String theory

[Inquisitive Stone]

The string theory is interesting, if it is true, how do we prove it. How many dimensions are out there.

[Blueflame0831]

How many dimensions are out there.

 

It is estimated that along with the four dimensions we live in; x, y, z, and time, another seven may exist. Although we can not concieve these other dimensions they are mathematically correct and possible.

 

The string theory is interesting, if it is true, how do we prove it.

 

Hopefully with the help of the LHC, we will be able to prove the string theory. If you haven't done so already, I suggest that you look into Brian Greene's book, "The Elegant Universe." In this book, he exquisitly explains the backbone of the string theory and everything associated with it. It would also be a good idea to go to PBS's website and search for "The Elegant Universe" series they have on their. Brian Greene narates it and is very interesting.

[ajb]

It is estimated that along with the four dimensions we live in; x, y, z, and time, another seven may exist. Although we can not concieve these other dimensions they are mathematically correct and possible.

 

 

Not estimated, but calculated. String theory predicts the number of dimensions. For a bosonic string it is 26 and for a superstring 10. I'll stress this again, this is calculated and not put in by hand.

[blazarwolf]

As I understand it, string theory cant be proven. It could be mathmatically discribed in whole however, and all simulations based on it would match the observations of our universe. It would become something that works and is freakin beatifull man:D

[AtomSplitter]

Is it even possible to concieve a fith dimension in our minds? by that i mean is it possible to imagine it? what would it be? what is it called?

[RyanJ]

As I understand it, string theory cant be proven. It could be mathmatically discribed in whole however, and all simulations based on it would match the observations of our universe. It would become something that works and is freakin beatifull man:D

 

Technically speaking, few theories can be proven as is shown by Gödel's incompleteness theorems. We more or less always have approximations anyway so nothing is ever exact enough to test with 100% assurance.

 

That is a good thing really as ever more accurate answers give better and better tests for existing theories.

[Sovereign]

The string theory is interesting, if it is true, how do we prove it. How many dimensions are out there.

 

What is your definition of dimension?

 

Mine is direction and orthogonality. Therefor there are 3 dimensions, length width and height.

[ajb]

Definition of geometric dimensions is "just" the number of local coordinates required to describe the space*. By direction you mean "pick one coordinate". So a geometric dimension is not really an invariant notion, but it is a useful one.

 

This clearly carries over to higher (and lower) dimensional spaces. Mathematically there is no problems here. I am quite comfortable working with spaces of any (including infinite if I don't think about it too much) dimension.

 

 

 

 

* Really I am thinking about manifolds.

[Severian]

I even routinely do calculations in non-integer numbers of dimensions.

[ydoaPs]

I even routinely do calculations in non-integer numbers of dimensions.

 

Like complex number of dimensions, or rational?

[Mr Skeptic]

Complex dimensions sounds like fun! Are those possible?

[10thdimension]

Is it even possible to concieve a fith dimension in our minds? by that i mean is it possible to imagine it? what would it be? what is it called?

our brains function in three dimensional perception. so no we can't fathom any higher dimensions then our own.

[npts2020]

our brains function in three dimensional perception. so no we can't fathom any higher dimensions then our own.

 

 

I disagree. That is what abstract thinking is about, concieving of something that must be imagined. I would agree that our conception is likely to differ from reality because of our three dimensional existence but I believe many people can and do concieve of other dimensions. When was time first posited as a fourth dimension? IMO somebody was fathoming higher dimensions.

[iNow]

our brains function in three dimensional perception. so no we can't fathom any higher dimensions then our own.

 

It's been shared before, but I'll share it again.

 

[10thdimension]

yeah i gues i should have added the real dimension and not our own perception of a dimension

[ajb]

I even routinely do calculations in non-integer numbers of dimensions.

 

You mean infinite dimensions? Or are we talking about something else "non-manifold"? It is known that some set can have non-integer Hausdorff dimension, such as fractals. But I don't think this is what you are talking about?

 

One can do "differential geometry" outside the category of set. Doing so must make it less clear what you mean be "dimension".

 

Another thing to think about is when working in the category of smooth manifolds, how often does the dimensions of the manifolds really come into play? If it is not important for your particular work, then I imagine we cold generalise to non-integer and even negative dimensions?

[Severian]

You mean infinite dimensions? Or are we talking about something else "non-manifold"? It is known that some set can have non-integer Hausdorff dimension, such as fractals. But I don't think this is what you are talking about?

