# The 11 dimensions of M-theory

From what I have gathered, M-theory states that there are 11 dimensions. We live in 3 of these dimensions(unless time is considered its own dimension), and I believe the common understanding is that these other 8 dimensions are incredibly small. At the time of the Big Bang, these 3 dimensions expanded along with the universe while the other remained small.

My question is this: Why did these other dimensions remain small? Also, if these dimensions had never expanded, does this mean that they would be found at the "center" of the universe?

In String Theory, the myriad of particle types is replaced by a single fundamental building block, a string'. These strings can be closed, like loops, or open, like a hair. As the string moves through time it traces out a tube or a sheet, according to whether it is closed or open. Furthermore, the string is free to vibrate, and different vibrational modes of the string represent the different particle types, since different modes are seen as different masses or spins.

One mode of vibration, or note', makes the string appear as an electron, another as a photon. There is even a mode describing the graviton, the particle carrying the force of gravity, which is an important reason why String Theory has received so much attention. The point is that we can make sense of the interaction of two gravitons in String theory in a way we could not in QFT. There are no infinities! And gravity is not something we put in by hand. It has to be there in a theory of strings. So, the first great achievement of String Theory was to give a consistent theory of quantum gravity, which resembles GR at macroscopic distances. Moreover String Theory also possesses the necessary degrees of freedom to describe the other interactions! At this point a great hope was created that String Theory would be able to unify all the known forces and particles together into a single `Theory of Everything'.

Supposedly, the energy level was enough for the three dimensions we know (plus time) to inflate. The other dimensions remain “compacted” and are thus everywhere embedded in space time.
However, although M theory is still alive, not all facets of the theory with extra dimensions still match the observations at the Large Hadron Collider and no evidence has been found for anything smaller than a quark…yet.

http://physicsworld.com/cws/article/indepth/44805

http://arxiv.org/abs/1012.3375

http://arxiv.org/abs/1010.4439

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Supposedly, the energy level was enough for the three dimensions we know (plus time) to inflate. The other dimensions remain “compacted” and are thus everywhere embedded in space time.
However, although M theory is still alive, not all facets of the theory with extra dimensions still match the observations at the Large Hadron Collider and no evidence has been found for anything smaller than a quark…yet.

Wait, so if the other dimensions are compacted, but everywhere, what is the difference between them and the other dimensions which are also located everywhere?

marcus
Gold Member
Dearly Missed
Cansay, M-theory has so far not been formulated as a definite theory. There are no equations defining the theory that you can point to, or calculate with to make predictions.
So it is a bit out of place, in cosmo forum, to be talking as if M-theory was something real, that you could fit observational data to.

Cosmology is an observational science, with huge masses of data. Millions of datapoints that the mathematical models have to fit. Mainstream working cosmologists do not incorporate M-theory in their models of the universe.
The models that one actually develops and fits observational data to, and calculates stuff with, like the darkmatter fraction or cosmological constant or age of U etc. these mainstream working models do not involve extra dimensions.

Speculative stuff like this is probably more suitable for the BTSM (beyond the standard model) forum.

However I'm not staff and this is just my personal opinion--- the mentors are the ones who sort things out category-wise.

Wait, so if the other dimensions are compacted, but everywhere, what is the difference between them and the other dimensions which are also located everywhere?

This is/was a problem I also grappled with in my head. At first I intuitively felt "well, if these dimensions are curled up/located EVERYWHERE and every time I move, I am moving through them (though they're just too small to notice) what is the difference between being small and being macroscopic? I had trouble seeing the difference, even if they were small, but everywhere then I thought there should essentially be no difference.

But I'm starting to feel more comfortable with the mental image of each tiny area being completely circumnavigated everywhere but individually and not leading to any observable macroscopic effect.

The other possibility I've wondered and perhaps take more seriously is that if these calabi-yau manifolds are sufficiently small as is most often suggested, then the only particles small enough to fit inside them are strings. The strings require these extra dimensions for their vibrational patterns to create the particles we now accept as the elementary particles. My thinking is that these elementary particles we know such as quarks are too large to fit inside of these tiny, curled up dimensions (calabi-yau manifolds) and thus there is no macroscopic effect because only strings and nothing larger enters these dimensions. This is hard to picture as I do understand your mentality that if they exist EVERYWHERE, what is the difference between that and being big. But picturing a curled up shape (no obviously you can't actually imagine visually a 6 dimensional curled up shape but the calabi-yau images that are usually made digitally at least make it somewhat easier to imagine), the string moves around throughout it, curving and grooving around turns, etc. It can enter a calabi-yau manifold, move through it, and leave it (circumnavigate) and then move into the next one immediately beside it and do the same thing. A larger particle will not be able to enter one, and thus cannot enter any of them. I hope this mental image helps, but wait for confirmation from someone else because this is just what I've concluded on my own as a viable solution to that problem.

I'd like if this could be moved to BtSM like Marcus said because I think a better answer would be given there (to help my understanding as well) and plus it is a bit out of place seeming in here for the reason marcus said.

