Peter,
You are right in that there is a problem with comparing the
weak, E&M, and gravitational forces to the strong force. The problem is
the strong force is linear while the other three obey the inverse square
law. Also, depending on energy density, the strong force can change to
a Coulomb-like force but then color screening makes it Yukawa type.
Very tricky business since this is non-perturbative QCD. Don't worry
everyone, I am not going any further than to say that anyone who
understands that should show up in Sweden next year for a medal.
I believe the quoted numbers like strong:gravity = 1:10^{-42}
comes from looking at the coupling constants. These would be G, alpha
(1/137), alpha_W (??), and alpha_S (which changes at different values).
Hope that helps and didn't confuse too much.
Sam Held
-----Original Message-----
From: Peter Vajk [mailto:vajk@IX.NETCOM.COM]
Sent: Saturday, May 22, 1999 6:29 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: Fundamental Forces
As I recall from my undergraduate physics a long time ago, "field" was
defined as "force per UNIT (mass/charge/hadron number, etc. -- take your
pick)", just as "potential" was "potential energy per UNIT (whatever)."
The field is then the gradient of the potential (if the potential can be
defined at all); the force is the gradient of the potential energy. In
thermodynamic terms, force is an extensive variable; field is an
intensive
variable.
As to relative strengths of the forces, gravity and E&M can be
"compared"
by computing the gravitational force and the electrostatic force
between,
say, an electron and a proton at a given distance apart (say, the Bohr
radius of the hydrogen atom). Since both forces scale the SAME WAY with
distance, this is a reasonable way to make a comparison -- except it
muddies the issue of whether it's the FORCES that are radically
different
strengths or that the CHARGES/MASSES are not "equivalent." Nonetheless,
the ratio of the grav. & E&M forces in the hydrogen atom is
illustratively
useful.
As to comparisons of these two inverse-square-law forces with the other
two, the comparison gets murkier. For the strong nuclear force, it's
probably reasonable to ask what the strong force between two protons IN
A
NUCLEUS is compared to the electrostatic repulsion between them. How
one
does this for the weak nuclear force (which governs beta-decay) I truly
don't see -- is it perhaps by comparison of energy density in the
fields?
Peter Vajk
St. Joseph Notre Dame High School
Alameda, CA