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 Bell's 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? Maudlin's 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?

Quantum non-locality and relativity

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion are discussed. Assuming the deformation scale $\lambda$ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigations of astrophysical phenomena such as gamma-ray bursts. We also outline a new approach to the construction of field theories on the noncommutative spacetime, with the noncommutativity equivalent under Fourier transform to non-Abelianness of the `addition law' for momentum in Feynman diagrams. We argue that CPT violation effects of the type testable using the sensitive neutral-kaon system are to be expected in such a theory.

Waves on Noncommutative Spacetime and Gamma-Ray Bursts

Nearly all theoretical approaches to the unification of quantum mechanics and gravity predict
 1,
 2,
 3,
 4
 that, at very short distance scales, the classical picture of space-time breaks down, with space-time becoming somewhat ‘fuzzy’ (or ‘foamy’). The properties of this fuzziness and the length scale that characterizes itsonset are potentially a means for determining which (if any) of the existing models of quantum gravity is correct. But it is generally believed
 5
 that these quantum space-time effects are too small to be probed by technologies currently available. Here Iargue that modern gravity-wave interferometers are sensitive enough to test certain space-time fuzziness models, because quantum space-time effects should provide an additional source of noise in the interferometers that can be tightly constrained experimentally. The noise levels recently achieved in one interferometer
 6
 are sufficient to rule out values of the length scale that characterizes one of the space-time fuzziness models down to the Planck length (∼10
 −35
  m) and beyond, while the sensitivity required to test another model should be achievable with interferometers now under construction.

Gravity-wave interferometers as quantum-gravity detectors

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski space–time [xi, t]=ιλxi. A natural wave equation is derived and the associated phenomena of in vacuo dispersion are discussed. Assuming the deformation scale λ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigations of astrophysical phenomena such as gamma-ray bursts. We also outline a new approach to the construction of field theories on the noncommutative space–time, with the noncommutativity equivalent under Fourier transform to non-Abelianness of the "addition law" for momentum in Feynman diagrams. We argue that CPT violation effects of the type testable using the sensitive neutral-kaon system are to be expected in such a theory.

Waves on noncommutative space–time and gamma-ray bursts

A handful of recent papers has been devoted to proposals of experiments capable of testing some candidate quantum-gravity phenomena. These lecture notes emphasize those aspects that are most relevant to the questions that inevitably come to mind when one is exposed for the first time to these research developments: How come theory and experiments are finally meeting in spite of all the gloomy forecasts that pervade traditional quantum-gravity reviews? Is this a case of theorists having put forward more and more speculative ideas until a point was reached at which conventional experiments could rule out the proposed phenomena? Or has there been such a remarkable improvement in experimental techniques and ideas that we are now capable of testing plausible candidate quantum-gravity phenomena? These questions are analysed rather carefully for the recent proposals of tests of space-time fuzziness using modern interferometers and tests of dispersion in the quantum-gravity vacuum using observations of gamma rays from distant astrophysical sources. I also briefly discuss other proposed quantum-gravity experiments, including those exploiting the properties of the neutral-kaon system for tests of quantum-gravity-induced decoherence and those using particle-physics accelerators for tests of models with large extra dimensions.

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Are We at the Dawn of Quantum-Gravity Phenomenology?

The measurability analysis of quantum electrodynamics performed by Bohr and Rosenfeld is generalized in order to be applicable to gravitation. After briefly restating our earlier argument for the measurability of the components of the quantum linearized Weyl tensor field taken separately, we demonstrate in detail their measurability taken jointly. In comparing the measurability analysis of linearized gravitation with that of quantum electrodynamics, we are able to exhibit the pervasive differences between the analyses necessitated by the equivalence principle.

Measurability analysis of the linearized gravitational field

The Einstein-Podolsky-Rosen (EPR) paradox and the correlated states it introduced comprise one of the central interpretive problems of quantum mechanics Because of the apparent nonlocal character of this paradox, it should be given a relativistic treatment The purpose of this paper is to provide such a treatment

A relativistic formulation of the Einstein-Podolsky-Rosen paradox

The procedures of Ashtekar and Goldberg to achieve a polynomial form of Dirac's canonical lapse and shift generators in general relativity involve a partial complexification of the canonical field variables, which in turn suggests consideration of a complex gauge group. This paper indicates possible approaches.

Gerrit J. Smith

Papers

Measurability analysis of the linearized gravitational field

A relativistic formulation of the Einstein-Podolsky-Rosen paradox

Complex phase spaces and complex gauge groups in general relativity.

Quantum blurring of cosmological singularities

Foundations of Space-Time Theories. Michael Friedman