The Quantum Measurement Problem and the Everett Interpretation
|June 21, 2012|
by Jeffrey A. Barrett
In the Spring of 2007, the journalist Peter Byrne interviewed Mark Everett (E of the band Eels) about Mark’s father Hugh Everett III. Mark did not know much about what his father had done for a living, and he knew even less about what he had done as a graduate student in physics at Princeton University. But when Mark’s father died in 1982, the family cleared his desk and files and put the documents they found, which included notes, papers, sketches and photographs, in a small handful of cardboard boxes. As the last surviving member of the family, Mark had the boxes in the basement of his Los Feliz home. After a quick examination of the contents, Byrne knew that he had stumbled across something of remarkable value.
As a graduate student, Hugh Everett III had formulated one of the most important and contentious physical theories of the last century. His theory was important because it might ultimately lead to a solution of the infamous quantum measurement problem. It was contentious both because of what it predicts in order to get a solution to the measurement problem, and because scholars have never been able to agree on the details of how Everett intended for his theory to be interpreted. After getting his PhD and a government job, Everett himself had remained silent in public as scholars debated the merits and best interpretation of his theory. But the documents in the cardboard boxes stacked among the empty guitar cases and personal belongings in Mark Everett’s basement showed that his father had continued to think about quantum mechanics until his death in 1982.
After graduating from Princeton, Everett went to work as an operations researcher at the Pentagon. He kept track of what people were saying about his theory and he collected letters, papers and his own notes on quantum mechanics. These documents and the work directly related to his original thesis ended up in boxes in Mark Everett’s basement. Many of these are collected in my book with Peter Byrne, The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980.
Mark Everett at Princeton, Parallel Worlds, Parallel Lives, BBC, 2007
Hugh Everett III was a student in his mid-twenties in 1957 when he presented his revolutionary formulation of quantum mechanics in his PhD thesis. Everett himself called his theory variously; pure wave mechanics, the relative-state formulation of quantum mechanics, and the theory of the universal wave function. His theory, however, came to be popularly known as the many-worlds interpretation, because it predicts that everything that might happen, does in fact happen. As the physicist Bryce DeWitt later described it, Everett’s theory predicts that our universe is composed of countless parallel universes that are each constantly splitting into yet further copies, and in the process, creating copies of each observer, each of which subsequently observes a different quantum universe and splits into further copies.
While a science fiction fan might embrace such a theory simply by dint of how cool it would be if something like that were true, one might naturally wonder what good scientific reason one might have for believing that our universe is in fact composed of countless parallel splitting universes. Part of the answer is that this is not quite what Everett proposed. What Everett did propose is every bit as exotic—it’s just more subtle.
The short story starts with the orthodox theory of quantum mechanics, the theory that Everett argued against. The orthodox theory was formulated by the physicist P.A.M. Dirac and the mathematician John von Neumann in the early 1930s. It arguably makes the best empirical predictions of any scientific theory we have ever had. Indeed, the standard collapse formulation of quantum mechanics makes correct empirical predictions to better than thirteen significant figures when we are able to make measurements with that degree of accuracy and precision. This is comparable to getting the distance between London and Los Angeles right to within 1/100 the thickness of a strand of human hair. And there is every reason to believe that the theory will continue to exhibit such empirical success when we are able to make yet more accurate and precise observations.
There is another aspect to the predictive success of the standard theory. In addition to making precise predictions, it predicts that when we look carefully, we will find that the physical world behaves in wildly counterintuitive ways. These predictions involve the behavior of physical systems in superpositions and entangled superpositions of classically possible states. The standard theory predicts that such systems will behave nothing like familiar classical systems, and, so far, it has predicted such counterintuitive behavior precisely right whenever the appropriate experiments can be performed to check its predictions. These predictions have included two-slit interference effects, quantum tunneling, EPR correlations, the Aharonov-Bohm effect and the oscillation of neutral K mesons, quantum teleportation, and a host of other breathtakingly counterintuitive behavior.
