The graph of interference pattern, computed by the sum-over-paths method, refers to the probability that a photon falls at a given point of detector. Thoughtful reader may object that one photon cannot create an interference pattern, which is spread along the detector, as probability per definition is the ratio of favourable cases to all possible cases. From this it follows that interference pattern is the result of striking by a lot of photons.
Fig. 21 Double slit interference pattern for 50 photons per detector point
With the program
The shape of the interference pattern varies with the number of photons striking the detector (Fig. 22). One photon per a detector point is not able to create a structured pattern what means that each point has an equal chance to be hit by a photon. With growing numbers of photons the interference pattern limits to the form that is the same as calculated by the
Fig. 22 Interference pattern related to the number of photons per detector point.
We may say that the sum-over-path method makes use of statistical results attained by the “machine gun model” and it relates they to one photon. This approach is similar to the die rolling when from the statistical distribution of their outcomes we conclude that the probability of a favourite result is 1/6 for one roll. We are aware that there remains an open question how the atoms save the photon “imprints” in the form of vector sum.
Let the things are the way or another way, behaviour of subatomic particles is mysterious for a man whose thoughts has been formed in a world of objects moderate in size and velocity. Nevertheless, sophisticated experiments speak in favour of photon passing two slits simultaneously. In the section Interference we offer Feynman’s probabilistic explanation of these experiments.