(I) Aristotle of Stagira (384-322 BC) 0) A closed geocentric spherical cosmology. (Adopted from the great mathematician, Eudoxus, c. 400 to 347 BC; via Calippus; but Aristotle unifies their separate schemes for different heavenly bodies). (Aristotle cites mathematicians as estimating radius of earth: in fact 200% of correct figure. Eratosthenes ca. 250 BC estimates radius of earth as 120% of correct).
There is no question that the theory of quantum mechanics is empirically successful. What the formalism of the theory says about the world, however, remains controversial. In this class, we will look at different theories of quantum mechanics. We will examine a range of philosophical issues that arise for the different theories, including the measurement problem, non-locality, the ontological status of the wavefunction and configuration space, the nature of probability, causation, and the compatibility of quantum mechanics with relativity.
How do we learn about the fundamental nature of the world from a mathematically formulated physical theory? To learn about spacetime, we follow this rule: posit the least spacetime structure to the world required by a theory’s dynamical laws. Applied to special relativity, for example, this rule tells us to not posit an absolute simultaneity structure. I suggest that we should use this rule for more than just spacetime structure. We should use the rule for statespace, positing the least statespace (...) structure required by a theory’s dynamical laws. Using this rule, I argue that a classical mechanical world has surprisingly little fundamental structure. Fundamentally, such a world does not have a Euclidean distance structure. This bears on more general questions: what physics tells us about the world; what possibilities are distinguished by a theory; what is in a theory’s fundamental ontology (which I suggest includes the statespace structure); and when two formulations of a theory are mere notational variants. (shrink)
How do we learn about the nature of the world from the mathematical formulation of a physical theory? One rule we follow, familiar from spacetime theorizing: posit the least amount of spacetime structure required by the fundamental dynamical laws. I think that we should extend this rule beyond spacetime structure. We should extend the rule to statespace structure. Using this rule, I argue that a classical mechanical world has a surprisingly spare amount of structure.
I argue that the fundamental space of a quantum mechanical world is the wavefunction's space. I argue for this using some very general principles that guide our inferences to the fundamental nature of a world, for any fundamental physical theory. I suggest that ordinary three-dimensional space exists in such a world, but is non-fundamental; it emerges from the fundamental space of the wavefunction.
Or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. “Time in thermodynamics” misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a “phenomenological science.” And to the extent that physics can tell us about the fundamental features of the world, including such things as the nature of time, we generally think that only fundamental (...) physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time; and in particular, the apparent asymmetry of those processes. The pressing question of time in the context of thermodynamics is about the asymmetry of things in time, not the asymmetry of time, to paraphrase Price ( , ). I use the title anyway, to underscore what is, to my mind, the centrality of thermodynamics to any discussion of the nature of time and our experience in it. The two issues—the temporal features of processes in time, and the intrinsic structure of time itself—are related. Indeed, it is in part this relation that makes the question of time asymmetry in thermodynamics so interesting. This, plus the fact that thermodynamics describes a surprisingly wide range of our ordinary experience. We’ll return to this. First, we need to get the question of time asymmetry in thermodynamics out on the table. (shrink)
We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)
We are used to talking about the “structure” posited by a given theory of physics. We say that relativity is a theory about spacetime structure. Special relativity posits one spacetime structure; different models of general relativity posit different spacetime structures. We also talk of the “existence” of these structures. Special relativity says the world’s spacetime structure is Minkowskian: it posits that this spacetime structure exists. Understanding structure in this sense seems important for understanding what physics is telling us about the (...) world. But it is not immediately obvious just what this structure is, or what we mean by the existence of one structure, rather than another. The idea of mathematical structure is relatively straightforward. There is geometric structure, topological structure, algebraic structure, and so forth. Mathematical structure tells us how abstract mathematical objects t together to form different types of mathematical spaces. Insofar as we understand mathematical objects, we can understand mathematical structure. Of course, what to say about the nature of mathematical objects isn’t easy. But there seems to be no further problem for understanding mathematical structure. Modern theories of physics are formulated in terms of these mathematical structures. In order to understand “structure” as used in physics, then, it seems we must simply look at the structure of the mathematics that is used to state the physics. But it is not that simple. Physics is supposed to be telling us about the nature of the world. If our physical theories are formulated in mathematical language, using mathematical objects, then this mathematics is somehow telling us about the physical make-up of the world. What is.. (shrink)
