Why More Than 3 Spatial Dimensions?

[one_raven]

I asked this in another thread on this forum, and did not get an answer, so I decided to make a thread of it.

Let me ask a question (phrased as mutiple questions)...
Please temorarily disregard the "Is time/spacetime a spatial, temporal or neither dimesion?" argument for the sake of this question...

What is the necessity of conceptualizing more than three spatial dimensions?
Other than to fill in the blanks of the vairous unnecessary string (or brane) hypotheses (I really wish people would refrain from refrring to them as "Theories" being that not one of them can rightfully be considered a theory), interesting sci-fi plot-lines and pretty pictures, what is the purpose of it?
What makes anyone think they exist?
What valid evidence is there to support, or even suggest, them?
(BTW, being a required integral aspect of incomplete conceptualized physics hypotheses does not count as valid evidence in my humble opinion)
Is there any independant evidence for them?
Simply...
Why?

 

[alkaline]

There are three camps:

1. small-higher-dimension camp: people who talk about string theory and related theories.
2. higher-dimensional geometry: higher dimensional polytopes, topology, etc
3. possibility of higher-dimensional life

I'm in camp number 3. It's a hobby to me, and i know that it's actually not possible for higher-dimensional life to exist (as far as we know). I just find it fun to think about how the world would work with a fourth spatial dimension - it's a very mind-expanding exercise, and it really works your brain. I have a webpage for it:

Fourth Dimension: Tetraspace

I'll let the other people speak for their respective camps.

 

[one_raven]

I have always pondered on the possibility (though, like you, don't really look at it as a relaity, just a fun possibility) that other beings share the same three dimensions with us, however interact with different vibration frequencies, therefore, in a sense, exist on a different "plane" (if you will) of existence.

For example, the resonant frequency of the matter these beings are made of would be around (slightly above/below) the frequency of what we refer to as "visible light".
Maybe this is what ghosts are?
Aliens?
etc.

Perhaps they can see us, perhaps not.
Maybe they can observe us, but can not interact or interfere with us in any way.

Blah blah blah.

So I do understand where you are coming from, and even appreciate all the work and thought you have put into it.

Anyway, thses things are fun to play with, but how much of a serious look do they deserve from science?

Where is the line between science and sci-fi?
Where is teh line between physics and meta-physics?
These lines seem to be getting more and more blurry with each new "theory".

 

[MythioS]

I'm not sure exactly where your coming from when you say you don't understand why there's more then 3 dimensions yet you want to disclude special theory of relativity or general relativity.. cause that pretty much goes into why another dimension was required to more accuratly describe gravity.

 

[one_raven]

I am sorry, I guess I wasn't being as clear as I was hoping (which sometimes happens when talking about such things).

I just didn't want to get into the typical semantics debate over whether time is a spatial dimension, a temporal dimension, not a dimension etc...

I am talking about beyond the three spatial dimensions and time.
Other than those 4 (or 3) dimensions, why add more?
What is the justification for it?

 

[selfAdjoint]

When physicsts invented the math of string theory they found that it had the dimension of specetime in it as a variable. The first kind of string theory they studied said that spacetime has 26 dimensions. The theory wouldn't work unless that was so.

The original sting theory couldn't do all kinds of particles, so they added supersymetry and invented superstring theory. This one said number of dimensions = 10. That's the number you hear most. There turned out to be 5 kinds of superstring theory, all with D = 10.

When they unified the 5 kinds and got M theory, they added one more dimension in the process, so D is now 11, and that's held up for several years now.

 

[whiterabbit]

I would like to clarify the explanation of the last post a bit.

The whole extra dimension business is actually quite old. It goes back (as for as I know) to ideas of Kaluza and Klein at the beginning of the last century [1,2]. They tried to unify general reltivity with Maxwells electromagnetic theory and had the idea to use an additional (comapct, i.e. circular) fifth dimension to account for the U(1) symmetry of em. The charge associated to this symmetry (Noether's theorem) is the electromagnetic charge.
Here starts the interesting part, which is essentially used like this for 80 years now. Take some (compact) space with internal symmetry and use it as additional space to the usual Minkowski spacetime. There are several subleties to play with (e.g. "warped" or "twisted" compactifications etc.) but the concept is always the same - you get the internal symmetries of your theory (e.g. the SU(3)xSU(2)xU(1) of the standard model) from the symmetries of your compact space.
All this stuff has nothing to do with string theory, not even qft. As mentioned in the last post - superstring theory needs 10 dimensions and then there is the mysterious eleventh one (but I would really appreciate if someone could explain me the deep reason for this, besides the fact that 11 is the maximal dimension for supergravity). Anyway - we need to get rid of them, because all we see are four dimensions - and here Kaluza and Klein come in again. Most ideas to compactify superstring theory or M theory involve compact six or seven dimensional manifolds (with special properties to get something like the standard model or a susy extension of it).

So what's the upshot? People are using extra (spacial) dimensions in the spirit of Einstein's big dream - the explanation of all physics in terms of geometry. And because physics has more interactions besides gravity and because of that more symmetries besides Poincaré symmetry it is tempting to use additional (comapact) dimensions for them.

