Interpretations of Quantum Mechanics

Making Sense of the Laws

The laws of quantum mechanics—Schrödinger’s equation and Born’s rule—tell us what to expect in various kinds of experiments. They give the correct predictions about what we’ll observe when photons pass through polarization filters or when electrons pass through tiny slits, for example. Yet, these abstract mathematical rules don’t fully explain why things happen the way they do. Why does Born’s rule give us the correct predictions about measurement outcomes, and why does the Schrödinger equation seem to be violated whenever we make a measurement? In order to make sense of what is happening in our experiments, we need to “interpret” the laws of quantum mechanics, and figure out what they really mean.

An interpretation of quantum mechanics is a theory that tries to explain how those abstract mathematical laws (Schrödinger’s equation and Born’s rule) relate to the structure of physical reality itself. In other words, an interpretation of quantum mechanics is just an attempt to make sense of quantum mechanics. There are many different interpretations of quantum mechanics, and they paint radically disparate pictures of the world.

The various interpretations of quantum mechanics tell dramatically different stories about what really happens at the most basic level of physical reality. Nonetheless, most of these interpretations are empirically equivalent, which means they give exactly the same predictions about what we will observe in any experiment. (Two theories are empirically equivalent if they give exactly the same predictions about observable phenomena: there is no possible scientific observation we could ever make, now or in the future, that would support one theory over the other.) In other words, there is no possible experiment or observation that could ever determine which of these many interpretations is correct. To judge between competing interpretations, therefore, we must rely on considerations other than direct scientific evidence. For example, we might consider which interpretations seem simpler, or more intuitive, or more explanatorily satisfying. For Christians, evidence from religious sources (e.g. theological doctrines or scriptural revelation) might also play some role in helping us to discern which interpretations are most likely to be true.

The Measurement Problem

A central goal of most interpretations is to explain why the Schrödinger equation apparently holds whenever we aren’t observing a system, yet is suddenly violated (so it seems) when we measure something. Remember, the Schrödinger equation implies that when a system in a superposition is measured, the measuring device itself should go into a superposition of all the possible measurement outcomes. Obviously that doesn’t happen. When we measure something that we know was in a superposition before the measurement (based on previous measurements and the predictions of the Schrödinger equation), we see just one outcome. We never find our measuring devices in a superposition of many different measurement outcomes. Measuring instruments and other macroscopic objects always appear to have determinate positions, momenta, and other observable properties. We never see “fuzzy” indeterminate states at the macroscopic scale.

Here’s another way of describing the issue. All three of the following claims seem true, yet it is logically impossible for all three to be true:

1. Physical systems do—or at least should—always obey the same fundamental laws of nature, regardless of whether they are being measured. (After all, measurement itself is a physical process, so it would be strange indeed if measurements violated the laws of physics!)
2. The Schrödinger equation is a fundamental law of nature.
3. Measurements have determinate outcomes.

At least one of those claims must be false, but it is far from obvious which one is false. This puzzle is known as the measurement problem.

In order to solve the measurement problem, all interpretations of quantum mechanics must reject at least one of the above three claims. So, we can classify different interpretations according to the claims they reject. Below is a simple classification schema, populated by five of the most commonly advocated interpretations of quantum mechanics.

Interpretations that reject claim 1

Some interpretations suggest that the Schrödinger equation is a fundamental law, yet is sometimes violated. Here are two of the most famous examples:

• The Copenhagen interpretation was developed primarily by Niels Bohr and Werner Heisenberg, who were working together in the city of Copenhagen, Denmark. This is the original, orthodox interpretation, which I have been calling the “traditional” view of quantum mechanics. According to this view, measuring an object causes it to collapse from a superposition to a definite state for the measured variable.

  The central problem with this interpretation is that it doesn’t even begin to explain what sorts of processes count as “measurements” or why these processes cause the wave function to collapse.

• The von Neumann–Wigner interpretation, named for its early proponents John von Neumann and Eugene Wigner, tries to explain what’s special about “measurements” by suggesting that the presence of a conscious observer somehow causes wave function collapse. In other words, it isn’t the physical process of measurement that causes collapse. Rather, consciousness causes the collapse.

  One problem with this interpretation is that it doesn’t explain why, how, or even exactly when consciousness violates the laws of physics. Also, most people (including me) find this hypothesis far-fetched. Both consciousness and quantum collapse are deeply mysterious phenomena, but apart from that similarity it isn’t easy to see any direct relation between them.

Interpretations that reject claim 2

Other interpretations attempt to explain the predictive accuracy of Born’s rule by suggesting that the Schrödinger equation isn’t actually a fundamental law. These theories are perhaps better described as alternatives to quantum mechanics, rather than interpretations of quantum mechanics, since they deny that the standard laws of quantum mechanics are correct. Here are two popular examples:

• Bohmian mechanics, proposed by American physicist David Bohm, claims that particles are never in superpositions. Particles always have definite positions, but are guided in their motions by “pilot waves,” which account for the apparent wave-like behaviors of particles. In the double-slit test, for instance, the electron just goes through one slit. But the electron’s pilot wave travels through both slits and steers the electron toward regions where the amplitude of the wave is highest (i.e., the regions corresponding to constructive interference).
  This is a common way of characterizing Bohm’s theory, but it’s slightly misleading. The waves in Bohm’s theory aren’t waves in ordinary 3-dimensional space; rather, Bohm is suggesting that the wave function itself is a real physical object, not merely an abstract mathematical representation of a system’s state. But the wave function exists in an infinite-dimensional Hilbert space! So Bohm’s theory implies that the fundamental structure of reality is radically different from what we perceive it to be.

