MadSci Network: Physics Query:

### Re: energy in relation to mass

Date: Wed Dec 30 12:39:31 1998
Posted By: Everett Rubel, Degree in Physics
Area of science: Physics
ID: 913661856.Ph
Message:

Alfred,

Thanks for the question.  The definitions of energy and mass can be tricky
when we look closely at them.  What I state here will certainly be
considered incomplete or inaccurate by some, but at least it will give you
an idea of what some of the issues are.

1.  Energy is the motion or frequency of matter.
Energy does not necessarily require the presence of matter or mass to
exist.  One example is a static electric or magnetic field.  Such a field
can store energy and we can talk about the energy density of the field.

2.  Photons have zero rest mass.
Another example of energy without matter or mass is electromagnetic
radiation (photons.)  It is confusing to talk about rest mass for a photon
however, since photons only travel at the speed of light c.  It is better
to say that the invariant mass of the photon is zero.  Also, to add to the
confusion,  a SYSTEM of photons with zero net momemtum could be considered
to have a nonzero invariant mass.  An illustration of this is the system
composed of the two oppositely directed photons created when an electron
and positron annihilate.  From the perspective of general relativity it is
possible for two massless photons to combine to form something that has a
mass.
Take a look at this link for a better explanation of what is going on:

http://math.ucr.edu/home/baez/physics/light_mass.html

3. Neutrinoes have recently been found to have mass.
Actually, the jury is still out on this one.  It appears probable that
neutrinoes have a small mass, but the results really need to be confirmed
by other experiments.  There are other probable massless particles however.
An example would be the graviton, the carrier of the gravitational force.

4. Is there any form of energy which has no mass?
From the examples mentioned I would say that energy does not have to be
associated with mass.   I think that what confuses many people learning
about physics and relativity is the famous relation E = m c^2.  The fact
that an equivalence between mass and energy can be defined does not mean
that a given amount of energy can be considered as a related amount of
mass, at least not in all circumstances.  This is particularly true with
regards to the photon.  Please see this related link where I have done most
of my research on this topic:
http://math.ucr.edu/home/baez/physics/mass.html

The relationship between mass and energy seems to be fairly complicated
once we enter the realms of special and general relativity.  I would
caution you to take explanations provided by any popularization of physics
with a grain of salt.  There are always many more details that the authors
don't have time to discuss.

Regards,

Everett Rubel

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