A guide to (not) understanding quantum mechanics

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How can we come to grips with a theory that doesn’t explain how anything works?

 

 

Enlarge / According to Werner Heisenberg and Niels Bohr, when it comes to the subatomic world, we’re just goldfish.

 

Quantum mechanics is simultaneously beautiful and frustrating.

 

Its explanatory power is unmatched. Armed with the machinery of quantum theory, we have unlocked the secrets of atomic power, divined the inner workings of chemistry, built sophisticated electronics, discovered the power of entanglement, and so much more. According to some estimates, roughly a quarter of our world’s GDP relies on quantum mechanics.

 

Yet despite its overwhelming success as a framework for understanding what nature does, quantum mechanics tells us very little about how nature works. Quantum mechanics provides a powerful set of tools for successfully making predictions about what subatomic particles will do, but the theory itself is relatively silent about how those subatomic particles actually go about their lives.

 

For example, take the familiar concept of a quantum jump. An electron in an atom changes energy levels and thus either absorbs or emits energy in the form of one photon of radiation. No big deal, right? But how does the electron “jump” from one energy level to another? If it moves smoothly, like literally everything else in the Universe, we would see the energy involved change smoothly as well. But we don’t.

 

So does the electron magically disappear from one energy level and magically reappear in another? If it does, name one other physical object in the Universe that acts like that. While you’re at it, please give me a physical description of the unfolding of this magic act. I'll wait.

 

Quantum mechanics is completely silent on how the electron changes orbitals; it just blandly states that it does and tells us what outcomes to expect when that happens.

 

How are we supposed to wrap our heads around that? How can we possibly come to grips with a theory that doesn’t explain how anything works? People have struggled with these questions ever since quantum mechanics was developed, and they’ve come up with a number of ways to make sense of the processes involved in quantum behavior. Let’s explore three of these interpretations of quantum mechanics to see if any of them satisfy our cravings for a "why" behind all this odd phenomenology.

The Copenhagen interpretation

Enlarge / The participants of the Copenhagen Conference in 1930. Niels Bohr is second from the left in the front row, and Werner Heisenberg is beside him on the right.

 

If you’re not the kind of person to sweat the small stuff, the Copenhagen interpretation is for you. Like the other two interpretations we’ll explore in this article (and the many more we won’t), there isn’t one precise, definitive Copenhagen interpretation—rather, it’s a collection of ideas that share a similar set of values.

 

In this case, those values are best expressed as “shut up and calculate.”

 

The Copenhagen interpretation was named in the 1950s, but it traces its lineage to some of quantum theory's founding figures who were based in that city in the early 20th century: Werner Heisenberg and Niels Bohr.

 

Heisenberg and Bohr argued extensively (and sometimes rudely) that subatomic physics is just plain weird. So weird, in fact, that it would be hopeless for our puny human brains to come up with pictures, visuals, stories, and descriptions of what’s really going on. We’re creatures of classical physics, after all, immersed in a macroscopic world. That macroscopic world doesn’t just inform our intuition; it also limits our very imagination.

 

Go up to a goldfish and ask for its thoughts on fluid mechanics. You may hear “blub blub,” but you probably won't get a lot of insights. According to Heisenberg and Bohr, when it comes to the subatomic world, we’re just goldfish. We may experience some of the output of this strange world, but we should count ourselves lucky that we were able to make any progress at all in understanding it.

 

As soon as physicists discovered that the subatomic world appears to play by different rules, the Copenhagen School would argue, we should skip trying to understand the "why" behind those rules and focus only on the results we get from our experiments. It’s straight-up hopeless to try to describe how a quantum jump actually unfolds; instead, we should console ourselves with the knowledge that it does happen and that we can make firm predictions about it.

 

So the Copenhagen interpretation stays as close as possible to the raw mathematics that powers the predictions of quantum theory. This makes it the most “popular” interpretation. (I used scare quotes here because it's the default interpretation taught in graduate school textbooks, and it has found some strong supporters. But the vast majority of physicists don’t even really think about interpretations in the first place, as they’re busy writing grant proposals anyway. In many ways, they’re living the Copenhagen interpretation.)

