4D Gravitational Constant

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4D Gravitational Constant

Postby Higher_Order » Mon May 28, 2012 3:42 am

Here's an interesting topic for discussion, 4D Gravity.

We all know "normal" gravity (G* (m1*m2/d^2)), where

G= Gravitational Constant (6.67*10^-11)
m1,m2 = two masses
d = distance

which changes to (G* (m1*m2/d^3)) in the 4th spacial dimension.

Here's my question (probably has a very simple answer) is the gravitational constant the same? I'm almost positive that it isn't, but then what is it?
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Re: 4D Gravitational Constant

Postby gonegahgah » Sat Jul 07, 2012 1:34 pm

To my mind the gravity and the gravitational constant along with it are related to volume.
So I would think that you would have to reduce the figure to one dimension and then enlarge it back up to the required number of dimensions.
I would do this by finding its cube root and then raising it to the power of four. ie.

G4D = (3√G3D)4.

Atoms would tend to pack themselves differently in 4D but I don't imagine this would affect the constant.
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Re: 4D Gravitational Constant

Postby quickfur » Sat Jul 07, 2012 3:29 pm

The value of the gravitional constant depends on the intrinsic strength of the gravitional force; it has nothing to do with how many dimensions it has. As far as I know, currently nobody yet knows what determines this value; it's one of the "magic constants" that physicists hope will one day be predicted by a unified theory of gravity.

The numerical value of this constant also depends on the units of measurement you're using, and I doubt you can simply carry over units of measurements across dimensions without some adjustment.
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Re: 4D Gravitational Constant

Postby wendy » Sun Jul 08, 2012 8:51 am

The real trick for N dimensional study, is to regard mass and charge as effects of volume and surface respectively, and that the 'real' measures are the point densities. We can thus write M as mSL, and Q as qS, where m and q are the point densities, S is surface, and L as volume.

With M = mSL, you get force = M.a = mSL²/T², and energy as force.length, as m.SL³/T². Also, pressure is m.L²/T².

Likewise, we see charge Q = qS, voltage is mSL³/T² divide qS = mL³/qT².

For the greatest part, the variation in velocity is much less than between L, (eg ft/s, km/h, mph, m/s vary over a lesser range than inch, foot), so we put

L = vT. M = mvST F = mv²S, E = mv² SL, pressure = mv², charge = qS, voltage = Lmv²/q.

Putting these into eg F = G MM / R^(N-1). The value R^(N-1) is simply S, so we get mv²S = G mvST . mvST / S

We cancel everything out to get G = 1/mT² (in all dimensions, 1/G is (density) × time².

For the coulomb relation F = kQ² / S (where R.S = R^N), we get

mv²S = K. qS qS / S , mv² = q²K K = mv²/q² eg Pascals / (c/m²)².

Since we decided already that m, v, q are all point-functions, then K is also of the nature of a point function.

With G = 1/mT², the size of G does not vary by dimension, but is a function of time.

In fps units, we get 4 pi K = 1.0167E-9 (ft pdl sec/vb²), and G = 1.069E-9 ft³/lb s². Both of these values are near 1/c, so

4 pi Kc = 1 (exactly), and c G = 1.05144 ft^4 / lb s³.
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Re: 4D Gravitational Constant

Postby Higher_Order » Wed Aug 15, 2012 2:46 am

Oh, ok. I get it now. I've been very busy for the past months, sorry for the late response.
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