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## Extra Dimensions in String Theory

Lisa Randall, in her book Warped Passages, takes at least one higher dimension very seriously. Her model is a bulk and boundary model; the standard model forces ( which of course includes all our biology) propagate in the boundary, identified with our 4-D spacetime, but the particles we see are projections or shadows of particle moving in the higher dimensional bulk (she has a precise mathematical description of this). She has calculated that the LHC ought to see clear signs if this model is correct.

 Quote by EL My question is though: would you call such extra dimension "real"?
Yes. If such particles are observed, I would be happy to call the extra dimensions real. However...does anybody want to make a bet on this?

Recognitions:
 Quote by Kea Yes. If such particles are observed, I would be happy to call the extra dimensions real. However...does anybody want to make a bet on this?
 Quote by Kea That's a very good question, Lelan. Some physicists persist in believing that it is more than a mathematical abstraction, and take the extra dimensions literally to be measurable in the simple way that you imagine. They are wrong, of course.
I'm objecting to! To me it sounded like you were saying that there could be no "real" extra dimensions, period.

So, what odds are you giving me for finding KK-particles at LHC?
Something like 1:100, and I'll consider taking it...

Also, if we find a deviation from the 1/r^2-gravity at small length scales, would you consider this as an indication of a "real" (although not universal) extra dimension ?

 Quote by EL So, what odds are you giving me for finding KK-particles at LHC? Something like 1:100, and I'll consider taking it...
Excellent. I have no problem with these odds (could we make it 10000:1 ?), but the question needs a little clarification: any particles that are predicted by the formalism to which I refer, prior to LHC results, should be exempt from being labelled as KK particles. Is that fair?

 Quote by EL Also, if we find a deviation from the $r^{-2}$ gravity at small length scales, would you consider this as an indication of a "real" (although not universal) extra dimension?
I'm afraid it isn't clear at all what you mean here. As far as this thread is concerned the 'reality' of dimensions is about the String formalism and the possible detection of KK modes at the LHC. If you want to give up Lorentz invariance then I fail to understand why you would believe in compactification.
 This is speculative: 1 - a square might be decomposed into 4 equilateral triangles - if bent along the triangles, such symmetry and dimensions may be viewed, but if not bent, remaining planar, these triangles are obscured with only the square viewed 2 - likewise a six sided cube may be decomposed into 24 equilateral triangles which might be bent into something resembling a torus by folding the top and bottom toward the interior while the front-back and left-right surfaces are folded outwards - but if not folded the equilateral triangles are obscured

Recognitions:
 Quote by Kea Excellent. I have no problem with these odds (could we make it 10000:1 ?), but the question needs a little clarification: any particles that are predicted by the formalism to which I refer, prior to LHC results, should be exempt from being labelled as KK particles. Is that fair?
Eh, no. You just agreed to that if we find KK-particles at LHC you would be happy to call the extra dimensions of the KK-theory real, and hence if the detected particle is predicted by both KK-theory and "by the formalism to which you refer" I should stand as the winner!
Let's make it 1:1000 then?

Recognitions:
 Quote by Kea I'm afraid it isn't clear at all what you mean here. As far as this thread is concerned the 'reality' of dimensions is about the String formalism and the possible detection of KK modes at the LHC. If you want to give up Lorentz invariance then I fail to understand why you would believe in compactification.
Where did I give up Lorentz invariance?

 Quote by EL ...and hence if the detected particle is predicted by both KK-theory and "by the formalism to which you refer" I should stand as the winner!
Could you give me some references of any KK particles (including precise masses) that have actually been predicted? The usual String hand-waving is not acceptable.

 Quote by EL Where did I give up Lorentz invariance?

