Quote:
Originally Posted by sjastro
If this idea is correct then physicists have been wasting their time since the early 20th century attempting to unify gravity with the other forces. A common feature with these theories (Kaluza-Klein and String Theories) is the extension of gravity into higher dimensions that allow unification to occur. Clearly stable orbits in higher dimensions occur in these theories.
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Steven,
It depends on whether these extra dimensions are compact or not. If the extra dimensions are not compact then there are no stable orbits. On the other hand if the extra dimensions are compact there is no effect on the force law. KK and string theory assume compact extra dimensions.
Quote:
Originally Posted by sjastro
Then there is the case of observation. The rotation curves of galaxies indicate that stars well away from the galactic centre do not exhibit familiar Keplerian orbits.
This indicates that the inverse square law doesn't apply either due to the presence of dark matter perturbing the stable orbits, or gravity doesn't need to be based on the inverse square law for stable orbits to exist.
In either case the observation contradicts the relationship between dimensionality and gravity.
Regards
Steven
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The rotation curves of galaxies don't invalidate the inverse square law. The inverse square law can result in non-Keplerian orbits depending on the form of the gravitational potential and thus ultimately on the mass distribution within the galaxy. An exponential disk potential amongst many others does not give a Keplerian radial profile.
Kepler orbits arise from spherically symmetric static potentials.
Cheers,
Tel