I mean, I welcome you guys into our private thread and all…
But we have an english only rule in force in here:) If you will kindly restate that in english, I would appreciate it.
The good Doctor was kind enough to take it slooooow with me. The abstract universe stuff intrigues me, but I never have anyone willing to field my questions.
Pre- General Relativity space and time were considered seperate, and I don’t know that time as a fourth dimension inexorably linked to the three familiar spatial dimensions was scientifically a line of thought.
That stuff happens, though, and General Relativity was the result. By “adding”[sup]1[/sup] time as a fourth dimension we “simplify” gravity, reducing it to geometry as opposed to the earlier “force” explained through Newton’s Law of Gravity.
Now, some time later these two chumps, Kaluza and Klein, were toying around with something-or-other and found that, like gravity, equations governing light were simplified by “adding” a fifth dimension. Many scientists, and indeed scienists in general, regarded this as a mathematical trick… that is, an expression that worked but bore no actual resemblence to physical reality. IE- “Where the hell is this dimension?” With the incredible success of Quantum Physics higher dimensional physics went the way of the dodo, at least for some time.
As the 80’s approached and arrived Quantum Physics was starting to get tapped out. It has been largely (but still not completely) tapped as far as theory goes, and work turned again to the “why” behind physics. Why four forces? Why so different? Etc.
The revival of the Kaluza Klein theory led to some of the more “popular” (and I’m sure you know why I put that in quotes) GUTs, or Grand Unified Theories. There was N=8 Supergravity, for instance, which supposed eight dimensions to unify, IIRC, the three forces but not gravity. Or something. Anyway, none were successful in unifying all forces[sup]2[/sup].
Enter Superstring theory, whose developmental ideas currenly escape me, even though I just read a book on it not two months ago. At any rate, there are two major breeds of them, the 10 dimensional and the 26 dimensional (10D being, IIRC again, a special case of the 26D). There are NDimensional “strings” whose vibrations, intersections, and splittings can account for the existence of all known particles.
1[sub] I put adding in quotes because there is significant ideological apprehension to using our mathematical models as factual representations. That is, are the dimensions really there or is it just a convenience to mathematically think they are? How well do theories represent reality when empirical data matches theoretical predictions?[/sub]
2[sub] How does adding extra dimensions allow for unified forces? I wish I could explain this clearly, but it is a tough read even having a contextual background behind it. Sufficient to say that there are matrices (algebra) whose components represent the forces acting on something. When we allow for a larger matrix, and hence extra dimensions, the forces become interchangable. I think. I’d have to reread this part again, though… for serious inquiry I have two excellent books which outline the ideas in a sufficiently non-mathematical way.
There is no contradiction here. A model has two kinds of properties: properties that represent the thing being modeled and properties that are artifacts of the model itself. A subway map is a model of the subway system. The 1,2,3,9 line is marked by a red line. This does not mean if I want to take one of these trains, I should expect to see an actual red line. The red line is an artifact of the model. Similarly, the higher dimension is an artifact of the model not a property of what is being modeled.
A hyper-sphere is a sphere of more than 3 (ususally 4) dimensions.
If a model with n dimensions makes accurate predictions about X, does it matter whether X “really” has n dimension? I don’t think it matters. What does “really” mean? (No, I’m not “really” Bill Clinton.)
Well, as I said, some consider our mathematical models to be just that: models. There is no underlying truth to them. If they say there are five dimensions, that’s just a way for our theories to get a handle on things.
Well, its a matter of taste, I think. I think the theories are correct in adding extra dimensions. I think those energies will one day be probed, and the unification of at least two forces will be tested. But, neither of us will live to see the day.
But this still leaves me wondering…do you really consider time as the fourth dimension? Is forward the first, sideways the second, and up the third? Again, I’ve never understood this lack of model-based truth things. If we probe down to the energies predicted by these multi-dimensional models and find what the models predict, what have we done?
Call Chronos over from GQ. He’s an expert on the Superstring Theory. Hey, Chronos, explain it again.
Disclaimer: I am not, repeat not, an expert on string theory. I think that the closest we have to that on the boards is my fellow SDSAB member Karen, who’s a penguinist (something to do with particle physics), but unfortunately, she doesn’t post much. (However, she and Dex do have a pretty good Mailbag answer relevant to this discussion.) I’m just a relativist, but I’ll take a stab at this.
First, we’ve got three familiar dimensions. You can number them in any order you want, they’re completely interchangeable. Then there’s time, which has some quirks to it (mostly in the form of minus signs where you wouldn’t expect them), but which is definately part of the same system as the first three. Anything above that, it just depends on how you want to do the math. Time as a dimension actually comes in from the much simpler Special Theory of Relativity, not the more complicated General Relativity, by the way.
