Extra Dimensions in String Theory

[Kea]

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?

 

[EL]

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?

It's your quote

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 ?

 

[Kea]

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?

 

[Kea]

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.

 

[Dcase]

How to hide dimensions?

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

 

[EL]

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?

 

[EL]

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?

 

[Kea]

...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.

 

[Kea]

Where did I give up Lorentz invariance?

I didn't say you had.

 

[EL]

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

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")?

 

[EL]

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...?

 

[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.

 

[EL]

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/Content/Chapters/AboutCERN/CERNFuture/WhatLHC/WhatLHC-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.

 

[Lelan Thara]

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. :)

 

[Kea]

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...

 

[ptalar]

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?

 

[EL]

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.

Eh, yes, we won't know what kind of particle we've found at the very first moment we detect any missing energy at LHC, but that holds for all new particle candidates, SUSY as well as KK-particles as well as...
The data analysis at LHC is very complex, and lot's of different new physics models are quite degenerate. But of course there are always differences (otherwise they would be the same theory) which we can nail down better and better the more we get to know about the properties of the new particle.
Remember that's only a five page paper not going into any details. Check the references (and the references in the references) for more details.

Because that's the only decent test of a theory.

What? That it should be derivable from a theory which we have no way to experimentally verify? You call that decent?

 

[Kea]

What? That it should be derivable from a theory which we have no way to experimentally verify?

I am well aware that String theory is not experimentally verifiable. That is the whole point. I fail to see how it competes with theories that are experimentally verifiable, especially if those theories have the capabilities of an M-theory and are able to reproduce the String models. This is a large claim, of course. Nevertheless, I am making it.

 

[EL]

So Kea, how much are you ready to bet?

 

[Kea]

So Kea, how much are you ready to bet?

We haven't yet settled on a properly formulated question. If you can give me a decent signature for KK modes which separates them from anything more plausible, I am quite willing to give you extremely large odds. In the interest of fairness, I should probably suggest that you take a look at the ideas I am talking about before you commit yourself to a bet. Moreover, I must confess to having no funds whatsoever to pay on loss, but I am sufficiently confident of my position to regard this as unimportant.

 

[EL]

If you can give me a decent signature for KK modes which separates them from anything more plausible, I am quite willing to give you extremely large odds.

I suggest that I'll win the bet if at LHC we'll find a new particle which is part of the KK mass spectrum. The mass of the lightest particle is of course arbitrary, and we need to find more heavier particles to verify that it's really a KK spectrum.
The first level of the KK-tower is really just kind of a copy of the standard model particles, but all with (tree level) masses raised an equal amount (with reservation for the radiative corrections to the masses.)
I think that even if we at first just find the lightest KK-particle at LHC, but have to wait for a while for more particles (to be found at LHC, or in some later experiments) to verify the KK-spectrum, I should win the bet.

However, I'll guess the easiest way to determine wheter it's KK-particles that have been found, is to see wheter the physics community will call them KK-particles or not...

Moreover, I must confess to having no funds whatsoever to pay on loss, but I am sufficiently confident of my position to regard this as unimportant.

I guess I'm in a lose-draw situation then. Say I bet 1$. If you win I'll afford to pay you. If I win, you'll never pay me my 1000$...

 

[Lelan Thara]

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?

In a sense yes, but in a sense no.

The "yes" part is when you talk about time as a dimension. Time is not "necessary and sufficient" to locate a spot in an instantaneous or conceptual volume - but in the physical world, it actually is necessary to have a time dimension to locate anything in space, since everything moves over time. Plus time is a measurement we can use in the physical world. Whether a dimension can be practically used for measurements - measurements that can't be duplicated in another dimension - is part of my conception of whether it's "real".

The important thing is that time is distinctly different from measurements of volume. In calling time a dimension, you are not simply reproducing dimensions that already exist under a new name.

But time standing still, or time moving backwards - I would not be inclined to call those extra dimensions - they seem like valid measurements on a single time axis. If there was some way to conceive of time moving sideways - whatever that might mean - then perhaps that would qualify as an additional time dimension.

