Pair Production, electron and positron from isolated photon

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Discussion Overview

The discussion revolves around the concept of pair production, specifically the creation of an electron-positron pair from an isolated photon. Participants explore the implications of conservation laws, particularly 4-momentum conservation, and the conditions under which pair production can occur, examining both theoretical and mathematical aspects.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about why an isolated photon cannot create an electron-positron pair, suggesting that 4-momentum conservation is a key issue.
  • Another participant argues that since there are reference frames where the photon has insufficient energy for pair production, it must be impossible in all frames.
  • A participant emphasizes the lack of time for an isolated photon, suggesting that events cannot occur for it, which complicates the idea of pair production.
  • One participant requests a rigorous proof of the violation of 4-momentum conservation in this context.
  • Several participants assert that 4-momentum is conserved, countering claims of its violation when considering an isolated photon.
  • Another participant points out that while photons can lead to pair production, this typically requires the presence of a nucleus, not an isolated photon.
  • One participant discusses the implications of using the center of mass frame for the electron-positron pair, questioning how a photon could have zero momentum in that frame.
  • Another participant raises a point about the energy requirements for pair production, noting that a zero momentum photon would also have zero energy, complicating the conservation argument.
  • There is a suggestion that a massless scalar field might decay into multiple scalar particles, indicating a potential avenue for further exploration.

Areas of Agreement / Disagreement

Participants express disagreement regarding the conservation of 4-momentum in the context of pair production from an isolated photon. While some assert that conservation holds, others argue that it leads to contradictions, indicating that the discussion remains unresolved.

Contextual Notes

The discussion highlights limitations related to the assumptions about reference frames, the nature of isolated photons, and the conditions necessary for pair production. There are unresolved mathematical steps and definitions that participants are grappling with.

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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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.
 
Cheers. What I'm really looking for though is a rigorous violation of the conservation of 4 momentum.
 
You won't find a "rigorous violation", since it is conserved.
 
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.
 
Can't photons of energy E>~1MeV lead to pair production?
 
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.
 
No, momentum is conserved.
 
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
 

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