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Register a new userThe universe would not be perfect without randomness: a quantum physicists reading of Aquinas
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Authors
Valerio Scarani
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Randomness is an unavoidable notion in discussing quantum physics, and this may trigger the curiosity to know more of its cultural history. This text is an invitation to explore the position on the matter of Thomas Aquinas, one of the most prominent philosophers and theologians of the European Middle Ages.
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We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.
We provide a novel perspective on regularity as a property of representations of the Weyl algebra. In Part I, we critiqued a proposal by Halvorson [2004, Complementarity of representations in quantum mechanics, Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who advocates for the use of the non-regular position and momentum representations of the Weyl algebra. Halvorson argues that the existence of these non-regular representations demonstrates that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. In this sequel, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.
We provide a novel perspective on regularity as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, Complementarity of representations in quantum mechanics, Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who argues that the non-regular position and momentum representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We show that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.
We give a conceptually simple proof of nonlocality using only the perfect correlations between results of measurements on distant systems discussed by Einstein, Podolsky and Rosen---correlations that EPR thought proved the incompleteness of quantum mechanics. Our argument relies on an extension of EPR by Schrodinger.
It is well-known that Bells Theorem and other No Hidden Variable theorems have a retrocausal loophole, because they assume that the values of pre-existing hidden variables are independent of future measurement settings. (This is often referred to, misleadingly, as the assumption of free will.) However, it seems to have gone unnoticed until recently that a violation of this assumption is a straightforward consequence of time-symmetry, given an understanding of the quantization of light that would have seemed natural to Einstein after 1905. The new argument shows precisely why quantization makes a difference, and why time-symmetry alone does not imply retrocausality, in the classical context. It is true that later developments in quantum theory provide a way to avoid retrocausality, without violating time-symmetry; but this escape route relies on the ontic conception of the wave function that Einstein rejected. Had this new argument been noticed much sooner, then, it seems likely that retrocausality would have been regarded as the default option for hidden variables theories (a fact that would then have seemed confirmed by Bells Theorem and the No Hidden Variable theorems). This paper presents these ideas at a level intended to be accessible to general readers.
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