From what I have gathered, M-theory states that there are 11 dimensions. We live in 3 of these dimensions(unless time is considered its own dimension), and I believe the common understanding is that these other 8 dimensions are incredibly small. At the time of the Big Bang, these 3 dimensions expanded along with the universe while the other remained small.

My question is this: Why did these other dimensions remain small? Also, if these dimensions had never expanded, does this mean that they would be found at the "center" of the universe?

Actually it is essential to include the time dimension if wording it they way you are. If you wanted to call m-theory a 10 dimension theory, ignoring time for the purposes of the conversation that would be different, but you can't consider it an 11 dimensional theory and ignore the time dimension because one of those 11 IS time. ex. if you said we lived in 3, and then there are 8 compactified dimensions, that is wrong. There are believed to be 7 extra spatial dimensions, not 8.

So we live in 3 space, 1 time, superstring theory predicts 6 small/curled up dimensions (most commonly referred to as a calabi-yau manifold, the shape that they take though we do not know which possible calabi-yau manifold configuration would be correct and there are many, if not an infinite amount of possibilities) and m-theory predicts one extra one. As for the properties of that extra dimension I can't really help on that with any confidence, I don't know enough about it. M-Theory does predict objects though called membranes which CAN be large/macroscopic in extent, they can be of different dimensions so for instance 2-branes, 5-branes, etc. and there is belief too of a 0-dimensional brane which seems to imply it is point-like, but a closed-loop string would be attached to it, giving it the needed planck-scale size string-theory says every object must have or exceed.

If you're interested in how m-theory relates to cosmology one route you could research is brane-world cosmology, which suggests that we could be living on a 3-dimensional brane and provides ideas for what caused the big bang, etc. But again as marcus said that still probably belongs in beyond the standard model, as this is 100% speculation. String theory doesn't even have fully known equations yet, but rather approximations with which to make predictions, much less m-theory which even less is known about so it isn't even a mathematical curiousity that might not be true but makes the correct predictions, it is only potentially a mathematical curiousity when we know the full equations, and that curiousity could potentially be a real theory.

Excuse me but I have some stupid questions. I am just a lowly mechanical engineer who enjoys cosmology and mainly reads a lot of the threads but these questions have been bothering me for some time. I hope somebody can answer: If we find that string theory is a workable theory by experiment do we have any theory that describes what strings are made of? What causes them to vibrate? And why would they vibrate in different modes to give the different particles? And what propogated the strings? Or have they always existed?

Excuse me but I have some stupid questions. I am just a lowly mechanical engineer who enjoys cosmology and mainly reads a lot of the threads but these questions have been bothering me for some time. I hope somebody can answer: If we find that string theory is a workable theory by experiment do we have any theory that describes what strings are made of? What causes them to vibrate? And why would they vibrate in different modes to give the different particles? And what propogated the strings? Or have they always existed?

As far as what strings are made of I understand that in string theory they are fundamental and not really composed of anything (verification from anyone?). I have no idea what actually makes them vibrate or chooses the pattern that they vibrate in, but there are some interesting ideas discussed here https://www.physicsforums.com/archive/index.php/t-356471.html

Thanks Taxonwrath. I appreciate the thread you shared. I suspected that the theory was not as developed as most people think. The string theory is a mathematical model that works for identifying a unified theory of the four fundamental forces of nature. Whether the mathematical model has any basis in true reality, I guess we will have to wait for experimental data.

Thanks Taxonwrath. I appreciate the thread you shared. I suspected that the theory was not as developed as most people think. The string theory is a mathematical model that works for identifying a unified theory of the four fundamental forces of nature. Whether the mathematical model has any basis in true reality, I guess we will have to wait for experimental data.

Well I am not really sure on how developed people think it is, but for the experimental data, I am not sure if we will see any given that it deals with a fundamental particle on the Plank length. However, it has offered working solutions to problems where there were none and that is about as close to experimental data as I think we will get (for a long while).

The data most people are holding out for though is along the lines of predicting the masses of particles. I believe Brian Greene addressed that somewhat in The Elegant Universe and may touch up on it more with his new book, about how that may be asking too much from a TOE.

Yes. I agree. I read somewhere we would need a particle accelerator the diameter of the Milky Way Galaxy in order to identify a string particle. There are indirect experimental methods they are trying to develop that would prove string theory by inference: If this, then that. I think, it is some sort of cause and effect experiment but I do not recall the details of the test at this point.

Apparently "dimension" has different meanings to different people. Simply speaking of dimensions other than that in which we live is outside human realm of definition and becomes philosophical theory unprovable in human terms.
There is much universal knowledge human intelligence is not priviledge to; perhaps for good reason; but equally as possible that human intelligence simply cannot fathom.
We just aren't smart enough to answer such questions; not to say that one day something will happen to make us smart enough; or the proof will somehow be made available; but until then; we can enjoy all manner of unproven theory and philosophy unfettered by human imagination.
Consider the possibility that things in other dimensions do not exist as those things in our dimension; that even human thinking is altered or even impossible in other dimensions; that even existence of anything in another dimension does not adhere to the physics of our current known dimensions; or even that our reality is anything but; simply a figment of our own boundless imagination.