Gravity in 4D

[gonegahgah]

We already know about our 3D gravity and spherical planets produce our closest gravitational experience.
From the surface of a planet gravity reduces approximately at g/r².

For a 2D world, where a planet is a circle, gravity reduces at only g/r.
For a 4D world, where a planet is a hypersphere, gravity reduces at g/r³.

So, for the 2Der, the gravitational decrease occurs at an even rate and for the 4Der gravity decreases even faster than it does for us.
However, this is compensated a little by the opposite effect on mass.

Comparison:
2D: M = G * pi * r²
3D: M = G * 4/3 * pi * r³
4D: M = G * 1/2 * pi² * r⁴ (I'm glad someone else worked that one out).

So, for the 4Ders, gravity will be much greater but will also taper off at a much faster rate.

[Keiji]

Yes, this is precisely why we don't have stable orbits in 2D, 4D or any other space that isn't 3D.

The lack of stable orbits is about the biggest stumbling block (that we know of) to a working higher dimensional universe...

[wendy]

Gravity, like electricity and magnetism, is a radiant flux system. What this means is that the force produced is a product of some intrinsic measure (charge) and an extrinsic measure, which is proportional to the surface of shell at radius r.

In 2d, F = c Qq / 2 pi r.
In 3d, F = c Qq / 4 pi r²
In 4d, F = c Qq / 2 pi² r³.

In these cases, the denominator is the surface of a sphere of radius r. The numerator c Qq is due to EM and gravitational waves travelling at the speed of light.

These formulae need an extra factor 1/z in SI, because that system is intrinsinicly incoherent elsewise.

[gonegahgah]

Your formulas are most likely more correct than mine Wendy though the trend is still there of course.
Though I have to admit that, in defiance of what is believed (I can say believed because it is unproven yet), I don't believe in gravitational waves.
Sorry Einstein, I think gravitational effect is immediate at any distance.

[quickfur]

Yes, this is precisely why we don't have stable orbits in 2D, 4D or any other space that isn't 3D.

The lack of stable orbits is about the biggest stumbling block (that we know of) to a working higher dimensional universe...

Well, that just means that we have to come up with a much more creative set of 4D physics laws than just directly generalizing from 3D. Sure there won't be planets and galaxies and stuff, but i'm sure we can come up with something else that still works. But it's obvious that it would be very alien to us.

[wendy]

You could have stable orbits in 4d, but you need to sneak in quanta. That's how they stabalised the Bohr atom. You should not imagine that our (lack of) knowledge of what 4d is, hinder this calculation.

Waves in gravity just needs a fast rotating massive pair of stars. There's plenty of them around. Even classical newtonian physics says there should be gravity waves.

On the other hand, relativity suggests that gravity travels at the speed of light. The instruments are only now becoming sensitive enough to test this. In general, there are lots of things that are more detectable than the relativistic speed of gravity, like the phases of the moon, passing trains, and bits of dense rock in the nearby ground. Typically, these are in the order of x E-9 / s², eg x nm/s² per horizontal metre. There's a unit called an Eötvös that looks after this.

The relativistic order of gravity is somewhat fainter on earth, although they do look at the passing of jupiter in front of bright quasars, such as what happened in 2002.

[gonegahgah]

Hi Wendy, you might want to check on that. As far as I know, and quickly could see on the web, classical Newtonian physics doesn't allow for any gravitational waves?
Well I guess if the instruments are now becoming sensitive enough then we should have our answer soon. So far all their indirect results are dependent on light and light and other things have been throwing them a few curve balls of late...

[wendy]

Waves are detected at a station by up-and-down motion of something, like the force of gravity.

A pair of stars spinning in millisecond orbit, should give rise to waves at millisecond rates. At any case, the tides are little more than the reflex of gravitional waves, or changes in intensity of gravity caused by the sun and the moon. This does not require einstein-relativity.

Still, newtonian physics is simply the limit of general relativity as c -> infinity. That we have magnetism implies that c is finite, and that there is co-gravity, implies that gravity too travels at a finite speed. It is usually rated as c, but i've been reading some articles which suggest that it could be somewhat less. Gravity, it is known, certianly does travel at a speed less than infinity, and probably at the length-time ratio of the Minkiskovski geometry.

