Pair Production, electron and positron from isolated photon

In summary, the conversation discusses the impossibility of creating an electron-positron pair from an isolated photon due to conservation of 4 momentum. Various arguments are presented, including the violation of conservation of energy and the impossibility of a photon having zero momentum. The conversation also touches on the idea of splitting a photon into lower energy photons, but ultimately it is determined that the creation of an electron-positron pair from an isolated photon is impossible.
  • #1
cooev769
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I don't completely understand why an electron positron pair cannot be created from an isolated photon. I understand it must have something to do with 4 momentum conservation, but I really can't see a problem given the photon has enough energy for the mass to energy vice versa conversion.\

The only seemingly sound argument I could seem to convince myself with is that if 4 momentum is conserved and we say pf=pi. And we take pi of the photon in the photons rest frame we have (0,0,0,E/c), but the electrons can never move at the speed of light and hence the 4 momentum of any two of the electrons will have a negative momentum value (-x,0,0,E/c) and hence it is therefore impossible. But I don't believe this is correct. Any suggestions appreciated thanks!
 
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  • #2
Pretty simple and trivial argument: equality of reference frames. You can always pick a reference frame where the isolated photon is Doppler shifted to have too little energy for pair production. Since the event must happen in all reference frames or in none of them, and there are frames where it is impossible, therefore it is impossible in all frames.

Even simpler argument: an isolated photon has no time whatsoever and therefore no events whatsoever can happen to it. Splitting a photon into several photons of lower energy traveling in the same initial direction would not violate conservation of momentum (unlike production of particles with rest mass) but it is still impossible because of no time at the speed of light.
 
  • #3
Cheers. What I'm really looking for though is a rigorous violation of the conservation of 4 momentum.
 
  • #4
You won't find a "rigorous violation", since it is conserved.
 
  • #5
No it isn't as an isolated photon cannot produce and electron and an anti electron, therefore writing the 4 momentum before and after will produce a violation in conservation of 4 momentum, which I know occurs, I just don't know the proof and I've been trying for a while.
 
  • #6
Can't photons of energy E>~1MeV lead to pair production?
 
  • #7
Yep, but apparently in the presence of a nucleus or something, not an isolated photon which is why I'm trying to prove it mathematically.
 
  • #8
No, momentum is conserved.
 
  • #9
cooev769 said:
No it isn't as an isolated photon cannot produce and electron and an anti electron, therefore writing the 4 momentum before and after will produce a violation in conservation of 4 momentum, which I know occurs, I just don't know the proof and I've been trying for a while.
Take as your rest frame the center of mass frame of the electron-positron pair. Their total momentum in this frame is zero. Now what is the momentum of the photon? If momentum is conserved, the photon would also have to have momentum zero. But the momentum of a photon can't be zero, since it would have to be standing still.
 
  • #10
No it isn't as an isolated photon cannot produce and electron and an anti electron, therefore writing the 4 momentum before and after will produce a violation in conservation of 4 momentum, which I know occurs, I just don't know the proof and I've been trying for a while

Just to follow up on Bill_K thread, it shows that momentum and Energy can't both be conserved. In the center of mass frame of the electron-positron pair their momentum is zero but there energy has to be at least twice the mass of the electron. A "zero momentum" photon also has zero energy and therefore can't have a four vector which is equal to the four vector of the electron-positron pair.

Splitting a photon into several photons of lower energy traveling in the same initial direction would not violate conservation of momentum (unlike production of particles with rest mass) but it is still impossible because of no time at the speed of light.

I'm not sure this argument is true. I think that in general a massless scalar field can decay to two collinear scalar fields ( or more)
 
  • #11
I'm not sure this argument is true. I think that in general a massless scalar field can decay to two collinear scalar fields (or more)

scalar particles not fields
 

1. What is Pair Production?

Pair Production is a process in which an isolated photon (a particle of light) is converted into an electron and a positron (a particle with the same mass as an electron, but with a positive charge). This process can occur when the photon has enough energy to create the mass of the two particles.

2. How does Pair Production occur?

In Pair Production, the energy of the photon is converted into the mass of the electron and positron. This is possible because of Einstein's famous equation, E=mc^2. The energy of the photon is equal to the mass of the particles multiplied by the speed of light squared. This allows the photon to create the mass of the particles.

3. What happens to the photon after Pair Production?

After Pair Production, the photon no longer exists as a particle of light. Its energy has been converted into the mass of the electron and positron. This process is known as annihilation, as the photon is essentially "destroyed" to create the particles.

4. Why is Pair Production important in particle physics?

Pair Production is important in particle physics because it is one of the ways in which new particles can be created. This process has been observed in high-energy environments such as particle accelerators and is crucial in understanding the fundamental building blocks of the universe.

5. Can Pair Production occur in everyday life?

No, Pair Production is a rare occurrence and can only happen in high-energy environments. In everyday life, photons do not have enough energy to create the mass of an electron and positron. However, Pair Production does play a role in natural processes such as gamma ray bursts from outer space.

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