And I also am not suggesting anything as philosophical as states of existence such as life and death being called dimensions.

What I've been trying to get a feel for here is this: I think most laymen don't fully grasp that the word "dimension" has a math definition that differs from the physical "necessary and sufficient measurement" definition. So laymen think of "other dimensions" as mysterious invisible places. What I've been asking is whether physicists see their extra spatial dimensions as laymen do, or whether their extra dimensions are mathematical conveniences to explain complex, indeterminate processes that can be physically located in a standard conception of volume and time.

I cannot accept the concept of observer created reality, and so I think a "hidden variables" model will ultimately be the answer to the quantum mysteries. And it seems likely those hidden variables are hidden in other dimensions. But I am afraid that if these hidden dimensions are always described with a mathematical formalism that doesn't reflect something we can measure in the physical world, we will remain mired in unprovable theories, as string theory currently seems to be.

Thank you for asking, ptalar

 

[ptalar]

Lelan,

I think the existing state of physics is to make the math work to support the theory. Then find a way to prove it experimentally. With math you can create as many theoretical conditions as necessary, such as degrees of freedom which is another word for dimensions. The number of degrees of freedom can be infinity.

Whether these dimensions exist and are physically measurable, I don't think we will know in our life time.

One of the hopes with the LHC is to indirectly prove string theory by creating certain conditions that would point to strings being the root cause. That would be the best we could hope for in our lifetime.

The amount of energy required to identify a string through a collision is astronomical and would take a collider the size of the milky way. Not very practical with todays technology.

Good luck in your quest.

I do believe time at t=0 and time in reverse are different dimensions just as x, y and z in the three dimensional world are dimensions in different directions. Yes they are not on the same line but they are different directions just as time can be in different directions.

As for life and death I don't know. I agree its philosophical but I thought I would throw it in for discussion and food for thought.

Phil

 

[Lelan Thara]

Lelan,

I think the existing state of physics is to make the math work to support the theory. Then find a way to prove it experimentally. With math you can create as many theoretical conditions as necessary, such as degrees of freedom which is another word for dimensions. The number of degrees of freedom can be infinity.

Whether these dimensions exist and are physically measurable, I don't think we will know in our life time.

The above is a good description of how things look to me as a layman. As for "our life time" - so much has changed in my lifetime that I remain optimistic

As for life and death I don't know. I agree its philosophical but I thought I would throw it in for discussion and food for thought.

Phil

It certainly is food for thought. I've read "The Tao of Physics", and I believe there are similar, more recent books. It seems many people would like to believe that modern physics leaves room for many metaphysical things that classical physics seemed to deny. Are heaven and hell in other dimensions? Do chakras represent our body's existence in higer dimensions? Are UFOs coming from other dimensions? Is ESP a sign of "spooky action at a distance" at work?

Who knows? Maybe some day we will find our spiritual and mystical beliefs are grounded in science.

But for now - I'm trying to demystify concepts that seem mysterious to me, not add another layer of mystery.

 

[arivero]

How do you understand time? Via a symmetry group. You do not see time, you see "forward in the time" and "back in the time". You recognise this as the elements of translations, and then you visualize time as if it were a line, because the translation generates lines. You see it is not related to the another three independent translations you recognize, so you set it apart as a 4th dimension.

Now, if string people postulate the 26 dimensions to be generated from a group of 26 "generators of translations" with the same mathematical (ie: logical) structure than the group of 4 generator you are used too, and the new dimensions having the same scalar product than old 3 spatial ones, then you have no right to discard as "no spatial" the new ones.

A different question should happen in models where the new dimensions compactify to a different structure. But in naive Kaluza Klein compactification, it is more of the same.

 

[Lelan Thara]

I understand time via a clock.

Arivero, what you have said, together with all else said here, makes it clear to me that the extra spatial dimensions are indeed mathematical abstractions.

I really appreciate the effort people have put in here to help me understand these extra spatial dimensions.

 

[Kea]

However, I'll guess the easiest way to determine wheter it's KK-particles that have been found, is to see whether the physics community will call them KK-particles or not...

Deal.

