# Intuitive “story” explaining how orientation of spin axis affects up/down observation?

Is there a "convenient fiction" that explains why the angle of an electron's spin axis affects the probability of it being observed in a spin up or spin down state?

By "convenient fiction", I mean a story or image that provides useful intuition to novices, even though it may not be technically accurate. For example the analogy of water flowing through a pipe is a convenient fiction used to introduce the concepts of current and voltage.

I imagine the electron being sent through a Stern-Gerlach device. It makes sense that the closer the spin axis is to vertical, the more strongly the electron is drawn up or down. But, I don't see what would induce the electron to ever move in the "unexpected" direction. For example, if the axis is 5 degrees off vertical, what ever induces it to move down?

Watching this Veritasium2 video leads me to imagine that the electron is constantly flipping its spin axis; but, that doesn't seem to explain how the angle of the axis affects the probability of being measured in the up or down position.

• Do you know about the Bloch sphere? – PM 2Ring Mar 30 '19 at 16:23
• Yes. I understand how it mathematically describes the expected observation. I'm having trouble developing a mental picture of how it describes what the electron is actually doing and why. (I know such a picture is probably not completely accurate --- hence the term "convenient fiction".) – Zack Mar 30 '19 at 16:28
• Penrose has a nice description of electron spin in relation to the Riemann sphere in The Emperor's New Mind, p. 342. – PM 2Ring Mar 30 '19 at 16:44
• I understand the mathematics; but, I'm still not seeing the intuition. – Zack Mar 30 '19 at 17:02
• What makes you think such a "convenient fiction" exists? I'm leaning towards not. – Elio Fabri Mar 30 '19 at 20:07

• The wave function is a representation on a certain basis of the state of a quantum system. In case of a spin, the wave function is simply given by the coefficients of the basis kets. In case of a particle in one spatial dimension it is a function of the coordinate $x$ in the position basis or a function of the momentum $p$ in the momentum basis. If you imagine the graph of the function, you visualize it. – Michele Grosso Apr 12 '19 at 21:04