Is space-time a continuous "solid" fabric or is it more like a grid where every possible discrete location in space-time is separated from every other?
The way we measure space and time, there are no such things as "discrete locations." You can plot a spatial or temporal coordinate down to any arbitrary decimal digit, or to any infinitely long irrational number that you can generate, even using a random number generator. It is indeed a "solid fabric," a continuum, at least in our model of the universe. A model came out about 25 years ago of an eleven-dimensional universe, if I've got that figure right. I think it was sort of a precursor to string theory, although it went off in a bit of a different direction. Anyway, the gist of it was that what we perceive as elementary particles are vibrating in a hyperplane through one (or more?) of those extra dimensions. When they show up here on their way back and forth, that's the only time we get to study them. So naturally there will be a discontinuity in their "existence," both spatially and temporally. I.e., most of the time they're not "here" at all, and when they are here they appear at discrete locations separated by the distance they moved when they were "not here." This had a tie-in with the Heisenberg Principle and other things that were over my head. I can see how this model of the universe might have discrete space-time. But apparently it was rather quickly rejected. I'm pretty sure that was the year I began to suspect that cosmology isn't exactly science, but more a melange of physics, theoretical mathematics, and philosophy. Nothing that's come along since then has changed my mind. Dark matter??? Expanding space??? Yeah right! Please Register or Log in to view the hidden image!
There is no such thing as the "space-time continuum". There is space and there is time, and the two are related. But since we do not know the dimensions of the former, and the latter has no dimensions at all, combining them in a meaningful way is not possible. Yes, I know, physicists do this all the time. They also speak of time-travel, wormholes, string theory, dark matter, dark energy and other nonsensical things.
swivel, I'm not familiar with your views, but I'd say you are just about 100-150 years behind in studying physics. -Richard Feynman, "Symmetry in Physical Law" in The Character of Physical Law, (1965). So while Lorentz and Einstein might write the Lorentz Transforms as: \( \left( {t' \\ x' \\ y' \\ z' } \right) = \left( \begin{array}{cccc} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} & \frac{-v}{c^2\sqrt{1 - \frac{v^2}{c^2}}} & 0 & 0 \\ \frac{-v}{\sqrt{1 - \frac{v^2}{c^2}}} & \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right) \left( {t \\ x \\ y \\ z } \right)\) Minkowski shows that it is simpler to write: \( \left( {ct' \\ x' \\ y' \\ z' } \right) = \left( \begin{array}{cccc} \cosh \phi & - \sinh \phi & 0 & 0 \\ - \sinh \phi & \cosh \phi & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right) \left( {ct \\ x \\ y \\ z } \right)\) where \(\phi = \tanh^{-1} \frac{v}{c} = \ln \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}\) Which is analogous to a two-dimensional rotation in the Euclidean plane: \( \left( {x' \\ y'} \right) = \left( \begin{array}{cc} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{array}\right) \left( {x \\ y} \right)\) where \(\theta = \tan^{-1} \mathrm{slope}\) (This is an example of a non-Euclidean geometry which makes physics easier.) Today this symmetry between space and time is called Lorentz Invariance and is tested in many cutting-edge physics experiments. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html http://relativity.livingreviews.org/Articles/lrr-2005-5/ Or you can go back to 1859: http://www.sciforums.com/showthread.php?p=2039656#post2039656
I don't know. Nonexistance. But if there is no separation, then you have the old problem of being able to half the distance between 2 points infinitely and having it take an infinite time to go from point A to point B.
by the natural interactions between objects themselves , the objects themselves , their movement(s) as a result of and the consequence(s) of
As long as we're quoting Feynman, I recall him stating somewhere that if someone suggests that spacetime is a grid of a kind, with discrete distances between of nodes or points, "we can prove immediately that is not so". By "we" he meant physicists. He might have been wrong, of course, and he didn't produce the proof in the essay, but it's definitely something that had been considered by him and others.
Lorentz is great, until you start trying to look at the Planck scale, where "time" and "distance", are sort of, well, non-existent. You have to switch to an abstract geometric view. Some theories of quantum gravity do this.
and it is because what people don't understand is that , dimension is NOT about the size of the thing but about the fundamentals of the necessity of three dimensional properties of the thing to always exist , length, breadth and depth , which also implies space ( I'm sure to get arguments here , but I'll wait , it can be complicated ) true hence above
