Sun, 21 Nov 1999 00:28:20 -0800
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Stephen and I had a very long talk. And some analogies which came
out, may be of interest. Particularly the last example.
There is a difference between ray optics as a particle model
(in terms of the orthogonality of the rays) and the Huygens construction
(in terms superposition and interference of waves).
There is a difference between filtered light (which is received
only subtractively through filters) and reflected light which
is received superpositionally (in terms of additive and subtractive
There is a difference between and electric circuit modelled
in terms of one the possible paths for an electron to follow
and the circuit modelled as a whole.
There is the difference between recorded (orthogonalized) time
and dynamic time (superpositional time).
The former cases are all distinctive or orthogonalized (particle) models
while that later models all allow for combinatorics in the superpositional
sense of interference (wave-like models).
There are many other analogs such as in terms of datagrams and streams
in network theory or in terms of fundamental or speculative stocks....
We try to connect these two extremes in each case together.
Special Relativity is a particle-like model with local times.
General Relativity is more of a wave-like model with a universal time
but it tries to include Special Relativity as a subset
(wave-like models include particle-like models as subset)
The particle models can be called slices of the wave-model.
The wave-particle model or unified model is a further consideration
of what happens when these two complementary models morph are allowed
into each other.
There is this same sense in Feynman's path integrals in terms of
local rays(paths) and the more global superposition (the extrema).
When looking at a painting (reflected light), two people see much
that is the same, and this is their global commonality analogous
to common or global time, and what they don't see in common is due
to superpositional interference and results in their local distinctions
or analogously their local times.
But if the two people look so closely at the painting that they
cannot each see the superpositional effects, then they will see absolute
frequencies, and not colors. Their _measurements_ and their times
become the same or common because they have eliminated the
interferences. They enter more closely into the same local system
with the same space-time reference.
Every electric circuit is based on fundamentals like resisters
capacitors and inductors. The different impedances create different
currents and so different "times" in the different branches of the
circuit. These different times in each branch can only be measured
statically by closing off power access to all the other branches.
This "branch time", expressed in terms of resistance or current, is
reversable because of the static nature of its measurment.
(This assumes we have infinite power to test each branch
parametrically; the power supply is distinct from the circuit's
There is also the "global time" of the circuit which
is measureable only dynamically in terms of the overall power
consumption and expressed as the impedance of the circuit
as a whole. This global time is not reversible because of the
dynamic nature of its measurement. (This assumes there is
a finite amount of power in the power supply when we test the
circuit as whole; we use the circuits power supply when we
test the circuit. We do not use an separate power supply)
The impedance is reactance + resistance. The reactance
is in terms of alternating current which obeys the superposition
principle and direct currents under resistance obey the mixture
or filtering principle.
When we try to combine dynamic and static measurements, we
are performing a power measurement which has an inherent
uncertainty in it at some level. But in a practical (empirical)
sense, it's not terribly important for electric circuits,
only at a theoretical level does it become important when
we try to unify all the analogs under the same model.
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