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Physics, Metaphysics, & Other Nonsense H.S. Hestevold Handout 15 Spring 2014 Quantum Mechanics: Philosophical Concerns, Part II VI. Wave function and wave function collapse Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 164.4-167 and diagram at the top of p. 168. A. What is a wave function? First, some review: the formula F = ma is a mathematical description of an object's force. One can determine the force of a particular automobile by multiplying the automobile's mass by the automobile's acceleration. Similarly, a wave function can be thought of as a mathematical description of an entity in superposition -- a description that allows us to make use of the bizarre status of an entity (e.g. an electron or photon) in superposition… whatever superposition may involve. B. LeClair: "What the Wave Function Means to Me:" We will have a few minutes of Show-And-Tell from LeClair: exactly, what can a wave function do for you? What payoff does it allow you to enjoy? C. How should one interpret the wave function? 1. Reminder: The wave function is a mathematical description that works. That is, using the wave function allows one to make successful predictions about the behavior of physical entities, and it allows one to solve real-world problems. 2. The task of interpretation. If you show 'F=ma' to the average middle-school student in Alabama, the student will have no understanding of what the letters and equality sign mean. To allow the student to understand and make use of the formula, you will need to provide the student with an interpretation of the formula. You will need to explain what the 'm' and 'a' represent, what the mass of an object involves, what the acceleration of an object involves, what the concept of force involves, and why the concept of the force of an object is useful. 3. Interpreting the wave function. Plugging values into a wave function works -- it allows physicists and engineers to make predictions and solve 1 problems. But what type of physical world is the wave function about? What type of physical world makes the wave function work? What are the photons and electrons like that behave so bizarrely and yet are describable by a wave function that is operationally sound? D. a. Is the wave function a description of nonparticle-like, non-wave-like material entities that don’t exhibit the standard intrinsic properties of sub-atomic particles? b. Is the wave function a description of the probabilities that certain measurements will be made if measurements are made at a particular place and time? c. Is the wave function a description of the way a particular material entity (e.g. photon or electron) behaves in different actual worlds at a given time? d. Is the wave function something else altogether? Wave function collapse. With respect to the double-slit experiment, assume that between leaving the electron gun at t1 and striking the detection screen at t8, an electron E1 is in superposition -- a state in which it lacks a definitive location with definitive intrinsic properties. Suppose that you want to know whether electron E1 is or isn't in particular spatial location S92. You put your detector in S92 at t6, and you will find that the particle is (or isn't0 there. You thereby cause a wave function collapse: you bring it about that there is no longer some non-zero and non-one probability that the E1 is in location S92. Rather, the detector reveals that the particle is in fact there (or not, as the case may be). 2 VII. The Copenhagen interpretation of QM Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 172.2-.175.2; Fib. 4.6 on p. 184. A. Is the wave function a description of the physical world? As I understand the Bohr/Heisenberg interpretation, the answer is No. It is a mistake to believe that the wave function is a mathematical description of a particle, a wave, or something that has the property of being in superposition (or in any other such state). Rather, the wave function is a description of the probability that certain measurements will be made at certain places at certain times. That is, the wave function may tell us that we have a certain probability of detecting that an electron E1 passing through the left slit with an upspin if we place a detector by the left slit at a given time. The wave function, then, is about the probability that certain measurements will be made, not the probability that there is a material entity at a certain spot with certain properties that would cause us to make certain measurements. B. What are detectors and what causal properties do they have? 1. According to some interpretations of QM, when one uses a detector to determine whether a particle is or isn’t within a particular region of space, the detector causes a “wave function collapse” -- i.e. it becomes a fact that the electron is within that region or it becomes a fact that the electron is not with that region. If no detector is employed, there is no fact (known or unknown) as to whether the electron is or isn’t within that region. 2. If, however, two electrons undergo a simple interaction with one another, no detector is involved and thereby there occurs no wave function collapse. That is, it would remain false that either electron has a definitive spatial location. 3. Detector mystery #1. What is the difference between a bunch of particles that constitute a detector and a bunch of particles that constitute doorknob? 4. Detector mystery #2. Is there a bizarre causal connection between consciousness and the state of the world at any given? (Please don't grow obsessed with this option.) 3 C. The Schrodinger/Einstein cat objection (Figure 4.6). VIII. The many-worlds interpretation of QM Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 193.4-195.2. A. Hugh Everett’s “many worlds” interpretation.1 1. Does the many-worlds interpretation allow a wave function collapse? 2. What the wave function describes. 3. Multiple actual worlds. 4. Reminder: the Deutsch/Lockwood model of time travel turned on the many-worlds interpretation of QM. B. Schrodinger's cat revisited: What does the many-worlds interpretation imply about Schrodinger's poor cat? C. Concerns. 