Gravity exibits an inverse square law, but EM has an inverse cube law.
Relativity is a 4D phenomena, but according to Kaluza-Klein, Electromagnetism is a result of 5D Relativity.
A cube is one dimension more than a square, and KK is one dimension more than GR.
Is there a connection?
Want to provide some background on how you arrived at the assertions preceding your question?
To address the first of the OP’s assertions, EM is an inverse square law, just like gravity.
Yep, EM is inverse sq., if you want to know if the two ar connected that’s beyond the knowledge of current physics, but I’m sure a theorist in superstring, M-theory or LQG would be able to give you some interesting ideas about this.
In four spatial dimensions, gravity would obey an inverse cube law. In general, for n spatial dimensions, gravity is as to 1/d[sup]n-1[/sup]. I assume EM works the same way.
:eek::o
Aha…let me amend my OP…MAGNETIZM obeys an inverse cube law.
Magnetism is a form of EM (it’s what the M stands for). Still inverse square.
Incidentally, tides do fall off as the cube of the distance. Perhaps this is what the OP was thinking of?
Well, the B-field from a magnetic dipole obeys a rough inverse-cube law. That’s probably what you’re thinking of, since there are no magnetic monopoles and all that. The same is true of electric dipoles. If you could get something with negative mass, the same would be true of gravitational dipoles. However, if you look at Maxwell’s equations, you’ll see that electric and magnetic fields have a very satisfying symmetry.
Now, you’re trying to draw a relation between Newton’s Law of Gravitation and the field law of a magnetic dipole. You can’t. It’s not a simple matter of changing a 2 to a 3 in the equation. Look at Equation 2. Yes, there is a 1/r[sup]3[/sup] there, but there’s also some junk with theta in it. Compare the Law of Gravitation and you’ll see there’s not a simple parallel to be drawn.