Apr 09, 2008
There’s a widespread belief that quantum mechanics is supposed to be confusing. This is not a good frame of mind for either a teacher or a student.
And I find that legendarily “confusing” subjects often are not really all that complicated as math, particularly if you just want a very basic—but still mathematical—grasp on what goes on down there.
I am not a physicist, and physicists famously hate it when non-professional-physicists talk about quantum mechanics. But I do have some experience with explaining mathy things that are allegedly “hard to understand.”
I wrote the Intuitive Explanation of Bayesian Reasoning because people were complaining that Bayes’s Theorem was “counterintuitive”—in fact it was famously counterintuitive—and this did not seem right. The equation just did not seem complicated enough to deserve the fearsome reputation it had. So I tried explaining it my way, and I did not manage to reach my original target of elementary school students, but I get frequent grateful emails from formerly confused folks ranging from reporters to outside academic college professors.
Besides, as a Bayesian, I don’t believe in phenomena that are inherently confusing. Confusion exists in our models of the world, not in the world itself. If a subject is widely known as confusing, not just difficult… you shouldn’t leave it at that. It doesn’t satisfice; it is not an okay place to be. Maybe you can fix the problem, maybe you can’t; but you shouldn’t be happy to leave students confused.
The first way in which my introduction is going to depart from the traditional, standard introduction to quantum mechanics, is that I am not going to tell you that quantum mechanics is supposed to be confusing.
I am not going to tell you that it’s okay for you to not understand quantum mechanics, because no one understands quantum mechanics, as Richard Feynman once claimed. There was a historical time when this was true, but we no longer live in that era.
I am not going to tell you: “You don’t understand quantum mechanics, you just get used to it.” (As von Neumann is reputed to have said; back in the dark decades when, in fact, no one did understand quantum mechanics.)
Explanations are supposed to make you less confused. If you feel like you don’t understand something, this indicates a problem—either with you, or your teacher—but at any rate a problem; and you should move to resolve the problem.
I am not going to tell you that quantum mechanics is weird, bizarre, confusing, or alien. Quantum mechanics is counterintuitive, but that is a problem with your intuitions, not a problem with quantum mechanics. Quantum mechanics has been around for billions of years before the Sun coalesced from interstellar hydrogen. Quantum mechanics was here before you were, and if you have a problem with that, you are the one who needs to change. Quantum mechanics sure won’t. There are no surprising facts, only models that are surprised by facts; and if a model is surprised by the facts, it is no credit to that model.
It is always best to think of reality as perfectly normal. Since the beginning, not one unusual thing has ever happened.
The goal is to become completely at home in a quantum universe. Like a native. Because, in fact, that is where you live.
In the coming sequence on quantum mechanics, I am going to consistently speak as if quantum mechanics is perfectly normal; and when human intuitions depart from quantum mechanics, I am going to make fun of the intuitions for being weird and unusual. This may seem odd, but the point is to swing your mind around to a native quantum point of view.
Another thing: The traditional introduction to quantum mechanics closely follows the order in which quantum mechanics was discovered.
The traditional introduction starts by saying that matter sometimes behaves like little billiard balls bopping around, and sometimes behaves like crests and troughs moving through a pool of water. Then the traditional introduction gives some examples of matter acting like a little billiard ball, and some examples of it acting like an ocean wave.
Now, it happens to be a historical fact that, back when students of matter were working all this stuff out and had no clue about the true underlying math, those early scientists first thought that matter was like little billiard balls. And then that it was like waves in the ocean. And then that it was like billiard balls again. And then the early scientists got really confused, and stayed that way for several decades, until it was finally sorted out in the second half of the twentieth century.
Dragging a modern-day student through all this may be a historically realistic approach to the subject matter, but it also ensures the historically realistic outcome of total bewilderment. Talking to aspiring young physicists about “wave/particle duality” is like starting chemistry students on the Four Elements.
An electron is not a billiard ball, and it’s not a crest and trough moving through a pool of water. An electron is a mathematically different sort of entity, all the time and under all circumstances, and it has to be accepted on its own terms.
