The two-spin enigma: from the helium atom to quantum ontology

The purpose of this article is to provide a novel approach and justification of the idea that classical physics and quantum physics can neither function nor even be conceived one without the other - in line with ideas attributed to e.g. Niels Bohr or Lev Landau. Though this point of view may go against current common wisdom, we will show that it perfectly fits with empirical evidence, and can be maintained without giving up physical realism. In order to place our arguments in a convenient historical perspective, we will proceed as if we were following the path of a police investigation, about the demise, or vanishing, of some valuable properties of the two electrons in the helium atom. We will start from experimentally based evidence in order to analyse and explain physical facts, moving cautiously from a classical to a quantum description, without mixing them up. The overall picture will be that the physical properties of microscopic systems are quantized, as initially shown by Planck and Einstein, and they are also contextual, i.e. that they can be given a physical sense only by embedding a microscopic system within a macroscopic measurement context.