QUOTE(Trick cyclist @ Wed 9th December 2009, 2:22am)
QUOTE(Milton Roe @ Tue 8th December 2009, 11:39pm)
Correct, but ...
This seems to be a matter of definition. What was matter (which of course has mass) is converted to energy which (by E=mc^2) still has mass. The total mass of the universe remains constant but matter is converted into energy. Sometimes energy is converted to matter too.
The real problems come in trying to define "matter." Why should "electrons" be counted as "matter" but "photons" not? This seems to be to be mainly fermion-o-centrism. Or, if you like virtualgaugeboson-ophobia. Due to the exclusion principle, fermions have a bit more "matter-like" quality than do bosons, but at the end of the day, particularly for virtual fields, there's not much difference. All "particles" have wave-like natures and waves have particle-natures, and which way you wish to see the world is up to you. If the math predictions are the same, it's just your prejudice. Physicists as great as Weinberg have chosen to see everything in nature in terms of fields, with "particles" as simply field excitations. Feynman chose to see it nature in terms of particles. The math is the same.
What you can't get away from is the fact that 98% of the mass of ordinary "matter" is not fermions, but just fermionic kinetic energy and perhaps the mass of some gluon "field".
The message of E=mc^2 is simpler: mass and energy are the same thing, and so neither one appears without the other. Energy always has mass, and mass always represents energy. The two are not interconvertable because they are separately conserved over time, and the amount of both of them in any isolated system never changes (and when you open the system, they both leave or enter together). And there you're done--- unless you make the mistake of trying to differentiate "matter" from energy. Mass is easily defined-- matter is not.
The only other wrinkle is defining the KINDS of mass and energy. Both remain the same value over time for the single observer. However, different observers may disagree (according to your definition) on what the value IS (even though all observers agree that it does not and cannot change). There's a type of E and M that varies with observer, and a type that doesn't.
The energy that changes with inertial frame and observer is called relativistic energy, and the mass that does this is called relativistic mass. The relationship between the two is E=mc^2.
The energy that does NOT change with inertial frame and observer is called invariant or rest energy, and the mass that does this is called invariant or rest mass. The relationship between these two is also E=mc^2.
However, it is NOT generally true that E=mc^2 where the E is of one sort, and the m is of the other. There is a momentum term which must be added in to get from one sort of energy and mass, to the other sort. Thus, the only time the two kinds of energy and the two kinds of mass are all four of them equal to each other (forget the factor c^2) is in the inertial frame where momentum of the system is zero. This is called the "center of momentum" or COM frame. Such a frame (call it a velocity point of view) always exists for any system of 2 particles or more, so long as they're doing different directions. When you get into this frame (travel at its constant velocity), everything is simplified, because all the different types of energy and mass are now equal. Also, interestingly, their value is minimized in this frame. So even though their value never changes over time in any frame and for any observer, you are free to choose a frame (or observer) where this value is minimized, and the COM frame is it.
Milton