Breaking Out of Eigenstates

An electron spin along the +x direction is a superposition of spin “up” and spin “down” along the z direction.

We humans love our dichotomies. “You’re either with us or against us!” “You either love it or hate it.” “A statement is either true or false.” “It’s a war between Good and Evil.” “Either you trust science or you trust religion.”

In quantum physics, there is a similar notion: “The spin of an electron can only be up or down.” This is incorrect. Like any other quantity with both magnitude and direction, the spin of an electron can point in any direction whatsoever. If you know a little quantum physics, you may say, “Yes, but it can only stay pointing up or down in a magnetic field.” True, but if there is no magnetic field present, it can stay pointing in any direction. This does not contradict the fact that an electron spin pointing in some other direction can be represented as a superposition of spin up and spin down along the z direction, whatever direction we choose as z. For example, an electron spin pointing in the positive x direction can be expressed as the sum of spin up and spin down eigenstates, divided by the square root of 2, as depicted above (below the title).

What happens to that electron spin if there is a magnetic field in the z direction? It evolves in time, rotating into the +y direction, then into the -x direction, then into the -y direction, then back into the +x direction, and so on. Around and around it goes, precessing about the magnetic field direction but always perpendicular to it. This time dependence is a much more interesting phenomenon than static eigenstates; when applied to protons instead of electrons it is the basis for the MRI machines that map your brain.

If you have read this far, you are probably wondering what the hell this quantum physics has to do with politics and psychology, where we started. Well, the metaphor is apt in most cases:

Love and Hate:

Few are the personal relationships that can be described as pure love or pure hate. Those few remain “stuck” in one eigenstate and do not evolve over time. Acknowledging the usual mixture of appreciation and annoyance makes things more interesting and allows for change.

Choosing sides:

My inclination is to be against anyone who demands that I choose a side. However, absent that impetus I am almost always a little for and a little against any initiative; and I really wish others would listen carefully to the arguments of “the other side” before picking up a club or a gun to decide the issue. The superposition of states allows, again, for evolution.

I should take this occasion to mention that there is another possibility in quantum physics that is neither pure “up” nor pure “down” nor a pure coherent superposition of both: the so-called “mixed state” describes a collection of independent spins, some of which are pure “up” and some of which are pure “down”. These may have an average z component of zero and yet not describe any state like |x+>. This is like a person “flipping” constantly between altogether “for” a proposition and altogether “against” it. It seems (to me) obvious that this sort of “averaging” does not constitute (or even allow) evolution of one’s point of view. The same would pertain to a person trying to maintain committed monogamous relationships with two partners; that is not the same as polygamy.

True vs. False:

Surely we can always make this distinction, right? Well, for sufficiently simple and testable hypotheses, sure! The statement, “The sun is currently shining where I am right now,” is true [trust me!] but its truth is time-dependent. The statement, “The less government, the better!” is sort of true-ish until a majority of citizens want to achieve something that requires more cooperation than is likely to emerge spontaneously. Most assertions have at least a kernel of truth, or no one would believe them; and most accepted “truths” include a lot of questionable implications, at the very least. I am fond of saying, “Every lie is constructed around a core of truth, and every truth collects a coating of lies.” Which is actually sort of redundant, but I like it anyway. An example would be, “There was fraud in the US 2020 presidential election.” Any collective endeavour of hundreds of thousands of people is certain to include some bad behaviour, but is there evidence of enough “fraud” to change the results of the election? No. This superposition of truth and falsehood has led to some quite “interesting” time-dependent behaviour — in this case not particularly constructive (so far). But every attempt at persuasion [including this one] is bound to reach beyond the boundaries of the empirically verifiable truth, or else nothing could ever change.