Abstract
The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre- and post-selection of states opens up a new, experimentally testable, sector of quantum mechanics, when combined with statistical averages of identical weak measurements. In this paper I apply the theory of weak quantum measurements combined with pre- and post-selection to cosmology. Here, pre-selection means specifying the wave function of the universe or, in a popular semi-classical approximation, the initial quantum state of a subset of quantum fields propagating in a classical background spacetime. The novel feature is post-selection: the additional specification of a condition on the quantum state in the far future. I discuss “natural” final conditions, and show how they may lead to potentially large and observable effects at the present cosmological epoch. I also discuss how pre- and post-selected quantum fields couple to gravity via the DeWitt-Schwinger effective action prescription, in contrast to the expectation value of the stress-energy-momentum tensor, resolving a vigorous debate from the 1970s. The paper thus provides a framework for computing large-scale cosmological effects arising from this new sector of quantum mechanics. A simple experimental test is proposed. [Editors note: for a video of the talk given by Prof. Davies at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-13.]
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Y. Aharonov, E. Gruss, Two-time interpretation of quantum mechanics (2005). arXiv:quant-ph/0507269
Y. Aharonov, D. Rohrlich, Quantum Paradoxes (Wiley-VCH, Weinheim, 2005)
J. Hartle, S. Hawking, Wave function of the universe. Phys. Rev. D 28(12), 2960 (1983)
N.D. Birrell, P.C.W. Davies, Curved Space. Quantum Fields (Cambridge University Press, Cambridge, 1982)
P.C.W. Davies, C.H. Lineweaver, M. Ruse (eds.), Complexity and the Arrow of Time (Cambridge University Press, Cambridge, 2013)
F. Hoyle, J.V. Narlikar, Electrodynamics of direct interparticle action. I. The quantum mechanical response of the universe. Ann. Phys. 54, 207–239 (1969)
F.J. Tipler, Cosmological limits on computation. Int. J. Theor. Phys. 25(6), 617–661 (1986). doi:10.1007/BF00670475
S.W. Hawking, R. Penrose, The Nature of Space and Time (Princeton University Press, Princeton, 1996)
H. Price, Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time (Oxford University Press, New York, 1996)
M. Gell-Mann, J.B. Hartle, Complexity, entropy and the physics of information, in Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology, vol. VIII, ed. by W.H. Zurek (Addison-Wesley, Reading, 1990), p. 425
D.N. Page, No time asymmetry from quantum mechanics. Phys. Rev. Lett. 70, 4034–4037 (1993)
C. Bernard, A. Duncan, Regularization and renormalization of quantum field theory in curved space-time. Ann. Phys. 107, 201–222 (1977)
Yu.V. Pavlov, Nonconformal scalar field in a homogeneous isotropic space and the method of Hamiltonian diagonalization (2000). gr-qc/0012082
T.S. Bunch, P.C.W. Davies, Quantum field theory in de Sitter space: renormalization by point-splitting. Proc. R. Soc. Lond. Ser. A 360, 117 (1978)
B.S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965)
D.G. Boulware, Quantum field theory in Schwarzschild and Rindler spaces. Phys. Rev. D 11, 1404–1424 (1975)
J.B. Hartle, B.L. Hu, Quantum effects in the early universe. II. Effective action for scalar fields in homogeneous cosmologies with small anisotropy. Phys. Rev. D 20, 1772–1782 (1979)
J.S. Dowker, R. Critchley, Effective Lagrangian and energy-momentum tensor in de Sitter space. Phys. Rev. D 13, 3224–3232 (1976)
B.S. DeWitt, Phys. Rep. 19C, 297 (1975)
S.W. Hawking, Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975)
R.B. Partridge, Absorber theory of radiation and the future of the universe. Nature 244, 263–265 (1973)
P.C.W. Davies, Is the universe transparent or opaque? J. Phys. A, Gen. Phys. 5, 1722–1737 (1972)
P.C.W. Davies, J. Twamley, Time-symmetric cosmology and the opacity of the future light cone. Class. Quantum Gravity 10, 931 (1993). doi:10.1088/0264-9381/10/5/011
Acknowledgements
I have greatly benefited from discussions with Alonso Botero, Jeff Tollaksen and Yakir Aharonov in preparing this paper. I would like to thank Katherine Lee and Saugata Chatterjee for their help reformatting and editing the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Italia
About this paper
Cite this paper
Davies, P.C.W. (2014). Quantum Weak Measurements and Cosmology. In: Struppa, D., Tollaksen, J. (eds) Quantum Theory: A Two-Time Success Story. Springer, Milano. https://doi.org/10.1007/978-88-470-5217-8_7
Download citation
DOI: https://doi.org/10.1007/978-88-470-5217-8_7
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-5216-1
Online ISBN: 978-88-470-5217-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)