I went back to post this link to the above post and my edit time had expired. Here is a link to a post in the Fringe that addresses the three explanations for the existence of the universe. It is from that perspective that I address the question of finite or infinite space and time: http://www.sciforums.com/threads/th...rse-cosmology-2014.141264/page-3#post-3262088
The paper is quite clear in identifying VSL theories as alternatives to GR. If the speed of light varies in the manner outlined in the paper, then it is an alternative to GR.
Here's Einstein talking about the speed of light again: Please Register or Log in to view the hidden image! quantum_wave: see what Einstein said in the second paragraph above. The speed of light is "spatially variable". It varies in space, and we model it all using the abstract thing called curved spacetime. It's important to avoid confusion between spacetime and space. The map is not the territory.
Since I have the honour of being on this moron's ignore list, let me explain something to any innocent reader Nobody in any course on General Relativity will have been taught that. They will have been taught that light speed is locally invariant And this is entirely back-to-front Spacetime is modeled as a 4-manifold with a semi-Riemann metric. At any point in this 4-manifod we have by definition a set of 4 independent coordinates, one of which is time t, or more specifically to match the units in which coordinates are measured, as ct. But if you want to talk about "speed" in GR you are using one of the coordinates (t) as an independent variable, and the other 3 (x, y, z) as dependent variables. Obviously you cannot use the time coordinate twice (hence Farsight's only correct(!!!) insistence that motion in spacetime has no mathematical meaning). But GR is a relativistic theory - or more precisely a generally covariant theory - so that for any other available coordinaate system we must have \(x'^2+y'^2+z'^2-ct' ^2 = x^2+ y^2+ z^2-ct^2 \) It follows that the speed of light "through" primed space as measured using primed time must be same as the speed of light through unprimed space using unprimed time. But noticing that \(x'^2+y'^2+z'^2-ct'^2 \ne x^2+y^2+z^2-ct'^2\), we have that the speed of light as measured from one set of spatial coordinates using a different a non-local time coordinate need not be the same as the speed of light as measured using the local time coordinate
Farsight, please stop lying about that paper. The paper you cite is speaking of a change to the speed of light at local measurements, not the speed over finite distances, as GR properly addresses.
Fortunately for me, and peculiar to my model, I replace the curvature of spacetime with the gravitational wave energy density hypothesis, i.e. where all objects have inflowing and out flowing gravitational wave energy. The energy density gradient of space contains the history of the gravitational wave energy out flow from objects. Therefore, there is gravitational wave energy traversing all points in space, at all times, at different directional densities. Light traverses that same space, and the directional speed of light is governed by the gravitational wave energy density gradient of the space it traverses. The speed of light is invariant in any frame, and will always vary between two frames in relative motion.
You keep claiming that you are not confused, that you do not misinterpret people, yet the link that you gave contradict all you have ever said about Light/photons BH's and FoR's...Oh, and at the same time support in general terms what I have been trying to tell you... Let's go through those points I have made again, and then I'll show you what two professors had to say..... [1] Light is never seen to be stopped, just generally redshifted beyond viewing capabilities. [2] From the local frame, nothing extraordinary ever happens, and the light following geodesics in the critically curved spacetime, crosses the EH and onward to the Singularity, the only possible path for it to take. [3]The only exception to this is photons of light that are emitted from just outside the EH, directly radially away. In that scenario they will always appear to "hover" forever, never secumbing to the BH, but never quite getting away. This is analogous to a fish swimming against a 10km/hr current, at 10km/hr [4]Light always travels at "c" in any and all local FoR's. Now interpret that to what the professors say that you yourself linked to.... "No, even with perfect instrumentation you cannot observe them forever. There is a ³last photon² that they emit/reflect before crossing the horizon. After that, there is no signal to detect. The same is true of a star that collapses to form a BH. This is a good in-practice observational definition of ³when the BH forms² . Don Marolf """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""" Prof. Moore: This is a good example of how intuitive models can go astray. The argument presumes that the light signal does not "slow down," but what exactly does that mean? An observer at rest relative to the star will always measure the outgoing light signal to have speed c *locally,* (that is, as the flash passes through a laboratory that is very small compared to scale over which spacetime is locally curved), but to talk about the speed of a signal emerging from the planet's surface and going all the way to infinity, one needs a *global* coordinate system (one that applies at all positions in spacetime, such as the Schwarzschild coordinate system) to talk about the signal's speed at various points. An observer using such a coordinate system will find that the light flash will move *slower* than c close to the planet's surface than it does at at infinity. This does not contradict the previous results, because time runs more slowly for observers close to the planet's surface than for those higher up, so what looks like something moving with speed c to an observer close to the surface looks like something moving slower to someone whose clock is running faster. As the planet's mass approaches the black hole limit, the signal emitted from the surface will seem to move more and more slowly away from the surface (and will also be seen to be increasingly red-shifted as observed from infinity). When the surface of the planet coincides with the black hole's event horizon, the signal will stop moving outward from the surface (and the redshift observed at infinity will go to infinity). So light no longer escapes. This also does not contradict the statement about an observer at rest on the surface seeing the signal to have speed c, because as event horizon moves beyond the planet's surface, that surface can no longer remain at rest, but in fact must go to r = 0 in a finite time (as measured by an observer on the surface), just as surely as the past must go towards the future. Even then, an observer on the surface will *still* see the light moving outward at speed c, but from the perspective of the global coordinate system, it is simply that the observer is falling faster toward r = 0 than the signal is. To understand all this fully, I strongly recommend that the questioner take a course in general relativity! Now Farsight, Professor Moore also gave you some good advice in the final sentence....That from memory was the second Professor to do so. You need to now swallow your pride, admit you are wrong just as Einstein did, and learn the way it really is.