[gonegahgah]

Well that's certainly the theory, whereas Newtonian physics says that the centre of gravity may wobble, but that will not really be noticeable by us because there would be almost no discernible change in gravitational difference between two points at our distance from that wobble. Certainly on the other hand gravitational waves predict a greater disturbance by many magnitudes than the centre of gravity model of Newtonian physics. So I guess its up to our mates with the gravity wave detectors now in space; though they have much greater localised effects to contend with that will also push at the survey ships. But anyhow, if they can overcome those and start looking for smaller and smaller effects than that is great. That will hopefully then give us an answer; though I'm sure a positive answer won't receive any of the skepticism that results like the neutrino ftl results have received; nor the apparent ftl particles that seem to bombard the Earth which are discounted without scrutiny. We see for our mate the Higgs Boson that they are running out of spaces for it to hide. Yet it has been held up as a necessary cornerstone of our standard model for so long. You may believe in this particles existance too; but again science may eventually prove itself to be wrong afterall on many things. Despite the self-assurance of science, I tend to see a house of cards. I always love the number of misapplied examples such as the Michelson-Morely experiment. How many times has been used as proof of other facts than the facts that it does actually prove. Anyhow, time will tell. What happens if there is no Higgs Boson? What happens if they never detect gravitational waves? What happens if the neutrinos prove to travel ftl? Would you waiver? Or, will you hold steadfast?

[wendy]

The whole point of centre-of-gravity is that it works only with spherical shells, not other mass distributions. That is, it's only spheres that approximate to concentrated masses at the centre, not all things.

A pair of stars rotating around each other, or indeed, any set of objects moving around each other, will create movements in the gravitational field, which will be noticed. The output wave is generally in terms or 1/r³, but it can be detected if it is looked for.

The weighing machines are now so sensitive that they can pick up the slow wave of the moon, and adjust for that in the calculations, and even detect the ripple in gravity caused by a fairly close train.

[gonegahgah]

Umm, last I knew anything can have a centre of gravity; even systems.

Well, they should give us your positive results no time soon then, hey?

[quickfur]

Sure, every system has a center of gravity... but only a spherical body with radially even distribution of mass will have a completely even gravitational field that fits 100% with the equations. An uneven system, like a binary star pair, will approximate a system with a center of gravity at very large distances, but the closer you get the more uneven the gravitational field becomes. If the pair is rotating, that amounts to changes in the unevenness of the gravitational field, which causes it to fluctuate.

[wendy]

One should not rely too much on the idea of 'centre of gravity'. It's really a con, and exists if the mass has a fairly symmetric distribution, including inversion.

The equalateral triangle has none, for example. It is true that one can draw a line through a triangle, which cuts its area in half, but all such lines do not cross at a single point. The exact process is there's a smaller copy of the triangle, at size sqrt(2)-1, and all bisecting lines cross through at least one of these vertices.

In four dimensions, even the approximation that a sphere can be reduced to a point is wrong.

In any case, just because an electric dipole has no net charge, it does not mean that it has no field. There is a field, which falls off as 1/r³. A rotating electric field, or even a rotating bar magnet, gives rise to undulating fields (waves), which is the basis of the dynamo. Since electric field is modeled on gravity, there should also be a gravity-dynamo, such as a pair of co-orbiting stars (a binary star).

Still, there is a gravity wave, in the order of something like 0.1 microhertz that causes neap tides and king tides on the earth.

[Shojin]

Let me see if I can phrase this question right. Let's take a tesseract sphere that has two points that are polar opposites equal distance apart. If we were to draw straight lines in the tesseract or hyper space, then distort that image into a three dimensional image, it should look like how we see magnets with poles work.

Also, imagine a sphere where two points opposite each other have equally flat areas, polar opposites. We'll rest the sphere on one flat pole so it is stable. Anything perfectly balanced, or resting within the boundaries of the flat spot on top would stay there if at rest with no external forces.

With these concepts, let us take gravity and make it polarized, but we put the two poles in a massive object, say a star or a black hole. This would represent the radius of the flat pole on the bottom of our sphere. The opposite side of that sphere would have a Lagrange like spot of equal size radius where matter would not fall into our massive object.

Now let's translate this idea as though our sphere represents the four dimensional tesseract hyper space, but from a perspective that we would observe in a three dimensional space. If the massive object were to be moved to the center of this tesseract hyper space, would not the polar opposite Lagrange 'area' appear as a disk of gravitational neutrality, a safe zone where matter would not fall into the massive object unless truly perturbed from our perspective in three dimensional space. Like a galactic disk, or the orbits of planets around stars.

Also, would this Lagrange space give a false gravity signature like what we call Dark Matter?
For me it appears that gravity works in both normal space as well as hyper space.
Is this a possibly viable hypothesis, or am I just crazed?

Edit: Or perhaps the Lagrange space is the negative gravity pole? (anti-gravity?)