Robert Spekkens: Leibniz’s principle of the identity of indiscernible as...

The speaker begins by expressing gratitude to the organizers for the opportunity to delve deeper into philosophical principles underlying their research on quantum theory interpretation. They introduce the concept of 'liveness' as a methodological principle central to their work, which posits that indiscernible entities should not be considered distinct. The talk aims to explore the relevance of Leibniz's principle in physics and its potential impact on quantum theory, using historical correspondence between Leibniz and Clarke to illustrate the principle's significance and its application in modern physics.

The speaker argues that Einstein's work, although not explicitly acknowledging Leibniz's principle, demonstrates a deep commitment to its ideals. Through examples from Einstein's papers on special relativity and the equivalence principle, the speaker shows how Einstein's theories align with the principle of ontological identity, rejecting models that suggest distinct scenarios with no observable differences. They also reference a philosopher of science who identifies similar methodological principles in Einstein's work, further supporting the connection.

The speaker addresses potential concerns that adherence to Leibniz's principle might lead to instrumentalism or a denial of realism. They clarify that the principle guides the inclusion of elements in reality based on observable criteria, rather than rejecting unobservable entities outright. The speaker also rejects an instrumentalist approach to quantum theory, using Simpson's paradox to illustrate the importance of distinguishing between correlation and causation, advocating for a realist position that seeks causal explanations.

The speaker emphasizes the importance of causal explanations in understanding quantum phenomena and discusses the challenge of inferring causal models from operational data. They introduce the formalism of circuit diagrams and directed acyclic graphs to represent causal structures and highlight the difficulty of discerning true causality from observational data alone. The speaker also presents the 'reckon box principle,' which insists all correlations must be explained causally.

The speaker explores how Leibniz's principle can be applied to address causality in quantum mechanics, particularly in the context of the Bell experiment. They argue that the principle challenges explanations involving superluminal causal influences and superdeterministic models, as these would imply ontological facts without observable consequences. The speaker suggests that Leibniz's principle can guide the development of causal models that are consistent with quantum theory's nonlocality.

The speaker discusses the concept of non-contextuality, relating it to Leibniz's principle, and uses it to explore how quantum theory deviates from classical theories. They describe experimental setups that test for non-contextual correlations and explain how quantum theory can violate the resulting inequalities, suggesting that Leibniz's principle can reveal deeper differences between classical and quantum realms.

The speaker proposes a research program to generalize causal models to accommodate quantum theory while preserving Leibniz's principle. They suggest that the causal structure implied by quantum experiments is correct but that the parameters describing unobserved nodes should be reformulated using density operators on Hilbert spaces. This approach allows for the violation of classical inequalities while maintaining the spirit of locality and non-contextuality.

The speaker acknowledges that the quantum generalization of Bayesian inference is not straightforward and requires a formalism that can handle pre and post-selection scenarios. They discuss the need for a quantum Markov condition that can justify the use of quantum conditionals within the causal framework and mention ongoing work with colleagues to develop such a condition.

In the concluding remarks, the speaker reflects on the ontological implications of their research program, suggesting that the focus should be on causal structure as the basis for ontology. They propose that the union of kinematics and dynamics in quantum theory might be better understood through a causal lens and hint at the possibility of a web of unitaries and causal structures serving as an ontology.