# How much radiation energy can a charge give off?

1. Aug 12, 2008

### kmarinas86

A charge has a mass-energy equal to the mass of the charge times the speed of light squared. So wouldn't there be a time which a charge undergoes a sufficient amount of acceleration such that the energy of the total radiation it emits (according to the Larmor formula) over a long period of time exceeds its mass-energy? In space, it is far more likely a particle to emit more radiation into deep space than to absorb from it, so it's concievable that the amount of energy the charge radiates over time due to changes in acceleration can accumulate in net amounts over time.

2. Aug 12, 2008

### blechman

a charge can only radiate when it's being accelerated, and the energy it radiates is taken from its KINETIC energy, not its mass (assuming, of course, that the particle doesn't decay). So the particle will radiate away all it's kinetic energy until it's at rest (or at least, no longer accelerating), but it won't lose any of its inertial mass unless, as I just said, it decays.

3. Aug 12, 2008

### blechman

i'm not sure I answered your question, so let me add: yes, it's true that an electron can keep radiating and radiating, but when you say "accumulate over time" - the energy had to come from somewhere - it's not spontaneously generated. So for example, a cosmic ray might harness energy from some large magnetic dynamo somewhere (and get accelerated), and then release that energy in the form of radiation. but then the energy came from the magnetic field, it didn't just build up out of nothing.

To put it another way: the radiated energy came from the force that did the accelerating, NOT from the particle's rest mass. So there's no conservation of energy issues.

I'm still not quite sure this answers your question, but if not, let me know.

4. Aug 13, 2008

### kmarinas86

If the radiation is ultimately due to the charged particles being accelerated by magnetic fields, then where does that radiation go? Is the radiation collected by other particles just as fast as it produced? Or does it accumulate in net amounts in vast intergalactic space of our apparently "expanding" universe?

5. Aug 13, 2008

### blechman

basically. it goes into the ever-increasing entropy of the universe.

6. Aug 13, 2008

### kmarinas86

Yet, somehow, the loose energy associated as "entropy" must have come from matter itself. How can charge with a mass-energy of 'x' joules increase the loose energy in the universe by a net amount greater than 'x' joules? It means that instead somehow the rate of this radiative dissipation must somehow decrease over time if the charge is going to remain as having mass-energy associated with it at all. If the "mass-energy" falls faster than the charge disappears, then it could mean that the force per mass increases, resulting in greater acceleration than otherwise expected, including its repulsive and attractive forms. The greater acceleration, in turn, further increasing the rate at which the radiation is produced. If the protons are not subject to the same acceleration however as electrons, they may (according to the Larmor formula) undergo a different rate of radiation emission. ?

But deductions aside, just what do you think are the true consequences of having net energy dissipation purely from acceleration of charged particles (even in the absence of nuclear and chemical reactions) with respect to cosmology?

Last edited: Aug 13, 2008
7. Aug 13, 2008

### blechman

i'm not following. the energy comes from whatever accelerated the charged particle in the first place. first law of thermo is still in effect: the energy was taken from whatever accelerated the particle and put into kinetic energy, and then the particle slowed itself down by shedding that energy in the form of (higher entropy) radiation.

i don't see where you see a break in energy conservation. and I don't see where the inertial mass of the particle comes in at all. perhaps I'm misunderstanding you...

8. Aug 13, 2008

### kmarinas86

I don't see a break in energy conservation - period.

The energy conservation is still there. Converting mass into energy doesn't delete the energy, it just makes it remote and distant and thus contributing to entropy. The thing is that if the charged particles in the universe have an inherent mass-energy in them, how could the production of net radiation through innumerable acceleration events conserve energy without having the mass-energy being reduced in the process? If that radiation "lost in space" will someday exceed two-fold the mass-energy that exists, in what previous form would that energy have been in? If not mass-energy, what other possibilities would we have? I could think that gravitational potential energy could be turned into radiation as a result of contributing to the acceleration of charged particles, but would that really come from the mass-energy of the accelerating particles or would it come from the externally-acting gravitational fields themselves (and likewise from magnetic fields). The obvious following question then is "where do these fields come from"? It might come from the same old-mass energy source! If not, then from what do they come from?

9. Aug 13, 2008

### kmarinas86

There is no absolute state of rest. Kinetic energy also is dependent on relative motion, so it is not constant for any object undergoing acceleration, whether repulsive or attractive. As long forces do exist, there will be acceleration (unless the universe is perfectly balanced).

Absolute state of rest of particles would also imply temperatures equal to absolute zero, which is thermodynamically impossible. At best, we can get objects to lose relative kinetic energy. But a loss in velocity with respect to one particle can be a gain with respect to another (and not necessarily in equal amounts)!

With radiative dissipation, we should expect the relative velocities of cosmological masses to reduce very slowly if mass is conserved as much of this kinetic energy would accumulate in empty space as radiation (if that's the way the radiation is produced). We know that gravitational potential energy can be converted into kinetic energy, as well as knowing that gravitational potential energy is due to the curvature of space time which is due to the energy density itself. But the curvature of space sees no sign of slowing down objects!

Last edited: Aug 13, 2008
10. Aug 13, 2008

### cesiumfrog

You're confusing inertial mass (which is also called relativistic mass, and includes the kinetic mass-energy component) with rest mass. The radiating charge will lose the former, but not the latter.

Magnetic fields do no work. So they redirect charges to trace helices, but as those particles radiate the transverse motion will decay, and the radiation will stop once the particles are no longer moving across the magnetic field (in the unique local reference frame where the electric field is zero).

I don't understand what you're trying to get at. But we started out in an improbable state, with massive gravitational potential. As matter collapses it heats up. As heat is radiated out, it can collapse further, and become even hotter (a run-away cycle). And so on until the remaining matter can collapse no further and the night sky warms to the same temperature as everything below it. And in the end, as all the energy seems locally to redshift away, the space per particle will increase, so expect entropy still to increase (unless some mechanism kicks in to renew the whole shebang).