# Gravity in higher dimensions

1. Sep 2, 2009

### wendten

according to string theory, gravity got the ability to escape the D-brane of witch all matter is bound. The reason is that the boson carrying the gravity is a loop-string, with no open ends linking to the brane.. this theory should explain why the gravity is so much weaker than the other forces.

but, the way gravity is decreasing by distance is spherical(3Dimensional), by newtons law of gravity:
$$F = \frac{G \cdot m_{1} \cdot m_{2}}{r^{2}}$$

witch indicates that there is no gravity lost to higher dimensions

my question now is: why does scientists state that gravity can escape our brane?

2. Sep 2, 2009

### humanino

Because the projection of a hypersphere on a three-dimensional "brane" still remains a sphere, the modification of the above formula for gravity is not in the exponent 2, it is in the coupling constant. The number 2 stems from the dimension of the projection of the hypersphere, it is our observable sphere. Gauss theorems still remains valid : whatever 99% of gravity which would have leaked out did leak out and we lost it there forever, whatever 1% of gravity which remains in our 3-dimensional subspace remains here.

3. Sep 2, 2009

### Finbar

Because the extra dimensions are said to be compactified or restricted to some small radius gravity will seem to be 3d at large distances. But for small distances we expect that the force law will change to $$1/r^{2+n}$$ where n is the number of extra dimensions.

4. Sep 3, 2009

### wendten

but won't the intensity be increased near the center of the sphere?
like if you are projection light though a glass sphere on a paper, where the geometrical form will be a filled circle, but with a darker fill in the center? as $$1/r^{2}$$

why? doesn't it has a higher dimensional angle, that will make it escape in a certain distance from the admitting source?

5. Sep 3, 2009

### wendten

ok, so not all higher dimensional angles are allowed? and only the fraction of the gravity following a path parallel to our brane, is experienced?

6. Sep 3, 2009

### Naty1

My reading supports Finbar's post # 4 answer....

Humanos posts includes: "Because the projection of a hypersphere on a three-dimensional "brane" still remains a sphere, the modification of the above formula for gravity is not in the exponent 2.."

Doesn't the leakage depend on the other dimensions... NOT the brane(s)....??,

Experiments to date (so far, that is) with Casimir apparatus confirms inverse square law...but the story ending has not yet been written.

Humano's post includes:

Can anyone explain?? This seems illogical on the surface but I'm not sure I understand it.

Last edited: Sep 3, 2009
7. Sep 4, 2009

### humanino

Whether the modification bears on the coupling or the exponent depends on the size of additional dimensions. If you have small additional compact dimensions, then as you probe gravity to scales comparable to the additional dimensions you do get modification of the exponent. If however we assume all dimensions are equivalent, in particular if we do not assume that additional dimensions should be compact, then the flux through our slice of the hypersphere remains constant, provided the flux is divergenceless, or say uniform on the hypersphere.

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