Darwin-L Message Log 7:9 (March 1994)

Academic Discussion on the History and Theory of the Historical Sciences

This is one message from the Archives of Darwin-L (1993–1997), a professional discussion group on the history and theory of the historical sciences.

Note: Additional publications on evolution and the historical sciences by the Darwin-L list owner are available on SSRN.

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<7:9>From rho@linda.CS.UNLV.EDU  Mon Mar  7 18:50:15 1994

To: darwin-l@ukanaix.cc.ukans.edu
Subject: Re: Superposition
Date: Mon, 07 Mar 1994 16:43:39 -0800
From: "Roy H. Ogawa" <rho@linda.CS.UNLV.EDU>

Quantum Mechanics and Optics both use the concept of superposition.  It
amounts to the sum of two functions.

For example, say that f(x,y,z,t) and g(x,y,z,t) describe solutions to the
relevant equations (Schrodinger's for QM and Maxwell's for Classical Optics).
If the relevant equations do not have any non-linear constraints, then the
linear sum of the two functions are also solutions:

        h(x,y,z,t) = af(x,y,z,t) + bg(x,y,z,t)

is also a solution.  This is the Principle of Superposition.  In the case
of QM, the functions are matter-waves (the major current interpretation
is that these are probablility distribution functions for the matter),
while in optics, these are the light waves.  Of course, in modern Optics,
based on QM with light as particle/wave, these are the same.

The descriptions you give above are consistent with a = b = 1 because
one can always imagine graphs of f, g, and h with g = h - f, giving
the appearance of an f-layer with a g-layer superposed (added) to give
the graph for the h-layer.

From whence I come, the term superposition used in geology or biology seems
odd.  But not anymore.

Hope this helps.

Roy O

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