 

Some of the statements you might find in a typical Copenhagen-like interpretation include:

 

• The subatomic universe is fundamentally non-deterministic. When electrons pass through a double-slit, for example, and land in a random spot on a screen, not even the electron knows where it’s going to land. The deep workings of the Universe prevent anybody from knowing the precise outcome of a quantum experiment beforehand.

 

• That said, we can make predictions about what might happen. For each subatomic system, we can lay out the probabilities for how it might evolve. These probabilities are given by a wave function, and the evolution of the wave function is governed by the Schrödinger equation. When we make a measurement, this wave function “collapses” and the system appears to be in a specific state.

 

• The macroscopic world does not play by these same rules, and there’s a transition scheme from the quantum to the classical realm known as the correspondence principle, so as you go about your daily life, you don’t have to sweat all this quantum weirdness.

The many-worlds interpretation

If you find the Copenhagen interpretation as filling yet unsatisfying as eating an entire bag of Cool Ranch Doritos in a single sitting (don’t judge), you’re not alone. The Copenhagen interpretation flat-out refuses to acknowledge how or why any of this stuff actually works. How does an electron travel through the double-slits? What happens to meld the quantum world into the classical one? And what the heck is going on with measurements to create a definitive state?

 

Enlarge / Erwin Schrödinger addresses the 5th World Power Conference in Vienna, Austria, in 1956.

 

That last question bugged Erwin Schrödinger to no end. Left to their own devices, the wave functions of quantum systems evolve according to Schrödinger’s equation, which spits out a potentially dizzying range of probabilities. But as soon as we “measure” the quantum system, the wave function collapses, evaporating with a poof, only to be replaced by a particle. Schrödinger asked what made measurements so special: How do quantum systems operate under two radically different sets of rules, one when nobody’s looking and one when somebody is?

 

Schrödinger’s argument culminated in his famous cat-in-the-box experiment, which he used to show just how ludicrous the growing consensus over the Copenhagen interpretation was. The refusal of Heisenberg and Bohr to answer the simple question of why measurement was so special eventually led Schrödinger to rage-quit the whole field altogether, concluding that he “was sorry he had anything to with it.”

 

But others took on the challenge. In the 1950s, physicist Hugh Everett looked at this measurement problem of quantum mechanics and came up with an elegant yet radical solution: What if there was no such thing as measurement? What if quantum systems simply evolve or interact via the Schrödinger equation at all times and in all cases?

 

It’s not that crazy. What we call a “measurement” is really just a series of subatomic interactions. The electrons hit a detector, where they interact with the atoms in the device, which interact with the electrons in the wire coming out the back, which interact with the photons spewing out of a display, which interact with the molecules in my eye, and so on. It’s all just quantum particles doing their thing—no weird “collapse” needed.

 

But when quantum particles interact, their wave functions overlap and can become entangled. They share a unified quantum state, a single wave function that describes both particles simultaneously. And if we follow any chain of interactions, we end up entangling the entire Universe with itself—a universal quantum wave function that subsumes the entirety of the cosmos.

 

Heavy stuff. But how do we reconcile the existence of this universal wave function with the probabilities that we observe in our experiments? If we shoot an electron at a screen, it will sometimes go left and sometimes go right. How does the Universe know which one to pick?

 

The universal wave function responds with, “Why not both?”

 

This is the “many” part of the many-worlds interpretation: Every time a quantum interaction takes place (which is, like, a lot) the universal wave function splits into multiple sections, with each section containing an identical copy of the cosmos except for the different outcomes of the interaction. In our example, one universe contains our electron going left, and another universe contains our electron going right. Both universes contain the observers (that is, us) who dutifully note the outcomes of our apparently random quantum experiment.

Lost in the multiverse

While brazenly straightforward and alluring, the many-worlds interpretation does have some drawbacks.

 

First and foremost, while this interpretation is usually spoken about in poetic terms, raising the tantalizing possibility of your doppelgängers living out all the alternative choices you faced in life, the true scope of the many-worlds interpretation is much less sexy. Every quantum interaction—and I mean every quantum interaction—leads to a splitting of the universe. Every time two atoms fuse in every star in every galaxy in the entire universe, every emission or absorption of radiation, every tiny little quantum jump inside the semiconductors of the device you’re looking at right now… all of them constantly, unceasingly split off more universes.

