what i recall Clay, is that it was YOU that first told me the name for
Planck Units:
http://groups.google.com/group/sci.physics/msg/e1d9352d0a6b64b3
and i thank you profusely. because you did that, i was able to do web
searches, found papers/web_sites/books by Michael Duff, Gabriele
Veneziano (pioneers of string theory), Lev Okun, John Baez, and John
Barrow and i've had several really neat email conversations with ALL 5
of these guys about the nature of fundamental physical constants (the
only ones that count are the dimensionless ones, any notions of a
"varying c" or "varying G" are not even wrong, they're meaningless,
and for those who can't see that, just think of everything measured in
Planck units). and then later i got into Gravito-electro-magnetism
(GEM) a little and some interest in the Gravity Probe B (which*still*
hasn't been able to conclusive say that frame-draggin or
gravitomagnetism or gravity waves can be measured, they are behind
schedule.)
none of that fun would have happened if you hadn't done that for me
nearly a decade ago. thanks.
discovered a word for that, too: "Nondimensionalization." there's a
wikipedia article on that also. i may have done a minor edit to that.
but dunno.
isn't normalizing the Rydberg constant have similar effect as fixing
the Bohr radius (with another dimensionless alpha tossed in)?
just curious.
r b-j
Hello Robert,
I'm glad my giving a name for Planck units put you on an interesting
course. I recall reading many years ago about Paul Dirac exploring the
ideas behind Planck units. And that is how I knew about them.
Studying Hydrogen has yielded some very interesting info. Balmer
empirically put together a formula that fits the spectral lines of
Hydrogen, but it offered no theory.
Bohr with his theory of the atom gave a theoretical basis for Balmer's
formula. But spectroscopists soon discovered a slight flaw in that
some of the energy levels had finely spaced details. A spectral "line"
under close observation turned out to be 2 or more lines very close
together.
Sommerfeld found by adding special relativity and elliptical orbits to
the theory, that he was able to explain the fine splitting (fine
structure) of the spectral lines. Bohr was of course ecstatic that his
theory was saved. Sommerfeld introduced the notion of the fine
structure constant, which in many older books is called the
"Sommerfeld fine structure constant", but now many have dropped
Sommerfeld's name - what a shame.
Alpha, as the constant is usually denoted, was discovered to be a
dimensionless number which may be expressed as (e*e)/(2*epsilon_0 *
h*c) and "e" is the charge of the electron, h is Planck's constant, c
is the speed of light in a vacuum, and epsilon_0 is the permititivity
of free space. We know alpha to be basically = 1/(137.0359895...). The
fact that it is much smaller than one allows perturbations to simple
systems to be expanded in series involving successive powers of alpha.
These series may be found by using Feynman diagrams.
Even though Sommerfeld discovered alpha with his work on Hydrogen, it
has turned out to be one of the most important fundamental constants
with consequences far beyond atomic physics. It shows up in many
places such as in the interaction of E-M fields with electrons and in
nuclear and particle physics.
In terms of atomic theory, the Bohr radius may be written as
(4pi*epsilon_0*h_bar^2)/(m*e^2), where m is the mass of the electron,
e is its charge, epsilon_0 the permititivity of free space, and h_bar
is Plank's constant h divided by 2pi.
A Hartree is simply alpha^2 * m*c^2 (27.2116 electron volts) and a
Rydberg is half of a Hartree. Again "m" is the mass of the electron
and c is the speed of light. Douglas Hartree did a lot of work in
computational atomic physics, and he gave us "atomic units." He even
built analog computers from a kid's toy called "mechano" to solve
atomic physics calculations back before WW2. [Mechano (UK) is a toy
very much like the Erector Set in the U.S.]
I've been working on a new algorithm to solve the Hartree-Fock
equations. So far the results have been quite encouraging. I.e., more
accuracy with less computation.
Clay
p.s. A book you may find interesting is "Universal Constants in
Physics" by Gilles Cohen-Tannoudji, 1993 McGraw-Hill. The parts on "h"
& "k" are interesting with "h" being the quantum of action and "k"
being the quantum of information.