In principle they could turn into a single photon but typically they instead form many particles, among them photons, of lower energies.
The same will be true for any anti-particle particle pair.

Thanks, klasm. One of my good friends thinks that photons are simply two electrons, one of which has been (somehow) 'flipped twice', as in some kind of gyroscopic action. I tried to explain that you can flip an electron any number of times, in any number of ways, but you'll never see it with a positive electrical charge. I also tried to tell him that spin isn't analogous to a spinning top, that it's either parallel or anti-parallel. So now I'll tell him that an electron-positron reaction more often forms many photons, and not necessarily a single photon. If I don't have it quite right, I'm grateful for any corrections, as well as any suggestions for any other reasons that photons couldn't be composed of two electrons (or an electron and a positron). Thanks!

A simple argument for why that is not possible is that photons move at the speed of light, not very surprising. Electrons however have a non-zero rest mass and can thus only move a speeds strictly less than the speed of light.

In principle they could turn into a single photon but typically they instead form many particles, among them photons, of lower energies.
The same will be true for any anti-particle particle pair.

Actually, an electron positron annihilation could not result in a single photon. The simplest annihilation process would result in two photons. The simple reason for this is the conservation of momentum. This can be seen most easily if we consider the annihilation as seen in the frame of reference of an observer moving such that he sees the two particles coming from oppisite directions at the same speed (that is, comoving with the center of mass of the system). If the annihilation could result in just one photon, it would have to carry all the energy from both particles - both masses, plus the kinetic energies. Using units where the speed of light is equal to 1, the magnitude of a photon's momentum is the same as its energy. So, the magnitude of the single photon's momentum would be equal to the total energy initially carried by the electron and the positron. The problem with this is that in the center of mass frame, the momenta of the electron and positron are equal in magnitude and opposite in direction, meaning that the total momentum of the system is initially zero (this is why the center of mass frame is often called the center of momentum frame). If the momentum is initially zero and only one particle is created in the reaction, that particle must have zero momentum, which we already have showed the photon cannot. With two photons, this problem disappears, because they simply move in opposite directions with momenta equal in magnitude.

A simple argument for why that is not possible is that photons move at the speed of light, not very surprising. Electrons however have a non-zero rest mass and can thus only move a speeds strictly less than the speed of light.

Oh, you think it would be that simple. Had a lively discussion and made some progress, I think. He's seen both billiards balls and ball bearings, with opposite angular momentum, run against each other and 'propagate' along straight and curved paths, and figures that when it happens with fundamental particles, their angular momentum is sufficient to cause propagation at c. I told him about mass, rest mass, Planck's constant, frequency, and of course, E = mc^2. But he has some idea that mass (what he calls "apparent mass") also comes from the interaction between angular momentum and (what else?) the ether. Tough cookie, but a good friend. Tomorrow's another day... Thanks again for your help and insight, klasm, it's a credit to the forum!

edit:

Quote:

...With two photons, this problem disappears, because they simply move in opposite directions with momenta equal in magnitude.

Hi, Solomon. Thanks for that. Looks quite irrefutable, and tomorrow's looking brighter! :)

Solomon, I agree that for an annihillation where the electron and the positron meet in a heads on collision preservation of momentum would exclude a single phtoton, in the way you describe.

If they meet at an angle of less than 180 degrees the original system would also have a non-zero momentum and this restriction is not quite as simple. At least in the presence of an electromagnetic field the time reversal of pair production should be able to take place.

It is always possible to find a Lorentz boast that will bring the total momentum to zero. So you can calculate the reaction in that frame and transform the results back to the original frame when you are done.
The spin angular momentum is just as important. Electrons and positrons each half integer spins which can point in any direction. An electron-positron pair can have their spin angular momentum anti-aligned (0 total spin angular momentum) or aligned (+/-1 tsam) or anywhere in between (mixed state). Photons have integer sam which must be either aligned or anti-aligned with their momentum vector. A pair of photons with zero total momentum must have a total spin angular momentum of -2, 0 or 2. So unless the original electron-positron pair had a tsam of 0 you would need at least 3 and probably 4 photons in the final state.
In the real world most often there are other particles present which can carry off some of the extra momentum and spin angular momentum. This makes the two photon outcome somewhat more likely and lowers the likelyhood that the pair will recoil elasticly. But as with all three or more particle systems calculating (and discribing) the exact result is more complicated than with just two.

Is is correct to say that an electron and a positron will annihilate into energy in the form of a photon which, after some time, can turn back into an individual electron and positron again? Does this allude to the composition of a photon, or is this oversimplified?

Sorry if someone else has already said this, but the electron-positron pair can annihilate to form a single photon which then turns back into an electron-positron pair within the time stated by the Heisenberg uncertainty principle.

As long as the photon exists for a suitably short period of time it does not violate conservation of energy and momentum.

Es99
the pair can become a temporary virtual photon which can never be observed.

Thanks Mark. Is that what Chipper was referring to? It was the only example I could think of where it would be possible to create a single photon.

Thanks Mark, Es99. It was a bit painful to hear a friend of mine saying that photons are composed of essentially two electrons. The example of annihilation (above) was what he cited as proof that it was that simple. I knew it wasn't that simple, and knew where to get good answers; I got 'em, and Bob's your uncle. :) He shoulder-surfed the responses from klasm, Mark, and Solomon earlier, agreed that he needs to reevaluate his ideas, and asked me to pass along his gratitude. Major step forward! I understand (and very much appreciate) your response, Es99, but I think I'll wait a while before mentioning it to him...