I don't know whether my confusing explanations helped to shed some light on this issue, but there are some nice popular articles on this issue, try for example John Baez's website for some serious information (try the physics FAQ): http://math.ucr.edu/home/baez/

[1] - T. Kaluza, On the problem of unity in physics, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) K1 (1921), 966-972
[2] - O. Klein, Quantum theory and five-dimensional theory of relativity, Z. Phys. 37 (1926), 895-906

 

[modmans2ndcoming]

there is a postulation

that has worked well for physicists, it is called symetry.

when an equation is balanced, it is considered symetric. symetric representations of the physical world correspond to real world observable events, so wehn you are trying to explain an observation of the universe, such as electromagnetic forces, the symetry of QED works eevry time so far for predicting what will happen, this leads us to believe that if we can accuratly predict what an event will do with an equation that is symetrical, it is probably true and it becomes a theory (though there is certainly more evidence built up than just a check mark on symetry and prediction, but this is a simple explanation so bear that in mind)

the equations involved in Super String Theory are symetrical and have explained things like what is matter and what is energy while holding true to what we can see about matter and energy.

so a lot of theoretical physics deals with analysis of systems of equations, and off of that, is what you begin to base a theory on. just because something is not the size of your TV does not mean it is not true.

 

[rtharbaugh1]

In one preceeding post Whiterabbit said:

"All this stuff has nothing to do with string theory, not even qft. As mentioned in the last post - superstring theory needs 10 dimensions and then there is the mysterious eleventh one (but I would really appreciate if someone could explain me the deep reason for this, besides the fact that 11 is the maximal dimension for supergravity). Anyway - we need to get rid of them, because all we see are four dimensions - and here Kaluza and Klein come "

Three dimensions could be curled up in a Planck sphere, and two of those curled up spheres makes six curled up dimensions. I would suggest one sphere could be thought of as the past (Planck time) instant, and one as the future instant. They are not really "smaller" you know, in any sense of containing less information anyway. They are seen as smaller for the same reason any other offset causes an apparent reduction. They are "farther away," where farther can and does take place in ways that seem to the observer to be matters of scale. By this trick of higher dimensional perspectives, we see, from any present instant position, a lower dimensional image which by benefit of previously set down decisions can be interpreted to have higher dimensional meaning. We do this as a regular and unappreciated habit when we look at an image on a screen. Then depth illusion can be enhanced by using a double image printed in two colors and very slightly offset, then wearing lenses over the two eyes to give the right eye a slightly different view from the left eye. Our brains are used to merging the two images into one "three dimensional" picture.

In fact it is possible to represent higher dimensionalities on lower dimensional structures in several ways. Shadows, projections, unfoldings, repetitions, movies are some examples. We are very used, is scholastic circles anyway, to looking at and interpreting many dimensions of information on limited surfaces.

Holographs are still somewhat crude, at least the ones I have seen, but do illustrate the concept. But once you have the concept of a hologram as a two dimensional presentation of three dimensional space, you should also be able to see how a movie camera panning along track can also present the higher dimensions of an object. I am thinking just now of the monorail at Disney, and how you curve around some groundscapes where topiary trees are visible to the minds eye, even years after the trip, from any direction. I can remember how the elephant's trunk curved above her back at an angle, and the reveal of a fountain.

So it is not a problem for most academics to see that there are many more than three dimensions available when describing an object. In fact part of the problem of description is that there are so many many ways to describe a thing. Part of the job of intelligence is to limit the data down to a summary statement that is concise. You want to be able to describe an object fully, but using as few a number of dimensions as possible.

I am trying to show that we are already higher dimensional creatures. We merely need to learn to identify the dimensions that are necessary and sufficient to the condition we are attempting to describe. Three dimensions of space is really all we need to describe our local events, and one of time. You see that the time line is a dimension also. However, when conditions close to singularities are considered, it is not enough to merely speak of the three spatial dimensions and one of time, because the space and time of the three dimensions is being warped and eventually crumpled. In such conditions it is no longer meaningful to speak of a length of say a meter, because with space bent so tightly, the meter is different in adjacent places. It is as if you might make a mark on a wall with the meter stick, then rotate the meter stick or move it about the room. When you go back to the wall and measure again, the meter stick will seem to be longer or shorter than before. Now you need to see another dimension, the dimension in which the surfaces are warped, before you can see that a meter is a meter. We like it when our meters stay the same. A watch is not much good if it is only correct twice a day. So in the neighborhood of singularities, we need to know about the ways that flat space can be made to crumple. Our universe is thought to be flat. What does it mean to bend three dimensions into a fourth dimensional space? The laboratory for our discussion of this topic has to be the black hole, the big bang, the Planck quanta, and perhaps the farthest ends of the universe. The only one of these four regions that is available to us right now in any useful sense is the Planck quanta. We can and do examine events on very small scales in real spacetime laboratories like Fermi and Chern and others. The impact of gold nuclei on each other at 99.99% c was discussed a few days ago on NPR Science Friday. These collisions are now said to have liberated quarks and gluons into a pre-nucleon plasma.

Thanks for any comments.

Richard