Dimensions

Recently saw a video that was pretty convincing that 10 dimensions are the maximum.

http://www.youtube.com/watch?v=qU1fixMAObI

Superstring theory is apparently based on there being 10 dimensions.

10 dimensions are required to make sense of the crazy math that is required to account for quantum weirdness. Therefor there are 10. Unless of course, the weirdness can be accounted for in some completely different way. In which case, we don't know ****.

I see that video on visualizing the 10 dimensions, and I wonder if in a hundred years people won't be looking back on us laughing at a system as seemingly absurd as the flat earth seems to us today.

We have, as yet, no reason to believe that there are more than the three space and one time dimension that we experience. Quantum theory does not require nor can it be modeled in higher dimensions. String theory, which was never a theory since it could not make observable predictions, or even calculate any physical quantity past the first level of approximation has been superseded by M-theory, which has the same issues as did the strings.

Interestingly it was the string theorist back in the late 80's that said that a conformaly invariant theory could not be made with higher dimensional objects than strings i.e. the membranes of M theory. After twenty years of trying to get string theory to work, with no luck, they suddenly got religion and moved to M-Theory

Short answer: the answer will be 3+1 = 4 dimensions for the foreseeable future. Hope that helps.

Thanks for the replies guys. I watched that video and it made sense on paper but i just can't seem to see how it would work in the real world. I can't concieve of a way to "bend or fold" through a dimension, considering that dimensions are not physical things.

That's because it's a theoretical construct, not the real, observable, world.

So if it is just a theoretical construct it doesn't apply to the real world?

If you are then that makes a pretty weak argument for the extra dimensions. This would mean that the # of dimensions is only limited by the amount people can visualize.

Maybe i should have worded my original post differently.

It seems that there are 2 answers to my question. There are a differing number of dimensions depending on what theory you read. But still only 4 real physical dimensions.

P.S - I realise that you may have just been pointing out the difference between the real world and the theoretical, just posting my train of thought.

Re: Dimensions


I began a similar thread some years ago. Here's the link, if you want to browse the responses I got there:

http://www.able2know.org/forums/viewtopic.php?t=80059

Mathematicians find 248-dimensional object.

i recently saw a very good and interesting documentary kind of movie "program". its called "The Elegant Universe". it talks about the different forces on earth (gravitational, electromagnetical) and tries to make a master formula to conect all these forces together, it somewhat talks about the creation of the universe and the dimensions of it. i think you should watch it (and any1 else interested). although it is 3 hours long, start watching it and im sure you would want to watch all of it (atleast i did)

The Elegant Universe | PBS

Hello there,

M-theory is a unified string theory so I wouldn't go about saying the latter has been discarded! Moreover the five string theories require 10, 11 or 26 dimensions.

If there are extra dimensions, they could be rationalized as follows:

1) "Ordinary" motion in these dimensions is infinitesimal.
2) Our minds and senses have a way of mapping everything onto 3-4 dimensions because they have no way of representing higher dimensions. Sort of like the mapping of 3 dimensions onto 2 as in a photograph.

Another possibility is that the mathematical representation of nature finds its most convenient expression in higher dimensionality but they are only a construct. I am reminded say of the thermodynamic potentials such as entropy or free energy which are not "real" in the sense that they can be directly experienced or measured. Similarly the "dual particle/wave" nature of light derives credence because of the ability to draw familiar metaphors. In reality light is neither like a particle nor a wave - it is like light.

You can think of string theory like quantum theory in that it makes predictions for extremely "unusual" circumstances such as the high energies between sub-atomic particles or at the center of a black hole (an object so massive that its atoms have actually collapsed under its own weight!).

Of course QM has made many many many correct predictions (without which this forum would not be possible). So even though it is rather crazy, it works quite well. The same can be said for the somewhat older theory of electromagnetism.

Physicists are working on developing instruments that are sensitive enough to test string theory. This requires probing exceedingly small (some would say useless) length and time scales.

/Kayyam

Re: Dimensions


Silus - what was the model with the 248 dimensions? If you're referring to E8 (Lie algebra) it doesn't really have 248 dimensions: the underlying dimensions never exceed 8 (eight) in any notional sense (the number 248 is just the number of roots to the equations involved, i.e. not real dimensions).
http://aimath.org/E8/e8.html

That's why it's called E8 to begin with

If you'd like something more advanced, these are 2 reasonably recent papers; not sure if they help with your question:



I'm posting abstracts of both papers as you may not be able to find them online:

1. We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates [.....] extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The "extra dimensions" are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb-Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe-Tucker action in curved C-space.

2. The octonionic geometry (gravity) ......... is extended to noncommutative and nonassociative space time coordinates associated with octonionic-valued coordinates and momenta. [.........] the energy-momentum dispersion relations without violating Lorentz invariance as it occurs with Hopf algebraic deformations of the Poincare algebra. The known octonionic realizations of the Clifford Cl(8), Cl(4) algebras should permit the construction of octonionic string actions that should have a correspondence with ordinary string actions for strings moving in a curved Clifford-space target background associated with a Cl(3, 1) algebra.

LOL - I got a PM telling me these later examples were too difficult, so here's the simplest one I can come up with:


http://math.ucr.edu/home/baez/lectures.html

That covers the (8+2=10) ten dimensions of the string theorists as well. So in answer to the original question: the number of dimensions is 10 at most, though for purposes of getting roots of equations we can assume there are more.

The most honest reply is we don't know. We have predictive models of reality that we can't fully validate yet.

Until we deeply understand our framework of existence we can't define its underlying structure such as number of defining dimensions.

Your question borders on search for the ultimate truth of all things, we really don't know is the only honest answer. We have many models at present - but they are a long way off being either complete or validated by any serious experimentation.