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Essays The Portal Podcast

Superposition

This essay appears in audio format at the beginning of The Portal Podcast, Episode 35.


Hi, it’s Eric with some thoughts for this week’s audio essay on the topic of superposition. Now, to those of you in the know, superposition is an odd word, in that it is the scientific concept we reach for when trying to describe the paradox of Schrodinger’s cat in the theory and philosophy of quantum measurement. We don’t yet know how to say that the cat is both dead and alive at the same time rigorously. So we fudge whatever is going on with this unfortunate feline, and say that the cat and the quantum system on which its life depends, are a mixture of two distinct states that are somehow commingled in a way that has defied a satisfying explanation for about a century.

Now, I’m usually loath to appeal to such quantum concepts in everyday life, as there is a veritable industry of people making bad quantum analogies. For example, whenever you have a non quantum system that is altered by its observation, that really has nothing to do with the Heisenberg uncertainty principle. Jane Goodall’s chimpanzees are almost certainly altered in their behavior due to her presence. But there’s likely no competent quantum theorist who would analogize chimps to electrons and Goodall to a Hermitian observable executing a quantum observation. Heisenberg adds nothing other than physics envy to the discussion of an entirely classical situation such as this. However, I have changed my mind in the case of superposition, as I would now like to explain.

To begin with, superposition isn’t a quantum phenomena. For example, imagine that you’d come from Europe to Australia, and that you had both euros and Swiss francs in your pockets. You might then be said to be in a superposition, because you have pocket change in both euros and francs rather than a pure state of only one currency or the other. The analog of a physical observable in the situation would be something like a multiple choice question found on the landing card about the contents of your pockets.

Here it is easy to see the danger of the setup. Assuming you have three times as much value in euros as you do in francs, what happens when you get a question that doesn’t include your situation as an answer? What if the landing card asked, “Is all of your change in A, euros, or B, Swiss francs?”, with no other options available?

Well, this, as stated, is a completely classical superposition problem, having nothing to do with quantum theory. Were you to have such a classical question asked of you like this, there would have been no way for you to answer. However, if the answer were on the multiple choice menu, there would be no problem at all, and you would give a clear answer determined by the state of your pockets. So if the state in question isn’t on the multiple choice menu, the classical world is forced to go mute, as there is no answer determined by the system. Whereas, if it is found on the list of allowable choices, the answer is then completely determined by the system’s state at the time that the question was asked.

Oddly, the quantum world is, in a way, exactly as deterministic as the classical one just described, despite what you may have heard to the contrary. In order to understand this, we’ll have to introduce a bit of jargon, so long as the system, now called the Hilbert State, is on the list of answers—technically called the system of eigenvectors—corresponding to the question, now called a quantum observable, the question will return a completely deterministic answer, technically called the eigenvalue, corresponding to the state eigenvector.

These are, in a sense, good questions in quantum theory, because the answer corresponding to the state of the system actually appears as one of the multiple choice options. So, if that is completely deterministic, well, then what happened to the famous quantum probability theory, and the indeterminacy that we hear so much about? What if I told you that it were 100% confined to the situation which classical theory couldn’t handle either. That is, quantum probability theory only becomes relevant when you ask bad quantum questions, where the state of the system isn’t on the list of multiple choice answers. When the landing card asked if all your change were completely in euros, or only in francs, the classical system couldn’t answer because three times the value of your Swiss francs were held in euros, so no answer could be determined. But if your pocket change was somehow quantum, well, then you might find that 75% of the time, your pocket coins would bizarrely turn into pure euros, and would be willingly turned into pure francs 25% of the time, just by virtue of your being asked for a measurement by the landing card.

In the quantum theory, this is due to the multiple choice answers of the so called observable represented by the landing card question, not being well suited to the mix state of your pockets in a superposition between euros and francs. In other words, quantum theory gets probabilistic only where classical theory went mute. All of the indeterminacy appears to come from asking bad multiple choice questions in both the classical and quantum regimes in which the state of the system doesn’t fit any given answer.

Quite honestly, I’ve never heard a physicist rework the issue of quantum probabilities in just this way, so as to highlight that the probabilistic weirdness comes only from the quantum being overly solicitous, and accommodating really bad questions. For some reason, they don’t like the idea of calling an observable that doesn’t have the state of the system as an allowable answer a bad question, but that is precisely why I do like it. It points out that the quantum is deterministic, where the classical theory is deterministic, and only probabilistic where the classical theory is mute. And this is because it is weirdly willing to answer questions that are in a sense that can be made precise, bad questions to begin with.