The speed of light is always at "c" it is in effect locally invariable and constant. If we observe the speed of light in another FoR to be anything other then "c", it is because light by law is always following geodesics in curved spacetime, and as such has a longer distance to travel. That is certainly settled.
The issue of the speed of light probably cannot be settled. It is possible to come up with theories that the speed of light at local areas was different in the past or could be different in the future. It is possible to test these theories (which puts the lie to the idea that the speed of light is completely tautological).
That is a touchy subject with some members, but I agree with the changing speed of light in our Big Bang arena over the ~14 billion years, and I would think that the rate that clocks would tick (show time passing, if you will permit that phrase) would have changed significantly over that same time period, and maybe in several epics. The energy density at t=10^-43 must have been near natures maximum, and as superlumninal expansion or inflation occurred, the density must have decreased proportionally. You can equate that decline in density with a flattening of the curvature of spacetime, and that would make the transformations between frames come out with less dialtion as time passes on the ~14 billion year clock, I think. I personally equate the decline in density due to expansion with a decrease in the gravitational wave energy density of the medium of space. As our high energy density home big bang arena expands into the surrounding low energy density space of the greater universe, I would expect to get the same change in the tick rate of clocks now vs. back then as one would expect when invoking curved spacetime. I think you bring that up as a reference to Farsight's words about tautology explaining the different speed of light at the ceiling vs. at the floor. Technically, until the experiments give us a new means to quantify the speed of light against some new constant or something, Farsight's explanation still seems appropriate.
That does not change the fact that the speed of light in any local frame, in any time period will always be "c" But note carefully, light/photons were literally bouncing around, being absorbed, reemitted leaving the Universe as opaque for at least 380,000 years, or until temperatures had dropped enough for electrons to couple with atomic nucleii. [I may be open for correction with that terminology, and would ask anyone more knowledgable for a better description?] Certainly. The closer we go back to t+10-43 seconds, the higher was the energy density, and the more curved was spacetime and consequently the more time dilation was in effect. The superluminal expansion was the period we call Inflation. Correct, and the speed of light still would have been "c" although this was still during the Opaque phase, and before the recombination era. That is wrong according to the BB. The BB was an evolution of space and time [as we know them] It says nothing about before t+10-43 seconds. So there was no arena to expand into, and no less energy density to apply. The only difference was when the superforce started to decouple and phase transitions were created within spacetime/Universe and false vacuums. This lead to excesses of energy and our first fundamental particles. Time dilation. But please note, time dilation, length contraction, and any variation in the speed of light are only obvious from another FoR. From the local frame, all appears as normal. Farsight's explanations are amiss in that he refuses to concede that the speed of light is always "c"from any local frame. As Only Me [I think] explained earlier, I, at the top of the ceiling, measure my speed of light at the top of the ceiling to be "c" You, on the floor, measure your speed of light to be "c" on the floor. I would like PhysBang to elaborate a bit on his statement though, as I don't believe it to be clear enough.
As Only Me [I think] explained earlier, I, at the top of the ceiling, measure my speed of light at the top of the ceiling to be "c" You, on the floor, measure your speed of light to be "c" on the floor. Does anyone have any argument with that?
No argument from me; it is correct. And you could add, that two identical clocks, synced at the start, with one moved to the ceiling and one to the floor, would show different times when brought back together (too tiny to measure in that scenario, but I'm speaking technically). The issue isn't if they show different times and different tick rates though, the issue is the cause of them ticking at different rates. Curved spacetime is an explanation, backed by near perfect math. Variable energy density is an explanation that could be described with some mechanics, albeit quite speculative. But let's not argue about something that can't be proven or falsified. Let's leave it that the math works, and that there might also be some mechanics at work that can't be observed.
I have made comment to that effect, if not those words.., somewhere. I have also said that I don't know with any certainty, that the local speed of light measured somewhere, say between galaxies, is the same as it is measured here locally... But when we interpret what we observe of the distant universe with the assumption that the speed of light IS the same in ALL local frames of reference, the conclusions we arrive at make sense... And I will add now, that I am unsure that would be the case, were the speed of light to be locally variable over great distances. I do certainly (not with certainty) believe that Farsight's space jelly, would muck things up.......
I am pretty sure that it will turn out to be an effect associated with inertia, whether that is viewed as an artifact of acceleration or as how a gravitational field creates a local inertial bias... That would kind of be an equivalence principle relationship.... But that is probably a subject for another time and thread.
Maybe, but with two objects moving relative to each other, does inertia become relative as well, depending on which is deemed to be in motion and which is at rest?
Farsight has given no real explanation. While it is true that GR takes the constancy of the speed of light as an axiom, if the speed of light were to change, then one can see a difference in the timing of some phenomena relative to others. In the time dilation of GR, all phenomena remain at the same rate. Farsight seeks to explain his idea of speed of light changing by saying that everything is made of photons. He has never been able to explain how everything is made of photons, he simply repeats that claim over and over. If everything is made of photons, as Farsight says, then there needs to be an explanation about how photons can behave like everything else. However, when someone asks Farsight how a photon, a spin 1 particle, can behave like other particles that have different spins, he never addresses the question. Farsight might be right, but there is no reason to believe his ideas until there is some evidence that his ideas can match what we observe in nature. It is not evidence that Newton once, in some remarks about alchemy, once wondered if light and matter were made of the same thing. Similarly, even though the Atomists of ancient Greece were roughly correct that the objects around us are made of atoms, they did not have good physics evidence for this claim.
All objects with mass are always affected by inertia, whether you are talking about atoms, baseballs, planets or even whole galaxies... Once in motion objects with mass tend to stay in motion, abscent influence from an additional force.
