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Re: SI and nothing else



Bob S. wrote:

But this doesn't define a definite interval of time unless the frequency
of the e.m. wave is specified. Or do I mis-interpret. (I never could make
sense out of this h=c=1 system!)

What I think Ludwik meant (or should have meant) was that one GeV^(-1) unit
of time is the time required for a photon of *energy 1 GeV* to go through a
phase change of 1 radian. This is 1/(2*[pi]) of the photon's period.

BTW, I would not characterize the GeV-based unit system of high energy
physicists as 'diabolical' (unless they really did set 1 = [pi]). No one
using those units really sets [pi] = 1 when doing any careful consistent
calculation. Occasionally, factors of [pi], 2, etc. are ignored when doing
a crude order of magnitude *estimate* (not real calculation). But ignoring
such factors is precisely what is supposed to be done in any crude Fermi-type
estimations of orders of magnitude.

Ludwik added:
Suppose I declare that v is dimensionless and equal to one. Why? Because
I am a spider who lives on this rope and v is my "universal constant".

The reason that velocities are dimensionless in relativistic calculations is
that velocities are just a particular variety of slopes of world lines in
spacetime. The reason that c = 1 in such calculations is that is simplest to
denominate all dimensions and directions of spacetime in the same units. The
real meaning of the factor c in physics is that it is a unit conversion
factor for converting intervals of spacetime denominated in seconds (or other
'time' units) to a denomination in meters (or other 'space' units). Doing
relativity with c not equal to one is like doing high school plane analytic
geometry where the x axis is denominated in miles and the y axis is
denominated in microns. It is doable, but it sure is more complicated. It's
hard enough to teach about the Pythagorean theorem, trigonometry and the
rotation of 2-vectors in the plane to high schoolers when both directions in
the plane are in the same units. Imagine the teaching nightmare that would
ensue if we insisted on teaching these subjects with all x values in miles
and all y values in microns. Every time we wished to find the Euclidean
length of a vector, to rotate a vector, to find the scalar product of 2
vectors, to find the slope of a line, or to do almost anything more
complicated than Cartesian vector addition we would have to keep inserting
the unit conversion factor of 1.609344 x 10^9 microns/mile throughout our
calculations. This is precisely the situation we are in if we insist on
teaching relativity where intervals along the 'time' direction in spacetime
are denominated in seconds and intervals along the 'space' directions are
denominated in meters. In this case the conversion factor of
c = 299792458 m/s keeps popping up in our calculations. Setting c = 1 makes
the subject of relativity more simple *not* more complicated.

And
I want to simplify things as much as possible. What can be more simple that
a system with only one fundamental unit?

A system with *zero* fundamental units is more simple than one with one
fundamental unit. Thus, Planck units are simplest.

Is c=h=1 an example of a simplification which makes things more difficult?

That depends one what you are trying to accomplish. It is a simplification
that makes the true underlying conceptual structure of physical theory more
transparent. It helps with the deep understanding of the concepts of
physics. If such understanding is not an objective then it is a
simplification that won't help. If the objective is just to turn out
engineers who are adept at making 'practical' calculations, then it is a
simplification that makes things more difficult (esp. if the answers of the
practical calculations must be displayed in practical units).

David Bowman
dbowman@gtc.georgetown.ky.us