From Osher Doctorow
Let's look at the "whole picture" using the FLT (force, length, time)
rather than MLT system of units because of the importance of force
(push, pull, etc.) in Causation or Cause-Effect:
1) Fg^a Fem^b Fs^c Fw^d Lx^e Ly^f Lz^h T1^i T2^j T3^k T4^l = constant
where g, em, s, w, x, y, z, 1, 2, 3, 4 are respectively subscripts
meaning gravitation, electromagnetic, strong nuclear force, weak
nuclear force, the usual x, y, z of 3 dimensional space (for example,
Euclidean), and the 4 time "unipolar" time dimensions forward (1),
backward (2), expansion (3), contraction (4). Exponents are a, b, c,
d, e, f, h, i, j, k, l.
Since we have arguably identified T = L^2 in the early Universe, we
can "cancel out" the L and T dimensions by just taking e = f = h = -8
and i = j = k = l = 3 and identifying Ly = Lx = Lz on the one hand,
and T1, T2, T3, T4 on the other hand to yield:
2) L^(-8) L^(-8) L^(-8) (L^2)^3 (L^2)^3 (L^2)^3 (L^2)^3 =
L^(-24)L^(24) = 1
which leaves (1) as:
3) (Fg)^a (Fem)^b (Fs)^c (Fw)^d = constant
Now a remarkable thing happens. Remember that we were able to
"cancel" L and T because we found T = L^2. Is there as simple or
simpler relationship(s) among the forces? Because of the simple form
of (3), when we identify the 4 forces, they would "cancel" provided
that simple opposite pair relationships exist among them. Now,
although the coupling constants (see for example HyperPhysics on the
internet) all have the same sign, so that the strengths of the forces
in the sense of coupling constants do not seem to be paired, the
scales of the coupling constants may simply be hiding the
relationships by making everything positive. But there is an "index"
which is so close to opposite pairing that it almost escapes us: the
ranges of the Fundamental Forces.
The range in meters of the Strong and Weak nuclear forces are 10^(-15)
and 10^(-18) respectively, which are remarkably close when we recall
that 10^(-15) is 1 divided by (1 followed by 15 zeros). However, the
electromagnetic and gravitational forces are usually considered to
have infinite range, and 1/(10)^(-15) = 10^15 = 1 followed by 15
zeros. It thus makes sense to pair Fs and Fw, on the one hand, and
Fg and Fem on the other hand, and using range as an "alias" for force
strength, we can use "effective forces" for Fg and Fem, truncated
(made finite) at approximately 10^15 or 10^18 respectively, so that:
4) Fg = (Fs)^(-1) (truncated or "effective')
5) Fem = (Fw)^(-1) (truncated or "effective")
The equation (3) is then satisfied by having all exponents equal to 1
and the constant k = 1.
That the weak and electromagnetic forces have already been "unified"
in the electroweak (EW) force is a bonus so to speak. A similar
result might be found for Fg (gravitation) and Fs (the Strong
force).
Osher Doctorow
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