## RE: In principle they could

)

Thanks, klasm. One of my good friends thinks that photons are simply two electrons, one of which has been (somehow) 'flipped twice', as in some kind of gyroscopic action. I tried to explain that you can flip an electron any number of times, in any number of ways, but you'll never see it with a positive electrical charge. I also tried to tell him that spin isn't analogous to a spinning top, that it's either parallel or anti-parallel. So now I'll tell him that an electron-positron reaction more often forms many photons, and not necessarily a single photon. If I don't have it quite right, I'm grateful for any corrections, as well as any suggestions for any other reasons that photons couldn't be composed of two electrons (or an electron and a positron). Thanks!

## A simple argument for why

)

A simple argument for why that is not possible is that photons move at the speed of light, not very surprising. Electrons however have a non-zero rest mass and can thus only move a speeds strictly less than the speed of light.

## RE: In principle they could

)

Actually, an electron positron annihilation could not result in a single photon. The simplest annihilation process would result in two photons. The simple reason for this is the conservation of momentum. This can be seen most easily if we consider the annihilation as seen in the frame of reference of an observer moving such that he sees the two particles coming from oppisite directions at the same speed (that is, comoving with the center of mass of the system). If the annihilation could result in just one photon, it would have to carry all the energy from both particles - both masses, plus the kinetic energies. Using units where the speed of light is equal to 1, the magnitude of a photon's momentum is the same as its energy. So, the magnitude of the single photon's momentum would be equal to the total energy initially carried by the electron and the positron. The problem with this is that in the center of mass frame, the momenta of the electron and positron are equal in magnitude and opposite in direction, meaning that the total momentum of the system is initially zero (this is why the center of mass frame is often called the center of momentum frame). If the momentum is initially zero and only one particle is created in the reaction, that particle must have zero momentum, which we already have showed the photon cannot. With two photons, this problem disappears, because they simply move in opposite directions with momenta equal in magnitude.

## RE: A simple argument for

)

Oh, you think it would be that simple. Had a lively discussion and made some progress, I think. He's seen both billiards balls and ball bearings, with opposite angular momentum, run against each other and 'propagate' along straight and curved paths, and figures that when it happens with fundamental particles, their angular momentum is sufficient to cause propagation at c. I told him about mass, rest mass, Planck's constant, frequency, and of course, E = mc^2. But he has some idea that mass (what he calls "apparent mass") also comes from the interaction between angular momentum and (what else?) the ether. Tough cookie, but a good friend. Tomorrow's another day... Thanks again for your help and insight, klasm, it's a credit to the forum!

edit:

Hi, Solomon. Thanks for that. Looks quite irrefutable, and tomorrow's looking brighter! :)

## Solomon, I agree that for an

)

Solomon, I agree that for an annihillation where the electron and the positron meet in a heads on collision preservation of momentum would exclude a single phtoton, in the way you describe.

If they meet at an angle of less than 180 degrees the original system would also have a non-zero momentum and this restriction is not quite as simple. At least in the presence of an electromagnetic field the time reversal of pair production should be able to take place.

## It is always possible to find

)

It is always possible to find a Lorentz boast that will bring the total momentum to zero. So you can calculate the reaction in that frame and transform the results back to the original frame when you are done.

The spin angular momentum is just as important. Electrons and positrons each half integer spins which can point in any direction. An electron-positron pair can have their spin angular momentum anti-aligned (0 total spin angular momentum) or aligned (+/-1 tsam) or anywhere in between (mixed state). Photons have integer sam which must be either aligned or anti-aligned with their momentum vector. A pair of photons with zero total momentum must have a total spin angular momentum of -2, 0 or 2. So unless the original electron-positron pair had a tsam of 0 you would need at least 3 and probably 4 photons in the final state.

In the real world most often there are other particles present which can carry off some of the extra momentum and spin angular momentum. This makes the two photon outcome somewhat more likely and lowers the likelyhood that the pair will recoil elasticly. But as with all three or more particle systems calculating (and discribing) the exact result is more complicated than with just two.

## RE: Is is correct to say

)

Sorry if someone else has already said this, but the electron-positron pair can annihilate to form a single photon which then turns back into an electron-positron pair within the time stated by the Heisenberg uncertainty principle.

As long as the photon exists for a suitably short period of time it does not violate conservation of energy and momentum.

Physics is for gurls!

## Es99 the pair can become a

)

Es99

the pair can become a temporary virtual photon which can never be observed.

## RE: Es99 the pair can

)

Thanks Mark. Is that what Chipper was referring to? It was the only example I could think of where it would be possible to create a single photon.

Physics is for gurls!

## RE: RE: Es99 the pair can

)

Thanks Mark, Es99. It was a bit painful to hear a friend of mine saying that photons are composed of essentially two electrons. The example of annihilation (above) was what he cited as proof that it was that simple. I knew it wasn't that simple, and knew where to get good answers; I got 'em, and Bob's your uncle. :) He shoulder-surfed the responses from klasm, Mark, and Solomon earlier, agreed that he needs to reevaluate his ideas, and asked me to pass along his gratitude. Major step forward! I understand (and very much appreciate) your response, Es99, but I think I'll wait a while before mentioning it to him...