Quote:
Originally Posted by cmsavage
Yes, it is due to the extra dimensions being compact. Take a look at this link: the gravitational potential scales as 1/r^(d+1) for r << L and as 1/r for r >> L, for d compact dimensions of size L.
The difference from a non-Newtonian force becomes highly suppressed at larger distances, with corrections on the order of (L/r)^2. If there was a "large" extra dimension of size 1 micrometer, then the variation of the force between the Earth and Sun (150 million km apart) would be about one part in 10^34, well beyond what we are capable of measuring (and may ever be capable of measuring). To search for extra dimensions, you want to look at variations of Newton's Law at small distances. However, gravity is pretty weak and it is difficult to measure it on such small scales since electromagnetic forces have such a huge effect on objects small enough to put only 1 mm or less apart (and Earth's gravity is a huge background that must be dealt with). That is why we currently only have upper limits of around mm's, even though we can see (using photons) much smaller distances (photons can be constrained to a brane and do not have to behave the same way as gravity).
I put "large" extra dimensions in quotes above because, in extra dimension papers and discussions, the "large" is relative to the Planck scale and is not associated with how we view the traditional 3 non-compact dimensions (which are obviously large). That is, an extra dimension can be 1/1000 the size of a nucleus, far smaller than the experimental limits, and would still be considered "large" because it is much larger than the Planck scale.
Because the variation gets smaller with larger distances, as noted above, the non-Newtonian effect is negligible on planetary scales, much less galactic scales.
If you have other branes near our brane that have massive objects, that is a different story. I suppose you can have gravitational interactions between particles on two different nearby branes (this has nothing to do with non-Newtonian forces), but I don't know enough about branes to say much about this. |
Sorry for the delay.
OK, I had a look at the link, and this is my interpretation on it:
The GaussīLaw holds for N spacial dimensions.
Ken G was right on that.
The inverse N-1 law for the field would hold for N spacial dimensions. An inverse N-2 law applies to the potential (as expected). Just N is ajusted on diferent scales for the number of spacial dimensions which still can count for something, as a result of the enclosing hypersurface the field has to cross being spaghetti-like.
If one or more (but not all) of the extra dimensions was bigger than Planck scale, we would have another different, intermediate variation on
r between the extreme scales (Planckīs and macroscopic). Cute.
Gravity potential spreads across all the dimensions in the brane, but no reference is made of gravity leaking across branes, at least in the linked page about hypergravity. Would have to look at the rest of the site though. And I still have the paper
Arituay mentioned to look at.
One thought: it looks like
stringbranists are using this to justify why gravity looks diminished. Unstated but implied is that they are comparing it to the electromagnetic field. But this poses two problems:
1. Why should gravity be comparable to the electromagnetic field? For peace of mind? I imagine they are trying at TGU but have they succeded? Why not to think that gravity has just its own order of magnitude? Would TGU really need gravity to be of comparable value to the other long range field?
2. If other (small scale, curled) dimensions exist, why would not EM spread through them just as gravity would? The only thing I can think that might prevent EM from doing so would be the elemental concentrations of charge having a size (do they really have a size?) bigger than the Planckīs lenght (since this is the size that it is postulated for the extra dimensions) while the elemental concentrations of mass would be smaller than the size of the extra dimensions. I donīt want to suggest singularities, but it looks close. The curious thing is that every particle with both a charge and a mass would have two different sizes, one for charge, one for mass.