As an interlude, I’ve just finished reading John Gribbin’s The Quantum Mystery (a short Kindle book). It’s very good. What it doesn’t do is bother with any of the maths. Instead, it sort of tells the human story, summarises the key experiments and focusses on the Scientists. I had been dwelling on entanglement, and ‘spooky action at a distance’, but had forgotten how strange the quantum world is right at its core. The double-slit experiments establish this very clearly. The original experiments were with light, and diffraction patterns – hence light is a wave, but other experiments showed that light is also particulate (the photon). This experiment was refined over time, and it became possible to fire one photon at a time at the slits and still observe a diffraction pattern build up as more and more photons are fired through the apparatus. The individual photons appear to know that there will be other photons following, and distribute themselves with a probability determined by the Schrödinger wave equation. Even more strange; if one of the slits is covered then the interference pattern disappears. And, if a detector is placed between the slits and the detector screen after the photon has passed through the slit, then the interference pattern also disappears (but how does the photon know it won’t reach the detector screen when it passes through the slit?). Now light is strange anyway (it travels at the speed of light and is subject to all sorts of strange relativistic effects).
But, in 2013, with the advance of nano-technology, it became possible to repeat these experiments using a stream of single electrons. And the same things were seen. So, this is a general quantum feature. Individual wave-particles appear to behave as if they know what their path through space will be in the future. How is that possible? We appear to be able to characterise the quantum world, but not understand it.