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Overview
In this book, Tim Maudlin, one of the world’s leading philosophers of physics, offers a sophisticated, original introduction to the philosophy of quantum mechanics. The briefest, clearest, and most refined account of his influential approach to the subject, the book will be invaluable to all students of philosophy and physics.
Quantum mechanics holds a unique place in the history of physics. It has produced the most accurate predictions of any scientific theory, but, more astonishing, there has never been any agreement about what the theory implies about physical reality. Maudlin argues that the very term “quantum theory” is a misnomer. A proper physical theory should clearly describe what is there and what it does—yet standard textbooks present quantum mechanics as a predictive recipe in search of a physical theory.
In contrast, Maudlin explores three proper theories that recover the quantum predictions: the indeterministic wavefunction collapse theory of Ghirardi, Rimini, and Weber; the deterministic particle theory of deBroglie and Bohm; and the conceptually challenging Many Worlds theory of Everett. Each offers a radically different proposal for the nature of physical reality, but Maudlin shows that none of them are what they are generally taken to be.
Product Details
| ISBN-13: | 9780691183527 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 03/19/2019 |
| Series: | Princeton Foundations of Contemporary Philosophy , #19 |
| Pages: | 256 |
| Sales rank: | 414,044 |
| Product dimensions: | 5.80(w) x 8.60(h) x 1.10(d) |
About the Author
Read an Excerpt
CHAPTER 1
Eight Experiments
Physics has traditionally been characterized as the science of matter in motion. Rough as this characterization is, it illuminates the standing of physics with respect to all other empirical sciences. Whatever else the objects of the various empirical sciences are, they are all instances of matter in motion. Every biological system, every economic system, every psychological system, every astronomical system is also matter in motion and so falls under the purview of physics. But not every physical system is biological or economic or psychological or astronomical. This is not to argue that these other empirical sciences reduce to physics, or that the other sciences do not provide an understanding of systems that is distinct from a purely physical account of them. Still, physics aspires to a sort of universality that is unique among empirical sciences and holds, in that sense, a foundational position among them.
The phrase "matter in motion" presents two targets for further analysis: "matter" and "motion." Present physics elucidates the "motion" of an object as its trajectory through space-time. A precise understanding of just what this is requires a precise account of the structure of space-time. The physical account of space-time structure has changed through the ages, and at present the best theory is the General Theory of Relativity. The nature of space-time itself and the geometrical structure of space-time is the topic of the companion volume to this one: Philosophy of Physics: Space and Time. The present volume addresses the question: What is matter? The best theory of matter presently available is quantum theory. Our main task is to understand just what quantum theory claims about the nature of the material constituents of the world.
As straightforward as this sounds, we must first confront a great paradox about modern physics. The two pillars on which modern physics rests are the General Theory of Relativity and quantum theory, but the status of these two theoretical systems is completely different. General Relativity is, in its own terms, completely clear and precise. It presents a novel account of space-time structure that takes some application and effort to completely grasp, but what the theory says is unambiguous. The more one works with it, the clearer it becomes, and there are no great debates among General Relativists about how to understand it. (The only bit of unclarity occurs exactly where one has to represent the distribution of matter in the theory, using the stress-energy tensor. Einstein remarked that that part of his theory is "low grade wood," while the part describing the space-time structure itself is "fine marble.") In contrast, no consensus at all exists among physicists about how to understand quantum theory. There just is no precise, exact physical theory called "quantum theory" to be presented in these pages. Instead, there is raging controversy.
How can that be? After all, dozens and dozens of textbooks of quantum theory have been published, and thousands of physics students learn quantum theory every year. Some predictions of quantum theory have been subjected to the most exacting and rigorous tests in human history and have passed them. The whole microelectronics industry depends on quantum-mechanical calculations. How can the manifest and overwhelming empirical success of quantum theory be reconciled with complete uncertainty about what the theory claims about the nature of matter?
What is presented in the average physics textbook, what students learn and researchers use, turns out not to be a precise physical theory at all. It is rather a very effective and accurate recipe for making certain sorts of predictions. What physics students learn is how to use the recipe. For all practical purposes, when designing microchips and predicting the outcomes of experiments, this ability suffices. But if a physics student happens to be unsatisfied with just learning these mathematical techniques for making predictions and asks instead what the theory claims about the physical world, she or he is likely to be met with a canonical response: Shut up and calculate!
What about the recipe? Is it, at least, perfectly precise? It is not. John Stewart Bell pressed just this complaint:
A preliminary account of these notions was entitled 'Quantum field theory without observers, or observables, or measurements, or systems, or apparatus, or wavefunction collapse, or anything like that'. That could suggest to some that the issue in question is a philosophical one. But I insist that my concern is strictly professional. I think that conventional formulations of quantum theory, and of quantum field theory in particular, are unprofessionally vague and ambiguous. Professional theoretical physicists ought to be able to do better.