But, while empirically successful, the standard collapse theory faces serious conceptual problems. Because of these problems, we know that the standard formulation of quantum mechanics does not in fact provide an accurate description of the physical world. This is not because it is counterintuitive. Quantum mechanics must be counterintuitive to make the right empirical predictions. Rather, as Everett argued, on a strict and literal understanding of the theory, the standard collapse formulation of quantum mechanics is logically inconsistent. This is the quantum measurement problem.
Everett characterized the measurement problem by considering how the standard theory’s two dynamical laws conflict with each other when one treats measuring devices as ordinary physical systems, then tries to describe their operation in the theory. In order to understand Everett’s argument, one first needs to get clear about what the standard collapse theory says.
The standard von Neumann-Dirac formulation of quantum mechanics can be expressed as a small handful of basic rules. To begin, it says that the physical state of a system is represented by a unit-length vector, or arrow, and that classically distinct physical states are represented by orthogonal vectors, or arrows at right angles to each other.
To see how this works, consider the Rosetta Stone. According to quantum mechanics, the state of the Rosetta Stone at a particular time is represented by an arrow of unit length. Different arrows represent different states. If one arrow represents the Rosetta Stone being inside the British Museum, another arrow, at a right angle to the first, would represent the Rosetta Stone being outside the British Museum. The representational and predictive power of quantum mechanics comes from the fact that, in addition to these two orthogonal arrows, there are an infinite number of other directions that the state arrow might point. These other arrows represent the Rosetta Stone as being in a superposition of being inside the British Museum and of being outside the British Museum.
Consider an arrow, for example, that is at a 45 degree angle to the arrow that represents the Rosetta Stone being inside the British Museum and at a 45 degree angle to the arrow that represents the Rosetta Stone being outside the British Museum. This arrow represents the Rosetta Stone in a superposition of being inside the British Museum and of being outside the British Museum, and, on the interpretation of states provided by the standard theory, in this superposed state, the Rosetta Stone is not inside the British Museum, it is not outside the British Museum, it is not both inside and outside the British Museum, and it is not neither inside nor outside the British Museum. Each of these four classically possible states has its own quantum representation, and none of these is the 45 degree arrow representing the superposition of being inside and outside the museum. Moreover, the standard theory tells us there are, at least in principle, interference experiments that would distinguish the Rosetta Stone in a superposition of locations from it being in any particular determinate location.
The standard theory describes two, very different, ways that the state of such a system might evolve. The theory tells us that, as long as the system is not measured, the state of the Rosetta Stone, or any other physical system, evolves in a smooth, continuous, deterministic way that depends only on its energy properties. Under this deterministic law, the arrow representing the state of the system wobbles around smoothly. But if the system is measured, if, for
example, someone looks for the Rosetta Stone, the theory tells us that its state instantaneously and randomly jumps to a state where the property that is being measured is determinate. If one looks for the Rosetta Stone when it is in the 45 degree arrow state described above, for example, the state of the artifact will randomly jump from being in a superposition of being inside the British Museum and being outside the British Museum to being either determinately inside or determinately outside the British Museum. For this 45 degree angle state, the probability of finding the artifact in the museum is 1/2 and the probability of finding it missing is 1/2. But, and the standard theory is absolutely clear on this, the Rosetta stone was not determinately inside and was not determinately outside the museum before one looked for it.
All this is a bit odd, but that’s not the problem. The problem is that the standard collapse theory tells us to use one dynamical law (the deterministic dynamics) to calculate the state when there is no measurement and to use the other dynamical law (the random collapse dynamics) to calculate the state when there is a measurement, but the two dynamical laws typically predict different resultant states and the theory does not tell us what constitutes a measurement. Worse, if one supposes, as Everett did, that observers are themselves physical systems like any other (and why wouldn’t they be?), then one gets a contradiction.
