Thread: Does anyone know of a geometric model of the four forces?

A 'plot' of the strengths of gravity, electromagnatism, weak, and strong forces?

Strength on the 'Y' axis, distance over which the act on the X axis?

Originally Posted by nmurphy24

A 'plot' of the strengths of gravity, electromagnatism, weak, and strong forces?

Strength on the 'Y' axis, distance over which the act on the X axis?

It would be nice if things were that simple, but unfortunately, these four forces aren't quite that simple.

Simple measurement such as temperature, distance, and mass are scalars, as they exist without respect to direction. Meanwhile, vectors include entities such as distance+direction, velocity+direction (change in distance over time), and acceleration+direction (change in velocity over time). The key is obviously one of direction!

While both scalars and vectors are themselves tensors, a tensor also describes relationships between scalars, vectors, and other tensors. Tensors are important in physics, because they describe the relationships between things such as elasticity, fluid mechanics, and general relativity (including gravity). Unlike scalars and vectors, tensors are also able to express density, as in gravimetric potential at a point, or the permeativity of various materials.

In answer to your question, there's no such plot. However, here is a chart depicting the relationship between the various forces in the Theory of Everything (one step beyond Grand Unified Theory).

One could make such a plot, but the "strength" of the individual forces usually determines the distance over which they act. So, it would be a little like plotting something versus itself.

But there's a more interesting answer.

When people (physicists, anyway) talk about the "strength" of a force, they are usually talking about the "coupling constant," and this is usually plotted versus energy. This was the focus of unification theories. When you make this plot and see that the coupling constants of two forces merge above a certain energy, then those two forces are considered to be "unified." It was hoped, several years ago that there was one energy where all of the constants meet, and the strong, weak, and electromagnetic forces would be unified.

Here's an example of a plot like I describe:

Grand Unification Theory

Now, the energy is usually associated with collider experiments, since these are the best instruments for probing this kind of physics. In colliders, when one raises the kinetic energy, one generally gets the consituents of the particles closer together (i.e. you are smooshing them together with more "force"). So, there is a distance scale implicit in these plots.

So, if you could re-make the constant versus energy plot as constant versus distance scale, that might be something like what you were asking for.

Oh, and I forgot to mention that this is related to something called the "Hierarchy problem," which can be summed up as: "Why to the forces have such vastly different strengths (coupling constants), and why are they in that order"

At least that's a hierarchy problem. The term is more general than just what I wrote above.