I have heard that there are an estimated 10-11 dimensions in the Universe. How was that number arrived at? And is it true that some of the dimensions are “curled-up” inside others?
And is there any way to explain it to a non-physicist/non-mathematician like me?
Let me explain. No, wait, is too complicated. Let me sum up.
Conventional models of physics can’t reconcile General Relativity with Quantum Mechanics. Either of them works wonderfully by itself, but if one were ever in a situation where both were relevant, nobody’s really sure what would happen. One very popular attempt (or family of attempts) at reconciling them is the String Model, or its relative M Model (often inaccurately called String Theory and M Theory, even though neither is actually a theory). I won’t say that the String Model is really all that great: In fact, it pretty well sucks as a scientific explanation. But everything else anyone has been able to come up with also sucks at least as much, if not more, so the String Model is sort of favored by default.
Well, one of the difficulties of the String Model is that it doesn’t work in 3+1 dimensional space: There’s simply not enough room for the strings to vibrate in enough different ways. The most common versions need at least 10, or at least 11, or I think in some cases at least 24, spatial dimensions.
But we don’t observe all those extra dimensions. Why not? There are several possible explanations. One, of course, is that they just don’t exist, and the String Model is bunk. Another possible explanation, though, is that the extra dimensions are curled up tightly, on scales too small for us to detect. Consider a drinking straw, for instance. If you look at it up close, you can see that it’s a basically two-dimensional sheet of plastic, rolled up into a tube. Zoom out, though, and it looks like just a line. The extra dimensions might all be like that, except that the diameter of the drinking straw is much smaller than an atom.
The prediction that the Universe has 10 dimensions comes from an as-yet unproven theory called “String Theory”. Basically, the idea is that all particles in the Universe — photons, electrons, quarks, neutrinos, etc. — are really just microscopic loops of string vibrating in different ways. So if your string wiggles in one particular way, it “looks like” a photon on our scale. If it wiggles in another way, it would look like an electron to us. If we were to get a super-duper microscope that could see things on the scale of these loops, we’d actually see that everything is just little loops of string.
Sounds pretty cool, right? The problem is when you try to make this consistent with two big well-established principles in physics: special relativity and quantum mechanics. It turns out (and this is where a buttload of mathematics is being swept under the rug) that if you take quantum mechanical effects into account, they imply that special relativity shouldn’t work the way it does… unless there are a total of 10 dimensions, nine spatial dimensions and one time dimension. The fancy phrase for this is the Lorentz anomaly; if a quantum theory has a Lorentz anomaly, then special relativity doesn’t work “right” in that theory. It so happens (sweep, sweep) that mathematically, the Lorentz anomaly vanishes if there are ten dimensions. In other words, if string theory is correct, you either need quantum mechanics to be wrong (not likely given how much experimental evidence there is for it), special relativity to be wrong (ditto), or for there to be ten dimensions to the Universe.
Well, that’s all well and good, except that we don’t have ten dimensions in our Universe. We have four. So does this mean that string theory is useless for describing our Universe? Well, maybe so and maybe no, but we can at least make string theory consistent with our Universe by postulating that the other six dimensions are very small and curled-up, so that we don’t notice them — if we move a fraction of a nanometre to the “left” in dimension #7, say, we would come back to where we started from. In other words, you can keep using string theory to describe our Universe so long as you’re willing to postulate that the extra dimensions are so small we wouldn’t notice them.
The alternative to spatial dimensions are time dimensions. From what I’ve read, more than one time dimension causes big problems with the math. (That’s not the same thing, apparently, as that the math for space works just as well if reconstructed as three time dimensions and one spatial dimension. Ah, math.)
Maybe this should be an entirely separate thread, but I wish I understood what “string” means in this context. I mean, what is it a string of? Obviously, it isn’t a string of wool or cotton, or even a string of electrons. So what is it, then?
Stranger than that, the heterotic strings actually have either 10 or 26 dimensions, depending whether or not you’re a fermion or boson, respectively! More accurately, the ‘left-moving’ oscillations of the string ‘see’ a different dimensionality than the ‘right-moving’ ones, but one should really only think of the 10 dimensions the superstring brings onto the table as space-time dimensions, considering the remaining 16 abstract mathematical entities (though from what I gather, it’s getting more common to think of the extra dimensions in string theory in general in a similar way – not all string backgrounds can be interpreted in a nice, geometric way).
