# Defining Superposition

I’d hope to keep this simple.

If we decide to measure electron spins along the vertical axis using a Stern-Gerlach device we get an overall even split between up and down.

Therefore it is said electrons are in an equal superposition before they are measured. Does this have any relation to reality though?

Why is it not sufficient to say a SG measuring device impacts electron spin?

(and leave the concept of superposition out entirely)

Assuming the electrons are prepared correctly, we know nothing at all about their spins prior to our measurement with the Stern-Gerlach device. (Except, of course, that each spin is $$\pm\hbar/2$$ along some direction.) That ignorance is captured by the idea of the equal superposition. Using that idea, when we calculate measurement probabilities in quantum mechanics, we get the right answers. That's why it's used.

In some sense, the Stern-Gerlach device does affect electron spin. As an example, consider the chain of devices that measure along the $$\hat{z}$$, then $$\hat{y}$$, then $$\hat{z}$$ directions. To see how this works, let's follow just one (of the eight total) sets of electrons through the experiment.

After the first device, half the electrons are in the $$|+\rangle_z$$ state. All of those electrons are spin-up in the $$\hat{z}$$ direction. Following those electrons into the second device, half are in the $$|+\rangle_y$$ state. Finally, putting that stream back through a $$\hat{z}$$ device finds that half of them are now in the $$|-\rangle_z$$ state! By measuring an orthogonal direction, the device destroyed all information about the spin in the $$\hat{z}$$ direction, allowing some of them to change their spins in that direction.

But we can't just rely on saying "the device affected the prior reality of the spin direction." How can there be prior reality when an electron can't hold a $$\hat{y}$$ and $$\hat{z}$$ spin at the same time? By measuring spin in one direction, you necessarily put the spin in the orthogonal direction(s) into an equal superposition. That is equivalent to saying a measurement destroys information in the orthogonal direction(s) -- in fact, that very lack of information is what the superposition means.

If you're unsatisfied by this explanation, you should feel free to look into the different interpretations of quantum mechanics. The fact is, quantum mechanics as a theory doesn't provide a "story" about what physically exists prior to a measurement. (Unless you take the superposition idea to be a concrete statement of reality, rather than a computational aid, which seems to be the preference of plenty of physicists.) I prefer to use the different interpretations as intuitive tools; I find a handful of different ones aid my intuition about different kinds of systems. Until one of them is experimentally proven, they're all fair game in this capacity* -- as long as you make sure to check your intuitions with the actual computations.

*Unfortunately, not all of them can reproduce quantum field theory, which is a deeper theory of nature, suggesting those interpretations are probably incorrect.

• So, I think you are saying that each set-up of the measuring device gives us one unit of information and by altering the set-up to obtain a different unit we negate the first unit. I think it is a very good answer. Jun 19, 2020 at 22:51
• That is one way of roughly, intuitively thinking about it, yes. Mathematically, it's because the Pauli spin matrices don't commute. But if you want to take the information idea further, I'd recommend the work of Ken Wharton, particularly his paper "Time-Symmetric Boundary Conditions and Quantum Foundations." He argues classical equations of motion have 2 time derivatives, hence 2 boundary conditions (pieces of information); but the Schrodinger equation has only 1. The halving of info yields the uncertainty principle. It's not a mainstream idea, but interesting & may help with intuition. Jun 20, 2020 at 3:54