Correspondence between particle and string vibration mode

[Blackberg]

Hi, my level of knowledge of string theory is the following :

I understand that to each elementary particle there corresponds a string vibrating at an associated frequency (mode).
So my questions are :

1. Is there some table yet that proposes a correspondence? Such as :
electron : so many Hz,
tau neutrino : so many Hz,
photon : so many Hz,
and so on.

2. What determines the length of a string?

3. I don't buy the curled up dimensions yet.
It seems to me that anything that is curled up can still be described with the known 3 dimensions.

4. As for time being a dimension, I'm rather at ease with time being nothing more that the number of rotations (or oscillations) an arbitrary reference body has made. Calling it a 4th (or 11th) dimension seems to me to be solely for mathematical purposes, and not sufficient to propose that we live in a pop-up book we all fail to properly visualize.

 

[bapowell]

3. I don't buy the curled up dimensions yet.
It seems to me that anything that is curled up can still be described with the known 3 dimensions.

Even something that's curled up on 10 dimensions? Are you perhaps taking the lower-dimensional analogies presented in popular science books and TV too literally?

 

[wabbit]

I am not particularly a fan of ST, but as I see it (no expert here, this interpretation may be incorrect), extra small dimensions aren't outrageous by themselves - there are in any case many extra dimensions needed to describe the world (e.g, t,x,y,z,E_x,E_y... including the values of the electromagnetic field). What is special here is that some of these dimensions (not the values of the EM field per se, this was more of an analogy) are unified with spacetime rather than being separate, somewhat like time was once unified with space. For EM, (Kaluza-Klein) theories with extra dimensions were proposed before, they weren't successful but their extra dimensions were not the issue.

 

[Doug Huffman]

Physicists, such as Richard Feynman,[6][7] Roger Penrose[8] and Sheldon Lee Glashow,[9] have criticized string theory for not providing novel experimental predictions at accessible energy scales.

The Standard Models of particle physics and of cosmology are not falsifiable, being modeled as towers of ad-hockery.

 

[bapowell]

I am not particularly a fan of ST, but as I see it (no expert here, this interpretation may be incorrect), extra small dimensions aren't outrageous by themselves - there are in any case many extra dimensions needed to describe the world (e.g, t,x,y,z,E_x,E_y... including the values of the electromagnetic field). What is special here is that some of these dimensions (not the values of the EM field per se, this was more of an analogy) are unified with spacetime rather than being separate, somewhat like time was once unified with space. For EM, (Kaluza-Klein) theories with extra dimensions were proposed before, they weren't successful but their extra dimensions were not the issue.

The extra dimensions in 10-dimensional string theory are quite literally extra dimensions of space.

 

[wabbit]

Physicists (...) have criticized string theory for not providing novel ' predictions at accessible energy scales.

Are there definite predictions of ST at (specific) higher energy scales?

 

[Doug Huffman]

Are there definite predictions of ST at (specific) higher energy scales?

Not that I know.

About extra dimensions; there is no evidence for dimensions beyond 3+1.

 

[wabbit]

The extra dimensions in 10-dimensional string theory are quite literally extra dimensions of space.

Hmmm... I guess my analogy was poor. In KK also the 5th dimension is spatial and the EM data lies in the metric, I need to work on this:) Still, I don't see extra dimensions as an issue in principle, more as one of experimental evidence.

 

[bapowell]

Still, I don't see extra dimensions as an issue in principle, more as one of experimental evidence.

Right, as it should be. It is certainly a key aspect of string theory that can in principle be tested. Sadly, the exact properties of the dimensions are not known and so no definite predictions can be made at this time.

 

[wabbit]

Hmmm... I guess my analogy was poor. In KK also the 5th dimension is spatial and the EM data lies in the metric, I need to work on this:)

Slightly improved (?) analogy: in KK, adding a fifth dimension allows EM to become a (metric) property of the (extended) spacetime manifold, like gravity is already in GR. Would it be roughly correct to say that ST takes a similar approach, but includes all standard model fields which become encoded in the manifold - and needs many more dimension to achieve that? Quite unsure about that, as about ST generally I must admit.

 

[bapowell]

Slightly improved (?) analogy: in KK, adding a fifth dimension allows EM to become a (metric) property of the (extended) spacetime manifold, like gravity is already in GR. Would it be roughly correct to say that ST takes a similar approach, but includes all standard model fields which become encoded in the manifold - and needs many more dimension to achieve that? Quite unsure about that, as about ST generally I must admit.

No, not as far as I know. There are scalar fields associated with the extra dimensions (so-called moduli) that are analogous to the scalar field appearing in Kaluza-Klein. The extra-dimensions are forced on string theory by the need for mathematical consistency (specifically, the cancellation of something called the world sheet conformal anomaly).

