# Extra dimensions -> power law lowering unification?

1. Jan 4, 2009

### karnten07

Is it true that the existence of extra dimensions can lower the unification scale to the GeV scale? Does this mean that the LHC would be in range to detect a unification of couplings if this were true?

2. Jan 5, 2009

### BenTheMan

Well, I think you mean (?) TeV, not GeV. And this is highly dependent on the size of the extra dimensions.

So, for example, to have unification at the TeV scale, the extra dimensions have to have radius of an inverse TeV (multiply by hbar and c, and appropriate powers of 10 to get meters). If you believe that string theory is correct, then you also need 5 other dimensions that have planck length radius, and you also have to explain this new hierarchy.

But, assuming you can explain WHY the dimension has a TeV radius (or, if you don't care), then there ARE definite consequences for the LHC, and it IS experimentally verifiable.

3. Jan 5, 2009

### Phrak

Are you saying: the bigger the dimension, the more we tend to notice it?

Last edited: Jan 5, 2009
4. Jan 5, 2009

### BenTheMan

Yes. The larger the dimension, the more it effects the experiments that we'll preform at LHC. We can also hide the extra dimension partially or completely by making it small enough.

5. Jan 5, 2009

### granpa

does this assume that forces like gravity spread through these extra dimensions?

6. Jan 6, 2009

### Phrak

Thanks, Ben, though I don't quite follow--the circumference of these dimensions can be changed?

I'm a bit curious about gravity as well, but in another way. It seems that in the early universe where the spacial dimensions are at Planck scales, gravity would unify with the other forces, but only because the gravitons would have to be far massive to fit. Is this right?

7. Jan 6, 2009

### BenTheMan

Gravity is always spread through the other dimensions. This scenario assumes that the regular particles (electrons, quarks, etc.) can live in the extra dimensions.

8. Jan 6, 2009

### BenTheMan

This is a model building issue. You usually pick the circumference of the extra dimensions to solve some problem.

I don't quite understand the question. What does "Far too massive to fit" mean?

9. Jan 7, 2009

### Phrak

Thanks, though I had hoped you'd droped a bombshell: dimensions of variable size.

I should have said 'energetic'--higher frequency. If space were small, the limited number of wavelengths that would fit would be higher frequencies. Does that make sense?

10. Jan 9, 2009

### BenTheMan

Sorry :) I'm not sure how this would work. I've thought about it for about ten minutes, and couldn't convince myself that I had any kind of an answer.

Yeah I understand now. Probably the answer is that the Plank length takes care of this. The radius of the compact directions is the Plank length, and the masses are quantized in units of the Planck Mass, which is 1/Planck Length. For a 2-d example, think about waves in a fishbowl, or something. If you set up a standing wave, there are exactly an integer number of waves in the fishbowl. You can think of the Planck mass resonances in terms of this---the lowest lying massive state corresponds to one wave in the fishbowl, etc.

11. Jan 9, 2009

### karnten07

Yes, i was just checking if it was at the GeV or TeV scale because this is really the issue i am confused about. The text says TeV which makes sense. But then for example in a paper by Dienes, Dudas and Gia Dvali where they discuss this accelerated power law, there is a graph showing the power law. But the scale is in GeV. Or does the TeV scale refer to unity which includes gravity by lowering the Planck scale?

12. Jan 9, 2009

### BenTheMan

I don't know offhand. Can you post a link to the paper?

I'm familiar with Dienes, Dudas, and Gherghetta, but not Dienes, Dudas and Dvali.

13. Jan 10, 2009

### karnten07

I'm sorry, i think thats who i meant. I think i get it now though, because unification is predicted to occur at 10^6 GeV which is 10^2 TeV? So with large extra dimensions unification occurs at the TeV scale. I think i was getting confused because the graphs were logarithmic. Thanks for the help though guys

Karnten07