This volume by Tim Maudlin is part 1 of a two-part series dealing with philosophical issues raised by our foundational theories in physics. This volume deals with space and time, covering aspects of Newtonian physics, the special theory of relativity, and the general theory of relativity. The central theme is the way in which our views about space and time, either commonsense or philosophical, have undergone forced revisions in the light of experimental science and the theories constructed to deal systematically with those empirical results. Both scientific results and philosophical ruminations on them are treated rigorously and clearly. There is an issue, I think, about the level of students for whom the book is intended, since the chapters on Newtonian theory and on general relativity will be much more easily grasped by students without much background in the formal sciences than will the chapter on special relativity.
Chapter 1 outlines some crucial aspects of the Aristotelian worldview, with the earth at rest in the center of the universe as the standard of rest and motion, and then contrasts that with Newton’s First Law and Newton’s Absolute Space and Absolute Time. The levels of our formal characterization of space (topological, differential, affine, and metric) are noted. Then Newton’s view is expounded with some of the wonderful parts of Newton’s own “Scholium to the Definitions” in the Principia quoted at length.
Chapter 2 takes up the evidence for Newton’s (astonishing to the relationists) view. The First and Second Laws are explored and the relevance of the spinning bucket and globes-on-a-rope thought experiments made clear. The history here seems to me a little thin. Galileo’s (false) “circular inertia,” grounded in his inclined plane experiments and useful to his attempt to rebut the dynamic arguments against the earth’s rotation, is contrasted with Newton’s “innovation” that true inertial motion is constant speed in a straight line. No mention is made of Benedetti or Descartes, who got much closer than Galileo to the final, correct straight line view of inertia in Newton. Well, to be sure, Newton in the “Scholium to the Laws” in the Principia credits Galileo with using the first two laws of motion in his study of projectile motion and never mentions Benedetti or Descartes.
After a useful section outlining how appropriate coordinates can be imposed on a space or space-time that allows them, there is an extended treatment of the dispute between Leibniz and Clarke. Leibniz’s use of the Principle of Sufficient Reason and the Identity of Indiscernibles (PII) is outlined, with useful quotations from the text. Then the demolition of Leibniz by the spinning bucket and Leibniz’s lame response are noted. Mach’s later relationist way out using the fixed stars and the development of the Machian idea by Barbour and Bertotti are noted.
At one point the author suggests that Leibniz need not deal with matter being situated in different locations in absolute space or having different motions relative to absolute space as having no empirical consequences to refute Newton by means of the PII, since if space exists its points, being alike, could not be distinct. But is it not the case that the PII argument needed by Leibniz in the arguments involving the position or motion of matter in space itself needs only the weaker (and more plausible) version of PII that claims two qualitatively identical possible worlds to be impossible, rather than the stronger principle that denies the possibility of qualitatively alike individuals in the actual world?
Chapter 3 digs deeper into the Newtonian problem of positing absolute uniform velocity as an unobservable feature of the world. The chapter reviews the issues and then culminates with a very clear and accessible explanation of Galilean space-time as providing the affine structure needed for absolute acceleration while denying any absolute rest frame as picked out from the class of equivalent inertial frames. This discussion provides the reader with a clear introduction to the space-time notion and shows how it plays a crucial role even in prerelativistic physics. It is a general theme that the process that eliminates unobservable structure in physics, such as that leading from Newton’s space and time to Galilean space-time, is a more modest and justifiable project than Leibniz’s grand application of epistemology to metaphysical ends. But might one also argue that such cases as the rejection of absolute rest in favor of the inertial frames of Galilean space-time lend weight to programs such as that of Leibniz by the familiar slippery-slope arguments?
The theory of special relativity is the subject of chapters 4 and 5. Here, it seems to me, a radical shift in pedagogical style takes place. The usual introduction to special relativity and Minkowski space-time is the familiar historical path. From the wave theory of light, bolstered by Maxwell’s equations, physics is led to the idea of a distinctive inertial frame in which the speed of light is isotropic and has its predicted value. From that, one is led to a search for the aether frame using round-trip experiments and, from that, to the shock of the null results of Michelson-Morley, Kennedy-Thorndike, et al. After that comes the Lorentz-Fitzgerald “compensatory” proposals, and only after that comes Einstein’s suggestion to reinstate the full equivalence of all inertial frames at the price of relativizing simultaneity.
