Quantenspiegelungen – Paths and probabilities in the quantum dimension

Paths and probabilities in the quantum dimension

In which sense is it justified to claim that light follows all possible paths, not only the straight one? Depending on the experiment, which of these paths are observable?

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Let us recollect the stepped pyramid and the possible routes, i.e. paths, that a classic particle can travel from A to B. The probability that the particle falls on one of the three paths into Box B is calculated as the sum of the individual probabilities for all paths to said box.

Our laser light, however, must be described based on the rules of quantum physics. That means that we need to carry out a complex extension of the observation probability P(x), to transform it into a probability capable of interference, in order to be able to make a statement on the probable location of a given light quantum. How do we achieve that? We associate a rotating wheel to each possible path. In such a way, we can form a vector sum on the square root probabilities of all possible paths to B. We thus add the vectors of the rotating wheels, and, in that way, obtain the amplitude in Box B. The square corresponds to the detection probability in Box B.

With this so-called path integral formulation, Richard P. Feynman developed an important theoretical pillar of quantum physics.

The path integral – Paths and probabilities in the quantum dimension

Paths and probabilities in the quantum dimension

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