String theory, string dimensions?

In summary: First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception because the p-brane boundary is a Clifford algebra).This sounds like it would be a difficult problem to solve.This sounds like it would be a difficult problem to solve.
  • #1
Nav
39
1
Strings are said to be one dimensional, due to the math. And I understand that there are problems in the math when they put the strings in 3 or 2 dimensions.
According to string theory, lengths smaller than Planck length have no physical significance.
Could it be that strings are 3 dimensional but their height and width dimensions are so small and insignificant they they cannot be taken into consideration or calculated by the mathematics?
 
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  • #2
Sure it could be. String theory is so far from making much in terms of verifiable predictions that anything is possible.

The word "theory" is only loosely applicable to the body of hypothetical work associated with strings.
 
  • #3
Nav said:
Strings are said to be one dimensional, due to the math. And I understand that there are problems in the math when they put the strings in 3 or 2 dimensions.
According to string theory, lengths smaller than Planck length have no physical significance.
Could it be that strings are 3 dimensional but their height and width dimensions are so small and insignificant they they cannot be taken into consideration or calculated by the mathematics?
It has not been possible to construct a quantum theory of objects having more than 1 dimension.
 
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  • #4
bapowell said:
It has not been possible to construct a quantum theory of objects having more than 1 dimension.
Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.
 
  • #5
Demystifier said:
Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.
Are you saying that it is possible for strings to have higher dimensions like branes?
 
  • #7
bapowell said:
I see. I thought it had something to do with stability: http://www.sciencedirect.com/science/article/pii/0550321389902149
A string can still have three dimensions it's just that those other two dimensions are insignificant.
It comes down to actual dimensions. 1-D is a mathematical convenience that often works if the size in 1 dimension is much larger than the other two.
Think of a real guitar string. If it is 24" long, but only 0.005" in diameter, a 1-D model is a good approx.
 
  • #8
bapowell said:
I see. I thought it had something to do with stability: http://www.sciencedirect.com/science/article/pii/0550321389902149
The other dimensions of the string are too small to be taken into account by the calculations and therefore are just portrayed to be one dimensional.
Branes are different, you can't construct a quantum theory on branes because all of its dimensions are taken into account by the calculations because they are so big.
 
  • #9
Nav said:
A string can still have three dimensions it's just that those other two dimensions are insignificant.
It comes down to actual dimensions. 1-D is a mathematical convenience that often works if the size in 1 dimension is much larger than the other two.
Think of a real guitar string. If it is 24" long, but only 0.005" in diameter, a 1-D model is a good approx.
I understand that a 3-dimensional object can look 1-dimensional, but these objects behave very differently when quantized. Are you saying that it is possible to quantize a 3-dimensional object without stability issues or other problems? In string theory, the other dimensions are not simply ignored -- the string is not "portrayed to be one dimensional" -- it actually is, exactly.
 
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  • #10
bapowell said:
I understand that a 3-dimensional object can look 1-dimensional, but these objects behave very differently when quantized. Are you saying that it is possible to quantize a 3-dimensional object without stability issues or other anomalies? In string theory, the other dimensions are not simply ignored -- the string is not "portrayed to be one dimensional" -- it actually is, exactly.
I never said that they are ignored, what i meant was that the other dimensions are too small to be considered in the calculations
 
  • #11
Nav said:
I never said that they are ignored, what i meant was that the other dimensions are too small to be considered in the calculations
Right, and I'm saying this is wrong. The strings of string theory are *exactly* 1-dimensional. If you add more dimensions, the quantization procedure is very different.
 
  • #12
Nav said:
Are you saying that it is possible for strings to have higher dimensions like branes?
No.
 
  • #13
Demystifier said:
Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.
Could you give a link where this is done or discussed?
 
  • #14
haushofer said:
Could you give a link where this is done or discussed?
I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.
 
  • #15
Demystifier said:
I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.
But what about the free field theory? I understand "UV divergences" only in the context of interactions.
 
  • #16
Nav said:
The other dimensions of the string are too small to be taken into account by the calculations and therefore are just portrayed to be one dimensional.
Branes are different, you can't construct a quantum theory on branes because all of its dimensions are taken into account by the calculations because they are so big.
Can you show me those "calculations"?
 
  • #17
bapowell said:
But what about the free field theory? I understand "UV divergences" only in the context of interactions.
Even for free theory there is a UV infinite energy of the ground state, but this can always be removed by normal ordering.
 
  • #18
Demystifier said:
I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.
Ah, ok, I understood your statement in the sense that these qft's are fully renormalizible.
 
  • #19
Demystifier said:
Even for free theory there is a UV infinite energy of the ground state, but this can always be removed by normal ordering.
Right, but those are just the normal divergences we find with any free quantum field theory. I had always read that there were stability issues when attempting to quantize fundamental objects of dimension greater than 1.
 
  • #20
bapowell said:
I had always read that there were stability issues when attempting to quantize fundamental objects of dimension greater than 1.
Can you give a reference on that stability issues?
 

What is string theory?

String theory is a theoretical framework in physics that attempts to reconcile general relativity and quantum mechanics by describing the fundamental building blocks of the universe as tiny, vibrating strings rather than point-like particles.

How many dimensions does string theory propose?

String theory proposes 10 or 11 dimensions, depending on the specific version of the theory. These dimensions include the three dimensions of space that we are familiar with, as well as time and 6 or 7 additional spatial dimensions that are curled up or compactified at a microscopic level.

What is the significance of the extra dimensions in string theory?

The extra dimensions in string theory are necessary for the mathematical consistency of the theory. They also provide a possible explanation for the weakness of gravity compared to the other fundamental forces, as they allow for the existence of higher-dimensional objects called branes which can interact with gravity in different ways.

How can we test the validity of string theory?

Currently, there is no experimental evidence for string theory. However, some predictions of the theory, such as the existence of supersymmetry and extra dimensions, can potentially be tested at high-energy particle accelerators. Other predictions, such as the holographic principle and black hole entropy, may be tested through observational data and astronomical observations.

Is string theory the only theory that proposes extra dimensions?

No, there are other theories such as Kaluza-Klein theory and brane-world scenarios that also propose extra dimensions. However, string theory is the only one that attempts to reconcile general relativity and quantum mechanics and has gained the most attention and support from the scientific community.

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