[SI-LIST] Re: Square wave harmonics
- From: "Doug McKean" <dmckean@xxxxxxxxxxxxxxx>
- To: "Signal Integrity Group" <si-list@xxxxxxxxxxxxx>
- Date: Mon, 3 Dec 2001 10:42:28 -0800
Just a side note ...
There's several "problems" with modelling by way of
Fourier or using Maxwell's equations. But in our reality,
for our purposes, they work just fine.
One, in Fourier Analysis, the use of negative frequency
to mathematically balance out a bilateral frequency
assumption for an integral has some conceptual problems.
Another, in Maxwell, the equations are just as happy to
use negative time in the time variable as positive time which
makes for some obvious causality problems.
The two mentioned above resulted from a prevailing scientific
analysis/philosphy which at the time presumed the universe to
be totally deterministic. I.e., all one needed to know was just
the state of the universe at the present moment and then one
could predict anything of it in the future or analyze anything
in the past. Or so they thought.
And again, with Maxwell, a couple of the equations require
the assumption of magnetic dipoles as a basis. Current
research into finding a magnetic monopole will require ALL
of Maxwell to be rewritten. Thus the reason why there's real
concern in their existance. The person finding magnetic
monopoles and subsequently rewriting Maxwell's equations
will put that person down in infamy.
Quantum mechanics, chaos theory and the various offshoots
from them have since challenged that deterministic model.
And it will be interesting to see how that all works out.
- Doug McKean
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