Philosophy of Physics: Space and Time,

An understanding of the nature of space and time is central to both philosophy and physics. Tim Maudlin, a professor of philosophy at New York University, is well qualified to review theories of space and time from both perspectives, and he is successful in doing so in this concise and highly engaging book.

In *Philosophy of Physics: Space and Time*, Maudlin begins with a discussion of Isaac Newton’s view of absolute space and time, including an interesting analysis of the Leibniz–Clarke correspondence, wherein Gottfried Leibniz attacked the notion of absolute space and Samuel Clarke defended it. Maudlin then explains the changes to the Newtonian view of space and time needed to incorporate Galilean relativity’s demand that absolute velocities have no meaning. Then he presents special relativity from a fully geometrical point of view. Maudlin concludes with a discussion of general relativity, but the presentation is extremely cursory and the choice of topics within general relativity is quite desultory. It is therefore hard to see how a reader who is not already deeply familiar with general relativity will be able to follow the discussion in a serious and meaningful way.

The main strength of the book is its presentation of special relativity, which is done without ever introducing a Lorentz transformation. Maudlin explains very clearly why commonly made statements like “time slows down for moving observers” are utterly nonsensical. His discussion of the twin paradox is excellent, and it corrects many of the wrong and confusing statements that have been made previously by a number of distinguished people. There also are several worked examples that concretely illustrate how calculations can be done in special relativity by direct use of the spacetime interval rather than via Lorentz transformations.

However, there is one significant flaw in Maudlin’s presentation. In chapter 4, the first of the two chapters dedicated to special relativity, he introduces a “clock hypothesis,” and constructs global inertial coordinates using the idealized clocks he thereby introduces. The fact that the coordinate speed of light is one light-minute per minute is then a tautology. But in chapter 5, Maudlin tries to explain that there is, in fact, a nontautological meaning to the statement that the speed of light is “constant in all frames.” To do so, he introduces the notion of (approximately) rigid rods as *physical systems* and then asserts that such rods would undergo a *physical* Lorentz contraction. By introducing the notion of physical Lorentz contraction, Maudlin edges backwards toward exactly the same type of confusing presentation of special relativity that he rightly criticizes in chapter 4. There is no justification for treating clocks and rods asymmetrically, so if it is appropriate to say that physical rods undergo a physical Lorentz contraction, then it must be equally appropriate to say that physical clocks undergo a “physical time dilation.” And that concession leads one back toward the usual discussions of the twin paradox that Maudlin demolishes in chapter 4.

It would be much better if Maudlin consistently stuck to the view that all of the structure of space and time in special relativity is described by the topological and differential properties of events together with the spacetime metric. Only that structure enters the laws of physics governing the dynamical behavior of matter and fields in spacetime, so the dynamical behavior of physical systems directly reflects the properties of the spacetime metric. The physical manifestations of the spacetime metric may then be nicely elucidated by stating how idealized clocks and rods would behave. (However, since rigidity cannot be maintained for general, noninertial motions, it is much more awkward to formulate a “rod hypothesis” than a “clock hypothesis,” since one would have to use arbitrarily short rods in such a formulation.) Of course, both real clocks and real rods are governed by the laws of physics for the matter of which they are composed. But one can make real clocks and rods that closely approximate the idealizations if the motion considered is not too extreme, so it is fine to base a discussion on idealized clocks and rods.

My expectation is that a perceptive reader will feel highly enlightened by the clear explanations in chapter 4, which uses clocks as idealized objects, but will likely feel uneasy after reading chapter 5, in which rods are introduced only as physical objects. Despite the above criticism, I would highly recommend * Philosophy of Physics* to anyone who wants to get a deeper historical and philosophical perspective on the nature of space and time, as well as to any physics student who has been confused by the twin paradox.

**Robert M. Wald** is the Charles H. Swift Distinguished Service Professor of Physics at the University of Chicago. He is the author of *General Relativity* (U. of Chicago Press, 1984; reviewed in *Physics Today*, May 1987, page 94).