Recognitions:
 Quote by Kea Could you give me some references of any KK particles (including precise masses) that have actually been predicted?
The masses in the KK-spectrum can of course not be predicted since they depend on the compactification radius R: (m(n))^2 = (n/R)^2 + (m0)^2, where m0 is the zero mode mass (SM-particle). All there is, is a lower limit set by electroweak precision tests. In principle the masses could be extremely high, if the extra dimension is tiny. But (generous as I am) our bet will only include the mass range of LHC (where the lightest KK-particle is to be found be found if it should be able to constitute the dark matter).
However, the theory predicts other properties of the particles.
I guess this quite recent paper could be something to look at:
http://www.arxiv.org/abs/hep-ph/0610057
 Quote by Phenomenology of Universal Extra Dimensions In this proceeding, the phenomenology of Universal Extra Dimensions (UED), in which all the Standard Model fields propagate, is explored. We focus on models with one universal extra dimension, compactified on an S1/Z2 orbifold. We revisit calculations of Kaluza-Klein (KK) dark matter without an assumption of the KK mass degeneracy including all possible coannihilations. We then contrast the experimental signatures of low energy supersymmetry and UED.
 The usual String hand-waving is not acceptable.
Why do I have to derive the spectrum directly from string theory? Aren't we talking about wheter there could be any "real" extra dimensions or not?
Yes, the subject is about the extra dimensions indicated by string theory, but I guess you wouldn't say string theory is ruled out just because we happen to find KK-particles (in which case you agreed to call the extra dimension "real")?

Recognitions:
 Quote by Kea I didn't say you had.
Well, to me
 If you want to give up Lorentz invariance then I fail to understand why you would believe in compactification.
sounded like you were implying that deviation from 1/r^2 gravity would spoil Lorentz invariance in some way...?
 I did a Wiki search on LHC and didn't come up with anything physics-related - can someone tell me what LHC stands for? Some of this discussion is going over my head, which is fine, but if I could make two points - The conversation is drifting back into "what is real" without an operational definition of "real". My particular interest is "what is necessary and sufficient to locate all points in an unbounded volume". Also, "real extra dimensions" is not a concept I object to - it's real extra spatial dimensions that I'm questioning.

Recognitions:
 Quote by Lelan Thara I did a Wiki search on LHC and didn't come up with anything physics-related - can someone tell me what LHC stands for?
LHC stands for the Large Hadron Collider, which is the new particle accelerator under construction at CERN.
http://public.web.cern.ch/Public/Con...hatLHC-en.html
It's the most amazing machine humanity has ever built, and the physics community are eagerly waiting for it take up operation.

 The conversation is drifting back into "what is real" without an operational definition of "real".
Good summary. My point is that if you call our usual dimensions "real", then there could also be extra dimensions we (IMO) should call "real".

 Also, "real extra dimensions" is not a concept I object to - it's real extra spatial dimensions that I'm questioning.
I guess I've left out "spatial" some times during the discussion, but when I've said "extra dimensions" I've ment "extra spatial dimensions". In string theory, the predicted extra dimensions are all spatial.
 Thanks, EL. It certainly gives a sense of scale to realize that the power of 1150 mosquitos will create the most powerful atom smasher we've ever had. :)

 Quote by EL However, the theory predicts other properties of the particles. http://www.arxiv.org/abs/hep-ph/0610057
I fail to understand how such a vague analysis as this can possibly compare to potential precise predictions (in the LHC range). The authors readily admit that it is difficult to separate ED effects from other possibilities.

 Why do I have to derive the spectrum directly from string theory?
Because that's the only decent test of a theory.

 ...but I guess you wouldn't say string theory is ruled out just because we happen to find KK-particles?
No. Rather, I actually expect quite a lot of interesting things to happen before then...

 Quote by Lelan Thara I did a Wiki search on LHC and didn't come up with anything physics-related - can someone tell me what LHC stands for? Some of this discussion is going over my head, which is fine, but if I could make two points - The conversation is drifting back into "what is real" without an operational definition of "real". My particular interest is "what is necessary and sufficient to locate all points in an unbounded volume". Also, "real extra dimensions" is not a concept I object to - it's real extra spatial dimensions that I'm questioning.
Lelan. I also agree that the extra dimensions may not be spatial. According to Einsteins theory of relativity time stops at the speed of light. Aren't we experiencing particles that are at t=0 when we see sun light? A fifth dimension? What about these imaginary particles, tachyons,that supposedly travel faster than the speed of light, isn't time going in reverse relative to the tachyon? A sixth dimension? What about existence in general, being alive vs. say being dead. Are these states of existence or dimensions? Is this where your trying to go?