Tim Maudlin

Quantum Non-Locality and Relativity

It is sometimes stated that composite quantum systems in entangled states are fundamentally ‘non-local’(i.e. a measurement on one component system can affect a spacelike separated system ‘instantaneously’) and therefore, non-relativistic quantum mechanics violates Relativity theory. This conclusion is usually thought to follow directly from Bells Theorem in quantum mechanics and the upper limit on velocities provided by the speed of light in Relativity. But exactly what if the conflict between the kind of non-locality exhibited by entangled quantum systems and either the Special or General Theory of Relativity? Maudlins Quantum Non-Locality and Relativity is a beautifully crafted book that attempts to answer this question by evaluating four purported restrictions imposed by Relativity. He also considers four attempts to formulate Lorentz invariant quantum theories and concludes that such accounts exact a high philosophical price. Maudlin has achieved his first goal: he gives a lucid exposition of the tension between quantum non-locality and Relativity theory which is accessible to the non-specialist. But is there a high philosophical price to be paid for Lorentz invariant quantum theories and can we afford it?

Completeness, supervenience and ontology

In 1935, Einstein, Podolsky and Rosen raised the issue of the completeness of the quantum description of a physical system. What they had in mind is whether or not the quantum description is informationally complete, in that all physical features of a system can be recovered from it. In a collapse theory such as the theory of Ghirardi, Rimini and Weber, the quantum wavefunction is informationally complete, and this has often been taken to suggest that according to that theory the wavefunction is all there is. If we distinguish the ontological completeness of a description from its informational completeness, we can see that the best interpretations of the GRW theory must postulate more physical ontology than just the wavefunction.

Buckets of water and waves of space: why spacetime is probably a substance

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newtons bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibnizs critique, a fact which has been obscured by the conflation of two of Leibnizs arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey the effect of the General Theory of Relativity and of plenism on these considerations.

Substances and space-time: What Aristotle would have said to Einstein

Abstract This essay consists of two parts. The first is an exegetical analysis of the “stripping” argument of Metaphysics Z.3. I contend that the passage is not in propria persona and that the resolution of the aporia depends upon a careful consideration of the metaphysical relationship between essential properties and the subjects of which they are predicated. The second part applies this conclusion to a problem recently raised by John Earman and John Norton about whether the general theory of relativity is compatible with both determinism and a substantivalist interpretation of space-time. I argue that their difficulty can be avoided by an Aristotelian account of the essential properties of space-time.

The Essence of Space-Time

I argue that Norton & Earmans hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newtons writings and consider how they can be updated to apply to the case provided by General Relativity.

Three Measurement Problems

The aim of this essay is to distinguish and analyze several difficulties confronting attempts to reconcile the fundamental quantum mechanical dynamics with Borns rule. It is shown that many of the proposed accounts of measurement fail at least one of the problems. In particular, only collapse theories and hidden variables theories have a chance of succeeding, and, of the latter, the modal interpretations fail. Any real solution demands new physics.

What Bell did

On the 50th anniversary of Bell?s monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier argument of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell?s inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?50 years of Bell?s theorem?.

Bell's Inequality, Information Transmission, and Prism Models

Violations of Bells Inequality can only be reliably produced if some information about the apparatus setting on one wing is available on the other, requiring superluminal information transmission. In this paper I inquire into the minimum amount of information needed to generate quantum statistics for correlated photons. Reflection on informational constraints clarifies the significance of Fines Prism models, and allows the construction of several models more powerful than Fines. These models are more efficient than Fine claims to be possible and work for the full range of possible analyzer settings. It also demonstrates that the division of theories into those that violate parameter independence and those that violate outcome independence sheds no light on the question of superluminal information transmission.

Healey on the Aharonov-Bohm Effect

Richard Healey (1997) argues that the Aharonov-Bohm effect demands the recognition of either nonlocal or nonseparable physics in much the way that violations of Bells inequality do. A careful examination of the effect and the arguments, though, shows that Healeys interpretation of the Aharonov-Bohm effect depends critically on his interpretation of gauge theories, and that the analogy with violations of Bells inequalities fails.

Space-Time in the Quantum World

Consider pairs of electrons produced in the singlet state and allowed to separate to a very great distance. We know from the work of Bell that no theory can predict violations of Bell’s inequality for spin measurements on those pairs if it satisfied two conditions. The first (condition a) is that the theory ascribe either a single initial state or a convex sum of states to the ensemble of pairs such that the initial states are statistically independent of the spin measurements later carried out on the electrons. The second (condition b) is most easily understood if expressed differently for deterministic and for stochastic theories. For a deterministic theory we require (condition b′) that the theory determine the results of each measurement solely on the basis of the initial state and the details of the measurement carried out on that particle. For a stochastic theory we demand (condition b*) that the theory assign probabilities for measurement results based solely on the initial state and the measurement carried out on a single electron, which probabilities are unchanged when one conditionalizes on the measurements and results obtained on the other particle in the pair. (Conditions b′ and b* are really the same condition, expressed in the one case appropriately to a deterministic theory, in the other for an indeterministic one. A theory which violates b′ also violates b* since conditionalizing on information about the measurement carried out on the second electron can render the result of the first measurement certain.) Einstein et al. (1935) had already pointed out the impossibility of a non-deterministic theory which obeys a and b* to recover the predictions of quantum theory, and so argued in favor of a deterministic theory. Bell showed that no deterministic theory obeying a and b′ could recover all of the predictions of quantum mechanics. The later work of Greenberger et al. (1989) showed that the reference to ensembles is otiose: there can be individual triples of particles such that no initial state of type a can recover all of the predictions of quantum mechanics if the theory is of type b′ or b*.