a few questions about gravity in 4D

[Plat]

I know that gravity can be extended to 4D but shouldnt there be modifications made because the reason why they come up with unstable orbits and atoms is because they take how gravity acts here in 3D physics and apply it the same way in the extrapolated 4D physics (thats extrapolated from our physics)? but we just dont know what kind of modifications can be made so we dont make any?...is this statement correct?

[Batman3]

Plat, I think the best way to extend 3d-gravity to 4d-gravity is to figure out exactly Why things work that way in 3d.

I think the reason 3d-gravity(or 3d-electric field) falls off as 1/r^2 as r increases is that the surface area of a sphere surrounding the central-point-source is prop. to r^2 (4 pi r^2). The reciever of the gravity would intercept an amount of the gravitons proportional to the area(i.e. mass) of the reciever over the area of the sphere at that distance.

Similarly the 4d-hypersurface around a central-point-source is prop. to r^3. Thus 4d-gravity is prop. to1/r^3. Then 4d-f =G m1m2/r^3. We have to put up with the consequences, whatever they may be.

Alternatively we could assume that gravitons work by accelerating when they hit the gravitee and the gravitee accelerates in the other direction. We could make various assumptions with results for 3d- and 4d- gravity but I think we should stick to those which are consistent with our 3d-gravity(and then of course extend to 4d-) One is that the graviton thins out in thickness as it moves out. I Think this comes to the same thing.

Alternatively if we assume QM(which I can't), the uncertainty principle might supply an energy of h bar/t where t is the distance of time between the source and the gravitee at speed of gravity cg. Then r(t)=t*cg. Thus E = h bar/cg/r. Taking the DIV operator, we get F=GM1M2/r^2 where cg=cg(G). If the 4d-E is also 1/r then 4d-f is 1/r^2 in contrast to 1/r^3 above. If so the orbits would be the same as 3d.

Wendy, this might help get units for 4d-cg if 4d-cg=3d-cg.

[pat]

I know that gravity can be extended to 4D but shouldnt there be modifications made because the reason why they come up with unstable orbits and atoms is because they take how gravity acts here in 3D physics and apply it the same way in the extrapolated 4D physics (thats extrapolated from our physics)? but we just dont know what kind of modifications can be made so we dont make any?...is this statement correct?

That statement is technically correct... but mostly meaningless.

Consider instead this question: In the absence of anything that forces a modification, how could you even consider making modifications?

Now, there is a point to be made (and Wendy has made it) that the fact that orbits don't work does force a modification. If we want there to be 4-d beings on 4-d planets with 4-d suns in a 4-d universe, then we have to start with the premise that orbits can work in 4-d. From there, we have to try to find some set of assumptions which fulfill that need.

It should be obvious that there is more than one set of assumptions that would make this work. There's also the possibility of 4-d universes without planets orbiting stars and in which the life forms on the planets get their energy from some other source.

So, then the question becomes, how do you cull? How do decide which possibilities are worthy of further inspection and which are "silly"?

You have to start somewhere. If you start with "gravity is a radiant field", your answer is "no stable orbits". If you start with "suppose there are stable orbits", your philosophic task is to justify the assumptions that make that possible.

(Of course, all of this said, there aren't any stable orbits in a 3-dimensional universe with more than two bodies either...)

[pat]

More succinctly....

Proposition: Gravity would act as a radiant field even if space had 'k' dimensions (for any positive integer k).

Give me a reason to believe that's not true.

[Plat]

I really dont know anything about physics, I was just thinking that is this conclusive enough?, I mean we dont know what else might pop up in a 4D universe, for sure it would be significantly different from our universe, 4D physics will also most likely allow for new physics that dont work in 3D. It also depends on the nature of the dimension, but I see what your saying that this is the only speculation that is not meaningless because as PWrong already told me that the people who think up of the equations try to change as little as possible to remind us of own things in our universe, and they do that by adding an extra dimension in there but thats the only change they make.

EDIT: So multi-dimensional universe would technically be "dead" then?, pat what do you think of there being new matters form in those universes?

[wendy]

The thing with "stable orbits" is that there must be a whole class of these, that one can change from one to another. In three dimensions, this is provided by elliptical orbits.

Supposing that gravity is a radiant flux, leads to the proposition that for any sphere, (surface area) * (specific force intensity) = (mass) * (constant) = (flux).

One then finds (surface area) = function(radius), and it is this that dictates the nature of radiant fields, not only in the higher dimensions, but also non-euclidean geometries.

Newton's mechanics are built on Euclidean physics by adding the notions of mass and time. One can add these notions to Hyperbolic geometry, or to 4D geometry, and let the underlying geometry do the talking.

Even the radiant field has its part to play. That the sky is black, is a sign that the heavens is not uniformly peppered with stars.

The only instances where a radiant force leads to set of stable orbits is in N=1, and N=3.

To create a kind of universe where stable orbits exist, then one has to suppose some kind of other element keeps the planets on track. This is not entirely unknown in our world, since the atom would collapse except for quantisation.

It could be that gravity is somehow quantised at a large scale, and that what we're seeing is GM.Gm = Nk, for some very large k, and that the planet is drawn to a stable orbit N. For people and rocks and so forth, we have N=0, so they're stuck on the surface.

I don't know, but even modern physics abounds with things that are not to our nature defined. For example, quarks have a force independent of distance, as like a string-tension. The Bohr atom is quantised, again unexpectedly.

There are of course other things that could conspire to make stable orbits in four dimensions: such as the swirl of clifford-rotation. (note, for example, that the orbit of planets follow the rotation of the sun).

In any case, my premise is to make all of this stuff a SEP (someone else's problem), and deal instead in trying to find what parameters are needed to be solved for. For example, the nature of 4d rotation was made by simply setting up a model and watching the night sky. In this sense, it is more real than supposing a pole etc as we have in 3d.

Even for relativity, Einstein did not have a clean slate to work with. The experimental evidence was already present, just waiting for an explination. Einstein just explained it, with formulae.

What i am doing is trying to find out the most earthlike kind of four-dimensions, and leave it to others, or point in the direction where i think an answer ought lie.

W

[Batman3]

What is wrong with the electron-in-jello plus nucleus model of the atom? Charge is conserved to 0, all motion=0 so magnetic forces do not apply. Why can't we create a new slowing and repulsice force of limited range to account for the atom? After all, that is what they do in nuclear physics.

[wendy]

"jello" is american for jelly.

Nothing is wrong with the jelly-model per se, but the whole thing is that to have planets and things, you need to have the thing unstuck. That's the point of the thing. So if you are going to have it unstuck, you might as well start down deep.

even the nucleus is a mob of quark bubbles. neutron stars have atoms nucleus sitting side by side. there are denser matter-states, when the quark bubbles break up, and the quarks sit side by side.

Wendy