Newton's Laws of motion, as described in Principia, only work under a range of circumstances. Both relativity and quantum mechanics are more general theories that include Newton's Laws as an approximation, accurate only for a range of conditions.

Newton's Laws and Maxwell's equations (which characterizes electromagnetic fields) seemed to contradict each other until special relativity came along. For example, consider two electric charges. A force couldn't propagate from an electric charge faster than the speed of light according to Maxwell's equations. However, Newton's Third Law implies that there is a reaction force immediately in the second charge, with no pause. Einstein showed that one could make a logical resolution by changing the concepts of time and space.
According to quantum mechanics, energy can be viewed as carried by particles or waves. This isn't part of relativity.

However, in pure relativity (no quantum mechanics), a field can store energy. A field is a region of space where a particle will experience a force. The strength of the field is the force on the particle divided by some numerical characteristic of the particle. By treating waves in a field as having "real" properties like mass, in other words treating the "wave" as real object like a particle, one could resolve the third law of Newton with the forces like electromagnetism.

Basically, SR presumes that waves in a field can have mass, energy, and momentum even if they aren't particles. The 1905 paper by Einstein has "field equations," which many casual readers like to skip. However, "field equations" are very important in relativity since they contain the forces that some critics say aren't in SR.

The question presumes that both quantum mechanics and special relativity are both at least partly correct. The implied assumptions are that there are photons (quantum mechanics), and that they obey E=mc^2 (SR). The mass in the "E=mc^2" formula is really called the "longitudinal mass." The longitudinal mass of a photon is NOT zero.

In SR, the "longitudinal mass" (the mass that you are talking about) is equal to the rest mass times a Lorentz factor. The Lorentz factor becomes infinite at the speed of light, and a finite number times infinity is infinity. So a particle of finite rest mass can't go at the speed of light. The rest mass is the energy that a particle would have as measured by an observer in the same inertial frame as the particle.

If the rest mass is zero, the "longitudinal mass" at the speed of light is zero times infinity which is indeterminate. It can be any number at all, so something else has to determine it. So a particle of zero rest mass has to move at the speed of light to carry energy.

One implicit assumption in SR (?) is that all observers have a nonzero rest mass. Therefore, an observer can't go at the speed of light (or else its "longitudinal mass would be infinite). Since a photon moves at the speed of light, no observer can be in the same inertial frame as a photon. So one can not measure a "zero rest mass" of a photon. Questions of the "reference frame" of the photon are meaningless because all observers have a finite rest mass.

Actually, I haven't actually read that asumption explicitly stated anywhere. Is there an implication in SR, as defined by the 1905 paper by Einstein, that all observers have a finite rest mass? Where is it written? I have seen beings of pure energy in science fiction, and even a creature made of 100% light in the old Outer Limits, but I suspect that this is impossible. However, if such a creature did exist, one would have to worry about the "rest frame" of a photon.

<font size=-1>[ This Message was edited by: Rosen1 on 2001-12-04 20:54 ]</font>