Max Jammer’s recent book, Concepts of Simultaneity: From Antiquity to Einstein and Beyond, traces the history of our ideas on simultaneity as they evolved alongside sweeping changes in our understanding of physics. One of the interesting lessons of the book is that, even as our physical theories have become increasingly successful, the question of the proper understanding or interpretation of those theories remains extremely puzzling. The central issue is this: Is the simultaneity of events a real feature of the world? (...) Or does it depend on the particular choice of reference frame, with any such frame as good as any other? In ancient times, Jammer suggests, most people took the notion of simultaneity for granted: Two events were simultaneous if they happened at the same time. Simultaneity was considered an objective feature of the world. This simple idea appeared con rmed by classical Newtonian mechanics. In Newtonian physics different inertial reference frames (ones that move at a constant velocity relative to one another) are equally good (the laws of motion hold in all of them), even though some attributes of an object, say velocity or momentum, differ from one reference frame to another. However, some features, such as simultaneity, hold in all allowable reference frames and are thus frame independent and in some sense more objective. But what if two events whose simultaneity is in question took place far from each other? How would you know whether they were simultaneous? One solution (available for the last few centuries anyway) is for the observers of each event to look at their (previously synchronized) clocks. The question then becomes, How can clocks that are distant from one.. (shrink)
In a recent paper, Malament (2004) employs a time reversal transformation that differs from the standard one, without explicitly arguing for it. This is a new and important understanding of time reversal that deserves arguing for in its own right. I argue that it improves upon the standard one. Recent discussion has focused on whether velocities should undergo a time reversal operation. I address a prior question: What is the proper notion of time reversal? This is important, for it will (...) affect our conclusion as to whether our best theories are time-reversal symmetric, and hence whether our spacetime is temporally oriented. *Received February 2007; revised March 2008. †To contact the author, please write to: Department of Philosophy, Yale University, P.O. Box 208306, New Haven, CT 06520-8306; e-mail: firstname.lastname@example.org. (shrink)
This book is a stimulating and engaging discussion of philosophical issues in the foundations of classical electromagnetism. In the rst half, Frisch argues against the standard conception of the theory as consistent and local. The second half is devoted to the puzzle of the arrow of radiation: the fact that waves behave asymmetrically in time, though the laws governing their evolution are temporally symmetric. The book is worthwhile for anyone interested in understanding the physical theory of electromagnetism, as well for (...) the views it presents on philosophical issues such as causation, counterfactuals, laws, scienti c theories, models, and explanation. While philosophers of physics tend to focus on quantum mechanics and relativity, Frisch’s book shows that there are deep foundational issues in classical physics, equally worthy of attention. That said, let me lodge disagreement on some key points. Frisch argues from an alleged inconsistency in classical electromagnetism— that Maxwell’s equations, the Lorentz force law, and the conservation of energy cannot be jointly true—to the conclusion that the standard view of scienti c theories as a formalism plus an interpretation is incorrect. Consistency is a necessary condition of any view on which scienti c theories give us an account of “ways the world could be” (Frisch, , ). Since classical electromagnetism is successfully used by practicing physicists, consistency must be just one criterion of theory choice weighed equally among others. This is an intriguing idea, but I am not sure that consistency can be given up so easily. That road leads dangerously close to accepting orthodox ‘Copenhagen’ quantum mechanics. Surely the inconsistency of.. (shrink)
I discuss the nature of the puzzle about the time‐asymmetry of radiation and argue that its most common formulation is flawed. As a result, many proposed solutions fail to solve the real problem. I discuss a recent proposal of Mathias Frisch as an example of the tendency to address the wrong problem. I go on to suggest that the asymmetry of radiation, like the asymmetry of thermodynamics, results from the initial state of the universe.
Huw Price argues that there are two conceptions of the puzzle of the time-asymmetry of thermodynamics. He thinks this puzzle has remained unsolved for so long partly due to a misunderstanding about which of these conceptions is the right one and what form a solution ought to take. I argue that it is Price's understanding of the problem which is mistaken. Further, it is on the basis of this and other misunderstandings that he disparages a type of account which does, (...) in fact, hold promise of a solution. (shrink)