"The Structure & Interpratation of Qunatum Mechanics" by R.I.G. Hughes

Follow @Aristeidis_K Of most book that I have read that attempt to introduce some of the peculiarities of QM, I have found the one by Hughes the most instructive and mostly for thisd reason I decided to include some comments here.

Hughes uses the Stern-Gerlach experiment as a means for demonstrating some of the peculiarities or ‘weirdness’ of quantum theory.
Very briefly, and omitting a considerable deal of detail, a collimated beam of electrons enters a non-uniform magnetic field produced by specially arranged magnets. What is observed is that the beam splits into 2 parts of equal intensity, one travelling upwards and the other downwards.



Using the ‘spin’ of the electrons we can account for this behaviour in classical terms. Half of the electrons in the beam posses spin -1/2 in the vertical direction, and the other half +1/2 (for simplicity Plank’s constant is set to 1). The ones with he negative-valued spin feel a net magnetic force downwards and the positive-valued ones a net force upwards. This is verified by simply blocking off one of the beams (up or down) and placing another similar set of magnets. As we would expect no further splitting is observed.[Hughes refers to this set-up as a ‘Experiment VV’, meaning that we force the beam to be split in the Vertical direction twice].

The problems start when we alter this set-up. By rotating the second apparatus by 90∘we force the incoming beam to be split into two horizontal components, spin-left and spin-right. [This set up would be ‘Experiment VH’ - H for Horizontal splitting]. Let’s assume that we have blocked the spin-up component from the first apparatus, and the spin-left from the second. It follows that the resulting beam has a horizontal spin-right component only, and a vertical spin-down component only. Therefore, if we passed this beam though yet another apparatus we would expect to see no further splitting.
This, however, is not the case. Placing a third apparatus set in the vertical direction, the emergent beam will be split into two. Therefore, there must be something faulty in this account we offered.
Hughes lists 4 separate (unwarranted) assumptions that might have found their way into this account.

1. When we assign a numerical value to a physical constant (in this case a specific component of spin), we can think of this quantity as a property of the system.

2. We can assign a value for each physical quantity to a system at any given time. For example we can say that the electron has both spin-up and spin-left.

3. The apparatus sorts out the atoms according to the values of one particular quantity, in other words according to the properties they posses.

4. As the apparatus does so, the other properties of the system remain unchanged.

Obviously, here something has to go. Here I think Hughes describes in less technical terms the notions of Value Realism (assumption 1), Value Definiteness (assumption 2), and Non-contextuality (assumption 3&4). Which assumption or assumptions have to go, modified, replaced, etc., is something I will postpone commenting on for two reasons. Firstly, because it will be more productive and clear if done after some more material is covered. Secondly and more importantly, I think it will depend on one’s ‘allegiances’ and research programme. Possibly someone supporting a more traditional scientific realism will not want to abandon the above assumption... or at least not without a serious fight. Someone on the opposite camp, an instrumentalist, would probably have no problems throwing them out of the window altogether.