Skip to comments.In search of hidden dimensions
Posted on 01/09/2005 12:26:51 PM PST by snarks_when_bored
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Gravity itself is a field. So travel doesnt apply. Its like saying how fast is the ocean between SF and Tokyo. However, gravity waves, according to general relativity (and some pretty strong evidence), travel at exactly the speed of light.
Rather it seems that if space can bend than it is more like a material.
The basic equation in Einstein's General Relativity places (essentially) the geometric structure of spacetime on one side and stress-energy on the other, that is, there is an equivalence between the mathematical (geometry) and the physical (stress-energy). So, yes, spacetime (not just space) is more like a material, at least in General Relativity.
if this is true then there should be some kind of equation with an = or an imbalanced >= which would do for space what E=MC2 has done for energy and matter...such that Space=Energy (something or other)
Space=Matter (something or other)
Quite correct. 'Gravitational disturbances' do the traveling.
...there should be some kind of equation with an = or an imbalanced >= which would do for space what E=MC2 has done for energy and matter...such that Space=Energy (something or other) Space=Matter (something or other)
Correct, there isI just didn't put it in my post to you. On the left side of the equation is the so-called 'Einstein tensor' (this keeps quantitative track of the geometric curvature of spacetime); on the right side of the equation is the so-called 'stress-energy tensor' (this keeps quantitative track of the 'matter/energy' or 'stuff' in spacetime). There are also some multiplicative constants, usually written on the right side, to make the units work out.
Check out the reference in my post #47 for much more info.
And although it has a hokey background, here's an image of a coordinate-independent version of Einstein's general relativity field equation (that's the Einstein tensor on the left, the stress-energy tensor on the right):
What controls the number of dimensions?
That's a tough question that nobody really knows the answer to.
Standard general relativity works with a 4-dimensional spacetime manifold (3 dimensions of space, 1 dimension of time). In order to get results that make sense mathematically, string theories require the postulation of an additional 6 spatial dimensions (these are the ones that are often characterized as being 'curled up' into tiny balls or other shapes). At the moment, it's not at all clear that it's going to be possible to describe the cosmos we inhabit using a string theory. So, as usual, we're not sure what the situation is as far as the dimensionality of the cosmos is concerned.
(I'm leaving out the stuff about 5-dimensional branes and the like. For one thing, I don't know enough about it, and, for another thing, neither does anybody else, apparently.)
What controls the number of dimensions?
Does extra dimension theory interface with Hawking's latest statements on black holes and information ("Hawking changes his mind on black holes; Galactic traps may actually allow information to escape, author says")?
Not as far as I can tell. Hawking's work (which is still being checked, by the way) uses standard techniques of general relativity and quantum gravity. I'll refer you to another page by John Baez (who, incidentally, is performing a real service for webizens by trying to explain difficult ideas in physics and mathematics in a way that non-experts have some hope of understanding). Baez attended the talk at which Hawking announced his result. Here's Baez' report on that talk (including a transcript of Hawking's entire presentation):
You probably won't understand all of it (maybe not even much of it)I only got glimpses and flashes of understanding when I read it, maybe a rough sense of the whole, but not many details. But just skip the parts you have trouble with and read the non-technical bits if nothing else. Baez has some interesting remarks later in the piece about the role of authorities in science (there aren't any 'Popes of science', as it wereeverything has to be checked).