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: they give exactly the same predictions about what we will observe in any experiment. 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.

I feel obliged to give a disclaimer here. There are substantial volumes of literature developing, defending, and critiquing each of the interpretations listed below. The descriptions I provide, and the problems I mention for each view, will seem embarrassingly simplistic to anyone acquainted with the relevant issues. The descriptions I have provided are intended merely to give readers a sense of the variety of interpretations on offer, and to highlight the radical dissimilarities between these interpretations. For that purpose, a cursory gloss of each interpretation will suffice.

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:

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:

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 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.