# Extra dimensions and weakness of gravity

1. Jan 22, 2014

### kochanskij

I often read about the weakness of gravity being explained by gravity leaking into extra space dimensions. But, if there is a large 4th space dimension that only gravity can access, that would make gravity follow an inverse cube law. Observation clearly shows an inverse square law that Newton predicted. More large space dimensions would produce an even higher inverse power law for gravity. So extra dimensions can not be large.

If the extra space dimensions are on the order of the plank length and are too small to observe, then the weakening of gravity due to leakage into the small dimensions would only become noticeable near the plank length. So gravity should be very strong at everyday scales. But it is not.

So how can leakage into extra dimensions be used to explain the weakness of gravity?

This is true if the 4th dimension is infinite; however, in most approaches that use extra dimensions to address the hierarchy problem/weak gravity, the extra dimensions are compactified at some scale, say $R$. Then, for point masses with a separation, $r \gg R$, one has $V(r) \sim 1/r$ because the gravitational flux lines do not extend through the extra dimensions. See the Arkani-Hamed-Dimopoulos-Dvali (ADD) model for more details.