Gravity in the fourth dimension

[Munkybob13]

is there any gravity in the fourth dimension? if so, how does it work? help greatly appreciated.

[jinydu]

It depends. So far, there is no experimental evidence for a fourth spatial dimension, so alkaline's site relies solely on hypothetical situation.

If you want to postulate a four-dimensional universe where gravity exists, you're free to do so. If you want to postulate a four-dimensional universe without gravity, you can also do that.

My 300th post! It's a long way from here to tetraspace citizen...

[wendy]

To the extent that we postulate some sort of equalivance of four-dimension like our own, then gravity exists.

We have the matter being attracted to matter.

The most likely form of gravity is an inverse-cube law, which arises from the radiance proposition. What this means is that we assume that a mass releases a shell, which increases as a sphere from the centre. This means that at distance r, the surface is r cubed.

[iki]

would gravity really matter in the 4th dimension becuase of the movement of ana and katta what would it matter to have gravity since you could pierce through objects and move to a new point in space without pierceing through those objects...which im sure everyone knows. but to say there couldnt be gravity would be impossible since the rotation of large objects causes gravitational pull so to lack gravity then the 4th deminsion would lack stars and planets or everything in space in the 4th dimension would collide having nothing to orbit or to keep it in its own galaxy. you might not understand what im saying but i tried to simplify it to minute terms

[jinydu]

Well, why does the fourth dimension have to have matter at all? As I said, your question can't be answered without further assumptions. Of course, if you want to postulate things so that the fourth dimension is similar to our own, then that's another matter. There are plenty of existing threads on this forum that address this question. Just look around.

[wendy]

gravity works in any dimension.

It is best treated as a weak radiant-vector field, which means, that the size of the force is proportional to, and points to the centre, of masses. Because it is weak, it requires so much mass.

For euclidean geometries, it means roughly, that f = GMm/r^(n-1). For 1 and 3 dimensions, we can approximate a large object to its centre. For all others the approximation does not work. Where dr (changes in r) is relatively small to r, we can treat the measure GM/r^(n-1) as a constant g, and have f = gm (eg 1 lbf = g * 1 lb, or in metrics, 1 kg = 9.80665 N

For a given planet, it can be treated as a field radiating upwards at uniform density: that is g is 32.175 ft/s at the bottom and top of tall buildings. This allows us to implement gravity in the model without having to resort to doing calculations in integrals of gm1m2/r^3.

Gravity would no more crunch four-dimensions than it would crunch three or five. We evidnetly still are here, so gravity has not had its way with us.

As for ana and kata, the notions here is that because we have three naturally derivable directions in 3d, this is always the case. This is false.

One has only two dimensions that are set by nature: gravity (up/down) and motion (forward/backward). Plants, which don't move, have no obvious forward/backwards construction, while animals generally do.

Anything over that is purely in the domain of "equal valid directions of motion" Where we have left/right in a clear parity on a line [although people confuse these], in four dimensions, there is no intrinsic nature drawing the third and fourth directions out. All one has is a sense of "go clockwise 75 degrees from the church".

For those having problems following this, imagine that you lay a lot of clocks on the ground. In four dimensions, this is the across-space. While we can set face-of-clock = up or down, we have no reason to set the 12o'clock position to the north direction (or any other).

Correspoindingly, while up/down and back/forward intrinsically translate, the directions of left/right does not. ie ana and kata make no sense to a 4d being.

Wendy

[Neues Kinder]

I believe gravity exists in the fourth dimension, only it would be a lot stronger because there is a lot more matter in one area because matter is more compact. There's gravity in the second dimension and the third dimension, so why wouldn't there be gravity in the fourth dimension?

[wendy]

In four dimensions, there is a lot of space for the radiant flux to get away as well. This means that to achieve the same effect that 1E24 lb does in Earth, you be looking closer to 1E32 lb in 4d.

W

[Neues Kinder]

Yeah, but being 4D and all, wouldn't matter have more surface area because of all the extra room? So wouldn't the atoms make more contact with each other, causing the matter to be more compact? And I figure that the atomic mass would be greater also, each factor would increase the strength of gravity a fairly large amount, and both of them together would increase the strength of gravity an enormous amount. Thus making the gravitational pull in the fourth dimension stronger than it is in the third dimension.

Wait, what you just said finally sunk in. I see what you mean. Nevermind.

[jinydu]

In four dimensions, there is a lot of space for the radiant flux to get away as well. This means that to achieve the same effect that 1E24 lb does in Earth, you be looking closer to 1E32 lb in 4d.

W

Well, it depends on the value of G. Of course, you can't really compare the value of G in 3D with the value of G in 4D, since they have different units...

[wendy]

When one deals with higher dimensions, it is best to deal with a new quantity V = volume, and set:

length = L
mass = DV (mass = density * volume)
time = T
charge = SV/L (charge is a surface thing ie, V/L * sigma)
volume = V = L^n

When one does this, it is much easier to get the correct numbers.


We have then that

F = MA = GMM/R**(N -1)
DVL/T2 = G DVDVL/V
G = 1/DT2

This means that we have G pretty much the same value in all dimensions, and that the size of the unit is felt.

Putting G = 1e-9 (as it is in the imperial system), we have

mA = GMm/R**(N-1) [ universal gravitation ]
A = GMR/V [ k = volume of earth in radius ^n ]
A = GdkVR/V [ d = density of earth ]
g = A = GdRk
k = pi2/2. d = 330, R = 3960 miles = 20 E7 ft.
g = 0.02 dk = 0.02*330*4.9348 = 32.569 ft/s2