Textbook quantum mechanics is a recipe for predicting the results of experiments. It works. Yet, as Tim Maudlin emphasizes in this philosophical monograph, a recipe is not a physical theory. A proper physical theory tells us what things exist and how they behave, without explicit regard in its formulation to observers or measurements. Having taken this stand, Maudlin simply walks away from the Copenhagen interpretation to focus on providing the reader with a critical introduction to three main alternatives: (a) spontaneous collapse theories (GRW after initiators GianCarlo Ghirardi, Alberto Rimini, and Tulio Weber), (b) the pilot wave theory of Louis de Broglie and David Bohm, and (c) the many-worlds theory initiated by Hugh Everett. These are not interpretations but rather “precise physical theories with exactly defined physical ontologies and dynamics that (if true) would explain why the quantum recipe works as well as it does.” They apply, at least in principle, to the observer or measuring apparatus as just another physical system, along with the system being observed or measured. Each theory is put to the test of explaining eight experiments, including double-slit interference, the Mach-Zehnder interferometer, the Einstein-Rosen-Podolsky paradox (as formulated by Bohm), and Bell's theorem-violating correlations among entangled particles. Shunning the usual abstract formalism in which measurements are characterized by Hermitian matrices, Maudlin takes us behind the veil for a closer look at how observed results come about, for example, how “certain marks or flashes are formed in certain places on a screen.”

In the textbook recipe, when a measurement is made, the value obtained is, with probability given by the Born rule, one of the eigenvalues of the corresponding operator, and the wavefunction of the system collapses to the corresponding eigenfunction. In GRW, collapses are occurring all the time, in which individual particles localize randomly to positions whose likelihood follows the square amplitude of the wavefunction, irrespective of any observation or measurement. For a given electron, localizations are so infrequent, perhaps once in 10^{15} s that it is unlikely to localize while traversing a double-slit experiment. The position of the electron in the interference pattern becomes entangled with the state of the detector array to the point where it affects the position of a macroscopic object such as a pointer that records the result. The pointer contains so many particles (whose positions are entangled) that one of them will localize almost instantly, taking the pointer with it and collapsing the superposition to give a definite result.

So an observation becomes analyzable in terms of fundamental processes, but at the price (as philosophers like to say) of requiring two new constants of nature. First is the timescale for localization of any fundamental particle. Second is a parameter characterizing the spread of the collapsed wavefunction: an electron can't be localized to a single point because by the uncertainty principle, it would likely acquire a huge momentum and we would be seeing high-speed electrons generated spontaneously in macroscopic matter. Regardless of how this parameter is adjusted, conservation of energy is forfeited in GRW, though by a small, perhaps unobservable amount.

In the pilot wave theory, the wavefunction never collapses but particles have definite positions at all times. Roughly speaking, the gradient of the wavefunction determines the velocities of fundamental particles, whose actual positions ultimately depend on initial conditions. As in GRW, particle positions are privileged over other observables.

According to this theory, in a double-slit experiment, the electron takes one path, whereupon the particles making up the measuring apparatus follow their own paths such that the result is recorded, and the particles making up human observers follow paths such that the result is recognized by them and leads perhaps to different choices of subsequent action. But! the wavefunction for all other paths continues to evolve, including the particle paths for measuring instruments recording different results, humans recognizing those results, etc. All this extra structure might not be remarkable if the wavefunction was merely a calculational device, but Maudlin makes clear that it is part of the physical ontology. Moreover, its evolution throughout configuration space is independent of the actual locations of the particles. It moves them but is unmoved by them, an asymmetry unfamiliar to physicists.

Everett had the insight that Schrodinger evolution by itself might account for our experience that quantum measurements have definite outcomes. Superpositions at the microscopic level entangle with macroscopic superpositions of measuring instruments and human observers who see different results. Further research clarified that decoherence would make the corresponding parts of the universal wavefunction highly unlikely to interfere in the future, leaving the way open to regard macroscopic superpositions as coexisting, independently evolving worlds.

Nevertheless, conceptual objections remain, and Maudlin presses two of them quite hard. One is that there can be no meaning to probability in a world where all possibilities actually occur. He finds it “not clear how Many Worlds can recover or vindicate Born's Rule as it was originally proposed (i.e., as a way to assign likelihoods to alternatives).” The other objection is that a wavefunction evolving in a many-dimensional configuration space is itself not, or by itself cannot account for, the familiar three-dimension world that we inhabit. Maudlin worries, “If tables and chairs and cats are structured collections of local entities in space-time, then stripping the local entities out from the theory strips out all the familiar material objects as well.”

I am not persuaded that these are real problems. Successive quantum measurements lead to successive generations of observers recording different sequences of results. Retrospectively for any given observer, the statistics of outcomes leads naturally to a concept of probability. Many-worlds theorists are under no obligation to derive the Born rule (after all, Born did not derive it either) but they have demonstrated that under fairly reasonable assumptions people can be expected to make decisions (or bets) in accordance with it. If the wavefunction is the reality, then patterns in the wavefunction are what account for our perception of tables and chairs. Maudlin calls this claim “astonishing.” I agree, but the history of science is replete with (at-the-time) astonishing claims that we now regard as discoveries. Nevertheless, it is a mark of pedagogical excellence that the author gives fair representation to arguments with which he disagrees, including long quotations from David Albert and David Wallace.

Relativistic considerations are addressed only in the concluding chapter, where GRW and pilot wave theories face more challenges. In many-worlds theory, if we have the correct wavefunction and its evolution, then it appears that we are home free.

To conclude: Maudlin has made a number of strategic choices in crafting this introduction to the philosophy of quantum theory. While no one would mistake the book for a popularization, by limiting mathematical manipulations to where they are essential, he has allowed the conceptual issues to command the center stage. The result is a compact, approachable volume that repays a careful study. Recommended for physicists and philosophers interested in alternatives to the Copenhagen orthodoxy.

*Allan Walstad is Associate Professor of Physics at the University of Pittsburgh at Johnstown and an Associate of the Center for Philosophy of Science.*