The Measurement Problem

In the last article, we looked at the “Measurement Problem” of quantum mechanics and how it poses a perplexing problem for physicists trying to work out what quantum theory actually tells us about the world. The crux of the problem is that we have two conflicting sets of rules determining how the quantum state of a system evolves. On the one hand we have unitary evolution of the Schrodinger equation, but this always seems to produce superpositions of measurement results which we don’t observe when we try to measure a system. On the other hand we have the second quantum rule: the “collapse postulate”. This tells us the probability of a particular measurement result given the quantum state. The Measurement Problem asks how can these two different rules be reconciled. How come we only ever observe one measurement result, when the Schrodinger equation tells us that the quantum state evolves as a superposition of different observations?

The Everett Interpretation

In 1957, the physicist Hugh Everett III (doesn’t his name sound much cooler with the roman numerals?) proposed a novel solution to the measurement problem. He suggested that the reason we only see one measurement outcome is because the quantum state describes more than just what we observe. Everett suggested that the superposition of different measurement outcomes in the quantum state isn’t a superposition of the various measurement outcomes in one world, but a superposition of many worlds, each seeing only one measurement outcome.

The easiest way to see this is by looking at a quantum state:

The above quantum state gives us the total quantum state of Schrodinger’s Cat. It’s a superposition of the cat being dead and alive. This quantum state is a superposition of distinct measurement results – the cat’s either being alive or dead. Instead of asking why the quantum state is in a superposition, yet we only ever see one measurement result, Everett said that we should notice here that there are two “branches” of the quantum state. In one branch of the quantum state, we have the cat alive, in the other we have the cat dead. Instead of associating the quantum state with a description of our world, it makes more sense to say instead that the quantum state describes multiple worlds, our world being one particular branch of the quantum state.

Whenever a quantum event occurs all possible outcomes happen, but these different outcomes are realised in separate worlds. This almost certainly sounds crazy, but the idea offers perhaps the most compelling resolution to the measurement problem. Everett’s original ideas have been developed a lot since he proposed them back in 1957, but we’ll sketch over the key features of his original proposal, and why they made such a compelling case for the existence of multiple worlds.

Taking Quantum Mechanics Seriously

If we’re going to postulate the existence of multiple other universes, none of which are, in principle, observable then we’d better have good reason! Physicists always like their theories to be as parsimonious as possible, explaining as much as possible whilst postulating the existence of the fewest independent entities. In simple terms, physical theories should not have any extra entities in them that don’t increase the explanatory power of the theory. In the Everett interpretation we have a huge increase in the number of entities, we’ve just postulated the existence of a potentially infinite number of other universes! The only way we can justify this is if they really do explain the structure of quantum theory much better than any alternative theory. So let’s see how introducing many worlds helps us to interpret quantum theory, and how this interpretation compares to other ones.

The main motivation behind the Everett interpretation was to “take quantum mechanics seriously”. From an Everettian’s point of view, the many-worlds interpretation is the only interpretation of quantum mechanics that stays true to quantum theory itself. Other interpretations either try to add something extra to the theory to solve the measurement problem, or deny that quantum mechanics actually describes the behaviour of reality. Let’s briefly introduce some of the other, major interpretations of quantum theory that have been proposed:

• Copenhagen Interpretation: Otherwise known as the “shut-up and calculate” interpretation. The Copenhagen Interpretation says that quantum mechanics should be taken seriously, but only to make predictions about measurement outcomes. We should not say that quantum theory is actually saying anything about how particles actually behave. This solves the measurement problem, in effect, by denying it exists. There is no problem of nature following two different rules, because quantum theory isn’t supposed to describe fundamental reality.
• Pilot Wave Theory: Suggests that quantum theory describes little, marble-like particles being carried along by a matter wave which evolves according to the wavefunction. Produces the same predictions as quantum theory, but has added new elements into the theory such as the pilot wave and the marble-like particle, the particle being a “hidden variable”.
• Dynamical Collapse Theory: Suggests that wavefunction collapse is a real physical process. Tries to add an extra term to the Schrodinger equation so that it can produce wavefunction collapse as well as unitary evolution in a single equation.

The “problem” with these different interpretations is that they’re either trying to amend quantum mechanics, or deny that it describes reality. The Copenhagen interpretation claims that quantum mechanics only predicts measurements and should not be used to tell us how fundamental reality behaves. But even if that were true, shouldn’t we instead develop a theory that did describe how fundamental particles behaved? Pilot Wave Theory and Collapse Theory on the other hand both say that we need to add something to quantum theory for us to be able to interpret it, but as we’ve explained before, quantum theory is one of our most accurate and successful theories of nature ever. Surely we should trust it’s formalism, instead of trying to change it so that we can provide a more intuitive interpretation of it?

The attractive feature of the Everett interpretation is that it doesn’t seek to add anything new to the already amazingly successful framework of quantum theory, and it attempts to take seriously what the theory may suggest about how reality actually works. To me, at least, this seems to be the most sensible approach. If we have an incredibly accurate theory that accords so well with reality, shouldn’t we take it seriously and try ti interpret it without adding entities?

So, what happens if we do take the theory seriously?

Taking Quantum Mechanics Seriously

If we’re going to take quantum theory seriously, then we need to take the Schrodinger equation at face value, without trying to amend it or add anything into it. If we allow the that the Schrodinger equation is a fundamental law of nature, and that it governs the evolution of systems at all times, then we’re faced with a key question.

The Schrodinger equation always produces superpositions of measurement results, but in the real world we only ever witness particular measurement results, not superpositions. How can we reconcile these two things? If we take a look at the structure of the quantum state, we see that it is a superposition of classical measurement results. These different measurement results can be called “branches” of the quantum state. What Everett saw is that the quantum state is made up of lots of these branches, but what we see is only ever one particular branch of the quantum state. If we take our universe to be precisely one of these branches, then that suggests that all the other branches must be universes on par with ours. Each branch is its own universe, and in each universe the observers see only one outcome, just like what we observe when we make a measurement.

This is the basis for the claim that the Everett Interpretation takes quantum mechanics seriously. If we do wish to take the theory seriously, as we should since it is so powerfully accurate, then we are led to the Many-Worlds Interpretation as the most “face-value” interpretation.