String theory and extra dimensions

[Santalum]

If all fundamental particles are one dimensional strings that vibrate ate various unique frequencies, characteristic of the fundamental particle in question, can some one please explain as simply as possible the relationship the 8 or so additional dimensions and strings.

[ajb]

The extra dimensions are needed because the theory will not work otherwise. The rules of applying quantum theory to strings determines the number of dimensions to be 10 for the superstring and 26 for the bosonic string. This is an amazing prediction of string theory.

[Santalum]

The extra dimensions are needed because the theory will not work otherwise. The rules of applying quantum theory to strings determines the number of dimensions to be 10 for the superstring and 26 for the bosonic string. This is an amazing prediction of string theory.

 

 

That much I know but I wish to attempt to understand it.

How does quantum theory determine that there are 10 dimensions for s super string?

Is there a way of explaining it in fairly basic terms without having to get into the complex maths?

Is there a suitable analogy perhaps?

 

I can picture a vibrating string in terms of a physical string being pulled taught by to volunteers and being twanged by one of them.

 

I could perhaps begin to comprhend how entanglement might work if there were perhaps 3 volunteers and two seperate strings with one volunteer holding the end of both strings and the volunteers at the other ends widley spaced.

 

 

But how would the extra dimensions fit into this analogy?

[ajb]

That much I know but I wish to attempt to understand it.

How does quantum theory determine that there are 10 dimensions for s super string?

Is there a way of explaining it in fairly basic terms without having to get into the complex maths?

Is there a suitable analogy perhaps?

 

I am going to say that there is no simple explanation here.

 

The technical issues you need to think about are called anomalies. Basically, a classical symmetry is said to be anomalous if it does not survive the quantisation process, a little more specifically regularisation.

 

For string theory the dimensions are such that the conformal anomaly of the worldsheet conformal field theory vanishes.

 

I suggest you need to learn a bit about anomalies in field theories.

[DrRocket]

That much I know but I wish to attempt to understand it.

How does quantum theory determine that there are 10 dimensions for s super string?

Is there a way of explaining it in fairly basic terms without having to get into the complex maths?

Is there a suitable analogy perhaps?

 

I can picture a vibrating string in terms of a physical string being pulled taught by to volunteers and being twanged by one of them.

 

I could perhaps begin to comprhend how entanglement might work if there were perhaps 3 volunteers and two seperate strings with one volunteer holding the end of both strings and the volunteers at the other ends widley spaced.

 

 

But how would the extra dimensions fit into this analogy?

 

String theory does not really predict the extra dimensions. Rather the theory requires the extra dimensions else it is demonstrably not self-consistent.

 

One problem is that no one has yet really been able to clearly define what string theory is. But apparently, whatever it is, it requires extra spatial dimensions -- the precise number being dependent on the particular string theory or M-theory.

 

As far as prediction go, string theory has yet to produce a testable prediction. Maybe someday it will, and maybe someday it will become a viable physical theory. But this is not that day.

 

Analogies are pretty useless with string theory. It is a VERY abstract and mathematical theory.

[Santalum]

String theory does not really predict the extra dimensions. Rather the theory requires the extra dimensions else it is demonstrably not self-consistent.

 

One problem is that no one has yet really been able to clearly define what string theory is. But apparently, whatever it is, it requires extra spatial dimensions -- the precise number being dependent on the particular string theory or M-theory.

 

As far as prediction go, string theory has yet to produce a testable prediction. Maybe someday it will, and maybe someday it will become a viable physical theory. But this is not that day.

 

Analogies are pretty useless with string theory. It is a VERY abstract and mathematical theory.

 

 

Bummer! Makes it difficult for us non-mathematicians.

 

Perhaps as the hypothesis is ironed out more it may become possible to form appropriate analogies. It seems that all working theories (relativity, quantum mechanics,...) thus far have been able to be very broadly explained through analogies.

[ajb]

Perhaps as the hypothesis is ironed out more it may become possible to form appropriate analogies. It seems that all working theories (relativity, quantum mechanics,...) thus far have been able to be very broadly explained through analogies.

 

For string theory people liken the notes played on a violin to particles. However, this and other analogies are exactly that, analogies. One has to be very careful with their use. In fact, I would say that on this site most of the key misunderstandings come from trying to take analogies too seriously.

 

The only "analogy" for quantum anomalies that I can think of is the similarity with the harmonic oscillator, assuming you know a little quantum mechanics. Well anyway, it is understood that the ground state for a classical harmonic oscillator has zero energy, i.e. the minima of the potential. However, when you quantise the harmonic oscillator the ground state no longer has zero energy, rather [math]\hbar \omega/2[/math].

 

This remarkable "lifting" of the energy cannot be seen at the level of classical Lagrangian. It is a true quantum effect.

 

This is much like anomalies. One cannot guarantee that a symmetry of the classical system survives in the quantum system.

 

Without getting too technical, some of these anomalies can be disastrous for the theory. The quantum theories become "sick" and are inconsistent. This is the case for string theory unless the dimensions are fixed to be 10 or 26, depending on the theory. A consistent theory of a free string can only be formulated in these dimensions.

[IM Egdall]

Analogies are pretty useless with string theory. It is a VERY abstract and mathematical theory.

 

Maybe this is the key problem with string theory. It is not based on a physical principle, like quantum mechanics (uncertainty principle) or special relativity (absolute speed of light) or general relativity (equivalence principle).

Edited January 24, 2012 by IM Egdall

[DrRocket]

Maybe this is the key problem with string theory. It is not based on a physical principle, like quantum mechanics (uncertainty principle) or special relativity (absolute speed of light) or general relativity (equivalence principle).

 

 

Quantum mechanics is not based on the uncertainty principle. That is a necessary part of the theory but hardly the basis.

 

Special relativity actually requires two postulates, and the invariance of the speed of light is one. The other is the invariance of the equations of physics in all inertial reference frames.

 

While the equivalence principle gets a lot of press, and it was philosophically useful to Einstein, it is not the true basis of general relativity and in fact it is pretty much logically irrelevant in modern treatments of the theory.

 

One key problem with string theory is that no one really knows what it is. There are deep conceptual issues associated with quantum field theories, but they pale in comparison with the issues in string theory. Another problem is that string theory has yet to produce a single new testable prediction. It may eventually become a viable theory of nature, but it is quite far from any such status at this time. But the biggest problem with string theory is the totally unsubstantiated assertions made by some proponents in popularizations -- statements that they could never get away with in from of a knowledgeable and critical audience.

[ajb]

One must not forget that the question "what is a quantum field theory?" has yet to have a full answer.

 

Classical string theory can be understood as a 2-dimensional (super)conformal sigma-model. So, the question of what is classical string theory becomes "was is a full 2-dimensional conformal sigma model?". Understanding this properly will give us the classical string.

 

Understanding the quantum string properly is extremely difficult.