Lu,
The natural units, c=h=k=1, does not eliminate the units from
the units just the calculations. In high energy physics, the time unit
is fm/c or just fm in natural units. Why? Because a most particles
produced (99.999999...% of them do) travel at c, so the distance gives
us a better understanding of the development of the collision region.
One can easily recover the proper units by inserting a factor of hc.
Any really good high energy or rel. kinematics book will discuss this.
Most text do not and take it for granted, so the instructor should cover
this. Ask your teacher why he didn't explain this.
Sam Held
----Original Message-----
From: luqiang [mailto:lqwy@263.NET]
Sent: Monday, May 31, 1999 9:53 AM
To: PHYS-L@LISTS.NAU.EDU
Subject:
There are four furthermental dimentions in physics. They are
space L, time T,
mass M, and temperature K. Other mechnics quantity can be represented in
terms of
these
four dimentional fundermentals. For instance, gravitation constant
[G]=L/M and charge
[Q]=(LM)^1/2, Where [quantity] represents the dimentaion of that
quantity. The
dimentions of these two quantities can be seen from expression
(1-2GM/r+GQ^2/r^2),
which comes from the caes of a charged black hole. M is the mass of the
blak hole.
Three main theory, special relativity, quantum mechnics, and
thermodinamic,
introduce three constants, these are c (the velocity of light c=0.998e8
m/s),
h (Planck constant h=6.628e-34 kg*m^2/s), k (the Boltzmann constant
k=1.381e-23 J/K).
If these three constants are set to be contant 1, correspondong, three
furthermental
dimentions are eliminated. Mass M and temperature K has energy
dimention. Time T and
space L has dimention of reciprocal of energy. So we choose energy
dimention E to be
the rest one. Then all physics quantities can be descripted by E.
The dimention of the gravitation constant G now is E^(-2). And,
[Q]=1. This is
natural units.
One may say that if there is a new theory which is able to introduce
a new
constant to eliminate the last dimention, this world will be a
mathmatical one. But
it is impossible, because, the process of elimination of one dimention
is depend on
another dimention. Thus there can not be another fundermental theory
which need to
introduce a new constant. Furthermore, this world was, is, and will be
never a
mathmatical one. But ...
But if we choose the space L to be the last fundermental dimention,
this world
is able to be descripted into geometry. Thus, all physics quantities can
be derived
from geometry quantities. For 4-dimention space, if distance and time
are not
independent, they have the same dimention. This conclusion is tenable as
well. My
opinion has no sufficient proof. I wish someone try to refute my opinion
and tells
me where does that original dimention come from.
Besides, I am a chinese student. Maybe my English writing is not
fine. If anyone
who find improper words and sentences, I wish he or she may correct
them. Thanks.