# E=MC2: quantum or relativistic effect?

1. Jan 19, 2004

### arivero

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 text book. 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?

2. Jan 19, 2004

Staff Emeritus
Relativity says this mathematical relationship, the energy = c times the square of the mass, holds in the rest frame of a massive particle. In a frame where the particle is moving, of course, more energy will be seen due to the motion.

But relativity says nothing about how to actualize this relationship. That's a subject for quantum mechanics and nuclear physics.

3. Jan 19, 2004

### Arcon

I disagree. This doesn't just hold in quatum and nuclear physics. It holds in classical mechanics and electrodynanmics.

You can actually analyze this from a purely mechanical point of view in some cases.

For an example from EM consider the fact that the mass of a capacitor increases with an increase in energy. Energy increases - inertia increases. This even holds for a system of two point particles. The increase in inertia in such a case can be calculated using only EM. In fact such a calculation is was done in 1979 by Timothy H. Boyer in the American Journal of Physics.

Griffith did something similar too.

4. Jan 20, 2004

### arivero

Arcon, do you have the reference for Griffith, or at least the complete name?

As for Boyer (do not confuse with M. Boyer, Spain ex-ministry of economics, also a physicist), there are in fact two related articles with a 20-year diference!

AJP -- Feb 1979 -- V 47, (2), pp. 129-131
Electrostatic potential energy leading to a gravitational mass change for a system of two point charges

and
AJP-- Oct 1998 -- V 66, (10), pp. 872-876
Example of mass-energy relation: Classical hydrogen atom accelerated or supported in a gravitational field

From the abstracts, the first one seems to use general relativity to get a change in mass. The second one neglects self-radiation, so perhaps a quantum conditions is hidden there. There are no copies of these papers online :-(

The gravitational emphasis strikes me, as E=mc2 works already with the inertial mass.

Last edited: Jan 20, 2004
5. Jan 20, 2004

### Arcon

Sure. Happy to

Mass renormalization in classical electrodynamics, David J. Griffiths and Russell E. Owen, Am. J. Phys. 51, 1120 (1983)

Yes. I've read them both. Excellant articles! I'm using them in some work I'm doing at the moment. In fact Boyer will be proof reading it for me when I've finished it.

6. Jan 20, 2004

Staff Emeritus
Arcon, Wow! I stand corrected. Since I don't have access to print journals, do you know of any online discussion of these classical electromagnetic effects>

7. Jan 20, 2004

### Arcon

Try sci.physics.research

I can scan them in and e-mail the papers to you if you'd like?