It doesn’t get rid of the mystery, but it recasts it so it doesn’t sound quite so weird. The new question is, why would a quantum system overcompensate for the lousy questions being posed, when the classical system seems to know not to answer?

So why bring any of this up? Well, the first reason is that I couldn’t resist sneaking in a personal reformulation of the quantum measurement problem that most people will have never considered. But the second reason is that I’ve come to believe that we are wasting our political lives on just such superposition questions.

For example, let’s see if we can solve the abortion debate problem right now on this podcast, using superposition, as it is much easier than the abortion problem itself. The abortion debate problem is that everyone agrees that before fertilization there’s no human life to worry about, and that after a baby is born, there’s no question that it has a right to live. Yet pro-choice and pro-life activists insist on telling us that the developing embryo is either a mere bundle of cells suddenly becoming a life only when born, or, a full fledged baby the moment the sperm enters the egg. You can guess my answer here. The question of “Is it a baby’s life or a woman’s choice?” is agreed upon by everyone before fertilization or following birth, because the observable in question has the system as one of the two multiple choice answers in those two cases. However, during the process of embryonic development, something miraculous is taking place that we simply don’t understand scientifically. Somehow a non-sentient blastula becomes a baby by a process utterly opaque to science, which is yet has no mature theory of consciousness. The system in utero isn’t a changing and progressing superposition tilted heavily towards not being a baby at the beginning and tilted heavily towards being one at the end of the pregnancy.

But the problem here is that we have allowed the activists, rather than the embryologist and developmental biologists, to hand us the life-versus-choice observable, with its two terrible multiple choice options. If we had let the embryologists set the multiple choice question there would be at least 23 Carnegie stages for the embryo before you even get to fetal development. But instead of going forward from what we both know and don’t know with high confidence about the system, we are instead permanently deranged by being stuck with Schrdinger’s embryo by the activists who insist on working backwards from their political objectives.

So does this somehow solve the abortion issue? Of course not. All it does is get us to see how ridiculously transparent we are in our politics that we would allow our society to be led by those activists who would shoehorn the central scientific miracle of human development into a nutty political binary of convenience. We don’t even think to ask, “Who are these people who have left us at each other’s throats debating an inappropriate multiple choice question that can never be answered?”

Well, in the spirit of The Portal, we are always looking for a way out of our perennial problems to try to find an exit. And I think that the technique here of teaching oneself to spot superposition problems in stalemated political systems brings a great deal of relief to those of us who find the perspective of naive activism a fairly impoverished worldview. The activist mindset is always trying to remove nuanced selections that might better match our world’s needs from among the multiple choice answers until it finds a comical binary.

Do you support the war on drugs? Yes or no?

Are you for or against immigration?

Should men and women be treated equally?

Should we embrace capitalism or choose socialism?

Racism, systemic problem or convenient excuse?

Is China a trading partner or strategic rival?

Has technology stagnated, or is it in fact racing ahead at breakneck speed?

Has feminism gone too far, or not far enough?

In all of these cases, there’s an entire industry built around writing articles that involve replacing conversations that might progress towards answers and agreement, with simple multiple choice political options that foreclose all hope. And, in general, we can surmise when this has occurred, because activism generally leaves a distinct signature, where the true state of a system is best represented as a superposition of the last two remaining choices that bitterly divide us handed us by activists.

So I will leave you with the following thought: The principle of superposition is not limited to quantum weirdness, and it may be governing your life at a level you’ve never considered.

Think about where you are most divided from your loved ones politically, then ask yourself, when I listened to the debates at my dinner table, am I hearing a set of multiple choice answers that sound like they were developed by scholars interested in understanding, or by activists who are pushing for an outcome? If the latter, think about whether you couldn’t make more progress with those who love by recognizing that the truth is usually in some kind of a superposition of the last remaining answers pushed by the activist. But you don’t have to accept these middlebrow binaries, dilemmas, and trilemmas.

Instead, try asking a new question. If my loved ones and I trashed the terms of debate foisted upon us by strangers, activists in the news media, could we together fashion a list of multiple choice answers that we might agree contain an answer we all could live with, and that better describes the true state of the system?

I mean, do you really want open or closed borders? Do you really want to talk about psilocybin and heroin in the same breath? Do you really want to claim that there is no systemic oppression, or that it governs every aspect of our lives? Before long, it is my hope that you will develop an intuition that many long-running stalemated discussions are really about having our lives shoehorned by others into inappropriate binaries that can only represent the state of our world as a superposition of inappropriate and simplistic answers that you never would have chosen for yourself.