Annihilation of electron positron pair

[devang2]

Suppose in thought experiment one electron positron pair is annihilated in the carriage of fast moving train while the other pair is annihilated on the platform . Will the frequency of the photon reaching the platform from the carriage will be same as given out by the other pair which which is annihilated on the platform

 

[Nugatory]

The motion of the carriage is irrelevant to this problem. What matters is the total energy of the electron-positron pairs in the platform frame, and you use $E^2=(m_0{c}^2)^2+(pc)^2$ to figure that.

In practice, we usually do these problems in a frame in which the center of mass of the interacting particles is at rest.

As an aside: the annihilation will produce two photons, not one - otherwise momentum wouldn't be conserved.

 

[pervect]

The frequency of any source will be doppler shifted by the motion of the train. Light/photons going in one direction will be redshifted, in the other blue-shifted.

See http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

There's nothing particularly special about using electron-positron annihilation as a source.

 

[Dale]

In practice, we usually do these problems in a frame in which the center of mass of the interacting particles is at rest.

To emphasize what Nugatory said, in this frame the initial system momentum is zero, so the momenta of the resulting photons will sum to zero. In another frame there will be nonzero momentum before and after, so the photons in one direction will be redshifted and blue shifted in the other.

 

[devang2]

thank you for the reply based on momentum Doppler effect which leads to the conclusion that there is no effect of increase in mass of electron and positron due to motion of train .If the increase in mass is considered the frequency of photon emitted from the carriage should be more than photon emitted by annihilation of stationary pair on the platform . Please let me know if i am right or wrong

 

[Nugatory]

thank you for the reply based on momentum Doppler effect which leads to the conclusion that there is no effect of increase in mass of electron and positron due to motion of train .If the increase in mass is considered the frequency of photon emitted from the carriage should be more than photon emitted by annihilation of stationary pair on the platform .

Energy still has to be conserved. The total energy of the moving pair is greater than that of a stationary pair, so the annihilation will yield higher-frequency more energetic photons.

If you're thinking in terms of relativistic mass increase (which is almost guaranteed to confuse you), then the masses of the particles, as calculated in the platform frame in which they're moving, will be greater than their masses as calculated in the train frame where they're at rest.

 

[devang2]

Thank you for the comprehensive reply that there is increase in frequency emitted by the moving pair . it may be due to mass increase or more momentum .Momentum of moving particle is calculated by using relative increase in mass.Am i correct.The basic relation between energyy of particle at rest . energy when particle is in motion and momentum is derived by using the the relative mass relation of moving oarticle .