Hugh Everett III (far right) with Niels Bohr
The argument goes like this. Suppose that the interaction between the Rosetta Stone and the museum visitor observing it is an ordinary physical interaction between two physical systems. In that case, we use the deterministic dynamics, and, according to the deterministic dynamics, if the Rosetta Stone begins in a superposition of being inside the British Museum and being outside the British Museum, the visitor herself will end up in an entangled superposition of recording that the Rosetta Stone is in the museum and of recording that it is not in the museum when she looks for it. But if we apply the random collapse dynamics to the same interaction, it predicts that the Rosetta Stone will randomly jump to a state where it is either determinately in the museum or not, and the visitor will then either determinately record that it is in the museum or determinately record that it is not in the museum. Since the standard theory does not say what constitutes a measurement, it allows one to justify either way of calculating the resultant state. And, as Everett carefully pointed out, the two ways of calculating the resultant state typically produce contradictory results.
While Everett did much to clarify precisely what the quantum measurement problem involved, he was not the first to worry about it. The physicist Erwin Schrodinger, who won a Nobel Prize in physics for his work on the deterministic quantum dynamics, believed that the collapse dynamics was blatantly ad hoc. After debating the point with the influential Niels Bohr, Schrodinger famously concluded, “If one has to stick to this damned quantum jumping, then I regret having ever been involved in this thing.” Einstein also disliked the ad hoc character of the collapse dynamics. But he also held that the instantaneous collapse of the quantum mechanical state “implies, to my mind, a contradiction with the postulate of relativity.” Since special relativity is our other best physical theory, any potential conflict between it and quantum mechanics is a serious matter indeed. And, as it turned out, Einstein was right. As described in the standard theory, the collapse dynamics is in fact incompatible with the dynamical constraints of relativity.
For his part, Everett’s insight was to note that one can get rid of the threat of inconsistency if one simply drops one of the two incompatible laws from the standard theory. And he agreed with both Schrodinger and Einstein concerning which law to sacrifice.
Specifically, Everett’s proposal was to solve the quantum measurement problem by dropping the random collapse dynamics from the standard theory then taking the resulting pure wave mechanics, where the evolution of physical systems is governed by the deterministic dynamics alone, as a complete and accurate physical theory. His goal then was to deduce the empirical predictions of the standard collapse theory as the subjective experiences of observers who are themselves treated as quantum mechanical systems described by pure wave mechanics.
Everett’s proposal clearly removes the potential for conflict between the two dynamics laws. It also has the advantage that pure wave mechanics is manifestly compatible with the constraints of special relativity. But without the collapse dynamics, it is unclear how pure wave mechanics might be understood as predicting any measurement results at all, let alone make the right quantum statistical predictions.
It is easy to say what pure wave mechanics predicts. If there is no collapse of the state, then the visitor who looks for the Rosetta Stone will end up in an entangled superposition of recording that it is in the British Museum and of recording that it is not in the British Museum, which is presumably not what happens to real museum visitors. On the other hand, one might note, it is not entirely clear what it would be like to be in an entangled superposition of recording incompatible measurement results. Perhaps we routinely end up in such entangled superpositions but simply never notice, which is precisely what Everett argued.
In his PhD thesis and notes Everett provided good reason to believe that if observers themselves are treated quantum mechanically, then pure wave mechanics predicts that they would not notice that they typically end up in entangled superpositions of recording incompatible measurement results. And he further illustrated a specific sense in which pure wave mechanics, without the collapse dynamics, provides a representation of all of the empirical predictions of the standard collapse formulation of quantum mechanics.
While the argument is subtle with numerous twists and turns, and while some steps in the argument are open to multiple interpretations, Everett’s remarkable achievement was in providing a compelling case that pure wave mechanics alone constitutes a complete and accurate physical theory that makes the same empirical predictions as the standard collapse theory. If he was right, then the quantum measurement problem was a misunderstanding generated by unnecessarily adding the random collapse dynamics to a theory that didn’t need it.
About the Author:
Jeffrey A. Barrett is Professor of Logic and Philosophy of Science at UC Irvine.
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