The author, instead, uses a “top down” approach to introduce the fundamental structures of Minkowski space-time. The presentation is rigorous, clear, and insightful. But it will be much harder for beginning students to assimilate. Basing the theory on anything having to do with speed or inertial frame is disparaged. Start with the empirical fact that the trajectory of light in a vacuum is independent of the state of the source and, hence, determined by the space-time structure alone, allowing for the definition of a light-cone structure. Characterize that space-time as four-dimensional and admitting of Lorentzian coordinates. Posit the connection of the space-time structure to fundamental material things by a Law of Light (the trajectory of a light ray in a vacuum emitted from an event is a straight line on the future light cone from the event). Posit a law of the Limiting Role of the Light Cone (the trajectory of any physical entity that goes through an event never goes outside the light cone of that event). Posit a Relativistic Law of Inertia (the trajectory of any entity subject to no external forces is a straight line in Minkowski space-time). Finally, introduce a Clock Hypothesis (ideal clocks measure the interval along their trajectories).
From these posits, the Twins Paradox can be explained clearly and simply. The exposition here is interrupted by irate comments about how Rindler and Feynman, among others, confuse and mislead by telling students that the key to the situation is the fact that one twin is accelerated and the other is not.
The treatment of the Twins Paradox is followed by a lucid and rigorous demonstration of how the posited Lorentzian coordinates for the space-time can be constructed using light rays in a vacuum, undisturbed moving particles, and ideal clocks. Once this has been done, Maudlin then offers equally clear and rigorous explanations of some of the familiar coordinate-dependent aspects of the special theory such as the relativity of simultaneity, coordinate-dependent time dilation of a moving clock, and the constancy of the speed of light over all inertial frames. Looking again at the twins situation, he finishes up chapter 4 by making it very clear how one must distinguish what one concludes from coordinate calculations and what one sees using light rays that are transmitted from one moving system to another.
Chapter 5 takes up further issues in connecting the Minkowski space-time structure to possible observations. The issue of what constitutes an ideal clock is handled by using as a clock light bouncing back and forth between two mirrors traveling parallel inertial paths. Maudlin remarks that “we are not here concerned to explain how we could know that the trajectories of the mirrors are parallel to one another: we simply take that as part of the physical specification of the system in question” (109–10). So no resort to a Marzke-Wheeler construction is explored here.
Maudlin then uses a simplified version of the Lorentz-style pedagogical technique favored by J. S. Bell in his well-known paper on teaching relativity, to, first, explain why such an ideal clock will remain ideal even if accelerated into a new inertial frame. The “physical Lorentz contraction” is central to the argument. These methods are extended to show the reader why the “constancy of the speed of light” will now follow from the structure of the Minkowski space-time and the response of measuring devices to that structure. Here, for the first time, Michelson and Morley and their famous experiment are briefly noted. Those who think that the null results on that experiment should not only be given a central place in presenting the history of special relativity but be seen as something crucial to our philosophical understanding of the theory will, I think, be disappointed in the treatment of the experiment as just another consequence of a now-posited Minkowski space-time structure and its relation to material measuring devices.
Chapter 6, introducing the reader to general relativity, reverts to the pedagogical style of chapters 1–3, with an easy introduction to non-Euclidean space-times and a historical approach to the discovery of the theory. Galileo’s work on falling bodies, Newton’s handling of the generalization of this by setting the gravitation charge as the inertial mass, and the follow-up experimentation to confirm this posit are all noted. Then we get a clear and straightforward account of how Einstein went from the Weak to the Strong Equivalence Principle. The way in which this allows for the geometrization of gravity is clearly explained. Examples of how the theory works, such as the Big Bang and black holes, are nicely treated. The “hole” argument in its Norton-Earman version is explained along with three philosophical responses to it. The chapter ends with the thought-provoking suggestion that “still, the argument might inspire some radically new metaphysical account of space and time. … To date, no such alternative has arisen. Only time will tell” (151).
Chapter 7 takes up the topology and the direction of time. Time-non-orientable space-times and space-like and time-like compactified space-times are illustrated. It is noted how the last of these gives rise to the curious possibility of closed time-like trajectories and the possibility of time travel. The possibility of consistent models of universes with closed time-like trajectories is noted as showing that time travel, by itself, does not necessarily give rise to paradoxes. There is a very brief introduction to the issue of the notion of “the direction of time,” including a sketch of the arguments to the effect that asymmetry in time of processes is somehow at the root of the notion of the intrinsic direction of time, but the problem is reserved for further discussion in the second volume of this introduction to the philosophy of physics. All in all the book is a clear, rigorous, and exciting introduction to the structure of space-times and to the issues that arise when this area of theoretical physics is subject to critical philosophical thought.
