Polarization of Light – Summary

Application of the four-quadrant scheme using polarization as an example: We distinguish experiments with very many quanta from those with single quanta. In theory, we distinguish observable probabilities from unobservable amplitudes in Hilbert space (the quantum dimension).

We can summarise the results of station U1-8 by applying our sheme of four quadrants.

In the first quadrant, the polarization of many photons is measured simultaneously. An intensity distribution emerges, which depends on the difference in the angle between two polarisation filters.

In the second quadrant, the polarization of individual photons is measured. A black-white random pattern for transmission or reflection emerges. The probabilities for transmission and reflection depend on the angle. For 45°, the probabilities both are 50%.

In the third quadrant, we sort the number of transmitted and reflected photons and arrange the resulting probabilities on a circle. In such a way, we obtain an angle-dependent probability distribution for transmission, which is proportional to the intensity distribution.

Before the interaction with the detectors, we cannot describe the state of the photon just using probabilities, as probabilities cannot interfere with each other.

In the fourth quadrant, we thus embark into the quantum dimension by generalizing probabilities by amplitudes, visualized by rotating wheels. An oscillation with one nodal line emerges, which describes the amplitude for transmission. The amplitude for transmission is zero at the nodal line, meaning that the photon is reflected in this angle with 100% probability.