New Paradox: Gamma Light & Relativistic Doppler Effect

[Alfredo Tifi]

A monochromatic gamma light source S emits photons with spherical symmetry. These photons have a little less energy than necessary to permit formation of particle - antiparticle couples (electron-positron couple) or “EPCs”. An inertial observer O moves towards S with a small fraction of light speed. O carries an experimental apparatus to detect EPCs. Due to relativistic Doppler effect his velocity is high enough to experiment blue-shifted photons arriving from the source, with a significant probability to create EPCs, which are eventually detected. Once O passes beyond S, getting farther and farther from it, he just sees red shifted gamma rays without any EPC creation event detected.
So, how can a phenomenon-event occur relatively to O for half trip while not occurring for the second half trip and from S’s POV? The photons don’t “know” who are watching at them!
PS the experimental apparatus does not interact with the photons, but only with electrons and/or positrons.

 

[Dale]

A single photon cannot create an EPC, regardless of energy. Energy and momentum could not be conserved. The EPC detector detects nothing in both frames

 

[pervect]

A monochromatic gamma light source S emits photons with spherical symmetry. These photons have a little less energy than necessary to permit formation of particle - antiparticle couples (electron-positron couple) or “EPCs”. An inertial observer O moves towards S with a small fraction of light speed. O carries an experimental apparatus to detect EPCs. Due to relativistic Doppler effect his velocity is high enough to experiment blue-shifted photons arriving from the source, with a significant probability to create EPCs, which are eventually detected. Once O passes beyond S, getting farther and farther from it, he just sees red shifted gamma rays without any EPC creation event detected.
So, how can a phenomenon-event occur relatively to O for half trip while not occurring for the second half trip and from S’s POV? The photons don’t “know” who are watching at them!
PS the experimental apparatus does not interact with the photons, but only with electrons and/or positrons.

I'm not seeing where the paradox is. Perhaps you're thinking the energy of a photon is a property of the photon alone? This is simply not true, the energy of a photon depends on who observes it. I'm not sure of your background, but there's a mathematical entity, the energy-momentum 4-vector, that can be regarded as an observer independent representation of the energy and momentum carried by the photon as it allows any observer to calculate the energy and momentum of the photon in his frame of reference. But the actual values for energy (and momentum) are frame dependent.

Perhaps that's not your issue, it's my best guess though. If that's not the issue, could you be more clear where the "paradox" is? I'm not seeing anythign that looks paradoxical in the situation you describe.

 

[Orodruin]

PS the experimental apparatus does not interact with the photons, but only with electrons and/or positrons

Yes it does. You cannot have spontaneous pair-production without exchanging momentum with something else, that would violate energy-momentum conservation.

 

[Alfredo Tifi]

Thank you Dale and Orodruin. I see now there is no paradox given that a single photon can’t undergo pair production. The paradox would have been of events (pair production) occurring for an observer but not for another one with only a slow motion. I was aware that energy of photons depend from the observer, and that was the possible source of paradoxes. A reference system associated to photons does not exist, but does exist one associated to the source of photons. So, Pervect, I am a chemistry teacher, and I’m going to study more about photon momentum, pair-production and quadrivectors and then to search for other possible paradoxes :-)