Questions and answers with Amit Hagar

Amit Hagar , author of Discrete or Continuous?: The Quest for Fundamental Length in Modern Physics (Cambridge University Press, 2014), is a professor in the department of history and philosophy of science at Indiana University in Bloomington. Born and educated in Israel, he received his master’s degree in philosophy at the Hebrew University of Jerusalem; his thesis was on the hole argument and the ontology of spacetime theories. Hagar’s PhD, also in philosophy, was obtained at the University of British Columbia in Vancouver. His dissertation, “Chance and time,” covered the foundations of statistical physics and was republished as an expository book on the philosophy of physics in Israel.

Hagar’s current research spans the foundations of modern physics—in particular, the origin and source of the probabilities in statistical and quantum mechanics, the philosophy of time, and the notion of physical computation, especially in the context of quantum information theory. He received an NSF Scholars Award, which funded his research on the history and philosophy of the notion of fundamental length in modern physics. That project led to Discrete or Continuous?, which is reviewed in this month’s issue of Physics Today. The book, writes reviewer Luis Garay, “takes the reader on an enjoyable journey—by turns historical, philosophical, and physical—in a quest to unravel many of the subtleties that underlie the concept of a minimum length in physics.”

Physics Today recently caught up with Hagar to discuss his new book.

PT: What motivated you to write this book?

Hagar: The project started as an NSF grant proposal. That grant was indeed awarded and contributed to the book writing. Delving, as I was, into the history of the notion of fundamental length, I slowly realized there was an interesting story to tell about how insights from millennia-old debates were reincarnated in early-20th-century theoretical physics and how our attempts at unifying general relativity with quantum mechanics could benefit from those old yet still relevant insights.

PT: What does your book cover that is not found in other works on this topic?

Hagar: Recent approaches to quantum gravity are widely covered in textbooks or more general reviews—I made no attempt at covering [the topic] in such detail. My goal was to emphasize how the notion of fundamental length entered into modern physics and how the problems it generated in field theories in the 1930s resurface in current attempts to incorporate that notion into general relativity. The motto here is a famous one: Those who do not know the history are bound to repeat it.

PT: How do you distinguish between the philosophical (or metaphysical) and physical implications of the discrete versus continuous debate?

Hagar: The discrete versus continuous debate can be seen as fueling many of the theoretical developments in modern physics, since it captures the tension between the physical world and the way we describe it mathematically. The continuum is by far the most fruitful mathematical invention, and it has been proven convenient in many physical domains. And yet, many feel uneasy with the stronger claim, namely, that the continuum is not only a convenient, but also a veridical, description of the world. Indeed, if you look around in physics, actual infinity is banned, singularities are avoided, and divergences are tamed.

The physical implications arising from this debate can be measured not only by means of new experiments or suggestions for new observations, but also by means of new mathematical methods that allow the supporters of the discrete view to reproduce the predictions of the continuum view. Such implications may be seen as “philosophical,” especially if they don’t immediately lead to new predictions. But here we must remember that we are dealing with orders of magnitude far below anything measurable in the history of physics, and so one should keep an open mind and allow such philosophical approaches to flourish. This interplay between the question about how the world is and how we describe it is, to my mind, what makes the topic of fundamental length so fascinating and so exciting for a philosopher of physics.

PT: What reaction to the book have you received, both from colleagues and from nonexpert readers?

Hagar: The book has received very positive reviews from mathematicians and physicists, and in particular from practitioners of quantum gravity, and it has also sold surprisingly well so far for such a niche topic. [Cambridge University Press] tells me that a paperback edition is coming up soon, which means that nonexperts are also interested.

Philosophers have been slower to respond, but I believe that as their appreciation of quantum gravity would increase, the philosophical issues that surround it would become more fashionable. After all, we have been debating such questions for more than two millennia, and we will probably still debate them in the millennia to come.

PT: What books are you currently reading?

Hagar: For my upcoming class on relativity and the philosophy of spacetime, I am rereading Robert Geroch’s General Relativity from A to B (University of Chicago Press, 1981) and David Mermin’s It’s About Time: Understanding Einstein’s Relativity (Princeton University Press, 2005). I’m also reading William Bialek’s Biophysics: Searching for Principles (Princeton University Press, 2012), since I am developing a new project on the biophysical modeling of cancer.

For personal reading, I have just finished David Grossman’s latest novel, A Horse Walks Into a Bar (in Hebrew; Hasifriya Hachadasha, 2014); I am plowing my way through Tim Weiner’s Legacy of Ashes: The History of the CIA (Doubleday, 2007); and I’m looking forward to devouring Amos Oz’s latest novel, The Gospel According to Judas (in Hebrew; 2014).