Posted on 01/09/2005 12:26:51 PM PST by snarks_when_bored
That would depend on both the model and initial conditions. Most of the time it does. (And all randomly generatied objects can be reduced to a uniform sample by use of the inverse cumulative distribution function; like looking at percentiles.) That's why I was surprised by the guy's comment; it needed more explanation though perhaps it was filtered throught the Journalist Transformation.
it has been conjectured that they're quite tiny (curled up into up into any of a myriad of possible shapes). The present article discusses the possibility of getting experimental confirmation of these extra dimensions.
Why is "dimensions" so much more popular "properties of space"???
Stretch a sheet of waxed paper on an embroidery frame and place its four corners on gimbals and sprinkle a bit of water on it the surface; now play with it...
"our universe is not accidental"What does he mean, I wonder. Does he mean that the universe was created by some intelligence? Or that it was fated to exi[s]t?
I don't think Steinhardt is a theist, so his use of the words 'not accidental' is a bit odd. But consider his second paragraph:
Historically, most physicists have shared this point-of-view. For centuries, most of us have believed that the universe is governed by a simple set of physical laws that are the same everywhere and that these laws derive from a simple unified theory.
What he's worked up about is the Anthropic Principle and its apparent consequence that our universe is just one among a truly vast number of universes, all the others of which are unobservable. Steinhardt says, with good reason, that this is not science.
Forgive me if I sound incredibly stupid..
Isn't Gravity simply a function of Mass? ( function, for lack of a better word. )
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.
John Baez has a nice tutorial on General Relativity, but it's not for the faint of heart:
General Relativity is our current best theory of gravity, so I'll refer you to my post #47 on this thread.
Has there been any experimental verification of string theory? What if this is a colossal dead end--what's Plan B?
No experimental verification of string theory yet (although certain properties of black holes have been deduced using string theory techniques). Perhaps string theory is a dead end, perhaps not. Either way, physics goes on. After all, what else is there to do?
I find it interesting that my original intent was to include "density" in my description..
( .. function of the density of mass.. )
While the short outline definition of Stress-Energy Tensor mentions "density" of energy and momentum...
Also "Newton's gravitational constant"..
More reading/study.. although I think that will be a dead end for what I'm trying to understand..
Thanks..
Gravity itself is a field. So travel doesn’t apply. It’s 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.
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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 is—I 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):
This Week's Finds in Mathematical Physics (Week 207) - July 25, 2004
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 were—everything has to be checked).
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