Quantum Beauty

Olivier Darrigol

Frank A. Wilczek

When I was asked to talk about quantum beauty I was a little startled, because the beauty of quantum theory is something that practising physicists, in the course of their work, rarely think about or mention. But when I gave the idea a chance, it really caught my imagination. And that’s why I’m here. Quantum beauty really is a wonderful, true thing to talk about. I’m going to sneak up on quantum beauty by putting it in historical context. The right context, I think, is a broader question: Does the world embody beautiful ideas? That is a question that people have thought about for a long time. Its intellectual history deserves volumes and syllabi. Here, though, I want to keep things brief and entertaining, so I shall spin a simple tale of heroes. Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell demonstrated how the world could embody beautiful ideas, in specific impressive cases. Finally, in the twentieth century in modern physics, and especially in quantum physics, we find a definitive answer: Yes! – the world does embody beautiful ideas.

Alastair Wilson

Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the unpopular ‘halfer’ answer in Sleeping Beauty. These considerations suggest that objective chance is playing an important and under-appreciated role in Sleeping Beauty. 1 Introduction 2 Confirmation in Everettian Quantum Mechanics 3 Sleeping Beauty 4 The Selection Model 5 Bradley’s Argument 6 The Right Route to ⅓ 7 The Breakdown of the Analogy 8 Alternative Diagnoses 9 God’s Gambling Game 10 Non-chancy Sleeping Beauty Cases 11 Conclusion

Jiaxuan Zhang

The Sleeping Beauty Problem (SBP) is a long-standing puzzle in classical probability theory and has been used to challenge the Many-Worlds Interpretation (MWI) of quantum mechanics, since both involve objective determinacy combined with subjective uncertainty about certain events. A common concern is that MWI yields a different answer to the quantum version of SBP than the widely supported Thirder position in the classical case. We argue that this concern is unwarranted. We show that in both the quantum and classical versions of SBP, the correct credence is given by the Halfer position. In the quantum (MWI) SBP, we show that if no unjustified renormalization is introduced, the correct credence is 1/2. We then extend this result to the classical SBP by refuting four major arguments for 1/3. First, we reject the Proportion Argument by distinguishing event weight from probability. Second, we rebut Elga's Variant Argument by extending an earlier critique that identifies the implicit introduction of additional information; we further clarify this point by constructing a new variant and explaining why the Principle of Indifference is inapplicable, drawing an analogy with a mistake by d'Alembert in the history of probability theory. Third, we identify a flaw in the Technicolor Beauty Variant Argument, which arises from treating overlapping events as disjoint. Finally, we argue that causal decision theory is inappropriate for SBP, rendering the Thirders vulnerable to a Dutch Book. Our results support the consistency of MWI under the challenge posed by SBP and suggest that the dominant position on SBP needs careful reconsideration.

Laura Berman

Jeffrey Strickland