Richard Muller’s Now: The Physics of Time is an ambitious undertaking that begins much like a popular account of relativity and quantum physics, but culminates by proposing a new theory of time. As in his acclaimed Physics for Future Presidents: The Science Behind the Headlines (Norton, 2007), based on a course he offers for nonscience majors at the University of California, Berkeley, the writing is entertaining and at times refreshingly idiosyncratic. Muller has a way of keeping a reader’s attention with provocative ideas or claims. Examples include sections entitled “Actually, There Are No Black Holes” and “Feynman Reverses Time” and an extended discussion on the entropic arrow of time. Skeptical readers can be assured that he wraps up his mysteries with sober resolutions, but intriguing lessons remain.
Other popular accounts have already covered much of what Now discusses, but the book stands apart because Muller, a professor at the University of California, Berkeley, is a leading experimental cosmologist. Although Muller’s lucid discussions of the behind-the-scenes difficulties of cosmological experiments make up only a small fraction of the text, they present important new insights to a general audience. It would not hurt if the Antaeus parable, which warns of the perils of losing touch with the ground, were declared required reading for any theoretical physicist.
The first parts of the book aim to introduce the basic physics of spacetime. Some crucial passages, however, may be hard to follow for a novice, as the treatment of relativity relies perhaps too much on difficult discussions of frames. For instance, someone not already familiar with local inertial frames is not likely to get much out of the statement, “If you are accelerating, handle the equations by imagining that your acceleration is essentially a continuous jumping of your proper frame from one reference frame to another one that is moving slightly faster.” It is also unfortunate that the book eschews spacetime diagrams on the grounds that they could undermine Muller’s new view of time by giving the impression of a spacetime without a dynamical flow.
Muller advises readers to be clear about frames of reference, but he does not always follow that important counsel. When he asks, “How far is it from the outside to the surface of the black hole?” he replies, “The answer is infinite.” He seems to be integrating the line element at fixed time, varying only the radial Schwarzschild coordinate, but that trajectory is not the worldline followed by the “falling surface” alluded to in his statement.
The main purpose of these introductory discussions is to set the stage for a new theory of time. In an attempt to avoid spoilers, I’ll let the brief quote “the explosion of the universe continually creates not only new space but also new time” suffice to indicate the main idea. Muller is open about the proposal’s weaknesses, such as the possibility of violations of general covariance. As the quote suggests, his proposal incorporates an incremental progress of time, which has been envisioned in some discrete theories of quantum gravity. Proponents of such theories are still struggling with the immense difficulties of making their proposals consistent with covariance.
Muller’s proposal is original and intriguing, and it has implications beyond physics. He dares to think in broad categories, connecting a physical theory about the universe with climate change and such unwieldy topics as free will. Potential observational tests of Muller’s new theory, however, receive rather short treatment. Some statements might be held against the theory if taken as specific predictions; for example, in chapter 22, Muller draws connections between entropy, empathy, and the electorate, and asserts that “the US voter does not want to elect a sociopath.” In addition, it sometimes seems that Muller is too quick to push aside competing theories. For instance, he argues that the immense entropy contained in black holes cannot matter for Arthur Eddington’s explanation regarding the arrow of time, because black holes are so far away from us. There may be much to criticize about Eddington’s proposal, but such quick dismissal is not entirely persuasive.
Nevertheless, Richard Muller’s new theory deserves a serious look, and his book presents important lessons in physics and beyond. Most readers will find intriguing new insights in Now: The Physics of Time. The book might even be useful to the future presidents in the title of Muller’s previous opus.
Martin Bojowald teaches relativity and quantum mechanics at the Pennsylvania State University. His research focuses on different physical and mathematical questions relevant for canonical theories of quantum gravity.