Now, as to that hypersphere that the good Dr was talking about. In everyday life, we’re used to thinking about curvature as an exterior property: This means that, for instance, if I have an inflated balloon, I’m likely to talk about it in terms of three dimensions, even though the surface of the balloon is just 2-D. However, we can measure curvature without having to step up a dimension, also. For instance, if you draw a triangle on the surface of a balloon, and add up the angles, you’ll find that they’re greater than 180[sup]o[/sup]. Based on the amount by whch they’re over, and the size of your triangle, you can determine the adius of the sphere, without ever even needing to know of the existance of the third dimension. Similarly, curvature of the Universe would have measureable implications, completely independent of any higher dimensions: We don’t need to ask some hyperbeing to tell us what the curvature does, we can see it for ourselves. It might so happen that the curvature that we measure is the same as one would expect from the “surface” of some figure in a higher-dimension Euclidean space, but it might also happen that we can’t identify it with any such. No worry either way.
Kaluza-Klein theory is interesting, but it doesn’t really do much for us. There’s no point trying to explain the electromagnetic force in the same framework as GR, because the standard, existing way of dealing with E&M is already simpler than GR. Of course, there’s some appeal to unification, but Kaluza-Klein theory seems to be a bit of a dead end in that regard: It works for gravity and electromagnetism, but it doesn’t tell us a thing about the nuclear forces.
Now, as to what the models really mean, and whether they’re “real” or not, that’s a question of philosophy, not physics, so I won’t go into that here. Wait a moment…
looks around, realizes he’s in GD, not his native GQ
OK, I will go into that here, then. If you’re going to try to argue that the models aren’t real, then you’re going to have a hard time arguing that anything is real. The fact of the matter is, the successful models of science are self consistent, and consistent with what we observe of the Universe. Sure, I don’t know if there’s “really” such a thing as force, or entropy, or any of these concepts, but then, I don’t know if there’s “really” such a thing as dogs, either. I think that dogs are real, because that explains why I seem to find shedded fur on my clothes every so often, and see droppings along the sidewalk. I think that concepts like force and entropy are real, because they explain other things that I observe.
Yeahhh, I guess I miffed that one, but no need to mention special relativity in RE to the forces of nature I thought.
Since I don’t work with them I can’t say for certain, but I thought the field equations set up around light were much simpler in the GR framework. By inspection, anyway.
I wasn’t aware of this… I thought, actually, that field equations governing the weak force have already been discovered. I am still uncertain about the strong force.
To my understanding, the large problems with TOEs is that gravity has not been successfully quantanized and the strong force has not successfully been incorporated into the GR style field equations. Any correction is welcomed.
I was debating whether the verb is “quantisized” or “quantized” and now I have to throw in “quantanized”?
You know, I betcha that, at this very moment, Star Trek writers are cutting and pasting random phrases from this thread and putting them into the scripts.
Perhaps I need to clarify a bit (gee, big surprise there, right?)… Maxwell’s equations (which govern light and other electromagnetic phenomena) are, indeed, simpler when expressed in tensor form, the same sort of notation used for GR. You’ll find them used that way in any upper-level E&M course. Kaluza-Klein theory goes a bit beyond that, though, and explains the causes of electromagnetic effects in terms of this 4+1 dimensional space. That’s what seems to be the dead end.
The field equations for the weak force are, indeed, well-known, and the strong force is mostly understood. However, neither one of them is expressed in the same form as gravity (or, if you want to look at it the other way, gravity isn’t expressed in the same form as the other three). The electromagnetic and weak forces are completely unified (indeed, there is no independent theory of the weak force, just of the “electroweak” force), and there’s considerable hope of tying in the strong, too, in the immediate future (there’s already several possibly workable theories that do that), but when you try to bring in gravity, things start looking awfully close to hopeless.
By the way, barbitu8, the word is “quantized”.
Hmm. Dead end as in… we cannot express the rest of the forces by having higher dimensions be the cause, or dead end because it doesn’t lead to testable conclusions… or both? Also, you say seems… what sort of ideas are lurking behind that word? Is it still a possiblity that the rest of the forces may be explained by higher dimensional equations?
Great. I have been using “quantanized” like a fool for, oh, ever. Haha. Ya learn something every day @ the SDMB!
With regards to G
Not that OP hasn’t been totally hijacked now, but surely cooling = creation if by creation you mean creation of what we call particulate matter (not light). The subatomic particles had a hard time staying together when the universe’s temperature was too high. Its not that the stuff wasn’t there, however.