Dissertation: Metaphysics of Quantum Mechanics
In my dissertation Essays on the Metaphysics of Quantum Mechanics, I trace various philosophical puzzles of quantum mechanics back to their source---the wave function. I first clarify how its mathematical representation relates to the physical world. In Chapter 1, "An Intrinsic Account of Quantum Mechanics: Progress in Field's Nominalistic Program," I show that the wave function represents four intrinsic relations on physical space-time, uniquely up to certain symmetries. Since my intrinsic account dispenses with any reference to mathematical objects, it extends Field's nominalistic program to the quantum realm. In Chapter 2, "Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function" (JPhil, 2017), I argue against configuration space realism, the view that physical space-time is "emergent" from the high-dimensional configuration space that the wave function lives on. Emphasizing the roles of dynamics and symmetries, I show that physical space-time is more fundamental than the configuration space. In Chapter 3, "The Best Summary of the Quantum World: The Universal Wave Function as a Humean Law," I defend a Humean proposal: the wave function is part of the Humean best system that supervenes on a separable mosaic. This defense provides a new geometric argument for the uniqueness of the wave function given the actual particle trajectories.
My dissertation brings together various themes in metaphysics and philosophy of science, including structuralism, fundamentality, explanation, objective probability, and laws of nature.
The Arrow of Time
I have started working on a new project: Time's Arrow in a Quantum Universe. I show that the arrow of time in our universe is crucial for understanding the ontological structure of quantum mechanics. In particular, I propose that we use the data in the "Past Hypothesis" to pin down a simple and unique initial quantum state of the universe. This proposal has interesting implications: it eliminates statistical-mechanical probabilities in the fundamental postulates of physics, unifies statistical and quantum mechanics, and reconciles Humean supervenience with quantum entanglement. The first part of the project is posted to the physics pre-print repository arXiv.
I am also working on a paper about time's arrow and de se (self-locating) probabilities. I show that (1) to explain the arrow of time, we need to add de se probabilities, but (2) the most straightforward way of doing so leads to radical skepticism.
Decision Theory and Infinite Values
I have been working, in collaboration with Daniel Rubio, on the foundations of decision theory and analyzing the paradoxes related to infinities such as Pascal’s Wager and the Pasadena Game (Nover and Hájek 2004). In our paper “Surreal Decisions” (PPR, forthcoming), we propose a decision theory framed entirely in John Conway's (1974) surreal numbers. By using surreal numbers as the values of the utility function and the probability function, we show that many paradoxes of infinite values disappear in finite state spaces. In particular, dominance principles are no longer in conflict with expected utility theory. We are working on a second paper that extends surreal decision theory to the more advanced setting of infinite state spaces, such as the Pasadena Game. As a decision theory that systematically handles infinities and infinitesimals, our surreal theory has applications in value theory, population ethics, and philosophy of religion.
Chinese Philosophy
I have two research projects in Chinese philosophy. The first one is at the intersection of classical Chinese philosophy and meta-ethics. In my paper “A Hybrid Voluntarist Interpretation of Xunzi,” I display tensions in the notions of xin (heart/mind), li (rituals), and dao (order) in the work of Xunzi, a prominent early Confucian philosopher, and I draw on Ruth Chang’s (2013a, 2013b) meta-ethical theory of hybrid voluntarism to help resolve these tensions. The second project is about issues related to the “Needham Question” about the history of science in China. I explore the connections (or disconnections) between Western concepts such as laws of nature with the Chinese concept of Dao (the absolute principle of nature), as well as the development of mathematics in ancient China and its influence on the Chinese philosophers.
In my dissertation Essays on the Metaphysics of Quantum Mechanics, I trace various philosophical puzzles of quantum mechanics back to their source---the wave function. I first clarify how its mathematical representation relates to the physical world. In Chapter 1, "An Intrinsic Account of Quantum Mechanics: Progress in Field's Nominalistic Program," I show that the wave function represents four intrinsic relations on physical space-time, uniquely up to certain symmetries. Since my intrinsic account dispenses with any reference to mathematical objects, it extends Field's nominalistic program to the quantum realm. In Chapter 2, "Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function" (JPhil, 2017), I argue against configuration space realism, the view that physical space-time is "emergent" from the high-dimensional configuration space that the wave function lives on. Emphasizing the roles of dynamics and symmetries, I show that physical space-time is more fundamental than the configuration space. In Chapter 3, "The Best Summary of the Quantum World: The Universal Wave Function as a Humean Law," I defend a Humean proposal: the wave function is part of the Humean best system that supervenes on a separable mosaic. This defense provides a new geometric argument for the uniqueness of the wave function given the actual particle trajectories.
