so, why exactly are extra dimensions needed by string theory?

Manifolds

>>8503553

/thread/

>>8503553
How exactly do manifolds relate to string theory?

>>8503553
>>8503557
What? This has nothing to do with "why" they are needed.

>>8503510
Various symmetries required for string theories to be physically realistic are broken if you the spacetime is not the correct dimension.

Because it sounds way cooler on the Discovery channel special

This seems like a good thread to ask for someone to post that two-frame image macro of a person with a calabi yau manifold for a head where the second frame says something like (yields applications in theoretical physics)

Plzthx

>>8503510
Fuck you that's why.

>>8503510
In the most general sense, a line contains useful properties that a point does not and can not, because it's a point.

It's like, if you had a curve projected on a 2-dimensional graph, and then you turned the graph sideways, so that you would have a surface in 3 dimensions which shares the slope of the curve. You can now express various properties which only exist in 3 dimensions, even though you were initially only looking at a curve.

This is why string theory is such a meme. In the same way that there are infinitely many ways which you can turn that 2 dimensional plane so that it is 3 dimensional, there are infinitely many solutions in string theories, so it's really just glorified mathematical cherry picking.

>>8503510

Because it's incompatible with reality.

>>8503659
Thanks for this.

>>8503510
The extra dimensions allow strings to do more things. For example, a string wrapped around a certain (compact) dimension gives it charge.

>>8503659
The problem in String Theory is not so much of dimensions themselves, as in not knowing exactly what they should be.

We know we probably want them to calabi-yau. And while we do know there exists only finitely many calabi-yau 1-folds and 2-folds (up to isomorphism) , whether that is true for calabi-yau 3-folds is an open problem.

This leaves us with the problem of having to choose between a very large number of vacua.

So until we have technology that could actually probe the necessary scales experimentally, the problem is essentially left to mathematicians.
And some stuff has been accomplished, through studying mirror symmetry and certain moduli problems. But there is a lot left to be done.

>>8503510
Because otherwise it wouldn't work. The objects that have the needed properties (whatever exactly they are) are 10 or 11 dimensional manifolds. That's just a mathematical requirement. How exactly those dimensions look in reality doesn't really matter, just imagine there these objects with some properties. It's not like string theorists are actual physicists, they don't give a shit whether their theory actually helps us understand how our world works. It's just a mathematical framework. In the end the physics part is "Yeah, there are these strings and I don't know, the dimensions are just really tiny, and they are somewhere, I don't know why"

File: 13d.jpg (41KB, 499x562px) Image search: [Google]

41KB, 499x562px

>>8503596

File: 13d.jpg (41KB, 499x562px) Image search: [Google]

41KB, 499x562px

>>8503681
Dont thank him, its completely wrong.

>>8503565
is correct OP, if you do the math for a string, you find that QM + special relativity gives you an equation where there's a term that breaks Lorentz invarience (and some other symmetries) that is equal to something like 1-(D-2)/24 with D the number of dimensions, depending on what theory you are working with, which forces you to have either 26 in the case of bosonic string theory or 10 in the case of superstring theory.

>>8503799
>thinking I'm wrong

Looks like someone doesn't understand the concept of dimensionality. I represented the idea of this symmetry breaking in a way that someone whose never heard of a Lorentz transformation can understand. It's obvious OP isn't well versed in the subject, so it's ineffective to communicate the idea in any way other than conceptually.

>>8504271
whatever you say champ

>>8503781
>they don't give a shit whether their theory actually helps us understand how our world works

That is exactly what they give a shit about.

>>8503510
simple answer: anomaly cancellation.
When you go from a classical theory to a quantum one, sometimes the symmetries that were present in your classical theory break down. This is called an anomaly. This is okay sometimes, but is fatal in the case of a "gauge anomaly". These occur when one of the gauge symmetries of your theory break down. Since gauge symmetries are not so much symmetries in the usual sense as they are redundancies in mathematical language, the breakdown of such symmetries leads to inconsistencies. To avoid these, it turns out that we need the extra dimensions.

>>8503659
>>8503681
There are only 5 consistent string theories. Not infinitely many.