to "tilt" the light-conei Force of gravity? What is that? Haven't you repeatedly referred to the article where John Baez says gravity is not a force? And gradient of what? Gravitational potential? If so, in all theories of gravitation, the potential (recall that in GR the potential is encoded in the metric tensor) the important operator is the divergence of the gradient - the so-called Laplacian operator in Newtonian theory, which is a second order differential operator acting on a scalar field of potentials. In the Newton-Poisson formulation this has the nice property that it satisfies the Laplace Equation in the presence of a field but in the absence of matter i.e \(\nabla^2 \phi =0\) In GR, where the potential \(\phi\) is replaced by the metric tensor \(g_{jk}\), the divergence of the gradient is given by \(R_{jk}-\frac{1}{2}R\) and the first term (curvature tensor) is first order in the connection which in turn is second order in the metric (the potential). Since these 2 sets of differential equations are defined with respect to different quantities, one can see that curvature is second order in the metric (the potential) So this is wrong Regarding your Einstein quote - the state of "empty space" is given by the 10 functions \(g_{jk}\) - please answer this question...... if by "state of space" he means it is a property of "spatial space" why does he need 10 functions? Surely, in its matrix representation a metris defined on only 3 coordinates is a 3 x 3 matrix, i.e. a maximum of 9 functions. (I know the answer, so don't try to flannel) Your pathetic attempts to patronize me (or anyone else that has studied differential geometry) are doomed unless you can do the mathematics - in spite of you poo-pooing mathematics, as PhysBang and others have rightly said your silly analogies and kindergarten pictures are woefully inaccurates

"No more abstract then your own misinformed childish analogies like "time cannot be seen to pass within a clock"[apologies if that doesn't align with the exact stupid wordage of what you did say] No., you have that arse about face and totally wrong. Light/photons follow geodesics in curved spacetime. That is GR and to deny that is to deny GR and the great man who you so often misquote. Farsight is actually the troll, and is cunningly deriding the mathematical proof because he is unable to understand or present that proof himself. What he fails to understand, is then according to his own delusions, wrong and need not be considered. As has been shown here, and in your total bannings elsewhere, you are obviously the person who needs to get it.

OK. Light goes straight. Parallel lines don't meet. Et cetera. Yep. True. You will be aware that I am not enamoured of this sort space/time switching inside black holes. And that I will point out that a light cone is an abstract thing. I cannot point up to the clear night sky and say look, there's a light cone! So what's your point? But there is no light cone. And there is no worldline. And no spacetime. And no coordinate system, and no metric. They're all abstract things. Space and energy and motion aren't. What's your point? Yes we all know about that. Gravity is not a force in the Newtonian sense, but people talk about the force of gravity. They also talk about g and 9.8m/s². Quit carping and make your point. And? It isn't wrong. Go and check your facts. Here's something for you: According to Eq. (8.5) tidal forces are second derivatives of the gravitational potential. You start with 4 x 4 spacetime terms, but reduce it to 10 because the metric is symmetric. Space and time are involved because you measure the "metric properties" of space using rods and clocks. At the fundamental level both employ the motion of light. For example you place light clocks throughout an equatorial slice of space, then plot the clock rates to depict Riemann curvature. Have you understood what I've told you yet? Your pencil doesn't fall down because the spacetime in the room you're in is curved. And it doesn't fall down because the space in the room you're in is curved, see Baez about that. Instead it falls down because....

No it doesn't. And you will not find Einstein saying that. Nor Quarkhead any more, because he now knows that spacetime is a static abstraction, and that light does not move through it. He now knows that light moves through space. What's been shown here is that my physics knowledge far surpasses Quarkhead's, who reacts with feather-spitting outrage. As for elsewhere, people like him are "moderators" elsewhere.

Here are two great quotes from Farsight: So metrics both don't exist and space has "metrical properties" that form the foundation of Einstein's work, including "inhomogeneous space". Yet whenever anyone asks Farsight to use these metrics to show us how the physics works, Farsight can't do it. Here is where Farsight always stops, because he can't explain why a pencil falls down!

Really? Because the beginning of chapter 4 of "The Meaning of Relativity" has this quotation from Einstein: "A material particle upon which no force acts moves, according to the principle of inertia, uniformly in a straight line. In the four-dimensional continuum of the special theory of relativity (with real time co-ordinate) this is a real straight line. The natural, that is, the simplest, generalization of the straight line which is plausible in the system of concepts of Riemann's general theory of invariants is that of the straightest, or geodetic, line." The "Riemann's general theory" of which Einstein speaks is the geometry that guides what we call "curved spacetime" today. Einstein then gives the formula for a geodesic as equation (90), which included the Christoffel symbol that indicates curvature. Later, Einstein writes, "A glance at (90) and (90a) shows that the [Christoffel terms] actually do play the role of the intensity of the gravitational field." Of course, Farsight might just say that I am cherry-picking and ignoring the context of Einstein's work and mathematics. I urge one to download the book and determine on one's own the context. (The work is available here (and at other places): http://www.gutenberg.org/ebooks/36276 ) Sure, if we define "physics" to be the contents of Farsight's fantasies without regard for the work of scientists or what one can observe, then Farsight is by far the expert.

Yay! Our work is done..... 1. Farsight asserts that "a field is a state of space" 2. Farsight admits that "a state of space" is given by a symmetric spacetime metric tensor whose matrix representation has only 10 independent components I assume the self-evidently true propositions 3. "Flat spacetime" has a metric that has only 4 non-zero components (in its matrix representation) {this is the so-called Minkowski metric} 4. A metric with 10 non-zero independent components describes "non-flat" spacetime 5. The field in 1) above is the gravitational field Conclusion - the exact equivalence between the gravitational field and non-flat spacetime. What's so hard about that?

I am beginning to think that at least part of Farsight's difficulty is that he is unable to think in abstract terms... And his attempts to compensate with analogy, lack suficient substance to be of any significant value. That aside, even in the math of curved spcetime, is not t a variable? Which at least implies the potential for motion... I mean if t varies, unless all 3 spacial coordinates are fixed, you are describing motion.., in a spacetime model.., no?