Solution Via Extra Dimensions
If we live in a 3+1 dimensional world, then we calculate the Gravitational Force via Gauss' law for gravity:
- (1)
which is simply Newton's law of gravitation. Note that Newton's constant G can be rewritten in terms of the Planck mass.
If we extend this idea to extra dimensions, then we get:
- (2)
where is the 3+1+ dimensional Planck mass. However, we are assuming that these extra dimensions are the same size as the normal 3+1 dimensions. Let us say that the extra dimensions are of size n <<< than normal dimensions. If we let r << n, then we get (2). However, if we let r >> n, then we get our usual Newton's law. However, when r >> n, the flux in the extra dimensions becomes a constant, because there is no extra room for gravitational flux to flow through. Thus the flux will be proportional to because this is the flux in the extra dimensions. The formula is:
which gives:
Thus the fundamental Planck mass (the extra dimensional one) could actually be small, meaning that gravity is actually strong, but this must be compensated by the number of the extra dimensions and their size. Physically, this means that gravity is weak because there is a loss of flux to the extra dimensions.
This section adapted from "Quantum Field Theory in a Nutshell" by A. Zee.
Read more about this topic: Hierarchy Problem
Famous quotes containing the words solution, extra and/or dimensions:
“There is a lot of talk now about metal detectors and gun control. Both are good things. But they are no more a solution than forks and spoons are a solution to world hunger.”
—Anna Quindlen (b. 1953)
“But that beginning was wiped out in fear
The day I swung suspended with the grapes,
And was come after like Eurydice
And brought down safely from the upper regions;
And the life I live nows an extra life
I can waste as I please on whom I please.”
—Robert Frost (18741963)
“I was surprised by Joes asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (18171862)