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From: Osher Doctorow on 5 Aug 2010 22:14
From Osher Doctorow

The "distraction" of theoretical physics through Germany and Denmark
and Austria in the early 1900s through now into Relativity (SR and GR)
and its generalizations/modifications and Quantum Theory, which
ultimately led to our concepts of "compacted" dimensions and
"invisible" dimensions such as Kaluza-Klein, Superstring/Brane/M-
Theory, Randall-Sundrum and their modifications, eliminated focus on
Dimensional Analysis as a Theory, "exiled" to be applicable to
Astrophysics, Mathematical Biology, and Engineering and to
"Phenomenological" rather than "Theoretical" Physics mostly (which
"Phenomenological" Physics largely explores new problems by giving a
"provisional" theory largely based on experiments which then is
ultimately replaced by the "Incorporated" (Inc., Ltd., etc.) Theories
which work "to the nth decimal place" (Relativity, Quantum Theory,
etc.) except that they often can't handle very new discoveries without
revolutionizing themselves and even their previous Axioms (recall
Einstein's "Principle of Verification"?).

Of course, Dimensional Analysis (of Buckingham, Bridgeman, etc.) only
postulated a few "Fundamental Dimensions", such as:

1) M (mass), L (length or spatial dimension), T (time)
2) M, L, T as in (1) as well as Theta (temperature)
3) M, L, T, Theta as in (2), as well as (or replacing Theta by) Q
(Electrical Charge).

If we double each of the 5 dimensions in (3) to account for either
"Anti-" or "Oppositely directed" dimensions, which may or may not be
the same as their Abelian (commutative) multiplicative inverses like
M^(-1), L^(-1), T^(-1), etc., then we already get 10 Fundamental
Dimensions arguably, which with one more can be the 10 or 11
dimensions of respectively Superstring or Supersymmetry Theories.

Admittedly, there is something "strange" about regarding M^(-1) as a
separate Fundamental Dimension from M, but then, the Universe is
strange. However, this is only one possibility, and unless I assume
it explicitly in some section or subsection, I do not assume it.

Now let us summarize Dimensionless Ratios discussed here and involving
respectively L, T, M:

4) L1/L2 (two L dimensions as in length of myelinated brain fibers/
earth-moon distance)

5) T1/T2 (this and L1/L2 are in Bode's Law, Dermott's Law, etc. for
adjacent planetary vs planetary or planetary vs Star/Sun or planetary
vs moon(s) or moon vs moon, etc. systems.

6) M1/M2 (for example Mass of white dwarf - Mass of Earth)/Mass of
Earth for Chandrasekhar limit used in Collapse and Supernovae).

Of course, we already know from Dimensional Analysis in Engineering,
for example, that Lx, Ly, Lz (for x, y, z subscripts) are 3 separate
dimensions of space when particular directionality in space is
relevant to a problem rather than homogeneity/isometry. And some
Physical Theories have come up with two time dimensions (not the
majority of such theories, but some). Two mass dimensions explicitly
identified seem to have escaped notice mostly.

Osher Doctorow

Osher Doctorow
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