And while it’s correct that ultimately, quantization considerations and preservation of Lorentz invariance picks out the number of dimensions for the quantum superstring, even classical superstrings don’t work in every dimension, but only in either 3, 4, 6, or 10 dimensions – the reason for this is related to the (normed) division algebras, i.e. number systems in which there are no two non-zero elements such that their product is zero (and consequently, division is possible), of which there are only four (the real numbers, the complex numbers, the quaternions, and the octonions), of dimensions 1, 2, 4, and 8 – add to that the number of dimensions of the string’s worldsheet (i.e. the area swept out by a strings motion), and you get the numbers above.
“Particles can’t be made of stuff, because stuff is made of particles!” (Hmm, I thought this was some well-known quotation, but google fails me in determining its origin…)
There was actually a proposal of constructing strings from ‘string bits’ (which I don’t think gained much traction), but of course, that just pushes the question back one step. I think it’s probably best to think of them in the abstract, as sort of a collection of properties: they have a length, a tension, are open or closed, etc. Typically, on composite objects, properties are due to their composition, but for a string, one must accept these properties as fundamental, sort of directly attached to the string itself – and anything that has these properties (and only these), is a string.
I don’t consider this personally very satisfying in the ‘last answer’ sense, either, but discussing this would take us too far into philosophy – and in the end, most objects stipulated to be ‘fundamental’ suffer from the same questions.
That’s one of the ones that sucks only the same amount as the String Model. But while both models are about equally bad, the String Model would also unify gravity with the other forces, while Loop Quantum Gravity purports to quantize gravity but not unify it. Unification of all the forces is favored by most theorists on aesthetic grounds, so the String Model tends to be favored for that reason (though of course, it’s quite possible that gravity is not unified with the other forces at all, and so any attempt to unify them must necessarily be futile).
“String” is just a name for a theoretical object here. Mathematicians and theoretical physicists have a habit of using ordinary words to refer to newly-thought-of concepts, rather than making up a new word. So, for example, quarks have “flavour” and “charm”, which have nothing to do with the ordinary meanings of those words: you can’t taste quarks, and quarks don’t have a rich social life.
On the contrary, quarks have an extremely rich social life. So rich, in fact, that you can’t tear them away from it. If you try, then the quark’s imaginary friends will just become real to compensate.
A model, basically, is descriptive. It’s a scientific construction that fits the collected data.
A theory, basically, is predictive. It’s a scientific construction that doesn’t just fit the collected data, but has been shown to be reliable in predicting what new observations will be.
I don’t think the terms ‘theory’ and ‘model’ really assign any empirical value. It’s just not really descritptive of the way the terms are used in science.
I’d say a theory is something that generally based around a small set of of relatively simple basic principles or postulates (e.g. the special theory of relativity), whereas ‘model’ is used more broadly (e.g. the standard model)
The Standard Model makes many predictions, BTW. That’s why a Theory of Everything in some form is necessary. Those predictions fall short of the totality of the universe. Model, theory, who cares? They’re only concerned about the math.
Scientists are generally almost as bad at using words as artists. (If you have a strong stomach, read the self-written cards artists place next to their pictures in an exhibit.) They have this mania for taking ordinary, common English words with a million other uses and senses and applying them to technical matters. That confuses everybody outside their specialties. Make it stop!
The theory/model distinction (especially in connection to String) is something of a personal crusade of mine, in response to the “it’s only a theory” so often directed towards evolution. I don’t mind the term “standard model” so much, even though that could properly be called a theory, because theories are a subset of models.
Also, I don´t think anyone has mentioned this yet, another possibility is that the extra dimensions are big but for whatever reason we cannot interact with them.
Under this theory we live on a 4D “brane” within X-dimensional space, and most forces and things like light can only move through our brane. But possibly some things like gravitons may propogate into the other dimensions (which IIRC was floated as a possible reason why gravity is so weak).
Disclaimer: This is all probably misremembered, misunderstood, out of date or some combination thereof