Nanotech Similitude Via E1/E2 = (w1L1F1)/(w2L2F2) and P1/P2 Forms
From: OsherD (mdoctorow_at_comcast.net)
Date: 01/28/05
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Date: 28 Jan 2005 00:20:41 GMT
>>From Osher Doctorow mdoctorow@comcast.net
I have argued on sci.stat.math, math-history-list (of Math Forum),
sci.physics, sci.eng.chem, and elsewhere that:
1) E = wLF
where E is complex energy E = E1 + iE2 with E1 the usual real
measured energy as in quantum theory and E2 the David Bohm quantum
potential and w is the Schrodinger wave function and L is length
or distance (either of an object or between objects) and F is
resultant force in one dimension (e.g., two oppositely directed
forces at a boundary point). It is interesting to combine this
with the Schrodinger equation and also to notice that:
2) EE* = /E/^2 = ww*L^2/F/^2
and recalling from quantum mechanics that ww* = P (probability),
we get:
3) /E/^2 = PL^2/F/^2
and dropping the / / for nonnegative real cases:
4) E^2 = PL^2F^2
We immediately get:
5) E1/E2 = (w1L1F1/(w2L2F2)
6) E1/E2 = (P1^(1/2)/P2^(1/2))(L1/L2)(F1/F2)
and when any two corresponding quantities are equal,
such as L1 and L2, a large number of similitude equations
results, such as:
7) E1/E2 = (L1F1)/(L2F2) (if w1 = w2)
or correspondingly for pairs of corresponding quantities:
8) E1/E2 = P1^(1/2)/P2^(1/2) (if L1F1 = L2F2)
This generates a wide variety of energy-force, energy-probability,
energy-distance, energy-length (of object), force-distance,
and so on relationships between large and small scale models.
Osher Doctorow
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