Re: Dynamical Systems and Expansion-Contraction

>>From Osher Doctorow

Max Jammer's (Bar-Ilan U. Israel, CUNY) The Philosophy of Quantum
Mechanics, Wiley: N.Y. 1974 argues quite effectively that HUP doesn't
hold in general for standard deviations or variances replaced by
(random) variables, but it could in my opinion hold in specific
scenarios or phases using random variables.

Let's look at the expression:

1) xp = k

where x is position and p is momentum, and consider p = mv with m
constant. Then:

3) xmv = k

and therefore:

4) d(xmv)/dt = 0

which yields:

5) mv^2 + xma = 0

so that for all energy E in kinetic form, (5) says:

6) E = -2xF

But x has dimension L, and writing L also for the variable x, (6) has
the form:

7) E = wLF

where w is -2 instead of non-real complex. This is a special case of
E = wLF that I discussed on an earlier thread. If m varies, we get a
generalization of (7) with an extra term xvdm/dt which when small or 0
yields exactly or approximaely (7).

Osher Doctorow

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