Abstract
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ``watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
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References
- [1]B. Freivogel, 2011 Making predictions in the multiverse, Class. Quant. Grav. 28 204007 [1105.0244]
- [2]D.N. Page, 2009 The Born rule dies J. Cosmol. Astropart. Phys. 2009 07 008 [0903.4888]
- [3]
- [4]J. Garriga and A. Vilenkin, 2013 Watchers of the multiverse J. Cosmol. Astropart. Phys. 2013 05 037 [1210.7540]
- [5]
- [6]
- [7]
- [8]T. Banks, W. Fischler and S. Paban, 2002 Recurrent nightmares? Measurement theory in de Sitter space J. High Energy Phys. JHEP12(2002)062 [hep-th/0210160]
- [9]L. Dyson, M. Kleban and L. Susskind, 2002 Disturbing implications of a cosmological constant J. High Energy Phys. JHEP10(2002)011 [hep-th/0208013]
- [10]T. Banks, TASI lectures on holographic space-time, SUSY and gravitational effective field theory, [1007.4001]
- [11]
- [12]
- [13]
- [14]S.R. Coleman and F. De Luccia, 1980 Gravitational effects on and of vacuum decay, Phys. Rev. D 21 3305
- [15]K.-M. Lee and E.J. Weinberg, 1987 Decay of the true vacuum in curved space-time, Phys. Rev. D 36 1088
- [16]
- [17]
- [18]
- [19]J. Garriga, A. Vilenkin and J. Zhang, 2013 Non-singular bounce transitions in the multiverse J. Cosmol. Astropart. Phys. 2013 11 055 [1309.2847]
- [20]
- [21]L. Susskind, The census taker's hat, [0710.1129]
- [22]A.H. Guth and V. Vanchurin, Eternal inflation, global time cutoff measures and a probability paradox, [1108.0665]
- [23]R.B. Griffiths, 1984 Consistent histories and the interpretation of quantum mechanics, J. Statist. Phys. 36 219
- [24]R. Omnes, 1988 Logical reformulation of quantum mechanics. I. Foundations, J. Statist. Phys. 53 893
- [25]M. Gell-Mann and J.B. Hartle, 1990 Quantum mechanics in the light of quantum cosmology, in Complexity, entropy, and the physics of information, W. Zurek ed., Addison Wesley, Reading U.S.A.
- [26]
- [27]B. d'Espagnat, 1989 Are there realistically interpretable local theories?, J. Statist. Phys. 56 747
- [28]
- [29]
- [30]C.J. Riedel, W.H. Zurek and M. Zwolak, The objective past of a quantum universe — part 1: redundant records of consistent histories, [1312.0331]
- [31]M. Gell-Mann and J.B. Hartle, Adaptive coarse graining, environment, strong decoherence and quasiclassical realms, [1312.7454]
- [32]J. Garriga, D. Schwartz-Perlov, A. Vilenkin and S. Winitzki, 2006 Probabilities in the inflationary multiverse J. Cosmol. Astropart. Phys. 2006 01 017 [hep-th/0509184]
- [33]G. Lindblad, 1976 On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48 119
- [34]
- [35]
- [36]D. Finkelstein, 1963 The logic of quantum physics Trans. N.Y. Acad. Sci. 25 621
- [37]J.B. Hartle, 1968 Quantum mechanics of individual systems, Am. J. Phys. 36 704
- [38]V.F. Mukhanov, 1985 On the many-worlds interpretation of quantum theory, in Proceedings of the Third Seminar on Quantum Gravity, Moscow U.S.S.R., 1984, M.A. Markov, V.A. Berezin and V.P. Frolov eds., World Scientific, Singapore
- [39]
- [40]
- [41]
- [42]E. Farhi, J. Goldstone and S. Gutmann, 1989 How probability arises in quantum mechanics, Annals Phys. 192 368
- [43]
- [44]