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:
“Let us begin to understand the argument.
There is a solution to everything: Science.”
—Allen Tate (1899–1979)
“When a lady of wealth, is seen roaming about in search of cheaper articles, or trying to beat down a shopkeeper, or making a close bargain with those she employs, the impropriety is glaring to all minds. A person of wealth has no occasion to spend time in looking for extra cheap articles; her time could be more profitably employed in distributing to the wants of others. And the practice of beating down tradespeople, is vulgar and degrading, in any one.”
—Catherine E. Beecher (1800–1878)
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)