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Power as a fundamental property

Given that dn=0 for the firmament, we can solve equations (4) and (5). Their solutions turn out to be identical. That is:

l^2 n^3 dm + 2mln^3 dl = 0

so that

l dm + 2m dl = 0

from (4), and

l^2 n^2 dm + 2mln^2 dl = 0


l dm = -2m dl

from (5). Hence we obtain:

l dm = -2m dl


dm/m = -2dl/l

Integrating (8) yields:

ln m = -2 ln l + K (Eqn. 9)

where K is a constant of integration (actually, it's a function of time but m and l are independent of time). We can rewrite (9) as:

m = K/l 2 (Eqn. 10)

which means that at this most fundamental level, mass is inversely proportional to area and directly proportional to K. In particular, this means that the more massive a particle, the smaller it is and vice-versa. So it is that an electron is larger than a proton, although the latter is much more massive. This is attested to by the observation that the electron "orbits" or "surrounds" the proton when the two are combined to form an atom. To see why this is so, note that as we subdivide the universe into smaller and smaller pieces, we eventually reach a point where we start "noticing" the firmament more and more. Eventually, at a size L~10-33 centimeter, any smaller cuts would only contain firmament. Equation (10) only holds for fundamental particles or scales where Planck's constant is relevant. This is so because the units of K, <K>, are actually <h>/<n>, that is, Planck's constant divided by a characteristic frequency n. So:

K = m l 2 = h / n (Eqn. 11)

We identify l as the Compton wavelength of the mass m, namely, h/mc. This is why physicists view mass as an area when dealing with cosmological (large-scale) and quantum mechanical (small-scale) problems.

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