Quantum Spin 1/2

 Let me repeat myself:  The map is not the territory.

Now, watch this video: "Electrons DO NOT Spin".  (I don't support PBS, but Spacetime is a really good show.)

Now, imagine a circle.  And a cosine wave.  And a sine wave.

What is a cosine (red) wave?  It's what you get if you attach a pen to the edge of a circle, and then roll the circle along in a straight line.  Note that the speed of rotation does not have to match the velocity of the center of the circle, but both must remain constant.  (A cosine wave is a sine (blue) wave, but 90 degrees off.)

Notice how the red "pen" starts at the top of the circle.  It moves along as the circle rotates until it reaches the bottom.  Notice what the sine (blue) wave does in that time.  It moves from zero to a positive peak and then back to zero.  Now look at where the red "pen" travels from the bottom back up to the top, completing one full rotation of the circle.  Notice how the blue pen, in that same time, moves from zero to a negative peak and back to zero.

This is what is going on with quantum spin 1/2.  The particle is rotating, but what the scientists are measuring is the sine function, because that's all they can detect.  You can only measure what you can see.

The map is not the territory.