 

No - much simpler and more practically minded. I do calculations in [math]4-2 \epsilon[/math] dimensions, where [math]\epsilon[/math] is small. Moving away from 4-d regulates the infra-red and ultra-violet divergences one gets in quntum field theories, allowing the infra-red divergences to cancel in physical predictions, or to renormalise the ultra-violet ones away. Then I take the limit [math] \epsilon \to 0[/math] at the end.

[ajb]

Dimensional regularisation, of course. That completely skipped my mind. (I have even used it in the past)

[AlphaNumeric]

It's been shared before, but I'll share it again.

 

I really don't like that. Yes, it's a nice way of viewing extensions of our space-time but the way those links extend space-time is not how string theorists do it or anyone else who works in extra dimensions. The extra dimensions are curled up and small but strings still move through those spaces like we move through the space we see.

Technically speaking, few theories can be proven as is shown by Gödel's incompleteness theorems. We more or less always have approximations anyway so nothing is ever exact enough to test with 100% assurance..

I think you are making reference to Godel's work incorrectly.

 

In mathematics, pre-Godel it was thought that any statement which can be constructed within some logic system would be either provable or falsifiable. Godel proved that there's always constructable statements which can be true but it is not possible to prove so, hence the label 'undecidable'. In maths you are given all your axioms and you work from there. You know the rules of the game.

 

In physics it's a different story. You are trying to discover the rules of the game. And no number of tests can prove that you've deduced a particular rule correctly, only increase your confidence you're at least close to the 'real' rule. You can never prove there isn't some additional caveat in Nature which will result in your rule not being completely squared with Nature.

 

For instance, quantum field theories were developed in the 1930s initially and people saw that Nature obeys a particular rule, there was no CP violation (see Wiki if you don't know what I mean). Loads of tests on on QED, no CP violation. Physicists said "Nature is invariant under CP symmetry". More tests done. No problems. Then in the 60s someone saw that the weak force didn't obey that symmetry. The caveat was found and the rule this shown to be not universally true. That is why there's a "It's not a proven fact" methodology in physics. There's no 'The Rules Manual' to check.

[Norman Albers]

Nature certainly does away with embarassing infinities. There is no Rules Manual, and we move forward with experimental poking around, and with mathematic insights to further representations.

Edited November 10, 2008 by Norman Albers

[AlphaNumeric]

Nature certainly does away with embarassing infinities.

But technically our theories never predicted infinities, the "Oh, we've got to renormalise this system" procedure means divergent quantities are a step on the path to the actual quantum field theory predictions, which are not infinite. It's fair to say (though it is somewhat of an assumption) that Nature is consistent, not 'it removes infinities' or however you wish to phrase it. When you work through the field theory calculations and end up get you prediction, you shouldn't have had to deal with actual infinities, just large finite quantities. [math]\infty - \infty[/math] is not something which appears in quantum field theory but you do get [math]\left( \frac{A}{\epsilon} + B + C\epsilon + \ldots \right) - \frac{A}{\epsilon}[/math] for [math]1>>\epsilon>0[/math]. The [math]\epsilon>0[/math] condition means your algebraic manipulation is well defined and then you take the limit [math]\epsilon \to 0[/math] after you've done that.

 

String theory takes a step towards not even having to consider these divergent quantities because, at least on heuristic grounds, it doesn't have the same UV behaviour as particle based theories. With scattering processes described by Feynman diagrams which are now 2 dimensional Riemannian surfaces, not branched graphs, there is no frame independent notion of an interaction point in space-time between two strings. The worldsheet 'smooths' this interaction out over a region (well, that's somewhat of an arm wavey description but the technicalities aren't important), removing the divergent quantities which might be seen as 'embarrassing infinities'.

[Severian]

Who is your supervisor at Southampton AlphaNumeric?

[Martin]

Who is your supervisor at Southampton AlphaNumeric?

 

Do you have to ask?

 

Almost has to be Beatriz de Carlos

 

woo woo

http://www.hep.phys.soton.ac.uk/~b.de-carlos/

[ajb]

Based on AlphaNumeric's interests I would also say Beatriz de Carlos.

[Norman Albers]

No - much simpler and more practically minded. I do calculations in [math]4-2 \epsilon[/math] dimensions, where [math]\epsilon[/math] is small. Moving away from 4-d regulates the infra-red and ultra-violet divergences one gets in quntum field theories, allowing the infra-red divergences to cancel in physical predictions, or to renormalise the ultra-violet ones away. Then I take the limit [math] \epsilon \to 0[/math] at the end.

So also AlphaNumeric states a limit process. This is intriguing to me, Severian, what are the infra-red divergences?