 

[wabbit]

OK I give up:)

 

[Haelfix]

String theory makes several unambiguous predictions near the characteristic scale where the theory lives. This is usually near the Planck scale. One of these would be a very specific 'Regge' like tower of vibrational modes that would be quite unmistakeable in an accelerator experiment. The exact details will depend on the type of solution string theory spits out, but very much like the standard model once you pin down several features, you quickly are in a position to make many more predictions and things would proceed very fast from that point.

As far as Kaluza-Klein goes, the type of compactification is not quite what happens in string theory. One gets the same type of general result (e.g. a spacetime dimension curls up and out pops a corresponding matter field(s) living in a 4d world) but the details are not as straightforward. The gauge group of typical string theories are too large to compactlify alla KK in even 11 dimensions, so other methods were discovered. The quantum geometry of all of this business is quite intricate and the exact solution corresponding to the real world is not known.

 

[Doug Huffman]

OK I give up:)

Oh, don't give up.

Read and understand physicist Alan Sokal's seminal essay 'Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity'

http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_singlefile.html

First published in the then well respected journal Social Text, #46/47, pp. 217-252 (spring/summer 1996). http://socialtextjournal.org/

 

[wabbit]

 

[arivero]

Slightly improved (?) analogy: in KK, adding a fifth dimension allows EM to become a (metric) property of the (extended) spacetime manifold, like gravity is already in GR. Would it be roughly correct to say that ST takes a similar approach, but includes all standard model fields which become encoded in the manifold - and needs many more dimension to achieve that? Quite unsure about that, as about ST generally I must admit.

No, not as far as I know. There are scalar fields associated with the extra dimensions (so-called moduli) that are analogous to the scalar field appearing in Kaluza-Klein. The extra-dimensions are forced on string theory by the need for mathematical consistency (specifically, the cancellation of something called the world sheet conformal anomaly).

Yep, this is one of the "wrong turns" of the development of String Theory. After nailing -with M theory- the number of extra dimensions, they did not work a way to exploit them as kaluza klein dimensions and instead they are a nuissance -well, in some models they hope to get the number of generations from the shape of the compactification-.

To understand why seven is the right number of extra dimensions it can be convenient to look to the unified groups SO(10), SU(5) and the partial unification SU(4)xSU(2)xSU(2) of Pati-Salam. Pretty obviously SO(10) is the group of symmetries of a sphere with 9 dimensions. SU(5) is the symmetry group of the manifold CP4, which is 8 dimensional. As for Pati-Salam, SU(4) is as SO(6) and SU(2)xSU(2) is as SO(4) algebraically, and SO(6)xSO(4) is the symmetry group of the producto of the 5-sphere times the 3-sphere, so again a 8 dimensional space. This product, S5xS3, is the clue used by Witten to show that in seven dimensions there are manifolds whose symmetry group, and thus the Kaluza Klein symmetry of the corresponding 7+4, is the same that the standard model, SU(3) x SU(2)xU(1).EDIT: what one should excpect is that the network of dualities (T-dual, etc) that interpolates between 9 and 11 dimensions is related to the chiral forces, because the "non chiral forces", namely the product of colour and electromagnetism, SU(3)xU(1), are the symmetry of a five dimensional manifild, CP2 x S1.

 

[wabbit]

(...see above...)

Thanks for your informative reply.

One gets the same type of general result (e.g. a spacetime dimension curls up and out pops a corresponding matter field(s) living in a 4d world).

Oh actually that's as far as I was hoping to get with my second analogy - thanks.

 

[wabbit]

@arivero - On the symmetries of SM emerging in a unified approach, Connes seems to get there by a different route (esp. his recent paper "Geometry and the Quantum: Basics", Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov, of which I can barely understand the introduction) so perhaps ST isn't the only contender to do that.

 

[wabbit]

As for time being a dimension, I'm rather at ease with time being nothing more that the number of rotations (or oscillations) an arbitrary reference body has made. Calling it a 4th (or 11th) dimension seems to me to be solely for mathematical purposes, and not sufficient to propose that we live in a pop-up book we all fail to properly visualize.

The pop-up book view is just as valid in Newtonian spacetime as in Relativity, and in the first case one can certainly dismiss it as just a mathematical tool, that says nothing deep.

Relativity however is different: here, space and time are truly merged into one, and there is no natural way to split them up - or rather, this way is different for each observer. So we do not live in a shared space and a shared time, only in a shared spacetime. The key fact that reveals this is "the relativity of simultaneity": things that happen at the same time from my viewpoint, do not from yours (at least if our relative velocity is high). And while you do have a well defined notion of your own time ("proper time"), the only thing you can always agree on with me is the mixed "spacetime interval", not time nor distance.

 

[haushofer]

If I'm not mistaken, string theory can also be formulated in 2+1 dimensions because the Lorentz algebra becomes simpler and hence no anomalies appear in the algebra.