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Terilien
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what in the name of the world made string theorists think that the universe is made of strings? what is the basis for this assumption?
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- removes UV divergencesTerilien said:what in the name of the world made string theorists think that the universe is made of strings? what is the basis for this assumption?
The 2d worldsheet of strings is the only manifold which gives local conformal invariance. To copy and paste a post I made on another forum (and pulled mostly from GS&W - Superstrings) :kvantti said:If you don't want to think of elementary particles as 0-dimensional "dots", you have to go with strings or with some other more fundamental structure of nature, e.g. branes or spinfoams.
Strings were found handy because they get rid of infinities in our current theories, such as the singularity in general relativity. Also, one vibrational mode of a string was realized to be the graviton, so it was the first glimpse of hope to include gravity into the quantum theory.
AlphaNumeric said:The 2d worldsheet of strings is the only manifold which gives local conformal invariance.
Of course. For example, this kills UV divergences in quantum loops. This is exactly why quantum gravity with strings works much better than that with point particles or fields.da_willem said:But there's reason a theory should have local conformal invariance right?!
AlphaNumeric said:The 2d worldsheet of strings is the only manifold which gives local conformal invariance. To copy and paste a post I made on another forum (and pulled mostly from GS&W - Superstrings) :
In string theory the Lagrangian can take a form roughly (up to some factors etc) of
[tex]\mathcal{L} = \int d^{n+1}\sigma \sqrt{h}h^{\alpha \beta}(\sigma) g_{\mu\nu}(X) \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}[/tex]
Not particularly pleasant, but it's very general and this form is used in standard quantum field theory where n=0, the objects are zero dimensional points with [tex]g_{\mu\nu} = \eta_{\mu\nu}[/tex]. This is just the mathematical extension to higher dimensions to see if anything is interesting. The integral is over n+1 dimensions because you're including time, so it's over an n+1 dimensional 'manifold' (just think surface or volume)
[tex]g_{\mu\nu}[/tex] is the space-time metric, the one which you'd see in general relativity. [tex]h_{\alpha \beta}[/tex] is the metric which describes the geometry of the n+1 dimensional manifold, basically the shape the quantum object 'sweeps out' as it moves through time and space, [tex]h^{\alpha \beta}[/tex] is it's inverse and [tex]\sqrt{h}[/tex] is the square root of the determinant of that metric. [tex]X^{\mu}[/tex] is the position function of the object. Just like [tex]\mathbf{x}=(x,y,z)[/tex] says where an object is in 3d space, [tex]X^{\mu}[/tex] does it in 10.
Local conformal invariance is sort of like a position dependent rescaling of the n+1 dimensional manifold (ie a rescaling of the surface where the rescaling changes with position) which leaves the integral unchanged. Specifically, it's the transformation [tex]h_{\alpha \beta} \to \Lambda(\sigma)h_{\alpha \beta} [/tex]. Crunching the numbers, this turns the integral into
[tex]\mathcal{L} = \int d^{n+1}\sigma \Lambda^{\frac{1}{2}(n+1)-1}\sqrt{h}h^{\alpha \beta}(\sigma) g_{\mu\nu}(X) \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}[/tex]
But we want invariance, so [tex]\Lambda^{\frac{1}{2}(n+1)-1} = 1[/tex] so [tex]\frac{1}{2}(n+1)-1 = 0[/tex], so n=1. Therefore the ONLY theory which has local conformal invariance is that which works with 2 dimensional manifolds, one dimension of which is time, so the object is extended through 1 spatial dimension, a string.
Because branes are not FUNDAMENTAL objects, but emergent effective ones. As known even from QFT, an effective theory does not need to be renormalizable and/or infinities-free.nrqed said:Very interesting post.
But then the obvious question is: what about branes?? We hear that string theory contains higher-dimensional objects than strings and your point makes it clear that this will destroy conformal invariance. So why is the theory of branes still viable?
Demystifier said:Because branes are not FUNDAMENTAL objects, but emergent effective ones. As known even from QFT, an effective theory does not need to be renormalizable and/or infinities-free.
String theory is a theoretical framework in physics that attempts to reconcile general relativity and quantum mechanics. It proposes that the fundamental building blocks of the universe are not particles, but rather tiny one-dimensional objects called strings.
String theory posits that these tiny strings vibrate at different frequencies, giving rise to different particles and forces. It also suggests that the universe has more than the three dimensions we can perceive, with 10 or 11 dimensions being necessary for the math to work.
At this point, there is no direct experimental evidence for string theory. However, it has provided a unified framework for understanding the four fundamental forces (gravity, electromagnetism, strong nuclear force, and weak nuclear force) and has made predictions that may be testable in the future.
As with any scientific theory, string theory cannot be definitively proven. However, it can be supported by empirical evidence and mathematical consistency. Further research and experimentation will be needed to fully validate or disprove the theory.
Some criticisms of string theory include its lack of empirical evidence, the difficulty of testing its predictions, and the fact that it has not yet produced any new experimental results. There are also ongoing debates about the number of dimensions required and the possibility of multiple universes within string theory.