

Photon Mass
Name: Daniel R.
Status: student
Age: 15
Location: N/A
Country: N/A
Date: 20002001
Question:
In your archive question # 24 you state that lasers have
a small amount of recoil due to the momentum of the photons leaving it.
But if a photon has momentum, doesn't it also have to have mass?
If so, then since it is traveling at light speed, wouldn't it's mass would
have to be multiplied by infinity? But this couldnt happen, because the
universe would collapse every time a photon was generated.
Also, why does magnetic field strength decrease much faster than the
inverse square of the distance like gravity? Is it because the force lines
have to curve back to the source? Is magnetism also carried by an
"imaginary" particle?
Replies:
This is several questions:
1. It a result of the theory of relativity that a photon has momentum, but
have zero mass. One of the worrisome aspects of relativity and quantum
mechanics is that we must abandon our graphic notions of Newtonian
mechanics, and also some of the notions of classical electromagnetic theory
of Maxwell. The problem you are asking about is only one of several notions
that has to be abandoned. In addition, there is the "fact" that the photon
has angular momentum  but from the classical picture, "something" has to
be spinning. What's spinning? And an electron orbiting a proton in the
hydrogen atom should spiral into the proton emitting electromagnetic
radiation, but it doesn't. Why not? The "why not" to all the above is that
our classical picture just does not correspond to observation, so we are
forced to reject our "picture" and adhere to the "observation" and not the
other way around. Richard Feynman
discusses the momentum of a photon in Vol. I  34  10 of his Lectures on
Physics.
2. The force generated by a magnetic field does not obey an inverse square
law  a fact. It obeys the force law associated with a dipole. When you ask
for a "Why?" modern physics is at somewhat of a loss because there really
isn't an easy answer. It doesn't (at least at our current state of
knowledge) and we have to live with that. I don't know that there is any
answer to the question "Why?" I believe it is important to always add, "At
least at our current state of knowledge." provision, because a few years ago
no one would have thought it possible to bring a photon to a dead stop, but
it has been done, and done so rather convincingly.
Sorry if this seems not to be very satisfying at a gut level, but we do not
have any direct experience with either quantum mechanics or relativity. We
see what the theories predict, do the experiment to confirm or deny, and
examine the experimental result. That is the only criterion of the validity
of the theory.
Vince Calder
Daniel,
You ask two very good questions.
For most average objects, momentum is truly mass x velocity. When motion
gets close to the speed of light, we find that the momentum relation p=mv is
only an approximation. It is only correct when speed (v) is much smaller
than the speed of light (c). The relation that works for all speeds is E^2
= p^2c^2 + m^2c^4. It is much less convenient to use, and doesn't help
figure anything out until you reach speeds of perhaps thirty million meters
per second. For a particle with no mass, the relation reduces to E=pc.
This works for a photon. For very small speeds, the system reduces to
E=mc^2 + (1/2)mv^2, and p=mv. This leads to relations with kinetic energy
and momentum: much more convenient to work with and just as accurate until
you reach speeds close to the speed of light.
As for magnetic field, there is no reason why it should behave like gravity.
For one thing, the strength of magnetic FORCE depends on the speed of the
particle being pushed or pulled by the field. Also, unlike gravity,
magnetic force pushes sideways, perpendicular to the field direction.
Gravitational force is just gravitational field multiplied by the mass being
pushed or pulled. Electric force is just electric field multiplied by the
charge being pushed or pulled. Magnetic force depends on the charge, speed,
AND direction of the charge being pushed or pulled, as well as the strength
of the field. It is a very different kind of force.
As for "carrying" the field, it is known that photons of light transmit both
electric and magnetic force. In fact, light is waves made of oscillating
electric and magnetic fields.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012

