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The parallel worlds of quantum mechanics

Modern physics is rich with speculation about multiverses and parallel realities. But there are very different ways that multiple universes might come about, and one of the most mind-blowing – the Many-Worlds formulation of quantum physics – is also one of the most plausible.

The English language rounded into shape long before modern physics came on the scene, so it’s no surprise that words like “world” and “universe” have ambiguous meanings. When you hear physicists talk about “the multiverse”, chances are they are thinking of the cosmological multiverse. That sounds pretty grand, and it is, but it’s not really a collection of distinct universes. Rather, it refers to a collection of regions of space, so far away that they are unobservable to us, where conditions of very different. There may be different particles, different forces, even a different number of dimensions of space from what we see around us.

The cosmological multiverse wasn’t invented because physicists thought it would be cool to have a bunch of universes out there. It arises naturally as a consequence of other speculative ideas, including string theory and cosmological inflation. But exactly because those ideas are themselves speculative, the cosmological multiverse should be thought of as speculative-squared. It may very well exist, but the only thing to say right now is that we don’t really know.

The multiple “worlds” of quantum mechanics are something else entirely. They are not far away – but only because they aren’t “located” anywhere at all. And they arise naturally from the simplest version of our most solidly tested physical theory, quantum mechanics. The many worlds of quantum mechanics, I would argue, are probably there. (Not everyone agrees with me about this.)

To see why, we have to think about how quantum mechanics works. Consider an electron, which is an elementary particle that has a certain fixed amount of a quantity called spin. When we measure its spin, we get only one of two possible answers: it’s spinning up or down, with respect to whatever axis we used to measure it.

That would be weird enough as it is – why only two possible answers? But even weirder is that we can’t always predict what that measurement outcome is going to be. We can prepare the electron in a “superposition” of spin-up and spin-down, such that there will be some probability of observing each outcome. Physicists describe the state of the electron in terms of a “wave function,” which tells us how much of the state of the electron is spin-up, and how much is spin-down. We can use the wave function to calculate the probability of each measurement outcome.

It’s natural to think that there really is some answer to how the electron is spinning, but we just don’t know what it is, and the wave function encapsulates our ignorance. That was the original hope of people like Albert Einstein. But it hasn’t worked out that way; the more we do experiments, and the more we understand the inner workings of quantum mechanics, the more it seems like the wave function really exists. It doesn’t just characterise our knowledge, it’s the real physical state of the electron.

That brings up a problem, namely, why do wave functions evolve differently when you’re looking at them and when you’re not? According to textbook quantum mechanics, a wave function by itself evolves according to a simple equation first written down by Erwin Schrödinger. But when we measure the system, it’s wave function stops being a superposition, and suddenly “collapses” to some particular measurement outcome, like spin-up.

That’s crazy talk. What do you mean by “measure”? Does it have to be a human being doing the measuring, or does any conscious creature count? Could it be a video camera? How quickly does it happen, and how does the system distinguish between measurements and any other kind of physical interaction?

These questions, collectively known as “the measurement problem” of quantum mechanics, bothered Hugh Everett, a graduate student at Princeton University in the 1950s. Everett’s idea was to keep in mind that observers – whatever they may be, from people to video cameras – are quantum systems in their own right. They are described by wave functions, and those wave functions can evolve into superpositions themselves.

And they not only can, they necessarily do, if you simply posit that everything obeys the Schrödinger equation, quantum mechanics’ fundamental equation. Consider some kind of apparatus that measures the spin of an electron, so it has as pointer that can indicate either “up” or “down.” If it’s an accurate device, whenever we feed it an electron that is purely spin-up, the pointer will reliably indicate “up.” And likewise for spin-down.

So what if we feed our apparatus an electron that is in a superposition of spin-up and spin-down? The prediction of the Schrödinger equation is completely unambiguous: the combined system of electron and apparatus will evolve into a superposition of “the electron is spin-up, and the apparatus measured it to be spin-up” and “the electron was spin-down, and the apparatus measured it to be spin-down.”

It doesn’t end with the apparatus. You obey the rules of quantum mechanics, so you have a wave function, and you can exist in superpositions. And once you glance at the pointer on your apparatus, you will become part of a superposition, where part features you thinking “I saw the electron measured to be spin-up” and another part has you thinking “I saw the electron measured to be spin-down.”

Everyone agrees that this is what the Schrödinger equation actually predicts. Where people disagree is what to do about it.

The founders of quantum mechanics reasoned, sensibly enough, that nobody had ever experienced being in a superposition like that. So they made up a new rule, according to which part of the wave function magically disappears, and that’s what we’ve been teaching our students ever since.

Everett’s move was straightforward and therapeutic. He simply said, “Both parts of the wave function exist, precisely as predicted by the Schrödinger equation. But they represent two distinct, non-interacting worlds.” The idea, in other words, is that every time you think a quantum measurement occurs, in actuality the universe branches into multiple worlds, each of which exactly the same except for the outcome of that measurement.

What’s important to emphasize is that Everett didn’t put in all the additional worlds; they were already there, the possibility of their existence opening up as soon as physicists started talking about superpositions and wave functions. All Everett did was to say “and that’s okay.” Not everyone agrees that it’s okay; there are numerous other formulations of quantum theory, each of which works very hard to get rid of all the other worlds.

But why bother? Once the worlds are created, we can’t interact with them any more. If for some reason we decide to base important life decisions on the measurement of an electron spin, we can ponder the idea that a version of ourselves in another branch of the wave function made the other choice and is living their life accordingly. But we can’t talk to them to compare notes. The other worlds are inaccessible to us. Their existence helps to simplify the maths, but they should affect how we go about living our lives.

There are many objections to Everett’s Many-Worlds formulation of quantum mechanics, of varying degrees of respectability. Some argue that it’s too extravagant, what with all those worlds. But the potential for the worlds is there in any version of quantum theory for which the wave function represents reality. Many-Worlds is actually the simplest and least elaborate version of quantum mechanics we can imagine. It’s just wave functions obeying the Schrödinger equation, nothing more or less.

Another objection is that the theory isn’t falsifiable, since we can’t observe the other worlds. But the worlds aren’t the theory; they are a prediction of the theory. To falsify a theory, we just have to do an experiment that is incompatible with one of its predictions. In the case of Everett, that’s simple; just find an example where a wave function doesn’t obey the Schrödinger equation even when it’s not interacting. In other formulations of quantum mechanics, that can happen, but not in Many-Worlds. Karl Popper, who popularised the idea that scientific theories should be falsifiable, was very impressed with Many-Worlds (and was a fierce critic of textbook quantum mechanics).

But there remain open questions that have not yet been fully resolved. Many-Worlds is a lean and mean theory, but it’s possibly too lean and mean; there is very little structure to rely on, so questions like “Why do probabilities behave the way they do?” and “Why is classical mechanics such a good approximation to the world we see?” are hard to answer.

That’s okay, physicists love tackling hard questions. We should be grateful that Hugh Everett has bequeathed to us a rich set of parallel universes, so that we will answer them all in at least some of them.

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