The universe is not wavering between using particles and waves, unable to make up its mind. It’s only human intuitions about quantum mechanics that swap back and forth. The intuitions we have for billiard balls, and the intuitions we have for crests and troughs in a pool of water, both look sort of like they’re applicable to electrons, at different times and under different circumstances. But the truth is that both intuitions simply aren’t applicable.
If you try to think of an electron as being like a billiard ball on some days, and like an ocean wave on other days, you will confuse the living daylights out of yourself.
Yet it’s your eyes that are wobbling and unstable, not the world.
The order in which humanity discovered things is not necessarily the best order in which to teach them. First, humanity noticed that there were other animals running around. Then we cut them open and found that they were full of organs. Then we examined the organs carefully and found they were made of tissues. Then we looked at the tissues under a microscope and discovered cells, which are made of proteins and some other chemically synthesized stuff. Which are made of molecules, which are made of atoms, which are made of protons and neutrons and electrons which are way simpler than entire animals but were discovered tens of thousands of years later.
Physics doesn’t start by talking about biology. So why should it start by talking about very high-level complicated phenomena, like, say, the observed results of experiments?
The ordinary way of teaching quantum mechanics keeps stressing the experimental results. Now I do understand why that sounds nice from a rationalist perspective. Believe me, I understand.
But it seems to me that the upshot is dragging in big complicated mathematical tools that you need to analyze real-world situations, before the student understands what fundamentally goes on in the simplest cases.
It’s like trying to teach programmers how to write concurrent multithreaded programs before they know how to add two variables together, because concurrent multithreaded programs are closer to everyday life. Being close to everyday life is not always a strong recommendation for what to teach first.
Maybe the monomaniacal focus on experimental observations made sense in the dark decades when no one understood what was fundamentally going on, and you couldn’t start there, and all your models were just mysterious maths that gave good experimental predictions… you can still find this view of quantum physics presented in many books… but maybe today it’s worth trying a different angle? The result of the standard approach is standard confusion.
The classical world is strictly implicit in the quantum world, but seeing from a classical perspective makes everything bigger and more complicated.
Everyday life is a higher level of organization, like molecules versus quarks—huge catalogue of molecules, six quarks. I think it is worth trying to teach from the perspective of the quantum world first, and talking about classical experimental results afterward.
I am not going to start with the normal classical world and then talk about a bizarre quantum backdrop hidden behind the scenes. The quantum world is the scene and it defines normality.
I am not going to talk as if the classical world is real life, and occasionally the classical world transmits a request for an experimental result to a quantum-physics server, and the quantum-physics server does some peculiar calculations and transmits back a classical experimental result. I am going to talk as if the quantum world is the really real and the classical world something far away. Not just because that makes it easier to be a native of a quantum universe, but because, at a core level, it’s the truth.
Finally, I am going to take a strictly realist perspective on quantum mechanics—the quantum world is really out there, our equations describe the territory and not our maps of it, and the classical world only exists implicitly within the quantum one. I am not going to discuss non-realist views in the early stages of my introduction, except to say why you should not be confused by certain intuitions that non-realists draw upon for support. I am not going to apologize for this, and I would like to ask any non-realists on the subject of quantum mechanics to wait and hold their comments until called for in a later essay. Do me this favor, please. I think non-realism is one of the main things that confuses prospective students, and prevents them from being able to concretely visualize quantum phenomena. I will discuss the issues explicitly in a future essay.
But everyone should be aware that, even though I’m not going to discuss the issue at first, there is a sizable community of scientists who dispute the realist perspective on quantum mechanics. Myself, I don’t think it’s worth figuring both ways; I’m a pure realist, for reasons that will become apparent. But if you read my introduction, you are getting my view. It is not only my view. It is probably the majority view among theoretical physicists, if that counts for anything (though I will argue the matter separately from opinion polls). Still, it is not the only view that exists in the modern physics community. I do not feel obliged to present the other views right away, but I feel obliged to warn my readers that there are other views, which I will not be presenting during the initial stages of the introduction.
To sum up, my goal will be to teach you to think like a native of a quantum universe, not a reluctant tourist.
Embrace reality. Hug it tight.