String! Theory! What is it good for ?!?

True, and these are being seriously confused in the exchanges above, but don't forget that extra dimensions give a route to extra 'universes'. Imagine a flatland universe (2 space + 1 time) embedded in our space-time (3 space + 1 time). You can have a limitless number of flatlands foliating our space-time (foliating meaning filling the space but without intersection, such as pages in a book, tree-rings in a stump, etc.)If we live in 5d, we can pick a point, pick a direction perpendicular to our 4d space-time, travel out a bit, then explore the 4d surface 'parallel' to our space-time. This doesn't imply extra universes, but it does give them somewhere for them to be.Edited by cavediver, : No reason given.

I think Mod has been doing a good job at defending the notion of what we mean by dimension when we speak of 'extra dimensions' - we are talking about the dimensionality of space-time. The problem is the utter vagueness that is introduced when talking in layman-ese. Bolder-dash is complaining about this, but failing to see that this is the fault of discussing cutting edge theoretical physics on an internet debate board with interested amateurs.When we talk about this in the academic departments, in the science papers, at the conferences - we know exactly what we are talking about. Yes, temperature in some circumstances can and is considered a dimension. As can and are many other concepts. This does not mean that when we talk about the extra dimensions of string theory, we are being vague as to our meaning. If you can't follow, then go do some learning. Claiming that string theory is weak because it doesn't explain the nature of the dimensions is like claiming that skyscrapers are bound to fall over, because you can't see any sign of any foundations. The limitations are in your understanding, not in our science

The dimensionality of space-time has always been just an observable property of the Universe - it has no theoretical underpinning. In other words, we don't know why it is 3+1 (3 space + 1 time)Nearly all theories constructed in the past 100 or so years can be constructed in d+1 dimensions, and still work. We have to set d=3 to get out the physics that is interesting and relevant to us. This shows that we are not yet that close to a deep understanding of why the Universe is the way it is. There has to be a reason it appears to be 3+1.The first consideration of extra dimensions came soon after Einstein published the General Theory Relativity, by Kaluza and Klein, who independently looked at formulating General Relativity in 5 dimensions, as in 4+1. When the extra dimension was considered as circular and too small to see, the five dimensional theory became an effective four dimensional theory. The miraculous part was that the 4d effective theory was no longer General Relativity, but General Relativity *PLUS* Maxwell's theory of electromagnetism!!!So, General Relativity in 5d gives us GR plus EM in 4d. This unifies GR and EM, and reduces them to one theory. For those of us deeply into our physics, it doesn't get sexier than this There are a few problems: there is an extra field that is introduced, the dilaton, which appears unrelated to the physics of our Universe; there are none of the other bosonic fields (weak, strong); there are no fermionic (matter) fields; and this is all still classical - this is no quantum gravity.But what it does show is that extra dimensions are possibly *the* key to the unification of all physics. And also, extra dimensions are not some new bizarre concept related to just string theory.The logical extension of Kaluza-Klein theory, and the resolution of its above issues, came much later with the Supergravity programme. Although Sugra ultimately failed on its own, it reappeared in String/M-Theory putting it on a much more solid foundation.So, extra space-time dimensions are a good thing. But our theories still don't tell us how many we have. Sugra started to, by giving limitations to the number of dimensions of space-time based on having well-behaved supersymmetry. This gave us the famous limit of 11 dimensions (10+1). Wrapping up an extra 7 dimensions gave plenty of ways to generate the observed bosonic and fermionic fields of the Standard Model. Unfortunately, it never quite worked out in this context...Then along comes String Theory. It is a mathematical physics theory of 2d space-times - tubes or pipes if you will, that can interconnect. If you take a constant-time slice through the tubes, you see lots of circles - the cross-sections of the tubes. These are the strings of String Theory. The tubes (or strings) can appear to be embedded in a virtual d+1 dimensional space-time by considering d+1 fields defined over the strings.When you do the calculations, you realise that this 'virtual' d+1 space-time contains General Relativity, and in fact much of the Supergravity we had been working on years before. This is the first miracle of String Theory: a simple 2d theory predicts a world like ours, in d+1 dimensions! More work shows that for the theory to actually stay consistent, d has to be a particular value...Wait, say that again. The theory tells us what d should be??? That is a first!!! d has always been an input to theories, but now the theory is telling us what d should be!!! This is the second miracle of string theory.In the toy version of string theory that only looks at bosons, d comes out to be 25 (so d+1 is 26), but in the real versions (Superstrings and Heterotic strings) d+1 comes out to be the famous 10. And ten dimensions is great for creating all the extra fields we need for the Standard Model, when we wrap up the extra six dimensions to get our 4d Universe.Of course, the fact that string theory says that the Universe is ten dimenionsal is regarded as a huge problem by those who don't actually understand the science and mathematics of quantum gravity. We just laugh at them The one valid embaressing point concerning Superstring Theory was the number of potential theories: Type I, Type IIa, Type IIb, and Heterotic. These are all ten dimensional. And there was the mysterious 11d Supergravity to which they seemed somehow related.My own subject area of string duality was what led to the realisation (principally proposed by Ed Witten) that all five theories were just different aspects of one master theory, or M-Theory.And that is where we are now - a mysterious M-Theory, that seems to sit, from a space-time perspective, in 11 dimensions. Below the 10d string theories lies the fundemental 2d theory of tubes. The nature of the fundemental theory underlying M-theory is yet to be determined.But the one thing that is in no way a problem for theory is the predicted existence of the extra space-time dimensions. They are the bonus!Edited by cavediver, : No reason given.Edited by Admin, : Typo.