1. The usual concerns about multiple-world views. 2. Tim Maudlin’s concern:2 to talk of the probabilities that are essential to QM is to talk about the probability that a wave function will collapse in a certain way. If, in fact, both ways do occur. Then, what are probabilities about after all? They cannot be about the odds that the world will be in one state but not another. (The probability is 1 that the cat is alive (in one world); and the probability is also 1 that the cat is not alive (in some other actual world). 1 See Tim Maudlin’s “Metaphysics and Quantum Physics," The Oxford Handbook of Metaphysics ed. by Loux and Zimmerman (2003), p. 467. 2 “Metaphysics and Quantum Physics," p. 468 4 IX. Determinism A. Determinism. D1 Event p is the sufficient causal condition for event q =Df It is physically necessary that if p occurs, q occurs.3 DET For any event e that occurs, there is a sufficient causal condition for e. B. Predictability. Some might be inclined to conclude that Determinism implies Predictability -- that if DET is true, then in principle, it is possible to predict at time t the state of the world at any time after t. This is what John Hospers wrote about the difference between Determinism and Predictability: Determinism... is a metaphysical theory: it has to do with what is, with what exists in reality; but predictability is an epistemological matter: it has to do with our knowledge of what is. To predict accurately we would require not only that everything have a cause but that we know in detail what these causes are and what are the laws connecting causes with effects. Predictability would be a consequence of determinism plus our knowledge of the laws, but it is not what determinism consists in.4 Hospers should have added that there could be no predictability unless it is in principle (physically) possible to have complete knowledge of the state of the world at a given time. If one couples such knowledge with complete knowledge of the laws of nature, then one could in principle predict future states of the world if DET were true. The following captures the difference between DET and predictability: 3 Alternatively, to say that p is the sufficient causal condition for q is to say that, in every possible world that has the same laws of nature as the actual world, it is true that if p occurs, q occurs. 4 John Hospers, An Introduction to Philosophical Analysis (2nd. ed.; Englewood Cliffs, NJ: Prentice-Hall, Inc., 1967), p. 328. 5 PRE (i) DET is correct; (ii) it is physically possible to have exhaustive knowledge of the laws of nature; (iii) it is physically possible to have exhaustive knowledge of the state of the world at any given time t; (iv) from exhaustive knowledge of the laws of nature and the state of the world at any time t, it is possible to deduce the state of the word at any time after t. Clearly, then, if DET is correct, it does not necessarily follow that Predictability is correct: for all we know, the world may be such that, it is in principle impossible for one to have exhaustive knowledge of the state of the world at some particular time t. And, if Predictability is true, there is no guarantee that one will be able to predict the future: though it may be physically possible to have exhaustive knowledge of the laws of nature and the state of the world at any given time, it may nonetheless be true that we lack the intelligence or technological means to have such exhaustive knowledge. C. X. For LeClair: What do the findings of QM imply about DET and PRE? Why is it that humans can’t solve these problems? A. The Kantian view. B. Logical empiricism (aka logical positivism). C. Are we simply not smart enough? D. The New Mysterianism. In writing about inability to understand the relation between consciousness and brain states, Colin McGinn writes: [T]he limits of our minds are just not the limits of reality. It is deplorably anthropocentric to insist that reality be constrained by what the human mind can conceive. We need to cultivate a vision of reality (a metaphysics) that makes it truly independent of our given cognitive powers, a conception that includes these powers as a proper part.5 Peter van Inwagen has also contemplated the question of why there seems to be no agreement among professional metaphysicians regarding the nature of space and time, consciousness, free will, etc.: 5 The Problem of Consciousness (Blackwell, 1991), p. 22. 6 One might hold that the human failure to achieve established metaphysical results is due to some special quirk of the human mind, a quirk that could be absent from the minds of Martians or intelligent dolphins. Evolutionary biology suggests that human beings possess a very specific set of mental talents and that other intelligent or rational species might possess a different but equally specific sets of talents. We, as a species are very good at physics, and -- all the evidence suggests this -- very bad a metaphysics. Perhaps we shall one day discover among the stars a species that is very good at metaphysics and very bad at physics. [Noam Chomsky has made this conjecture.] It may be that the best human metaphysicians are like acrobats. Acrobats are people who in virtue of long training and arduous discipline, can do what arboreal apes do much better without any training at all. Acrobats achieve what they do achieve by taking capacities of hand, mind, and eye that were “designed” for purposes quite unrelated to swinging through the air and pushing these capacities to their limits. Perhaps human metaphysicians are like that: they work by taking human intellectual capacities designed for purposes quite unrelated to questions about ultimate reality and pushing these capacities to their limits. It may be that a comparison Samuel Johnson used for a rather different purpose applies to the human metaphysician: such a person is like a dog walking on its hind legs. “It is not done well,” said Dr. Johnson, “but you are surprised to find it done at all.”6 6 Metaphysics (3rd ed.; Westview, 2009), p. 14. 7