Quantum Gravity 111.1: F, K.E., Momentum in Constraints On Accelerating Universe Via Riccati
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 30 Mar 2007 15:44:09 -0700
From Osher Doctorow
Now let's return to:
1) dv/dt = a = A(t) + B(t)v + C(t)v^2
and multiply both sides by mass m which is held constant or close to
constant and let C(t) incorporate the factor (1/2) and A(t)
incorporate m, yielding:
2) ma = F = A(t) + B(t)p + C(t)KE
where F is force, p is mv (momentum), KE is kinetic energy classically
((1/2)mv^2).
Arguably, we can include a potential term from A(t) and combine it
with KE to obtain a total energy E, so let's write (2) as follows with
A(t) still used to designate the non-velocity term:
3) F = A(t) + B(t)p + C(t)E
It must be stressed now that if (3) is found to hold classically, then
Quantum theory including Quantum Gravity arguably has to reduce to (3)
for the appropriate forces either directly or as a limiting case.
But (3) has more significance than just that. The variables F
(force), p (momentum), and E (energy) have a curious ability to
generate the 3 MLT dimensions of M (mass), L (length, distance), and T
(time), as follows with [ ] meaning "dimension(s) of":
4) [E/F] = L
5) [p/F] = T
6) factor of F or p or E = M
So (3) arguably introduces 3 fundamental dimensions alternative to MLT
as well, namely F, p, and E.
Osher Doctorow
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