 

As you read this, trillions upon untold trillions of you's are being created right now, living exactly identical lives except that in some random star in some random galaxy, a random dumb hydrogen nucleus went this way instead of that way.

 

While this fact doesn’t rule out the many-worlds interpretation, it does demand a certain level of intense commitment to the idea. (And yes, there are physicists with that level of commitment.)

 

And then there’s the problem of probabilities. In many-worlds, you’re guaranteed to experience certain results, but in quantum mechanics, we have only uncertainties. Remember the whole cat-in-the-box thing? What if we changed things up and put you in the box? You go in the box, and there’s a 50/50 chance you’ll be alive when we open the box again. To sweeten the deal, let’s say you'll get a billion dollars if you live.

 

Why might you hesitate to take that bet? Because the possibility of your death seems very real. But in the many-worlds interpretation, the version of you that dies won’t be around to experience it—you will only experience the reality where you wake up and walk off a billion dollars richer.

 

So why don’t you take the bet? Why hasn’t anyone taken the bet? As I said, it’s tough to square up the experimental fact of random probabilities with the guaranteed outcomes given by this interpretation.

The pilot-wave interpretation

But perhaps there’s a different way to tackle the problem. The Copenhagen interpretation says the wave function is a mere mathematical trick, just a way of assigning probabilities to outcomes. The many-worlds interpretation elevates the wave function to ultimate supremacy, saying there’s nothing but wave functions forever entangling with each other.

 

Here's a third approach: Perhaps the particles of subatomic physics are real—but so are their wave functions. This idea was first proposed by Louis de Broglie, the physicist who got the idea of wave-particle duality for matter in the first place. He suggested that every particle is associated with its own wave. This wave evolves as waves are wont to do, propagating and reflecting and so on, and those waves guide the particles to their final trajectories.

 

Enlarge / French physicist Louis de Broglie, winner of the 1929 Nobel Prize in Physics, circa 1930.

 

Eventually, de Broglie would abandon this idea in favor of the growing consensus around the Copenhagen interpretation (whether through his own conclusions or the bullying of Heisenberg and Bohr, it’s not clear). But decades later, the physicist David Bohm would pick the idea back up and flesh it out.

 

This pilot-wave interpretation (also known as de Broglie-Bohm mechanics or Bohmian mechanics) says that the true locations of the particles are hidden from us, even though they always follow set trajectories. Thus, the non-determinism of the Copenhagen interpretation is wiped away: Both the pilot waves and their particles always follow deterministic paths; we just don’t get to know about it.

 

Like the many-worlds interpretation, there’s no collapse of the wave function here because the waves themselves really exist. You still get the same chain of interactions and never-ending entanglement that consumes the universe, so some critics have argued that the pilot-wave theory is simply the many-worlds theory but with extra steps.

 

Just like the other interpretations, there’s trouble when you look closer. For example, in this interpretation, the positions of particles—not just their quantum states—become entangled. That means the motions of a hydrogen atom in the Andromeda galaxy literally influence the molecules inside your body.

 

While entanglement seems to be entrenched in any interpretation of quantum mechanics, many people argue this level of entanglement is a bridge too far. It completely destroys any notion of locality; how can we trust the results of our most basic experiments if the motions of particles within them are influenced by forces across the entire Universe?

 

There’s also the issue of the relationship between the waves and their particles, which is decidedly one-way. Didn’t we decide way back with Newton that for every action, there’s an equal and opposite reaction? Why do the waves act on the particles but not the other way around?

 

The focus on positions also poses problems for relativity, which says that position and momentum should be on equal footing. Without that, it’s incredibly difficult to build a relativistic version of the pilot-wave theory, which is kind of important. None of these issues are necessarily deal-breakers, but they do make pilot-wave theory somewhat unpalatable.

 

Ultimately, all the interpretations have their strengths and weaknesses. All of them attempt to explain the weirdness of the subatomic world, but all of them have aspects you either have to gloss over or hope that some future physicist can untangle.

 

What does quantum mechanics teach us about subatomic reality? Given our current state of knowledge, it’s up to you to choose which interpretation you prefer. No matter what, the supreme lesson remains: Quantum mechanics just doesn’t seem to make sense. Perhaps we’re just goldfish, after all.

 

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