Bell's complaint is that the predictive recipe found in textbooks uses such terms as "observer" and "measurement" and "apparatus" that are not completely precise and clear. This complaint about quantum theory does not originate with Bell: Einstein famously asked whether a mouse could bring about drastic changes in the universe just by looking at it. Einstein's point was that some formulations of quantum theory seek to associate a particular sudden change in the physical state of the universe ("collapse of the wavefunction") with acts of observation. If this is to count as a precise physical theory, then one needs a precise physical characterization of an observation. As Bell put it: "Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for a better qualified system ... with a Ph.D.?"
These imprecisions in the formulation of the quantum recipe do not have noticeable practical effects when it comes to making predictions. Physicists know well enough when a certain laboratory operation is to count as an observation, and what it is an observation of. Quantum theory predicts the outcomes of these experiments with stunning accuracy. But if one's main interest is in the nature of the physical world rather than the pragmatics of generating predictions, this ability is of no solace. For the recipe simply does not contain any univocal account of the world itself. To illustrate this, the standard recipe does use a mathematical operation that can be called "collapse of the wavefunction." But if one asks whether that mathematical operation corresponds to a real physical change in the world itself, the recipe does not say. And practicing physicists do not agree on the answer. Some will refuse to hazard an opinion about it.
Bell's complaint might seem incredible. If the problems with quantum theory are not "merely philosophical" but rather consist of the theory being unprofessionally vague and ambiguous as physics, why don't the physics textbooks mention this? Much of the problem has been papered over by a misleading choice of terminology. A standard retort one might hear is this: Quantum mechanics as a physical theory is perfectly precise (after all, it has been used to make tremendously precise predictions!), but the interpretation of the theory is disputable. And, one might also hear, interpretation is a philosophical problem rather than a physical one. Physicists can renounce the desire to have any interpretation at all and just work with the theory. An interpretation, whatever it is, must be just an inessential luxury, like the heated seats in a car: It makes you feel more comfortable but plays no practical role in getting you from here to there.
This way of talking is misleading, because it does not correspond to what should be meant by a physical theory, or at least a fundamental physical theory. A physical theory should contain a physical ontology: What the theory postulates to exist as physically real. And it should also contain dynamics: laws (either deterministic or probabilistic) describing how these physically real entities behave. In a precise physical theory, both the ontology and the dynamics are represented in sharp mathematical terms. But it is exactly in this sense that the quantum-mechanical prediction-making recipe is not a physical theory. It does not specify what physically exists and how it behaves, but rather gives a (slightly vague) procedure for making statistical predictions about the outcomes of experiments. And what are often called "alternative interpretations of quantum theory" are rather alternative 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.
Not every physical theory makes any pretense to provide a precisely characterized fundamental ontology. A physical theory may be put forward with the explicit warning that it is merely an approximation, that what it presents without further analysis is, nonetheless, derivative, and emerges from some deeper theory that we do not yet have in hand. In such a case, there may be circumstances in which the lowest level ontology actually mentioned by the theory is not precisely characterized. In the rest of this book, I will treat the theories under discussion as presenting a fundamental ontology that is not taken to be further analyzable, unless I indicate otherwise.
A precisely defined physical theory, in this sense, would never use terms like "observation," "measurement," "system," or "apparatus" in its fundamental postulates. It would instead say precisely what exists and how it behaves. If this description is correct, then the theory would account for the outcomes of all experiments, since experiments contain existing things that behave somehow. Applying such a physical theory to a laboratory situation would never require one to divide the laboratory up into "system" and "apparatus" or to make a judgment about whether an interaction should count as a measurement. Rather, the theory would postulate a physical description of the laboratory and use the dynamics to predict what the apparatus will (or might) do. Those predictions can then be compared to the data reported.
So far, then, we have distinguished three things: a physical theory, a recipe for making predictions, and the sort of data or phenomena that might be reported by an experimentalist. What is usually called "quantum theory" is a recipe or prescription, using some somewhat vague terms, for making predictions about data. If we are interested in the nature of the physical world, what we want is instead a theory — a precise articulation of what there is and how the physical world behaves, not just in the laboratory but at all places and times. The theory should be able to explain the success of the recipe and thereby also explain the phenomena.
Our order of investigation will start with some phenomena or data. We will try to report these phenomena in a "theory neutral" way, although in the end this will not quite be possible. But, as Aristotle said, any proper scientific investigation should start with what is clearer and more familiar to us and ascend to what is clearer by nature (Physics 184a16). We start with what we can see and try to end with an exactly articulated theory of what it really is.
Our phenomena are encapsulated in eight experiments.
Experiment 1: The Cathode Ray Tube
The two ends of an electrical battery are called "electrodes." The positive electrode is the anode, and the negative one is the cathode. Run wires from these electrodes to two conductive plates, put an open aperture in the anode, place a phosphor-coated screen beyond the anode, and enclose the whole apparatus in an evacuated tube. Finally, add a controllable heating element to the cathode. This apparatus, minus the heating element, was invented by Ferdinand Braun in 1897 and later came to be called a cathode ray tube (CRT). The heating element was added in the 1920s by John B. Johnson and Harry Weinhart.
