### On the Foundations of Quantum Mechanics, The Netherlands

Thursday, November 15th, 2007

Originally uploaded by hzenilc.

Models and Simulations 2

11 – 13 October 2007

Tilburg University, The Netherlands

I attended this conference one month ago. Among several interesting talks, one in particular caught my attention. It was given by Michael Seevinck from the Institute for History and Foundations of Science at Utrecht, The Netherlands. His talk was about the foundations of Quantum Mechanics, and there were many NKS related topics that it brought to mind. He talked about reconstructing Quantum Mechanics (QM) from scratch by exploring several restricted models in order to solve the so-called measurement problem, to deal with the nonlocality of quantum correlations, and with its alleged non-classicality, there being no consensus on the meaning of Quantum Mechanics (Niels Bohr said once: “If you think you have understood quantum mechanics, then you have not understood quantum mechanics.”—More quotes of this sort on QM here). The restrictons chosen in order to reconstruct the theory must be physical principles and not theoretical assumptions. In other words, one approaches the problem contrariwise than is traditional, taking the least possible restrictions and exploring the theories that can be built thereon. The speaker characterized this approach as the “study [of] a system from the outside” in order to “reconstruct the model”. It is basically a pure NKS approach: “Start from a general class of possible models and try to constrain it using some physical principles so as to arrive at the model in question (in this case QM).”

One can then proceed to ask such questions as how one might identify QM uniquely, what it is that makes QM quantum, what set of axioms in the model is to be used, and which of them are necessary and sufficient? The question of meaning, previously asked of the formalism, is removed, and bears, if at all, only on the selection and justification of first principles. Seevinck came up with the following interesting statement: “The partially ordered set of all questions in QM is isomorphic to the partially ordered set of all closed subspaces of a separable Hilbert space” (one of Mackey’s axioms in his axiomatisation of 1957). He added: “They (the principles)have solely an epistemic status. The personal motives for adopting certain first principles should be bracketed. One should be ontologically agnostic. The principles should be free of ontological commitment.” And further: “…axioms are neutral towards philosophical positions: they can be adopted by a realist, instrumentalist, or subjectivist.” He cited Clifton, Bub and Halverson who provided the following quantum information constraints used to derive quantum theory:

1. No superluminal information transfer via measurement.

2. No broadcasting

3. No secure bit commitment

Seevinck’s methodology in further detail is: Start with a general reconstruction model with a very weak formalism. Gradually see what (quantum) features are consequences of what added physical principles, and also see which features are connected and which features are a consequence of adding which principle. One thereby learns which principle is responsible for which element in the (quantum) theoretical structure.

One can generate further foundational questions over the whole space of restricted models, e.g. how many of them:

– forbid superluminal signalling?

– allow nonlocality, and to what extent?

– solve NP-complete problems in polynomial time?

An important question which arises concerns whether intrinsic randomness would be of a different nature in different models or whether all of them would yield to deterministic randomness.

His talk slides are available online. Highly recommended.

Among other interesting people I met was Rafaela Hillebrand, of the Institute for The Human Future at Oxford University. The Institute’s director, Nick Bostrom, has proposed an interesting theory concerning the likelihood that our reality is actually a computer simulation. I have myself approached the question in my work on experimental algorithmic complexity, in particular in my work on the testability and the skepticism content of the simulation hypothesis. I will post on that subject later. The subject of thought experiments–in which I have an interest– was one that came up frequently.