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If they have infinite lifetimes then does each one carry a memory of it's creation event? When I burn a log in my fireplace and a cinder flares and pops creating a spark, does the photon exist after the spark energy flares out and the cinder is no longer illuminated enough to be detected by my eyes?
If photons are infinite then harvesting light would be the first step in deciphering the complete history of the universe. All that would be left for us to do would be to derive the algorithms to unravel and categorize each photon into discrete groups based on their historical particle paths.
If we wanted to harvest light to test whether photons have infinite lifetimes we would need to design a structure that forms a light trap using materials with different refractive indices so that photons entering are forced onto paths from which they perfectly reflect in a lossless manner.
If photons are infinite then mirrors may have a memory if we can trap and monitor the photons that pass through them and force them to unravel their travel paths. Why can't I step in front of the mirror and have it replay every event that the mirror has seen? It would be a better replacement for photo or video mementos of lost loved ones if we could simply take the mirrors from their homes and spin back to watch their happiest moments forever by reconstructing the photon impingement history of the glass and mirror substrate.