Our first experiment consists of adjusting the heating element so the cathode warms up. When the cathode is quite hot, a bright spot, roughly the shape of the aperture in the anode, appears on the phosphorescent screen (Figure 1a, 1b). As we turn the heating element down, the spot gets dimmer and dimmer. Eventually, the spot no longer shines steadily, but instead individual flashes of light appear in the same area (Figure 1c). As the heat is further lowered, these individual flashes become less and less frequent, eventually only appearing one at a time, with significant gaps between them. But if we keep track of these individual flashes, over time they trace out the same region as the original steady spot.
These are the phenomena or data. They immediately suggest certain hypotheses about what is going on inside the tube, but for the moment, we want to distinguish any such hypotheses from the data themselves. The phenomena suggest, for example, that something is going from the cathode (where the heating is applied), through the aperture in the anode, and to the phosphorescent screen. We can test this hypothesis by moving screen toward the anode while the spot is steady. The spot remains steady, and it narrows and brightens as it approaches the anode. Just in front of the anode, the spot is the same shape as the aperture. One can place a screen between the cathode and anode, where it will light with a larger, brighter, more diffuse glow. So there does seem to be something emitted from the cathode and going to the screen. Originally, this something was called cathode rays.
When we turn down the heat, these cathode rays exhibit a sort of discrete or grainy character, producing one flash at a time. We could not have predicted this behavior: The spot might have just dimmed uniformly without ever resolving into individual scintillations. These individual discrete events suggest a further hypothesis, namely, that the cathode rays are composed of a collection of individual particles. These hypothetical particles were eventually called electrons, and the whole cathode/anode apparatus is sometimes referred to as an electron gun.
The model suggested by the term "electron gun" is strengthened by the following fact. Increasing the voltage of the battery increases the "speed" of the cathode rays in the sense that if we measure how long it takes between connecting the battery and seeing the spot, it takes less time for higher voltages. This relation yields a narrative: Heating the cathode boils off electrons, which, being negatively charged, are repelled by the negatively charged cathode and attracted to the positively charged anode. The greater the voltage difference between the two, the faster the electrons will go, with some passing through the aperture in the anode and continuing on to the screen.
It is indeed difficult to resist this particle hypothesis, but for the moment, resist it we must. The postulation of individual particles that travel from the cathode to the screen is not itself part of the data, although it might be part of a theory meant to account for the data.
Skepticism about the physical existence of individual discrete particles in this experimental situation may seem excessively cautious, but our next two experiments point in another direction.
Experiment 2: The Single Slit
If individual particles are flying from the cathode to the screen, then an object placed between the cathode and the screen might be able to affect these particles. As our first test of this hypothesis, we place a barrier with a single slit. The spot on the phosphorescent screen becomes long and thin, much as one might have anticipated (Figure 2a). Making the slit thinner in what we will call the z-direction initially makes the image thinner, again as one would expect. But beyond a certain point, a peculiar thing happens: making the slit even thinner results in the spot becoming wider and more spread out in the z-direction (Figure 2b). (In addition, the image starts to show some variation of brightness, with dark patches emerging. We leave that aside for now).
Our initial hypothesis of particles would not have hinted at this new development, but it is reminiscent of the familiar behavior of waves called diffraction. When a series of plane water waves hit a wide gap in a barrier (wide relative to the wavelength, i.e., distance between the crests), the wave train that gets through continues largely in the same direction, with just a little dissipation around the edges. But when it hits a very narrow gap, it creates a circular wave pattern on the other side that spreads farther upward and downward (Figures 3a and 3b). Crests are indicated by solid lines and troughs by dotted lines.
Since diffraction occurs when the size of the hole is small compared to the wavelength of the wave, the diffraction can be reduced by shortening the wavelength. And we find that the diffraction of our cathode rays is reduced as we increase the voltage between the cathode and the anode. So in this respect, our cathode rays behave somewhat like water waves, with the wavelength going down as the voltage goes up.
(Continues…)
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Table of Contents
Introduction ix
Chapter 1 Eight Experiments 1
Chapter 2 The Quantum Recipe 36
Chapter 3 The Wavefunction and the Quantum State 79
Chapter 4 Collapse Theories and the Problem of Local Beables 94
Chapter 5 Pilot Wave Theories 137
Chapter 6 Many Worlds 173
Chapter 7 Relativistic Quantum Field Theory 205
References 227
Index 231
What People are Saying About This
“Tim Maudlin is one of the world’s leading experts on the philosophy of physics, and he has a gift for digging deeply into foundations and explaining clearly what is there. This excellent book will be very valuable to students first encountering the philosophy of quantum mechanics. Maudlin’s strategy of introducing the subject through eight experiments is itself worth the price of admission.”—Sean Carroll, California Institute of Technology “This is an exceptionally clear account of a specific line in the interpretation of quantum mechanics, one that Tim Maudlin has been championing with increasing precision and care for twenty years, and which has found many adherents in the philosophy of physics community. The book also does a very good job of explaining, in nontechnical terms, the main conceptual puzzles of quantum mechanics in a style very conducive to understanding by philosophers. And Maudlin’s way of getting at quantum weirdness through eight experiments is beautiful.”—David Wallace, University of Southern California