I guess I'm in a lose-draw situation then. Say I bet 1$. If you win I'll afford to pay you. If I win, you'll never pay me my 1000$...

Well, maybe my luck will have changed by then. One never, never knows.

 

[Hans de Vries]

..., makes it clear to me that the extra spatial dimensions are indeed mathematical abstractions.

It's all a bit of a word play I guess. Nevertheless, mathematical abstractions
or not, they are all supposed to work just like real extra dimensions. Look
around for instance in the most used introduction for string theory:

http://books.google.com/books?vid=I...thor:zwiebach&sig=F8uUPfn2kaCq4cJRP7qp4PQ-ySw
https://www.amazon.com/dp/0521831431/?tag=pfamazon01-20

A First Course in String Theory by Barton Zwiebach.
Regards, Hans

 

[EL]

what you have said, together with all else said here, makes it clear to me that the extra spatial dimensions are indeed mathematical abstractions.

If that's your conclusion, why don't you call our ordinary three spatial dimensions "mathematical abstractions" also?
What makes exactly the number "3" the most real? Don't get fooled by the fact that our brains are used to a 3-dimensional flat world.

As Hans said, this is really a word play. In principle all physics quantities are just "mathematical abstractions", but we have do draw the line for what to call "real" somewhere. IMO it's a bit of a contradiction to call extra dimensions "unreal" at the same time we call our usuall 3 spatial dimensions "real"...

 

[EL]

Deal...Well, maybe my luck will have changed by then. One never, never knows.

Maybe if I bet just 1 cent. Then at least I have a fair chance of getting my 10$ if I win?

 

[Kea]

Maybe if I bet just 1 cent.

Oh, all right, then. I'm not greedy. A win of $10 will do fine.

 

[ptalar]

How do you understand time? Via a symmetry group. You do not see time, you see "forward in the time" and "back in the time". You recognise this as the elements of translations, and then you visualize time as if it were a line, because the translation generates lines. You see it is not related to the another three independent translations you recognize, so you set it apart as a 4th dimension.

Now, if string people postulate the 26 dimensions to be generated from a group of 26 "generators of translations" with the same mathematical (ie: logical) structure than the group of 4 generator you are used too, and the new dimensions having the same scalar product than old 3 spatial ones, then you have no right to discard as "no spatial" the new ones.

A different question should happen in models where the new dimensions compactify to a different structure. But in naive Kaluza Klein compactification, it is more of the same.

What makes some dimensions compactify and others to not compactify? Is there some Darwinian logic to these dimensions that decide which dimensions compactify? Why are we in a 11 dimensionsal world with 4 dimensions expanded and 7 compactified? Is it the least energy principal where all matter seeks its lowest energy state? Could that be where we are now with 4 dimensions? Must time always be one of the surviving dimensions that do not compactify? What circumstances must exist for the other 7 dimensions to decompactify? Would we still be alive if they did decompactify? I believe Lelan is on the right track. These are all theoretical exercises. Which is needed for physics to move forward. But must be validated experimentally for the theory to be science fact. Otherwise, it becomes another religion.

 

[EL]

Oh, all right, then. I'm not greedy. A win of $10 will do fine.

Deal! Guess you'll have my cent about 2010-2020 then!

 

[arivero]

Arivero, what you have said, together with all else said here, makes it clear to me that the extra spatial dimensions are indeed mathematical abstractions.

But note they obey all the equations of the non-extra dimensions. So for a mathematician, they are in equal footing than the rest. You could say that the non extra dimensions are "mathematical abstractions thar happen to coincide with ordinary experience" while extra dimensions are "mathematical abstractions than do not coincide with ordinary experience".

A mathematician can single out time (it has a different sign in the metric matrix) but it can not tell you any difference between an extra dimension and a ordinary one. Of cours, this comes to a conflict, at the very end, with the goals of compactification.

 

[EL]

Another thing to note is that the basic structure of string theory itself does not say those 7 extra spatial dimensions need to be compactified (at least that's the impression I've got), but are treated mathematically on equal footing as our ordinary 3. However, due to the fact we havn't observed any extra dimensions, we make the conclusion they need to be compactified.