My dissertation brings together various themes in metaphysics and philosophy of science, including structuralism, fundamentality, explanation, objective probability, and laws of nature.
The Arrow of Time
I have started working on a new project: Time's Arrow in a Quantum Universe. I show that the arrow of time in our universe is crucial for understanding the ontological structure of quantum mechanics. In particular, I propose that we use the data in the "Past Hypothesis" to pin down a simple and unique initial quantum state of the universe. This proposal has interesting implications: it eliminates statistical-mechanical probabilities in the fundamental postulates of physics, unifies statistical and quantum mechanics, and reconciles Humean supervenience with quantum entanglement. The first part of the project is posted to the physics pre-print repository arXiv.
I am also working on a paper about time's arrow and de se (self-locating) probabilities. I show that (1) to explain the arrow of time, we need to add de se probabilities, but (2) the most straightforward way of doing so leads to radical skepticism.
Decision Theory and Infinite Values
I have been working, in collaboration with Daniel Rubio, on the foundations of decision theory and analyzing the paradoxes related to infinities such as Pascal’s Wager and the Pasadena Game (Nover and Hájek 2004). In our paper “Surreal Decisions” (PPR, forthcoming), we propose a decision theory framed entirely in John Conway's (1974) surreal numbers. By using surreal numbers as the values of the utility function and the probability function, we show that many paradoxes of infinite values disappear in finite state spaces. In particular, dominance principles are no longer in conflict with expected utility theory. We are working on a second paper that extends surreal decision theory to the more advanced setting of infinite state spaces, such as the Pasadena Game. As a decision theory that systematically handles infinities and infinitesimals, our surreal theory has applications in value theory, population ethics, and philosophy of religion.
Chinese Philosophy
I have two research projects in Chinese philosophy. The first one is at the intersection of classical Chinese philosophy and meta-ethics. In my paper “A Hybrid Voluntarist Interpretation of Xunzi,” I display tensions in the notions of xin (heart/mind), li (rituals), and dao (order) in the work of Xunzi, a prominent early Confucian philosopher, and I draw on Ruth Chang’s (2013a, 2013b) meta-ethical theory of hybrid voluntarism to help resolve these tensions. The second project is about issues related to the “Needham Question” about the history of science in China. I explore the connections (or disconnections) between Western concepts such as laws of nature with the Chinese concept of Dao (the absolute principle of nature), as well as the development of mathematics in ancient China and its influence on the Chinese philosophers.
Articles
(Some papers are in multiple categories; most are available upon request.)
Philosophy of Physics, Philosophy of Science, Metaphysics:
Decision Theory, Probability, Formal Epistemology:
Chinese Philosophy:
Philosophy of Mind:
(Some papers are in multiple categories; most are available upon request.)
Philosophy of Physics, Philosophy of Science, Metaphysics:
- Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function, Journal of Philosophy, 2017 [Penultimate] [Journal]
- An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part I [PhilSci-Archive]
- The Best Summary of the Quantum World: The Universal Wave Function as a Humean Law [draft]
- Time's Arrow in a Quantum Universe I: On the Simplicity and Uniqueness of the Initial Quantum State [arXiv]
- Realism about the Wave Function (commissioned by Philosophy Compass, in preparation)
- Our Knowledge of the Past: Some Puzzles about Time's Arrow and Self-Locating Probabilities [draft]
Decision Theory, Probability, Formal Epistemology:
- Surreal Decisions (with Daniel Rubio), Philosophy and Phenomenological Research, forthcoming [Penultimate]
- Great Expectations: Introducing Surreal Decision Theory (with Daniel Rubio), Proceedings of the 5th International Workshop on Logic, Rationality, and Interaction (LORI-V), Springer-Verlag, 2015. [Proceedings]
- Surreal Decisions II: Infinite State Space (with Daniel Rubio) [draft]
- Our Knowledge of the Past: Some Puzzles about Time's Arrow and Self-Locating Probabilities [draft]
Chinese Philosophy:
- A Hybrid Voluntarist Interpretation of Xunzi [draft]
Philosophy of Mind:
- Comparativism about the Mind: From Metaphysics of Quantities to the Nature of Mentality [draft]