Introduction
My reference is the Wiki page on the famous Stern Gerlach experiment. It describes 3 stages where a silver atom beam was (supposedly) redirected 3 times by an applied inhomogeneous magnetic field. Interesting! Yet further research seems to reveal that stage 2 and 3 described in the wiki page were never ever actually performed. In fact it was later experiments like Frisch and Sevre which had the relevent second and third stages. Not the original 1922 Stern Gerlach experiment.
Original Stern Gerlach experiment:
The original Stern Gerlach experiment applies an inhomogenous magnetic field to a beam of silver atoms and ‘splits’ the beam. No other experimental setup is described beyond this in the original paper. Below is described a classical explanation for the observed beam deflections in the 3 stages.
Classical explanation for S-G
How to do this? To start with do not use the rather antiquated classical theory of what in 1925 was thought as the basis for a “classical” explanation. A centuries old outdated classical model where imaginary electrons and imaginary spin were invoked to describe what appears under scrutiny to be a simple case of the dipole magnetic fields of atoms interacting with the applied inhomogenous fields of the experiments.
Use simple logic based on facts only. Instead one must use only observed macro “ real life” behaviour of magnets reacting to externally applied magnetic fields.
In the original experimental 3 stages using the Stern Gerlach apparatus the beam is split into two in stage 1. Unaffected in stage 2. And split again into 2 beams in stage 3.
To explain this classically using magnetic fields only is as follows:
At the experiments source the beams silver atoms on emission have their atoms magnetic field directions point in random directions. On average 1/2 have their N poles point towards the S part of the inhomogenous magnetic field generated by the S-G apparatus. And 1/2 have their N poles point towards the North Pole of the field in the S-G apparatus.
What logically would one expect to happen based on actual experimental observations of moving magnets interacting with external magnetic fields? Logically the silver atoms in the beam with their North poles facing the north pole of the S-G apparatus would be repelled from the North Pole of the S-G apparatus. And the other half then would be attracted to the South Pole of the S-G apparatus. This is facilitated by the fact that the beam is not an infinite narrow beam. It has width. Which implies that each silver atom is always slightly closer to one pole or the other of the external applied field. A 50/50 divide. And so an atom which is slightly closer to the North Pole of the applied external field but whose North Pole also points more towards the North Pole of the applied field, will have a net repelling action on the atom. And its path will be deviated at a certain angle towards the South Pole of the applied external field. Any of the other atoms which are closer to the North Pole of the applied external field but whose magnetic south pole faces the externally applied North Pole...will attracted to the external North Pole in equal amounts and be deviated at the same angle but towards the North Pole of the externally applied field. Which allows a classical model using magnetic fields only with no imaginary spin or electrons, to correctly model and predict the split beams observed in stage 1.
To make stages 2 and 3 also consistent with a classical model one then assumes that after stage 1, as outlined above, all the silver atoms are aligned with polarities that match the inhomogenous field of stage 1. So when travelling through stage 2 which is also has the same direction of applied external magnetic field as stage 1, no overall repelling or attracting magnetic forces will be observed on the particle beam in stage 2. Seeing as the beam of silver atoms polarities are now lined up with both the stage 1 and 2 fields. And the silver atom beam would then proceed unchanged to stage 3. And this confirmation of classical model is observed in stage 2 in Frisch and Segre.
After which the alignment process resets in stage 3 and starts over again to repeat the process seen in initially in stage 1. Because the beam entering stage 3 has all atoms polarities in the beam now aligned at right angles to the applied inhomogenous field in stage 3. And therefore in stage 3 the beams atoms magnetic fields will all have to be flipped again either + or - 90 degrees, ie orthoganally as they were flipped in stage 1, to form the two new + and - beams to make them realign to the externally applied inhomogenous magnetic field in Stage 3.
And this is what is observed. The single beam in stage 3/is split in two. And depending on the strength of the applied field the split lines vary in distance and width from the Center. The stronger the magnetic field. The stronger the attraction to each pole and the larger the deviation from the path for each beam. One doesn’t need QT to explain the behaviour of interacting magnetic fields of varying strength.