Science > Physics > Quantum Gravity Via Expansion-Contraction 14.0: Convergence of the 2+1 GR and 3-diml QFT and 2-diml Riccati Differential equation
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Science > Physics |
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"OsherD" |
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23 Aug 2006 04:47:43 PM |
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Quantum Gravity Via Expansion-Contraction 14.0: Convergence of the 2+1 GR and 3-diml QFT and 2-diml Riccati Differential equation |
From Osher Doctorow
Why is the Riccati Differential equation so simple?
The answer appears to relate to 't Hooft's Holographic Principle and to
something pointed out by Sir John D. Barrow, Douglas J. Shaw, and
Christos G. Tsagas (respectively of Cambridge U, U.K., Cambridge U.,
and U. Thessaloniki Greece) in "Cosmology in three dimensions: steps
towards the general solution," gr-qc/0606025 v2 10 Jun 2006. As they
point out in their last (discussion) section, p. 33, the 2+1 GR (2
space and 1 time dimensions), to which the "three dimensions" in the
title of their paper refers, considerably simplifies the search for the
general solution of GR in several interesting situations. They also
point out that the 2+1 GR is also motivated by the current perception
that QFT is more natural in 3 rather than 4 dimensions.
The solutions and related solutions in Barrow et al (2006) are more
complicated than the usual Riccati Differential equation solutions, but
there are quite a few similarities both in the equations and solutions.
This is especially the case for the exponential function or sums or
differences or ratios of exponential functions as in sinh, cosh.
The paper by Sir John D. Barrow et al (2006) is a review paper of
research in 2+1 GR by one of the top researchers in that field
(Barrow), and in fact all authors are closely related to astrophysics
and astronomy which are among the most Creative and least Bureaucratic
fields in the physical sciences.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 14.0: Convergence of the 2+1 GR and 3-diml QFT and 2-diml Riccati Differential equation |
23 Aug 2006 05:10:07 PM |
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From Osher Doctorow
Looking back at the history of physics and mathematics and engineering,
the leading positions of astronomy and astrophysics as causes of
discovery become apparent as well as the leading position of practical
building/construction requirements. Although these causes are helped
by experiment wherever possible, it is more accurate to say that
experiment and/or observation combined with real goals rather than
purely abstract goals were critical causes. This doesn't mean that
"purely abstract mathematics" is not very valuable, but rather than
there are two types of abstraction:
1) abstraction unrelated in goals to the
physical/biological/behavioral/social Universe
2) abstraction related in goals to the
physical/biological/behavioral/social Universe
Despite the current and recent fads of algebraic geometry and algebraic
topology, algebra in itself arguably belongs to the first type of
abstraction, while probability and combinatorics and statistics and
differential equations/analysis and geometry and topology and logic
belong to the second type of abstraction.
Curiously enough, Bureaucracy including Bureaucratic power structures
in nations and Academia and other institutions and groups/classes has a
tendency to be more inclined toward (1) above than toward (2). This
arguably explains the persistence of poor strategies that do not adjust
to current realities, because the users of these strategies are mostly
using them out of habit (including deference to "superiors" and
"founding fathers") rather than out of "reality". I'm assuming here
that self-destruction for the sake of self-destruction is not a
"reality" goal.
Osher Doctorow
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