Are extra dimensions provable?

[Niaboc67]

I understand that we live in a 3D world. X,Y,Z...Up-Down, Left-Right, Frontwards-Backwards. But I hear theoretically ideas of the 4th dimension, time? As well as String Theory with as many as 11-dimensions. Are any of these higher/lower dimensions provable? And is the 4th dimension that is talked about fairly often correlated with the 4th dimension of the 11-dimensions of String Theory? As well is our 3D space the first 3 Dimensions of the 11-dimesional string-theory world? or is this something completely different?

Thank You

 

[Simon Bridge]

Depends what the "extra dimensions" mean.

We can certainly prove that we need more than three orthogonal axes to keep track of things the regular space ... even without invoking relativity we need space vs time graphs.

I remember an example from a lecture - a 10-speed bike can be modeled by giving it one exis for each degree of freedom for it's motion. So it can occupy positions on the road surface, which is 3D. Then it has 10 gears ... for 10 discrete points on another axis. Then it may tilt - that's another axis. The front wheel rotated with the handlebars... I count 6 dimensions so far: see what I mean? That's a perfectly ordinary object.

The note that we need a 4D (we actually say 3+1D) space-time comes from the demonstration that we can mix up space and time dimensions a bit like we can mix up two space dimensions (by going diagonally).

This should not be confused with the "travelling to other dimensions" in SciFi or the metaphorical "higher dimensions" in pseudoscience or mysticism.

 

[nejibanana]

From what I've read on string theory, extra dimensions would alter our law of gravitation. For our typical 3-D universe, the law of gravitation is an inverse square law. For 4-D it would be an inverse cubic law, 5-D is an inverse quartic and so on. The main problem is that the higher the dimension, the smaller the scale that these deviations from the inverse square law are applicable. Since gravity is such a weak force, it is hard to do an experiment to test this, because electromagnetic forces dominate at those scales. There are some experiments that have tried to test this, however they don't measure down to a small enough scale.

Zwiebach's Introduction to String Theory has a good section on this stuff.

 

[Chronos]

We have no compelling evidence of extra dimensions, despite their appeal.

 

[DriftGlass]

As nejibanana says, there are in theory ways to test their existence. Our experimental ability isn't anywhere near sensitive, however. If extra dimensions are compactifed very small then there should in principle be discrepancies in energy levels of states and of gravitational strength as measured above.

As for whether our dimensions are the same as those included in the 10 or 11 dimensional theory, one would hope so! Otherwise it wouldn't be a very realistic theory, albeit interesting. Ours wouldn't necessarily be the "first 3" spatial dimensions of string theory; rather they would be any arbitrary 3. Any perpendicular dimensions can just be relabelled and "first" has no meaning.

 

[Chronos]

In science, you first establish the need for some hitherto unknown property of the universe, then you confirm its existence by empirical methods. String theory provides a theoretical basis for extra dimensions. What is lacking is evidence of their existence. That, of course, is subject to change. There was some hope the LHC would provide evidence in the form of some unknown, exotic particle. No such particle has been detected to date. See http://home.web.cern.ch/about/physics/extra-dimensions-gravitons-and-tiny-black-holes for discussion.