Guerra Bobo (2013) has questioned whether Lüders conditionalization for quantum probabilities supplies a notion of conditional probability worthy of the name. I agree in large part with Guerra Bobo's critique; indeed, I show how her critique can be sharpened. But while valuable in itself, the main virtue of the critique derives from the fact that it prompts questions about the nature of quantum probabilities that engage some of the more important and contentious issues in the foundations of QM. I show how understanding the role of Lüders conditionalization in quantum probability theory helps to illuminate these issues.Guerra Bobo (2013) has questioned whether Lüders conditionalization for quantum probabilities supplies a notion of conditional probability worthy of the name. I agree in large part with Guerra Bobo's critique; indeed, I show how her critique can be sharpened. But while valuable in itself, the main virtue of the critique derives from the fact that it prompts questions about the nature of quantum probabilities that engage some of the more important and contentious issues in the foundations of QM. I show how understanding the role of Lüders conditionalization in quantum probability theory helps to illuminate these issues.

Apr 15, 20190 citations

Properties of Invariant Set Theory

Jonte R. Hance, Sabine Hossenfelder, T. N. Palmer

In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor $ψ$ -epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor $ψ$-epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.

arXiv:2108.08144Aug 18, 20210 citations

Perspectives on Quantum Theory

David Glick

Foundations of PhysicsDec 12, 20250 citations

Critique of the Quantum Power of Judgment

Hernán Bruno Pringe

The Critique of the Quantum Power of Judgement analyzes the a priori principles which underlie the empirical knowledge provided by quantum theory. In contrast to other transcendental approaches to quantum physics, none of the transcendental principles established by Kant is modified in order to cope with the new epistemological situation that arises with the asumption of the quantum postulate. Rather, by considering Bohr’s views, it is argued that classical concepts provide the mathematical formalism of quantum theory with physical reference through symbolic analogies in the strict Kantian sense. The main result of the investigation is the determination of the highest principle under which quantum objects are subsumed. This principle states that the conditions of the possibility of the systematic unity of contextual experience are at the same time the conditions of the possibility of quantum objects. Upon this principle rests the possibility of any a priori synthetic knowledge of quantum objects. Therefore, the Critique of the Quantum Power of Judgement yields the prolegomena to any future quantum metaphysics.The Critique of the Quantum Power of Judgement analyzes the a priori principles which underlie the empirical knowledge provided by quantum theory. In contrast to other transcendental approaches to quantum physics, none of the transcendental principles established by Kant is modified in order to cope with the new epistemological situation that arises with the asumption of the quantum postulate. Rather, by considering Bohr’s views, it is argued that classical concepts provide the mathematical formalism of quantum theory with physical reference through symbolic analogies in the strict Kantian sense. The main result of the investigation is the determination of the highest principle under which quantum objects are subsumed. This principle states that the conditions of the possibility of the systematic unity of contextual experience are at the same time the conditions of the possibility of quantum objects. Upon this principle rests the possibility of any a priori synthetic knowledge of quantum objects. Therefore, the Critique of the Quantum Power of Judgement yields the prolegomena to any future quantum metaphysics.

De Gruyter eBooksDec 31, 200713 citations

On quantum theory

Berthold‐Georg Englert

arXiv:1308.5290The European Physical Journal DNov 1, 201356 citations

ψ

-epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.