Why Gravity is Weak

Perhaps you are familiar with some of the more exotic and far-out theories that attempt to explain why gravity is so weak compared to, say, electromagnetism. One of my favorites involves gravitons hiding in extra dimensions. The logic is as follows: if gravitons weren't hiding in extra dimensions, gravity would be much stronger. It's analogous to someone screaming at the top of his lungs. The intensity of the sound is very strong until you hide that person away in a broom closet and lock the door.

As much as I like this theory, it has a problem that can't be hidden in a closet or extra dimension: there is no empirical evidence of extra dimensions. That begs the question: is it possible to explain gravity's weakness without using extra dimensions? Yes! When doing physics, I prefer taking an Occam's razor approach and using concepts and ideas that are testable and/or have been tested and confirmed. The end result is not as exciting as extra dimensions--but more likely to be true.

Let's begin with Einstein's field equations:

To simplify matters we equate the left side of equation 1 to K:

In equation 3 above, we have energy density (T44) multiplied by a constant that consists of G and c. Why do we need such a constant? Why can't we get by using equations 4 and 5 below?

The constant in question is a very small number and substantially reduces the value of K, the spacetime curvature. Perhaps equations 6 through 8 can shed some light on the subject:

Imagine energy (E) interacting with a cubic meter of spacetime. Equation 6 shows that spacetime energy density (Ts) is a tiny number. Since curved spacetime causes gravity, and since spactime's energy is so weak, is it any wonder that gravity is weak? Let's see if the math agrees. Equations 7 and 8 are the average radius of a nucleus and the nucleus volume respectively. Why are these numbers important? Imagine energy (E) added to a cubic meter of spacetime. To see how that energy interacts with spacetime, it's easier to take all spacetime's energy and reduce it to a particle. We do the same with the added energy. So we have a particle interacting with another particle within a cubic meter. Spacetime's total energy is equivalent to a proton's. We can imagine it having an approximate radius of e-15 meters and a volume of e-45 cubic meters. Our energy particle will have the same dimensions.

To provide a simple visual demonstration of the interaction between matter and spacetime, let's pretend that the volume of our spacetime proton is .25 cubic meters and that the energy particle we add has a .25 probability of interacting with it.

Because the probability of interaction is .25, the average energy ends up being .25 the total energy. To get the proper value for K, we would need to multiply E/m^3 by a constant of .25. So K is weaker than E/m^3. To illustrate the point further, let's distribute the energy evenly throughout the cubic meter. This time it will be a field of isotropic energy interacting with our spacetime proton:

At any given time, only 25% of the energy field interacts with the spacetime proton. The remaining 75% contributes nothing to the value of K. To drive this point completely home, let's cut up the spacetime proton and evenly distribute it within the cubic meter:

As you can see, it matters not how we distribute the matter energy and spacetime energy. In the case above, only 25% of the total matter energy interacts with the spacetime energy. Our constant of .25 remains constant. Now, let's stop pretending and let's replace the .25 constant with the volume of a nucleus, which is approximately e-45 m^3.

If e-45 is the right constant, then that means only e-45 of the energy contained in T44 contributes to K. Let's check it:

It looks as though it's in the ballpark of the actual constant used in Einstein's field equations. So it's highly plausible that gravity is weak due to energy interacting with very weak spacetime energy.