A little confused about photon decay

• phalanx123
In summary, the conversation discusses relativistic expressions for energy and momentum, specifically the invariant expression E^2 − p^2c^2 in the Special Theory of Relativity. The conversation also explores the behavior of particles colliding and decaying, and how the Doppler effect for light can be used to calculate their energy. The final part discusses different approaches to solving the problem.

phalanx123

I have this question.

Give relativistic expressions for the energy E and the magnitude of the momentum p of a particle of mass m moving at speed v. The expression E^2 − p^2c^2 is an invariant in the Special Theory of Relativity. Explain what this means and state the value of the invariant for a single particle.

A particle of mass m moving at speed 3/5c collides with an identical particle at rest, and forms a new particle of mass M which moves off at speed v. Show that v = 1/3c and find an expression for M.

The particle of mass M subsequently decays into two photons, one travelling
in the direction of incidence of the mass m, and the other traveling in the opposite direction. Determine the energy of each photon.

If instead the decay produces photons of equal energies, what are their
momenta and directions?

I have no problem in answering the first two parts of the question. the last part I know how to solve too: by saying photons are moving in opposite directions along the y-axis in the zero momentum frame. It is the third part where photons are moving parallel to x-axis which I don't get. The way it asks is implying that the two photons have different energies. Well fine if it is not a massless particle, in which case the speed of each particle in the stationary frame will have different speed and thus different kinetic/total enery. But with photons and such their speed is fixed, and they don't have mass, so in the zero momentum frame the two photons will have equal magnitude of momentum but in opposite directions and this will be the same in the stationary frame, since there is no change in velocity. So because E=p/c for photons, than they will have the same energy!? I am confused, could somebody sort me out please. thanks a million.

What do you know about the Doppler effect for light?

oh i see, why didn't i not realize that before! thanks a lot. So I say that in the zero momentum frame, each photon has same amount of energy i.e. half of the original energy, so use this energy the original emitted frequency can be calculated, than use the Doppler effect for light calculate the observed frequency for each photon, and thus the energy. Is my logic right? thanks ^_^

phalanx123 said:
oh i see, why didn't i not realize that before! thanks a lot. So I say that in the zero momentum frame, each photon has same amount of energy i.e. half of the original energy, so use this energy the original emitted frequency can be calculated, than use the Doppler effect for light calculate the observed frequency for each photon, and thus the energy. Is my logic right? thanks ^_^

That is one way to approach the problem. I don't think it would be difficult for two photons to do the calculation directly in the lab frame using conservation of energy and momentum, which would be another approach.

1. What is photon decay?

Photon decay is a hypothetical process in which a photon, which is a particle of light, splits into two or more particles with lower energy. This process is not observed in nature and is still a topic of research and debate among scientists.

2. Can photons really decay?

According to the current understanding of quantum mechanics, photons are considered to be stable particles and do not decay. However, there are theories that suggest the possibility of photon decay under certain extreme conditions, such as in the presence of a strong magnetic field or in the early universe.

3. How does photon decay affect our daily lives?

Photon decay is not a phenomenon that affects our daily lives. As mentioned earlier, it is a theoretical concept that is still being studied and has not been observed in nature. In our daily lives, we encounter and interact with photons constantly, but they do not decay.

4. What are some potential implications of photon decay?

If photon decay were to exist, it could have significant implications for our understanding of the fundamental laws of physics. It could also have implications for cosmology and the evolution of the universe, as well as potential applications in technology and energy production.

5. How do scientists study photon decay?

Scientists study photon decay through theoretical models and experiments. These experiments involve high-energy particle collisions, measurements of cosmic rays, and observations of distant objects in the universe. However, due to the elusive nature of photon decay, it has not been directly observed, and much of our understanding of it remains theoretical.

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