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, "Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State" (BJPS, forthcoming), I show that, by using the Past Hypothesis to pin down a simple and unique quantum state, we discover a new way of thinking about the relationship between the quantum state of the universe and the arrow of time. My proposal leads to a new class of quantum theories that dispense with certain objective probabilities and reconcile Humean supervenience with quantum entanglement.
My dissertation brings together various themes in metaphysics and philosophy of science, including structuralism, fundamentality, explanation, objective probabilities, and laws of nature.
The Arrow of Time
The last chapter of my dissertation is the first part of a new project: Time's Arrow in a Quantum Universe. The key idea is that the arrow of time in our universe is crucial for understanding the meaning of quantum mechanics. I propose that the quantum state of the universe is a special "mixed state," represented not by a wave function but by a special density matrix. I am currently working on several papers explaining how this proposal (1) unifies time's arrow and quantum ontology in the Humean framework, (2) eliminates statistical-mechanical probabilities in the fundamental postulates, (3) reconciles Lorentz invariance with quantum entanglement, (4) sheds light on various notions of empirical equivalence, (5) suggests new interpretive possibilities for the many-worlds interpretation of quantum mechanics (including a live possibility for strong determinism), and (6) provides a new perspective on the reality of the quantum state, especially in relation to the PBR theorem.
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, 2018), 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.
Metaphysics of Mental Qualities
I have another research project about metaphysics of quantities and philosophy of mind. Mental qualities (such as being painful and being conscious) are usually taken to be absolute and monadic. In my paper "Comparativism about the Mind: From Metaphysics of Quantities to the Nature of Mentality," I propose a new hypothesis about the nature of mental qualities: they are fundamentally comparative; for example, being more painful than is more fundamental than being painful. I call this the Comparative Mentality Hypothesis (CMH). CMH is motivated by comparativism about the physical as well as some theories about the mind-body problem. I use color qualities as the main example for CMH, and I provide an axiomatic foundation of color hues in terms of two comparative relations: cyclic-betweenness and cyclic-congruence. They turn out to have the same comparative structure as wave-function phases (Chen 2017a). I draw some consequences from CMH for Spinoza's mind-body parallelism, reductionist physicalism, and what David Chalmers (forthcoming) calls micro-idealism. In future work, I will apply CMH to other mental qualities and contrast it with comparativism about subjective probabilities.
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, "Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State" (BJPS, forthcoming), I show that, by using the Past Hypothesis to pin down a simple and unique quantum state, we discover a new way of thinking about the relationship between the quantum state of the universe and the arrow of time. My proposal leads to a new class of quantum theories that dispense with certain objective probabilities and reconcile Humean supervenience with quantum entanglement.
My dissertation brings together various themes in metaphysics and philosophy of science, including structuralism, fundamentality, explanation, objective probabilities, and laws of nature.
The Arrow of Time
The last chapter of my dissertation is the first part of a new project: Time's Arrow in a Quantum Universe. The key idea is that the arrow of time in our universe is crucial for understanding the meaning of quantum mechanics. I propose that the quantum state of the universe is a special "mixed state," represented not by a wave function but by a special density matrix. I am currently working on several papers explaining how this proposal (1) unifies time's arrow and quantum ontology in the Humean framework, (2) eliminates statistical-mechanical probabilities in the fundamental postulates, (3) reconciles Lorentz invariance with quantum entanglement, (4) sheds light on various notions of empirical equivalence, (5) suggests new interpretive possibilities for the many-worlds interpretation of quantum mechanics (including a live possibility for strong determinism), and (6) provides a new perspective on the reality of the quantum state, especially in relation to the PBR theorem.
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, 2018), 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.
Metaphysics of Mental Qualities
I have another research project about metaphysics of quantities and philosophy of mind. Mental qualities (such as being painful and being conscious) are usually taken to be absolute and monadic. In my paper "Comparativism about the Mind: From Metaphysics of Quantities to the Nature of Mentality," I propose a new hypothesis about the nature of mental qualities: they are fundamentally comparative; for example, being more painful than is more fundamental than being painful. I call this the Comparative Mentality Hypothesis (CMH). CMH is motivated by comparativism about the physical as well as some theories about the mind-body problem. I use color qualities as the main example for CMH, and I provide an axiomatic foundation of color hues in terms of two comparative relations: cyclic-betweenness and cyclic-congruence. They turn out to have the same comparative structure as wave-function phases (Chen 2017a). I draw some consequences from CMH for Spinoza's mind-body parallelism, reductionist physicalism, and what David Chalmers (forthcoming) calls micro-idealism. In future work, I will apply CMH to other mental qualities and contrast it with comparativism about subjective probabilities.
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
(Most are available upon request.)
Philosophy of Physics, Philosophy of Science, Metaphysics:
Decision Theory, Probability, Formal Epistemology:
Chinese Philosophy:
Philosophy of Mind:
(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]
- Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State, The British Journal for the Philosophy of Science, forthcoming [arXiv]
- Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities, in Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, World Scientific, forthcoming
- 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]
- Realism about the Wave Function (commissioned by Philosophy Compass, in preparation)
- Review of The Quantum Revolution in Philosophy by Richard Healey (commissioned by The Philosophical Review, in preparation)
Decision Theory, Probability, Formal Epistemology:
- Surreal Decisions (with Daniel Rubio), Philosophy and Phenomenological Research, 2018 [Penultimate] [Journal]
- 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]