Re: h bar and Lorentz transformation
From: robert bristow-johnson (rbj_at_audioimagination.com)
Date: 03/19/05
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Date: Sat, 19 Mar 2005 08:03:09 +0000 (UTC)
in article 1111009776.161148.65590@g14g2000cwa.googlegroups.com,
pointlike@gmail.com at pointlike@gmail.com wrote on 03/18/2005 13:38:
> The constancy of the speed of light is usually mentioned as one of the
> corner stones of special relativity.
there are some variable speed of light (VSL) theories, but they sound like
cold fusion to me.
> How about the constancy of h_bar, it is like c, a universal constant
> too but it is never mentioned as a corner stone of quantum mechanics!!!
well, it is. check out http://xxx.lanl.gov/pdf/physics/0110060 or
http://arxiv.org/pdf/physics/0110060 .
> is there any physical principle behind that?
one important physical principle is that ultimately the only physical
quantities that we measure in physical experiments or even in our
perception of reality are dimensionless quantities. a simple everyday
example is when one measures a length with a ruler or tape measure, that
person is counting tick marks on that ruler. that person is measuring
this physical quantity against another like dimensioned physical
quantity that might be called a standard or unit.
Planck's constant, h_bar, the speed of propagation of E&M or gravity, c,
the Newtonian gravitational constant, G, the Boltzmann contant, k, are
all dimensionful "constants" whose numerical value depends on the units
we use to measure them. i've always understood this regarding the
Boltzmann constant, k. you can set k to whatever you want by defining
the unit temperature so that k can have any numerical value. i did not
look at temperature as a distinct physical quantity but simply as a
measure of kinetic energy per particle per degree of freedom.
people on this newsgroup might remember that i had a tougher time coming
to that conclusion regarding h_bar, c, and G. but J Lodder, T Bunn, and
J Baez (as well as a few direct email conversations with Michael Duff,
Lev Okun, and some others) set me straight about that. the problem with
h_bar, c, and G, as opposed to k is that the relationship of k to the
unit temperature is simply a one equation, one unknown thing. sorta
like defining the Newton as the unit of force that will accelerate one
kilogram at a rate of one meter/sec^2 with no scaling constant in F=m*a.
you could do the same thing for the unit temperature to make the
scaling constant, k, be anything you what, including 1.
but with h_bar, c, and G, setting those to prescribed values (say 1, if
you want to get rid of them in equations) require 3 equations with 3
unknowns (dimensionful physical units) and there *are* 3 arbitrarily
defined, anthropocentric units that we can redefine to change the values
of h_bar, c, and G to whatever we want. those units are the unit of
length, time, and mass. if you want h_bar, c, and G to all be 1, the
units of length, time, mass we get are the Planck Units
http://en.wikipedia.org/wiki/Planck_units .
> or is there something special about c? a historical reason may be?
it is the natural unit of speed that we ultimately measure all other
speeds against. they have now, since 1987, defined the meter to be the
distance that light travels in 1/299792458th second. that's a
historical decision that will set c to the constant 299792458 for all
time (as long as they stick to that definition of the meter).
quoting Frank Wilczek in June 2001 Physics Today:
"We see that the question [posed] is not, 'Why is gravity so feeble?' but
rather, 'Why is the proton's mass so small?' For in Natural (Planck)
Units, the strength of gravity simply is what it is, a primary quantity,
while the proton's mass is the tiny number [1/(13 quintillion)]."
( http://www.physicstoday.org/pt/vol-54/iss-6/p12.html )
paraphrasing: "the speed of propagation of light (or gravity) simply is
what it is, a primary quantity, while the human unit of time (the
"second", about the time between heartbeats) is the large number."
something similar could be said for h_bar.
besides the paper cited above, you might want to look at
http://arxiv.org/pdf/hep-th/0208093 and
http://www.teorfys.uu.se/courses/exjobb/varconst.pdf
and, of course, NIST http://physics.nist.gov/cuu/ to get the low-down on
how the anthropocentric units have been defined in the past and how they
are defined today and what some of these universal physical constants
are, in terms of those units.
> Does the term "universal constant" necessirely mean, it is the same in
> all inertial frames?
probably the differentiation to make is dimensionful universal constants
(that end up being constructions of and anthropocentric system of units)
and *dimensionless* universal constants (whose values do not depend on
the system of units). h_bar, c, G, and k are examples of the former
and they can be anything, depending on the units we use to describe
them. the Fine-structure constant, alpha = e^/(h_bar*c*4*pi*epsilon_0)
is an example of the latter and is about 1/137.036, no matter what units
you use to describe h_bar, c, e, and epsilon_0.
if we were to measure time and length and mass in terms of Planck units
(or some constant multiple of them), even if h_bar, c, and G were to
change, they would stay the same, from the POV of these units.
-- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
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