The Everett-Wheeler interpretation and the open future

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new (though I expect correction on this), but they are natural and intuitive, and relate to traditional naive ideas of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open.Comment: 11 page

The future's not ours to see

An account of determinism and indeterminism in physics, addressed to non-physicist readers, leading up to proposals for how to understand statements about the future and single-event probability, motivated by quantum mechanics

Einstein and Tagore, Newton and Blake, Everett and Bohr: the dual nature of reality

There are two broad opposing classes of attitudes to reality (realist vs idealist, material vs mental) with corresponding attitudes to knowledge (objective vs subjective, scientific vs romantic). I argue that these attitudes can be compatible, and that quantum theory requires us to adopt both of them

Philosophical lessons of entanglement

The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern scientific thought. There are two kinds of statements about the world: those made from inside the world, and those from outside. The conflict between contradictory statements which both appear to be true can be resolved by recognising that they are made in different perspectives. Probability, in an objective sense, belongs in the internal perspective, and to statements in the future tense. Such statements obey a many-valued logic, in which the truth values are identified as probabilities.Comment: Talk given at 75 Years of Quantum Entanglement, Kolkata, India, 10 January 201

Time, chance and quantum theory

I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.Comment: 16 pages, to appear in "Probing the Meaning and Structure of Quantum Mechanics: Superpositions, Semantics, Dynamics and Identity", edited by Diederik Aerts, Christian de Ronde, Hector Freytes and Roberto Giuntini. The ever-helpful arXiv will alert you to substantial text overlap with some of my previous papers. arXiv admin note: substantial text overlap with arXiv:1103.4318, arXiv:1009.391

Yangian Construction of the Virasoro Algebra

We show that a Yangian construction based on the algebra of an infinite number of harmonic oscillators (i.e. a vibrating string) terminates after one step, yielding the Virasoro algebra.Comment: 5 pages, AMS-Latex 2