- #1
arivero
Gold Member
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The conversion of energy into mass is usually seen in nuclear or atomic binding. We have two particles of mass M,m and then they form an stable compound of binding energy -E, so the new coumpound shows an inertial mass of M+m-E/c^2.
Things that amaze me:
a)It works. It is clear for instance from mesurement of atomic masses, and even from almost-XIX-th century measurement of molar weights.
b)I have never seen this calculated explicitly in a textbook. One should decompose the movement between center-of-mass plus internal, and then to show that while the internal movement uses the usual reduced mass, the center of mass uses the new bound-state mass. Also, the internal energy would equilibrate or at least contribute to the bound-state energy.
c) Relativity textbooks work only with kinetic mass/energy relationships, and mostly between inertial systems. As a bound state does suffer a constant acceleration, it is not easy to see how the SR equations can be applied. Still one wonders if and how a gravity, GR, bound state (moon-earth, say) gets a mass correction from gravitational binding (thus a minor correction to solar orbit), but I guess it is a more complex calculation that just m times c square, is it?
d) On the other hand, it is easy to envision that a quantum binding of, say, a electron and a proton is done via emision of a photon having exactly the binding energy, thus the relativistic mass of the photon leaving the system is exactly the mass lost by the new state. But here we need, it seems, *quantum* radiation theory, do we?
Things that amaze me:
a)It works. It is clear for instance from mesurement of atomic masses, and even from almost-XIX-th century measurement of molar weights.
b)I have never seen this calculated explicitly in a textbook. One should decompose the movement between center-of-mass plus internal, and then to show that while the internal movement uses the usual reduced mass, the center of mass uses the new bound-state mass. Also, the internal energy would equilibrate or at least contribute to the bound-state energy.
c) Relativity textbooks work only with kinetic mass/energy relationships, and mostly between inertial systems. As a bound state does suffer a constant acceleration, it is not easy to see how the SR equations can be applied. Still one wonders if and how a gravity, GR, bound state (moon-earth, say) gets a mass correction from gravitational binding (thus a minor correction to solar orbit), but I guess it is a more complex calculation that just m times c square, is it?
d) On the other hand, it is easy to envision that a quantum binding of, say, a electron and a proton is done via emision of a photon having exactly the binding energy, thus the relativistic mass of the photon leaving the system is exactly the mass lost by the new state. But here we need, it seems, *quantum* radiation theory, do we?