by **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.