Re: A Stringy Nature Needs Just Two Constants

robert bristow-johnson wrote:

i think it is part of this conversation:

http://xxx.lanl.gov/abs/physics/0110060
"Trialogue on the number of fundamental constants"

between the author (GV) and Michael Duff and Lev Okun.

Thanks for the link to this very interesting paper.
I am finding the contribution by M. Duff most
convincing. It is in the spirit of a paper
by J.M Levy-Leblond, Riv. Nuovo Cimento, Vol.7, 188 (1977)
which had much influence on me. Levy-Leblond sated that
our progress in understanding the nature follows the
direction of eliminating from theories various
(inessential) numerical constants with the improper name
"fundamental" constants. In fact those constants
are merely the constants which result from our
unnatural choice of units, the choice due to our
incomplete understanding of the unified theory behind.

and i don't know diddley about string theory, but i would think that
any physical theory can be scaled in such a way that Planck units are
the units which makes "c", "G", "hbar", and "4*pi*epsilon0" all equal
to one. then they just go away in expressions of physical law, and
any numbers that remain are truly fundamental constants.

It is precisely what I played with. So I calculated the conversion
factors between the MKSA units and the units in which those four
constants are equal to one. It is incredibly useful in actual
calculations. So I am using those tables whenever I wish to do some
numerical work with the quantities entering the equations, which may be
written in the units in which c=G=1, or in the units in which
c=G=hbar=1, etc. One can simply put all fundamental constants to one,
perform calculations in the units in which c=G=hbar=4 pi epsilon =1, and
then convert the result into MKSA units.

Calling those units in which all four constants are equal to one
units D, one has

1D = (\hbar c/G)^{1/2} = 2.1768269 \times 10^{-8}$ kg
1D = (\hbar G/c^5)^{1/2} = 5.3903605 \times 10^{-44} s
1D = (\hbar G/c^3)^{1/2} = 1.6159894 \times 10^{-35} m
1D = (4 \pi \epsilon_0 \hbar c)^{1/2} = \alpha^{-1/2} e
= 1.8755619 \times 10^{-18} As
1D = c^3 (4 \pi \epsilon_0/G)^{1/2} = 3.4794723 \times 10^{25} A
1D = c^2 (4 \pi \epsilon_0 G)^{-1/2} = 1.0431195 \times 10^{27} V
1D = c^2 (\hbar c/G)^{1/2} = 1.9564344 \time 10^{9} J
1D = 1.41702 \times 10^{32} {}^0 K

I first published this (together with some discussion of how various physical
quantities transform under dilations) in Appendix of my
book "The Landscape of Theoretical Physics: A Global View;
From Point Particles to the Brane World and Beyond, in Search of
a Unifying Principles" (Kluwer, May 2001) which is now available
on arXiv: http://arxiv.org/abs/gr-qc/0610061

.

Relevant Pages

  • Re: Different laws of physics
    ... laws of physics. ... Each physical theory has a number of fundamental constants. ... is considered to have our laws of physics if those fundamental constants ... end up with a universe in which there are no atoms heavier than hydrogen ...
    (rec.arts.sf.science)
  • Re: reliability of error bars for fundamental constants
    ... Jonathan Thornburg wrote: ... > be given as known to within certain specified uncertainties (more precisely, ... Any chance it might have been in Physics Today? ... articles on fundamental constants there occasionally. ...
    (sci.physics.research)
  • On absolute units
    ... In October 2005 issue of Physics Today Frank Wilczek ... a triple of fundamental constants. ... including the electromagnetic field and electric charge, ... Numerical calculations with units D are ...
    (sci.physics)
  • Re: Fundamental constants and the fine-tuning argument
    ... The fine-tuning argument claims that the fundamental constants of ... nature and physics are evidence of design because they are ... The design inference assumes that at one time ... demonstrate that it is possible for these fundamental constants to be ...
    (talk.origins)