(posted below; thought I'd bring this to the top as is here for comments from anyone)
Off the top of my head; a quick explanation of quantum spin:
In a traffic jam on a highway, the following pattern may occur:
(Consider flying along in a helicopter above the straight highway). Down below, suppose that you see a series of cars progressively closer spaced and slower moving, as you fly along above the highway looking at the traffic. Then you see a number of stationary cars, and then increasingly-spaced and increasingly-faster-moving cars.
You may represent this as a series of dots in a straight line that are densely-packed in the middle and more-spread-out towards the ends.
You may consider the spreading-out at the ends to continue to plus infinity and to minus infinity, to match the math of the delta function.
The pattern of cars involves deceleration followed by acceleration.
The pattern of cars is like simple harmonic motion
and like a compression wave.
Suppose a similar traffic jam (imaginary if you like) is superposed at right angles to the first jam.
If you take a position of a car in the first jam, and take a position of an imaginary car in the at-right-angles-imaginary jam; having decided to track the relationship of these two cars you may superpose all the possible positions of cars in both jams into a grid.
(This may correspond to the "all possible ways an event may happen" that occurs in the Schrodinger equation).
(Making a MATCH between a car from each jam, this may correspond to the idea of "definition". A philosophy text tells us that "defining" something involves a broadening and a narrowing to find where the defined object intersects several categories.)
O.K., you have a grid showing a sequence of lines of jam 2 and of jam 1. Now you can see that on this grid your car-in-1/car-in-2 match traces out a curve over the grid.
Suppose you now ROTATE that curve so as it appears to you as a line (just as you can rotate a hula-hoop till it looks like a line.) Now your curve looks like a new linear simple harmonic motion (or deceleration-acceleration line).
Now you may imagine a new imaginary traffic jam at right angles to your line (to the line that was the SUM OF HISTORIES of your MATCHED cars from your first two jam-lines).
Now you started with jam 1, imaginary jam 2. You chose a car position in 1, and you chose a car position in 2. You decided to track the relationship of these matched cars through both jams superposed. This gave you a curved line (whereas the jam-lines are just at right angles to each other forming a grid of superposed lines.)
You rotated the curved line summing the first two lines, so far as your match-cars were concerned; that is you rotated your curved-path sum-line. You rotated that till it appeared end-on so looked like a new linear simple-harmonic motion pattern.
Call this sum-line jam (1,2).
Now you superpose a new (jam 3) imaginary traffic jam at right angles to this (1,2) sum line. You chose a car position in jam 3 and track its relationship to a choice of car position in jam (1,2).
This gives you a MATCH-cars sum-line that tracks the pair 3, (1,2). Note how a pattern like nesting Russian dolls is building here. Note how the framework of this system is all 2-D, or complex numbers. Note that a sum-of-histories system is building. Note that Schrodinger's equation as described by Roger Penrose, seems to fit this scenario.
O.K.; you now have the new curve; so you ROTATE the curve till it appears end-on. It now appears like a simple-harmonic-motion in a straight line.
By the way don't they call this business 'complex linear superposition?" Name fits it seems.
O.K.; obviously you can keep superposing more and more imaginary traffic jams at right angles. Each time you chose a car position in one jam and you choose a car position in the at-right-angles jam.
You track your chosen relationship. You get a curve. You ROTATE the curve till it looks linear.
Now given that all along you can choose ANY car position in ANY jam; but MUST STAY WITH THE CHOSEN CARS ONCE THE RELATIONSHIP IS A DEAL (John Cramer's "hand-shake quantum theory here I think")
you are faced with this scenario:
Take any starting position ("car"); take any ending position ("car"): the process by which you arrived at the end car from the start car may have involved a number of imaginary traffic jams (quantum linear superpositions) along the way.
It may have involved many rotations, in many different directions.
This looks roughly like what is called "quantum spin".
Entanglement occurs as it does with the circularity of word-definition in a dictionary.
The comparing and matching of patterns that physicists do, involves it seems a circularity of pattern-matches like the circularity of word-matches in a dictionary.
The Dirac delta function is inherent in this it appears.
Hopefully a lot of physics can be clarified.