# Multi-dimensional grand unification?

Einstein used reinman geometry (a kind of non-euclidean geometry where there are no parralel lines and other stuff) to describe how mass warps a four dimensional field (length, width, depth, time) and thus describes gravity.
this is the General Theory of Relativity

http://library.thinkquest.org/27930/media/metrictensor.gif

Later, The kaluza-Klein theory arose by adding one dimension to the General Theory of Relativity to give both gravity AND electromagnetism, the force which manifests itself as electricity, magnetizm, light, and chemical bonds.

http://feynman.physics.lsa.umich.edu/seminars/oklecture/oklecture11.gif

Eventially, you could add another twodeminsions to give the weak nuclear force, which is responsible for some kinds of nuclear decay, and finally four more dimensions to describe how quarks form together to make protons and neutrons.

Now, there is another little thing called the Standard Model:

which describe elementary particles by their mass, charge and spin.

A dimension is simply a linear measurement.

If space and time are dimensions, can mass, charge and spin be dimensions, too?

If so, can 11-D supergravity/supersymmetry/superstrings/M-theory have the additional three standard model dimensions added to it and yield more discoveries?

Physics grad student chiming in. What you’ve stumbled on is an idea that physicists use all the time, we call it “phase space.” Let’s say I’m studying a system composed of discrete particles that can move only in one dimension. I can plot their locations on a standard x-and-y-axis graph with x as position and y as time. OR, I can put x as position and y as momentum. That second graph is phase space.

Basically, any two (or more) quantities you can put on an axis can form their own phase space. Chemists have a graph of where the elements are plotted with nucleus size vs. stability that clearly shows the regions of extremely unstable nuclei.

As far as mass, charge, and spin goes, it’s more complicated than that. Not only does each particle have an electric charge, but also a “charge” for the weak nuclear force and for the “strong” nuclear force. Mass may be considered as the gravitational “charge.” All it means is that each particle interacts more or less strongly with the different forces in a way that we can quantify.

But while particles can move through space and time, they cannot change their rest mass, their spin, or any of their charges. So while it might be useful to plot the known particles on graphs with those axes (to see, for example, if there’s a clear sign of a particle we haven’t observed yet), they’re not dimensions like the spatial and temporal dimensions are.

Nitpick: Riemann.
Reinman geometry would be more like “parallel lines meet on ‘The People’s Court,’ gotta watch Wapner.”

Well, not exactly. “Charge”, for instance, doesn’t occupy some spatial dimension, but it does correspond to an extra dimension. What the parameters describe is gauge group representations, and those representations certainly do give extra dimensions worth considering.

As an example, electromagnetic interactions are governed by the gauge group U(1) – rotations of the circle. All simple representations of this group are one-complex-dimensional, and they’re parametrized by a single integer, which we interpret as charge (in units of the fundamental charge).

In fact, we don’t need the whole complex plane, since everything is determined by how the group acts on the unit circle. So we clip another copy of the unit circle (on which the group will act) to each point in spacetime to get five dimensions.

Mathochist, you’re correct of course (I’m actually just learning about this stuff in a math course, yay!), but what I meant was that while a particle can change its position by moving in a spatial dimension, it cannot change its charge by moving in a “charge dimension.” So in that sense it is different from the spatial and temporal dimensions.

Where does anti matter fit in?

In the context of the previous posts, you can think of the antiparticles being in that same “charge dimension,” but on the other side of the axis. For every particle, there exists an antiparticle with opposite electric charge. So if I draw the number line and put the electron at -1, the positron is at +1.

Further pushing the math angle, antimatter corresponds to dual representations of the gauge group.