Reflection probability – Probabilities for reflection and transmission

We cannot accurately predict the measurement result when looking at an individual measurement. We can only specify a probability, namely 50% for White (□), and 50% for Black (■). We see, in the image, 64 measurement results for 64 photons on the beam splitter. If we assume a 50:50 percentage probability, can we also conclude from this that we have 32 black fields and 32 white fields? Let us count up the fields. Doing so gives N(■) equal to 31 black fields and N(□) equal to 33 white fields. Theoretically, we expect the value P equal to 50% for either black or white. However, this value is not arrived at exactly in the experiment. Random fluctuations occur, which fluctuate around the theoretical value. The size of the fluctuations depends upon the total number N of measurements. The more measurements are conducted, the smaller the fluctuations around the anticipated value of 50% This follows from the central limit theorem. P(experimental) approximates P(theoretical) as N approaches infinity.

For our observations in everyday life, that means that we see too many photons simultaneously. As a result, the intensity fluctuations and thus quantum randomness become invisible. Only in the quantum optics laboratory, this fundamental quantum randomness can be proven with single-photon experiments.