Do we know if the extra dimensions predicted by string theory (a total of eleven?) are spatial in nature? Is it possible that they are temporal instead, or of some type that we haven’t seen before, or a mix of these?
They are generally believed to be spatial. When you have exactly one temporal dimension, or all but one temporal, you get something which seems like our world. But if you have any other number of temporal dimensions, especially if some of them are compact, things get wonky. I don’t think that there’s any sort of mathematical framework consistent with the observed Universe by which they could be anything other than spatial or temporal.
I thought there was one worked out theory with two temporal dimensions. I’ll try to find a cite.
I thought that three time-like dimensions and one space-like dimention gives you exactly the same answers to the equations as three space-like and one time-like.
It’s true that no other combination will work, AFAIK.
You can have as many as you like total, as long as there’s exactly one different from the others. And you’re right that it doesn’t really matter which is the odd man out; 3+1 does indeed give the equivalent results to 1+3. It’s largely just a matter of arbitrary convention.
And I have seen theories with two temporal dimensions, or even with one temporal dimension and one that varies from spatial to temporal. You can do the math with them, but they inevitably give results which are drastically at odds with our Universe. The notion of causality, for instance, doesn’t exist in such universes.
They’d either be spatial or temporal, since a nondegenerate bilinear form over R is congruent to a diagonal one with only 1s and -1s on the diagonal. 1 means spatial, -1 means temporal.
Hmmm… this may have no connection to real dimensional theory, but I always had the notion that there wasn’t a real difference between the dimensions that are spacial and temporal, so much as how we… (as organisms, as material objects, whatever,) related to them.
We move freely in three dimensions and unilaterally in a fourth.
From what I understand about other dimensions, they aren’t really a part of our continuum, so wouldn’t they behave far more differently than BOTH space and time (from our perspective) than space and time behave themselves??
Just a thought.
Do these so-called “extra dimensions” actually exist, meaning that they can be manipulated or traversed, or are they just theoretical constructs to satisfy equations that otherwise have no solutions?
I’m not ashamed to admit that I have problems conceptualizing extra dimensions. This is neither my line of work nor a particular area of consuming interest. But when someone starts talking about a dimension being (for example) “curled up so small as to be insignificant,” to me it sounds as meaningless as folding an X-axis or crimping a Y-axis.
If anyone has any links to material that can explain this better, I’d enjoy reading it.
M-theory (or Brane theory, or twistor-augmented string theory or whatever you want to call it) is just a conceptual framework to tie together the “nature” of all forces/particles/whathaveyou into one comprehensive model. The addition of “compactified” dimensions is a mathematical treatment that allows you to make adjustments to the model that would not be mathematically possible otherwise (though Witten’s revival of twistors seems to promise a treatment that doesn’t involve a bunch of invisible dimensions, or so I’ve read.)
The problem(s) with M-theory et al is that it is essentially non-falsifiable (by altering a number of purely arbitrary constants you can make a system that will model any particle behavior) and it is impossible, currently, to verify any predictions that it makes. It certainly demonstrates compatibility with the observable world, but only because it has been “tuned” to demonstrated the very characteristics that make it compatible. Whether the theory is an accurate representation of what is going on “under” our current understanding of the physical world, or just a simulation that seems accurate from our superficial understanding is, and will be for the forseeable future, unverifiable. To make an analogy, you can create an animation that looks like the real world, but which isn’t based on anything like the same principles. In this way, we are amused by the coyote that doesn’t fall after running off the cliff (until he looks down) but we wouldn’t take that as evidence that we could remain suspended in the air.
As for cites, start with Wiki (look under M-theory, superstings, brane theory, Edward Witten, et cetera.) You’re going to find a less than cohesive explaination online, though, because everyone seems to have a different notion of what and how string theory should be expressed. There are a number of books that have been published over the last few years that deal with the topic in a non-technical way, the foremost of which is probably Greene’s The Fabric of the Cosmos and Lewis’ Our Superstring Universe. (There’s another one I’m thinking of–I can visualize the bloody cover but can’t think of the title or author–that I’m sure someone else will post.) If you’re a little more inclined to get into the math, you could triy A First Course In String Theory, which I haven’t read but it has a cool Mathematica-esque graphic on the cover, so it must be good, right? :dubious:
I tried to get into (rather than just read about) M-theory a few years ago, and got a bit into it, but the concepts and math were beyond my junior-level modern physics reading, and I eventually found other interests, like beer and sleep. It’s an interesting revolution in physics, but there’s also a good chance that it’s a conceptual black hole, metaphorically speaking.
Stranger
Thank you for the lengthy and explanation, it helped me understand things better.
As someone who’s tried coming at this from a rational, mathematical perspective, you can omit the word “online”.