# Are small extra space-time dimensions represented correctly?

1. Jun 13, 2013

### bpmirsch

Are "small" extra space-time dimensions represented correctly?

This is my first post, I searched briefly but I apologize if this is a commonly covered topic!

The following is written in the spirit of the "aether" -- that, being an overcomplication with no evidence.

One of my biggest stumbling blocks so far in learning about various ‘modern physics’ topics is the premise of extra space-time dimensions. My background is in Mechanical Engineering with a concentration in Robotics; I understand mappings and I can see how physical state variables may be physical in nature but not dependent in the vector sense.

i.e. a robot with a x,y,z position and roll,pitch,yaw headings – these are six physical dimensions in a configuration space that are ultimately still linearly independent.

When I hear talk of necessary extra dimensions that are assumed to be space-time constituents, explanations sometimes talk of ‘tiny circles’ or ‘really small dimensions’ or ‘travelling across the universe and ending up where you started’, etc. I must be missing something, though, because in all of those explanations, you are only travelling in the previously defined x,y,z,t dimensions, albeit via strange or miniscule trajectories. This, to me, does not constitute independent dimensions.

The issue here is not that the mathematics requires the extra dimensions, but are these dimensions explicitly defined in "physical" terms? Are there units of distance? Are these just layman explanations or is this the extent of the leading theories in physics?

2. Jun 13, 2013

### fzero

Yes, these dimensions would have a size that could be expressed in physical units. Since extra dimensions have not been observed, the best we can do with experiments is put limits on their size. In the sense that, had the dimensions been larger than a certain length scale, they would have already been observed. These limits depend on the particular model that you are studying. In a common class of models, the limit is roughly that the dimensions must be smaller than around $10^{-17}~\mathrm{m}$. See http://profmattstrassler.com/articl...mensions/how-big-could-an-extra-dimension-be/ for a discussion.

3. Jun 13, 2013

### bpmirsch

I glanced the link you gave (I obviously haven't thoroughly read it) and it illustrates my issue perfectly... The graphics shown with a large boat fitted into a canal contrast with a small boat moving in two dimensions supposedly "contained" within the canal is inherently faulty from the beginning:

Let's say the giant boat moves in the X dimension; it is unaware of the Y dimension.
The small boat moves in the X and Y dimensions, it is aware of these dimensions.

True, the Y dimension is linearly independent from the X dimension and would be considered a novel discovery in that universe. However, every analogy I've seen to purport 'extra' space dimensions in OUR universe results in a linearly dependent analogy by saying "an extra dimension would be such and such smaller than this already discovered dimension".

"Small" displacements and limiting "small" sizes seems flawed to me because we are defining them as ratios of previously known dimensions. In the boat example, the boat can remain in the same X coordinate for any Y coordinate... if we can only measure in the X coordinate, we have no way of detecting this new Y coordinate. Where does the literature say that extra dimensions in our universe HAVE to be measured in distance? That's really my question, I suppose.

4. Jun 13, 2013

### bpmirsch

also I didn't mean to imply that I WONT read the material you provided... :) I will be reading that to see if it explains things a bit.

5. Jun 13, 2013

### fzero

This should be a bit clearer if you get through the tougher parts of that link (and further discussion on other pages on Strassler's site). The particle physics experiments that attempt to measure extra dimensions do not directly measure the dimensions as we would with a ruler. They rely on the notion that an extra compact space dimension would lead to so-called Kaluza-Klein particle states. For each particle we have observed, such as the electron, there is a tower of KK-states coming from quantum states that extend into the extra dimension. The mass of these states depends inversely on the size of the extra dimension. We can say that not having yet observed a KK-particle at LHC energies means that the size of the extra dimensions must be at least as small as the figure quoted.

6. Jun 14, 2013

### bpmirsch

OK, I am thinking of the projection of a shadow onto a piece of paper, mapping 3D to 2D.

Can you point me in the direction of the equations/theorems that explicitly give these extra dimensions units of length?