Some Insights – with my own verbiage – from Strange World of Quantum Physics -. Also read The Scales at which Quantum Amplitudes Apply

Raw Count leads to probabilities

Instead of talking about PROBABILITIES of a magnetic moment getting through,  let us talk about the NUMBER of magnets (raw count) that get through.

Think of two possible exits for a Stern Gerlach apparatus. Half of ALL incoming will go through EXIT 1 and half of ALL incoming will go through EXIT 2. This leads to PROBABILITY 0.5 of the moment going through any one exit.

Now, that it has gone through a certain exit (say EXIT 1), let us focus on all those coming out of EXIT 1 (and ignore the ones from EXIT 2).

If we now ASK The SAME question again (send ALL these OUTGOING into another INCOMING apparatus) – we get the same answer. 100% pass through EXIT 1.

If we ASK a DIFFERENT QUESTION (rotate the apparatus by say 90 degrees), we get an UNKNOWN answer. The reason is that we are now asking a DIFFERENT QUESTION – and the state for this SECOND question is AS UNCERTAIN as the state for the FIRST question was prior to the FIRST experiment.

EACH VARIABLE is a different question – and just because ONE apparatus has answered ONE question,  it doesn’t mean the other  questions have been asnwered?

SINGLE Stern Gerlach

Consider a SINGLE stern gerlach appartus.

A Spin Entering this apparatus can have any orientation – including a ZERO degree orientation with respect to the axis of the apparatus. The ZERO degree is the ‘pass through’ case – and  the most common orientation possible.

Other orientations are up down – and anywhere in between UP and DOWN.

So – a natural expectation would be for the SPIN to take any of those orientations.

Back to Back (Double) Stern Gerlach Apparatus – Same Orientation

Back to Back (Double) Stern Gerlach Apparatus – Reverse Orientation

The reverse orientation provides the first clue that something isn’t quite normal about the way these experiments work.

If the axis is inverted, the result is also inverted. You may wonder – how did the spin that was pointing up – suddenly – and with 100% accuracy, point DOWN? The simplest answer is that the result responds to the question (the axis being measured).

But wait, it gets weirder still…

Back to Back (Double) Stern Gerlach Apparatus – Angled Orientation – 90 degrees to start with

Back to Back to Back (Triple) Stern Gerlach Apparatus –

Angled Apparatuses  – And John Bell’s Insights into the Predicted Results

When we say that the probability for angled exits is proportional to cosine ( angle between the axes), what does that mean?

That means – ON AVERAGE  (i.e. when you send a WHOLE BUNCH of particles in through successive detectors), the number that will come out with +1 (versus -1) is cosine ( angle).

Individual measurement  ALWAYS reveals +1 or -1. It is never a projection of any sort (like cosine theta). The result is always UP or DOWN. It is just that the overall distribution of the +1s and -1s follows a pattern – that of cos (theta)