Please, no replies to this message. Let's keep discussion focused on the topic and not on the people discussing the topic. --Admin really? Would you care to point to anything that I cannot follow? Do not mistake a desire to not be drawn into conversing in bullshit, with not being rather well versed in a subject. Hmmm... Sounds a lot like someone have opinions on something about which they know nothing...Hint: Opinions are the building blocks of ignorance - asking questions is the way forward. And Mod has given you some very good answers. If you don't find them satisfactory, then there's not much that can be done. The world of science won't lose sleep because you don't understand a concept.Edited by cavediver, : No reason given.Edited by cavediver, : No reason given.Edited by cavediver, : No reason given.Edited by Admin, : Post short note at top in red.

Ok, I can see why this is confusing The 2d pipes are completely separate from any discussion of the dimensions of our space-time. In a sense, the whole of our space-time (4d, 10d, 11d, 26d, whatever) lives as a virtual existence on the 2d pipes! Our reality is like a program running on a computer. At least, that was how some of us we looked at it in the days before M-Theory. M-Theory has thrown that picture into disarray, and now I really have no clue. That's why I said that we don't understand the underlying theory to M-Theory.The 11d of M-Theory is "simply" our observed 3+1 plus another 7 space dimensions. And the 10d of String Theory is 3+1 and another 6 space dimensions.More later...

Yep, spot on. But this may or may not be the way reality works.By the way, this reminds me of how you spot cranks, at least in my field - they say, "my theory solves everything!", we say "my theory is great here and here, but it's a bit crap over there, and I'm really not sure what the hell is going on down there... but hey, it's great!"Bear that in mind as you read recent posts around here

Yep, exactly And refering back to your previous post, this is not the same as our 2d tubes - they're not part of this picture, at least not at this basic level. Yes, not bad at all. Well, here it gets much more complex. EM is easy as it is the gauge field of the circle - known as U(1). The complexities of the SU(2)xU(1) geometry of electroweak sector are much harder to describe, and require quite a few extra dimensions to build the necessary framework. Similarly with the SU(3) geometry of quantum chromodyanmics (strong). This is going a bit beyond what we can talk about here, but I might come back to describe why an extra dimension gives rose to what we call electromagnetism and the photon, as it's rather cool.