  The biggest problem for this theory is that—unlike the other interpretations listed here—it can’t be straightforwardly generalized to the context of quantum field theory, which has superseded particle-based theories in contemporary physics. (In quantum field theory, fields are the fundamental components of physical reality, and “particles” are merely disturbances in these fields.) Quantum field theories have proven more precisely accurate than any other theories in the history of physics, so until someone comes up with an equally successful version of Bohmian mechanics, this interpretation isn’t a serious contender. Nevertheless, advocates of Bohmian mechanics are actively working to develop such an extension of the theory.

• The Ghirardi–Rimini–Weber (GRW) interpretation was developed by Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber. It replaces the Schrödinger equation with a probabilistic law, which says that the wave function of any physical system can collapse spontaneously (regardless of whether the system is being “measured”). The wave function of an individual particle rarely collapses, but when many particles are entangled together, collapses occur much more frequently. Macroscopic objects consist of billions upon billions of fundamental particles, so they are collapsing almost constantly and never get “fuzzy” enough for us to notice.

  This also explains why we never see our measuring instruments in a weird superposition of various possible measurement outcomes. Whenever we measure a particle with our macroscopic instruments, the particle becomes entangled with the measuring instrument and is forced to collapse to a definite state. For example, an electron in the double-slit experiment may be in a superposition as it passes through the slits; but as soon as it strikes the detector film, it becomes entangled with the film’s molecules and is forced to collapse to a definite position. The collapse has nothing to do with measurement per se. It is merely a result of the fact that the measuring instrument (in this case, a detector film) consists of billions of molecules, so it is almost certain to have a very precise position state at all times.

  I’ll come right out and say it: this is my personal favorite interpretation of quantum mechanics. It does face some potential problems, though. For one, it isn’t empirically equivalent to traditional quantum mechanics: there are at least some possible experiments for which its predictions disagree with those of the Schrödinger equation. To date, so far as I am aware, no experiment has shown which of the two equations—the Schrödinger equation or GRW’s probabilistic one—yields more accurate predictions. I’m hoping GRW wins, but we’ll have to wait and see.

Interpretations that reject claim 3

Finally, some interpretations deny that measurements have determinate outcomes. What does that mean? Well, the Schrödinger equation implies that if a system is in a superposition when it is measured, the system should remain in a superposition and the measuring device itself should go into a superposition of all the possible measurement outcomes. This last category of interpretations claims that this is in fact what happens!

So, why don’t you see your measuring instruments (and other macroscopic objects) in superpositions? The answer, according to some physicists, is that you do see superpositions all the time. You just don’t notice, because you are in a superposition too! In other words, there are many “copies” of you, each observing a different outcome of the measurement. One copy of you sees one outcome, another copy sees a different outcome, and so on. There are infinitely many copies of you, but each copy of you thinks it’s the only copy and that the outcome it sees is the only outcome of the measurement. That’s why you don’t think you see superpositions. But in fact you do see them—or so some physicists have suggested.

All interpretations in this category are variations of the same basic idea, which was first proposed by American physicist Hugh Everett in 1957:

• The Everett interpretation, also called the many worlds interpretation, says that whenever a system goes into a superposition (regardless of whether anyone measures it), new copies or “branches” of the universe are created: one branch for each of the infinitely many possible values of the variable that has gone into a superposition. When an electron hits the detector film in the double-slit experiment, for instance, its superposition doesn’t collapse. Instead, the electron hits one point on the film in one branch of the universe, another point in another branch, and so on for each of the infinitely many points where the electron could have landed. The scientist, too, goes into a superposition, and each copy of the scientist sees just one dot on the film, so she thinks the electron collapsed to a definite position. In fact, however, collapse never occurs, and the universe is constantly branching into infinitely many new copies of itself.

  This is the most outlandish of all interpretations of quantum mechanics, and that may be reason enough to reject it. From a Christian perspective, the theory also seems theologically problematic. It isn’t easy to make sense of your own personal relationship with God, for example, if there are infinitely many copies of you, all doing different things.

  The Everett interpretation also faces numerous technical problems. One serious objection is that it can’t explain why Born’s rule works so well. If all of the possible outcomes of a measurement actually occur, then in what sense are some of them more likely than others? Proponents of the Everett interpretation have tried to account for the predictive success of Born’s rule in various ways, but it is controversial whether any of these attempts have succeeded.

The five interpretations mentioned above are some of the most popular, but literally dozens of other interpretations have been proposed. And remember, most of these are empirically equivalent: no experiment could possibly determine which interpretation is correct.

I hope this little sampling of interpretations was enough to convince you that science raises many more questions than it can answer, and some of the deepest questions—even questions specifically about the workings of the physical world—cannot be answered by science alone. We’ll return to this point in later chapters.