From Osher Doctorow
Daegene Song of Korea Institute for Advanced Study, Seoul, Korea, has
presented what appears to be a good argument for what I would call
"Observer-Observed Cancellation" in Energy, Dark or otherwise, when
the Observer oscillates and so does the "Observed" (object).
In "Comments on vacuum energy of harmonic oscillator," quant-ph/
0703124 v1 14 Mar 2007, 6 pages, he begins with a discussion of the
classical harmonic oscillator, and then moves to the quantum harmonic
oscillator. In the first case (classical), a particle in a 1-
dimensional harmonic oscillator has position:
1) x(t) = A cos(wt + phi)
and Observer sits on a second harmonic oscillator with different
amplitude B but the same phase phi etc.:
2) y(t) = B cos(wt + phi)
With A and B nonnegative and B < = A, the Observer would observe the
particle's position as:
3) x(t) - y(t) = (A - B)cos(wt + phi)
and would observe the energy E_obs to be:
4) E_obs = (1/2)mw^2 (A - B)^2
If B isn't 0, then the energy of the observer's oscillation is not 0,
but this value fails to contribute to E_obs, and only the difference A
- B contributes. Furthermore, when B is very close to A, E_obs is
very close to 0, and if B = A, then E_obs = 0.
A similar situation appears to hold for the quantum harmonic
oscillator.
The relevance to Dark Energy and also the electromagnetic-
gravitational scenarios is obvious, especially if as indicated in my
recent Section of this thread, Ohm's Law is everywhere local but not
necessarily global. If Ohm's Law is global, then the argument of Song
paper could still be used.
Osher Doctorow
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