### Re: does a particle have mass if it does not move?

Date: Thu Sep 6 17:49:23 2001
Posted By: Randall Scalise, Faculty, Physics, Southern Methodist University
Area of science: Physics
ID: 998256532.Ph
Message:
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Dear David,

Particles that acquire their mass through the Higgs mechanism do NOT
need a velocity relative to the Higgs field in order to interact with
the Higgs field.  The masses of quarks, leptons (electrons, muons, and
tauons), and the carriers of the weak nuclear force (W+, W-, and Z)
are all proportional to the so called "vacuum expectation value of
the Higgs field".  I will explain below.  But none of the particle
masses depend on the relative velocity between the massive particle
and the Higgs field.

Now to explain the vacuum expectation value of the Higgs field.
For most fields, the configuration with the lowest possible energy
is to have zero field everywhere throughout the Universe.  For example,
the lowest energy state for the photon field is no photons anywhere.
But the Higgs field is different; the lowest energy state for the
Higgs field is to have some Higgs particles present.  It would actually
cost you energy to eliminate all the Higgs particles from the Universe.
Particles like the electron interact with this lowest energy Higgs
configuration and as a result acquire a mass.

The increase of mass with speed is purely a Special Relativistic effect
and has nothing to do with the Higgs field.  Here is an easy way to
see that the Higgs field is not involved:
1)Measure the mass of an electron that is at rest relative to you, and
call the mass m.
2)Next shoot the electron out of a gun at nearly the speed of light
(let's say 0.994987 times the speed of light).  If you measure the
mass of this moving electron, you will find appoximately 10m.
3)Now run alongside the electron at the same speed.  The relative speed
of the electron with respect to you will be zero, and the mass you
will measure will again be m.

In summary, the number that multiplies the "rest mass" of a particle
(10 in my example) depends on the speed of the particle relative to
the observer.  The rest mass itself (m in my example) depends on the
lowest energy state of the Higgs field.

--Randall J. Scalise    http://www.phys.psu.edu/~scalise/

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