OnlyMe
Spacetime is an abstraction. It is a 4D geometric model that describes and predicts the dynamics of the interaction of gravitationally significant masses. It is not a description of any curvature of space or time.
And that is simply wrong. Relativity is a description of the Universe as we see it behave. The only constructs exist in our minds. The thing being described is the reality, and the construct and the reality are two different things. Just like evolution is an observed fact, the Universe is an observed fact. And just like Darwin's theory of evolution is a construct describing the fact of evolution and it's proposed mechanism, Relativity is a construct that describes and explains the observed facts of the Universe. Curved spacetime is an observed fact, any valid construction will have to include that fact. Lightspeed is always c from any source no matter it's movement or acceleration, any valid construct will have to deal with that fact. Space length changes in the direction of movement, time dilates, mass cannot go lightspeed because it gains mass with speed, taking more energy to go each increment faster in an endless positive feedback loop that tends toward infinite mass and energy, but infinite energy is not available so not even a single proton can travel at lightspeed(though Cosmic Rays try ever so hard), and that is a fact that also must be included. I could go on, but why bother? Fortunately we have a construct that explains all of these things. Relativity. And Relativity says you are wrong, nothing personal.
Science is not a popularity contest. Amateur opinions are not as valid as informed opinion, and no one is entitled to their own facts or to ignore facts already in evidence(constant speed of light being a big one). Any construct that does not include lightspeed being always c is DOA, we know it to be false(we've known it for over 200 years). Ditto for time dilation, mass increase, length contraction, lightspeed limit, etc. These are not theoretical anymore like some were in 1906, existing only in the abstract, they are observed facts, as is spacetime curvature. We are about to directly observe Gravity Waves which cannot exist without spacetime to wave. That is the LAST prediction that Relativity made that has not proven to be true, yet, though we have indirectly detected them in the CMB from the very first second after Expansion.
The abstract spacetime model of GR, has been a very successful model, helping us to understand and explain most of what we observe at scales ranging from everyday classical experience to many associated with cosmological dynamics. The later in some cases requiring some modification to our conceptual understanding of mass and energy to remain consistent with GR... And no success in providing any real insight into the dynamics of gravitation at either extreme, existing at quantum scales or within the event horizon of what we call black holes. In both cases GR begins to run into difficulties, in the form of infinities. This is perhaps the greatest problem with attempts to conceptually project the abstract spacetime of GR, onto reality as an accurate description of space and, time.
All theories are imperfect and get revised as more evidence or better understanding comes along. Relativity is no exception. But it is a process tending toward perfection, which, like infinities, may not actually exist. That is a strength of the scientific method, it weeds out erroneous dogma over time, constantly distilling the theory down to it's essence. All that constant questioning, testing and comparing to the reality. One of the first major revisions was dropping the ad hoc Cosmological Constant from the math.
Also, there are problems between Relativity and Quantum Mechanics that we don't yet understand, but the bulk of the theory is an excellent model of how the Universe behaves. I think they may be on the right track at the LHC to solve those misunderstandings, we'll see.
One of the arguments that has been tossed back and forth, in this discussion has been whether in the context of GR the speed of light is constant or variable. The answer is of no importance for GR itself.
It is constant,
that is one of only two postulates on which SR was built, and
GR extended that to acceleration/gravity. It is VITALLY important. That's like saying the motor has no importance in a car.
Postulate-Accept the fact, or truth of (something) as a basis for reasoning, discussion, or belief.
If that postulate is ever shown to be wrong Relativity has been the biggest farce and prank ever. The possibility does not keep me up nights.
Both SR and GR together make up Relativity, the first dealt only with inertial systems, the second added gravity/acceleration and light travels at c, always. That is the answer, there can be no argument about that if talking about Relativity is what you are trying to do. You will find it on the first page of text in "On the Electrodynamics of Moving Bodies" by Albert Einstein(third paragraph) and it applies equally to GR. If you just peruse the diagrams I posted you can see for yourself. I've explained it to you guys the exact same way I taught it straight out of the physics textbooks for 30 years. I hate math(dyslexic), but math is only the framework, I talk about the whole building, the meaning behind the math. And there is only the facts and then there is everything else. I'll be sticking with the facts.
That was why understanding the difference between coordinate speed and c is important. Again, my diagrams show why that is.
Coordinate speed does vary, c does not. A bent path is longer than the straight path between the same two coordinates. Every photon in a vacuum in the Universe that we have ever measured moves at c, period. That has been confirmed for over 200 years. But if their path is bent then their coordinate speed is slower, their actual speed never varies. Calculation of the difference will tell you how much longer the bent path is, it's curvature, it's curvature is a direct measurement of acceleration/gravity field strength(which are described in the same terms). Two such measurements at different points in the direction that you are accelerating, simultaneously, give you gradient, which in turn gives you the mass if in a gravity field, but if they are the same you are in an accelerating inertial frame which has no gradient(IE in a spaceship, both clocks are in the same accelerating frame, on Earth they are in two different frames with the higher one ticking faster due to less acceleration.).
But SR, is only functionally accurate within the context of GR, when the abstract spacetime curvature of that model can be neglected as insignificant.
In an inertial frame you are not under gravity's influence or you are coasting, you are in free fall, you follow the zero energy line through spacetime just like light does, and without gravity a straight line in spacetime is as straight as in Euclid. So all you have to deal with are speed, energy/mass gain, length contraction, and Doppler effects. This is a special case in Relativity, thus it is called Special Relativity(Einstein did not yet understand accelerated frames and gravity, he knew SR was not the complete picture, but it was an accurate description of moving bodies). Acceleration and gravity were tied into that still valid special case in GR, the math was harder, but lightspeed remaining at c in all frames is still just as valid and as essential in GR. Dude, constant c is the basis of all the math in Relativity,
without constant c there is no Relativity, because
everything is related to that value(that's what relativity means), energy is to mass as the square of c, the speed limit of mass in the Universe? c. When does time slow to a stop? At c. At what speed would the dimension of space in the direction of travel reach 0(in the viewpoint of a stationary observer, you wouldn't notice)? c (if you could reach it). Do you not think there might be something important about this value that keeps appearing in the math that describes the way the Universe actually behaves? You might want to look into it before speaking further. Some people can learn new things, I hope you are one of those.
Grumpy
