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According to the photon model, light carries its energy in packets called quanta or photons. Why then don't we see a series of flashes when we look at things?

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We do see things in a series of flashes. One photon excites one rhodopsin molecule in our retina and our optic nerve sends a signal every time this happens.

However under normal circumstances the number of photons per second detected by the eye is so large that the signals received by the brain are effectively continuous so we don't see any oscillation in our vision.

The question What is the minimum optical power detectable by human eye? asks whether our eyes can detect single photons, though without a firm answer. In any case you have to bear in mind that our vision is entirely a construction carried out by our brain, and the brain applies all sorts of postprocessing. For example we see films as continuous despite the fact they are really a sequence of still images.

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    $\begingroup$ Or, as mentioned recently in chat, "Your brain is continuously and egregiously lying to you about what your eyeballs have actually detected". $\endgroup$ – Emilio Pisanty Sep 7 '17 at 9:50
  • $\begingroup$ Another example of how your eye/brain interprets individual photons is how a combination of red photons and green photons is yellow. $\endgroup$ – Bill Alsept Sep 7 '17 at 15:56

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