Science > Physics > Quantum Gravity Via Expansion-Contraction 33.1: Complex and Laurent Series Paradox
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Science > Physics |
| User: |
"OsherD" |
| Date: |
12 Nov 2006 10:16:36 PM |
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Quantum Gravity Via Expansion-Contraction 33.1: Complex and Laurent Series Paradox |
From Osher Doctorow
Since Laurent Series are the complex version of real power series and
the former have negative as well as positive and zero powers, the idea
of Section 33.0 generalized to complex variables appears to indicate
that the non-real complex variables are inherently anti-Causal (if we
include the fact that even non-holomorphic functions have formal
Laurent series).
Although we can "save the day" by considering that Quantum Theory
involves a "different phase" or a different Universe/Multiverse, just
as Special Relativity appears to involve a different phase in the
possible Superluminal regime when v^2 > c^2, a more conservative and
strictly scientific idea would be to exclude complex variables from
Quantum Gravity formulations, at least in preliminary versions at the
present stage.
We thus have exponentials replacing logarithms, f(x)/Dn...n(f(x))
replacing its inverse, x^(-r) eliminated from physical laws for r > 0
and replaced by "proximity" functions, and restriction of Quantum
Gravity to real variables with real values and real coefficients at
least in the simplest one-phase theory of Quantum Gravity.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 33.1: Complex and Laurent Series Paradox |
12 Nov 2006 10:26:13 PM |
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From Osher Doctorow
I should perhaps mention that the classical Graduate School text on
complex variables, Walter Rudin (U. Wisconsin) Real and Compled
Analysis, McGraw-Hill: N.Y. 1966, saw fit to only devote 2 of its 412
pages to Laurent Series, which would quite possibly have helped
generations of researchers (had Laurent Series been explored more) to
discover simpler real models of Quantum Gravity.
Rudin's style of writing mathematics texts resembled Birkhoff and
MacLane's style in real analysis, basically leaving the "work" to
students to figure out and trying to minimize overt logic and physical
reality in favor of "covert" homework/tests. That was before Sputnik
forced the USA to teach generations of engineers rapidly, at which
point mathematics texts almost overnight became crystal clear in the
1970s and 1980s and after except for some texts for liberal arts and
life science students.
Osher Doctorow
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