University of Illinois, Urbana-Champaign Philosophy Professor Christopher Weaver is an affiliate member of the Illinois Physics faculty and a member of the Illinois Center for Advanced Studies of the Universe (ICASU). ICASU Director and Illinois Physics Professor Nicolás Yunes notes, “One of our main objectives when we formed this center was to bring people together who can challenge each other and ask each other new questions. Scientists have a lot to gain by confronting our own assumptions and biases. Perspectives from people in other disciplines, such as philosophy, can help us do just that.”
Weaver spent Spring 2021 as a visiting fellow at the Center for Philosophy of Science at the University of Pittsburgh. This competitive fellowship offers faculty from around the world an opportunity to participate in the scholarly activities of the center and to focus exclusively on research for either one or two semesters. In response to the COVID-19 pandemic, fellows participated remotely this year.
Weaver says, “The University of Pittsburgh has one of the top philosophy departments in the world, and the Center for Philosophy of Science in particular has extraordinary people working there. So, I was very excited and honored to have this opportunity.”
As a visiting fellow, Weaver continued to work on questions he explored in a paper entitled “In Praise of Clausius Entropy: Reassessing the Foundations of Boltzmannian Statistical Mechanics,” published recently in Foundations of Physics.
Weaver explains, “The second law of thermodynamics tells us that the entropy—or the disorder—of a system will increase until it reaches a state of equilibrium. Thanks to Ludwig Boltzmann, that law is stated probabilistically. That is, we say the chances of entropy decreasing are so small as to be virtually impossible.
“I argue that we need to make a slight adjustment to how we state the second law, because there are some instances where we can guarantee entropic increase. In some cases, it is not merely the most likely outcome, it is a guarantee. That’s an important distinction. Boltzmann’s H-theorem allows that for that, and I believe I have found a way to hold on to the H-theorem while also addressing the reversibility paradox.”
Weaver offers the following explanation of the reversibility paradox: “Consider a gas system that begins in a small corner of a container and then expands homogenously to fill that container, thereby increasing in entropy over time. The motions of gas molecules in this system are governed by equations that are time-reversal invariant. Thus, if the gas were to shrink back from its homogeneous distribution in the container to the small corner of the container from which it started, the governing laws would not be violated. The problem is that the possible reversed evolution looks like a violation of the H-theorem, since that theorem—if applicable—guarantees that entropy increases over time.”
According to Weaver, Boltzmann always remained committed to a mechanical explanation for the second law of thermodynamics, despite the prevailing historical account that he gave up on it when faced with the reversibility paradox.
Weaver says, “If I’m right, then we have a mechanical explanation of the second law of thermodynamics. We don’t need a statistical explanation. In other words, I think I’ve come up with what Boltzmann should have said when confronted with this paradox.”
Weaver’s work on Boltzmann is an extension of his previous work on the role of causality in areas ranging from Einstein’s theory of general relativity (GR) to quantum chromodynamics (QCD). According to Weaver, “GR should be interpreted causally. Even Einstein thought that GR was about cause and effect. It’s not just about one event following another. It’s not that this is simply what happens in the world. One event causes the other.”
Weaver looks forward to collaborating with the ICASU faculty as he continues to seek causal interpretations of physical laws. In addition, he is interested in questions regarding the origins of the universe, as well as what constitutes an exact mathematical solution. Weaver says, “I was excited when I heard about this new center, because it’s interdisciplinary, and because it addresses the kind of fundamental questions that I have long been interested in.”
“In Praise of Clausius Entropy: Reassessing the Foundations of Boltzmannian Statistical Mechanics." Foundations of Physics 51: Article number 59 pp. 1-64.