# converting electrons into photons

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So E = mc2 right? That means that matter can be converted to energy, and visa-versa. What particles does this apply to? It must apply at least to electrons, protons, and neutrons, which in turn means it applies to quarks. Now what form does this energy take once an electron or quark is converted to it? Would it be a photon? How many photons per particle? This must mean that electrons and quarks can be converted into photons and visa-versa.

Am I right?

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So E = mc2 right? That means that matter can be converted to energy, and visa-versa. What particles does this apply to? It must apply at least to electrons, protons, and neutrons, which in turn means it applies to quarks. Now what form does this energy take once an electron or quark is converted to it? Would it be a photon? How many photons per particle? This must mean that electrons and quarks can be converted into photons and visa-versa.

Am I right?

According to 'E=mc^2' by David Bodanis, Einstein did not say 'converted'; Einstein said energy and mass are the same.

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So E = mc2 right? That means that matter can be converted to energy, and visa-versa.

No, that's not what it means. The letter "m" means mass, not "matter". You cannot convert matter into energy in the same spirit that you cannot convert a block of iron into blue. It means that mass contributes to the total energy.

What particles does this apply to? It must apply at least to electrons, protons, and neutrons, which in turn means it applies to quarks. Now what form does this energy take once an electron or quark is converted to it? Would it be a photon? How many photons per particle? This must mean that electrons and quarks can be converted into photons and visa-versa.

I think that any reaction for which

a) energy and momentum are conserved and the relationship $E^2 = m^2c^4 + p^2c^2$ holds for each in-particle and out-particle individually,

b) the total number of quarks and leptons is conserved (anti-particles count negative),

holds should be possible in principle within the standard framework of particle physics. In practice, the probability of a certain reaction to happen can be negligible, tough (rules of thumb: The less kinetic energy the reaction products, the less probable; the more reaction vertices needed in the smalles Feynman diagram, the less probable). The only reason E=mc² matters at all in the process is that it contributes to the contraint a).

To answer your individual questions: An electron-positron pair (total lepton and quark number =0) can annihilate into 2+ photons (total number of quarks and leptons being zero, each). A single photon is not possible due to constraint a) - it might be interesting for you to figure out why. Same goes for quarks. The backwards-reactions are also possible except that here the photons must bring at least the mass of the leptons/quarks as kinetic energy to satisfy constraint a). Annihilation products do not need to be photons, in processes where the total quark or lepton number is non-zero it in fact cannot be photons only.

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Is it true that matter in motion = energy?

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Is it true that matter in motion = energy?

It is true that matter in motion has energy. Energy is a property of "stuff".

But remember that constant motion (i.e. no acceleration) is not a Lorentz invariant notion, and thus nor is energy.

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(edited:) Whatever; see ajb's post which you'd probably like more.

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Ah, so an electron just is energy; not convertable to energy (in the form of a photon). But still, the question lingers: has any material particle (electron or quark) ever been converted to energy (i.e. in a usable form) experimentally? I mean, one of the reasons E=mc2 is so exciting is because it points towards the potential prospect of actually harnessing huge quantities of energy from only small amounts of matter. Is there any hope of this at all?

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Ah, so an electron just is energy; not convertable to energy (in the form of a photon).

No. It has energy pretty much the same way that it has some electric charge. Some mass-energy (it's called "mass" - I am just emphasizing that it is just a form of energy) and possibly some other energy, say kinetic energy. Particles can be converted into other particles. A photon is not energy either - although it is quite a common misunderstanding that it was. It is just another particle that has energy, the only difference being that the energy of a photon is purely kinetic with zero contribution from (zero) mass.

Sidenote on different conventions: Some people call the total energy of a photon (or any other free particle) "relativstic mass". As you see, I don't.

But still, the question lingers: has any material particle (electron or quark) ever been converted to energy (i.e. in a usable form) experimentally?

Like I said: You cannot convert matter to energy. You can convert mass (a form of energy) into kinetic energy (another form of energy) via converting particles into other particles. Assuming mass and kinetic energy to be the only energies possible: When the resulting particles have less mass than the initial ones, the total kinetic energy of the resulting particles must be larger than that of the initial ones such that total energy is conserved.

The first process that comes to my mind here is nuclear fission. At the heart of the process, a neutron and a nucleus are converted into 2 (maybe also more?) other nuclei and some neutrons and possibly some other crap. The resulting particles have a high kinetic energy and can then heat water that drives a heat engine.

You could in principle store electrons and anti-electrons in two different containers, let them combine and form two photons with high kinetic energy that you then harvest. The basic reason why this is not done that it's just not practical.

I mean, one of the reasons E=mc2 is so exciting is because it points towards the potential prospect of actually harnessing huge quantities of energy from only small amounts of matter. Is there any hope of this at all?

Yes. In the case of the sun it even happens without significant risks due to radioactivity.

Note: Since I can't edit my previous post anymore: Electric charge also need to be conserved under any process. I forgot that in my previous post. I am currently not sure to what extent conservation of angular momentum (which is conserved) is important, too.

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So E = mc2 right? That means that matter can be converted to energy, and visa-versa.

The "m" stands for mass, which in certain circumstances can be converted into energy. For example, annihilation of matter and anti-matter into photons.

What particles does this apply to? It must apply at least to electrons, protons, and neutrons, which in turn means it applies to quarks. Now what form does this energy take once an electron or quark is converted to it? Would it be a photon? How many photons per particle? This must mean that electrons and quarks can be converted into photons and visa-versa.

Am I right?

Yes, but certain conservation rules need to be followed. There is:

1) Conservation of mass-energy.

2) Conservation of momentum.

3) Conservation of angular momentum (aka spin).

4) Conservation of electric charge.

There's also conservation of quark and lepton number, though I am somewhat suspicious of those.

Anyhow, the easiest way to satisfy all of those is to collide a particle with its antiparticle, which will have all the properties (except mass) the reverse of the particle, and then ensure the resulting photons or other particles conserve mass-energy and momentum.

If Hawking radiation is real, then matter can be converted into energy using a black hole. I made a thread on this, but as an energy source it seems impractical.