This is wrong as stated. I think that you meant something else. I believe that current usage of the word "mass" by physicists usually means the "longitudinal mass," and that you are probably thinking of mass as the "rest mass." I will make a painfully long winded explanation of the difference.

When physicists today speak of mass, they are usually speaking about what Einstein called the "longitudinal mass" in his 1905 paper. This is defined assumming an observer in an inertial frame who sees a particle or closed system move relative to him at a velocity v. By "system" moving at v, I am talking about a set of particles and waves where the center of mass is moving at v. Both Newton's Laws and Maxwell's equation apply to the observer, albeit in a highly modified manner.

One of the modifications to Newton called mass or inertia is anistropic. That is, there is one "mass" for the moving system in the direction of motion called the "longitudinal mass," and another "mass" for the system in the direction perpendicular to the direction of motion (the "transverse mass)." The equation:
F = ma
still applies. However, if the force is in the direction of the velocity v then "m" is the longitudinal mass, and if the force is perpendicular to v then the "mass" is the longitudinal mass.I don't remember the formula for transverse mass right now, but it isn't very important for this discussion. The equation for longitudinal mass m_L of a particle or system
m_L = m_0 /sqrt(1-(v/c)^2)
where m_0 is a parameter known as the "rest mass." Now, in these terms, the famous formula can be written as:
E = m_L c^2
where E is total energy of system, as measured by an inertial observer, and c is the speed of light.

One place the use of longitudinal mass can be seen is in a closed system. Imagine an almost rigid box (i.e., as rigid as SR allows) where the is a mixture of particles bouncing back and forth near the speed of light, in addition to light particles (photons) bouncing back and forth at the speed of light. Consider an inertial observer in the rest frame of the center of mass of the box.

To this observer, the box is standing still (i.e., |v|=0). He can examine it by pushing or pulling it. For him, the longitudinal mass of the box is exactly the same as the rest mass. He can used Newton's Laws up to the point that the center of mass goes close to the speed of light.

However, suppose he does experiments to find out what the inside of the box is like. The particles inside have a longitudinal mass almost as large as the speed of light. Their rest mass is NOT their longitudinal mass. The rest mass of the photons is definitely NOT the longitudinal mass. The rest mass of a photon is zero. However, the energy of a photon is given by quantum mechanics (Plancks constant times frequency of light wave) so the longitudinal mass can be found by the E=mc^2 formula. Every particle in that box has both a rest mass and a longitudinal mass.

How would one find the "rest mass" of this slow moving box from the microscopic examination. Well, the longitudinal mass of the system is equal to the sum of the longitudinal mass of its components. Since for the entire box (moving at slow speeds) longitudinal mass is equal to rest mass, the rest mass is equal to the sum of the longitudinal masses of the component particles. It is this mass that is conserved, even if the box should prove not so rigid and bust apart. If it explodes, the sum of the "longitudinal masses" will be preserved.

Note: This doesn't work if we use the word "mass" to mean rest masses. None of the photons have a rest mass, so they don't count. Even if the longitudinal masses of the photons add up to a ton of light, they can't be part of the summation. The high speed particles also are underrepresented by rest mass. The concepts of mass as an additive property means longitudinal mass.

I have ignored the energy stored in the stress fields of the box itself (i.e., the almost rigid surface). However, the longitudinal mass of the surface of the box is also is part of the summation. I don't want to get into relativistic rheology in this discussion, but the energy in the stress fields should be included in a real calculation of total longitudinal mass. I only mention this because some critics of relativity try to show a "contradiction" by doing a calculation without the energy of the surface.


Since Einstein wrote his paper, the word "mass" as used by relativistic physicists has come to mean "longitudinal mass." The usage is somewhat inconsistent. When I say the mass of a proton, I don't give a velocity because everyone knows the context implies rest mass. However, the conservation of mass applies strictly to the "longitudinal mass." So when I refer to either a conservation law or the E=m c^2 formula, I always use the longitudinal mass. You can see that, interpreted this way, the law of conservation of energy is really the same as the conservation of energy.


<font size=-1>[ This Message was edited by: Rosen1 on 2001-12-08 03:10 ]</font>