Accordingly, we note that curl *does* work in 4d, but it is over three vectors, not two.
One must also understand that other things come into play as well: for example, the classic Bohr model of atoms are stabalised by quantum effects. It is not at all inconcievable that some kind of spacial quantisation or a rotating rod-like structure might lead to an intense radiadiation of a field perpendicular to the body: this would produce the inverse square law and its attendent stable elliptical orbits, at a level where life might evolve.
The correct approach is not so much to dismiss the theory according to the deeper understandings of 3d, but rather to try and replicate this understanding in 4d. What _are_ the conditions needed to make 4d stable is the real question.
wendy wrote:What _are_ the conditions needed to make 4d stable is the real question.
1. Assume it works.
2. Let it run a bit
3. See why it works
it quite might be the case that the radiant field might not affect planets as much as some other kind of local planet-form thing, that has a inverse square law.
Since we normally expect gravity to be an attractive force, the gravitational field should point towards the origin.
I have a feeling the only way to prove it is by extending Newton's shell theorem. This page has one proof of the theorem. There is also a similar proof that uses potential energy instead of force.
http://teacher.pas.rochester.edu/phy121 ... ter14.html
I've tried both ways, but I get different answers each time. The integral doesn't cancel out nicely with either method.
PWrong wrote:Well, what this means is that the radius of a spherical object doesn't make any difference to it's gravitational pull, only the mass is important.
For instance, if you compressed the earth into the size of a tennis ball, without changing it's mass, it wouldn't affect the moon's orbit.
how is then 'looking at points outside of the sphere' formally different from 'looking at points inside the sphere' ? or you mean surface/volume distinction ?
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