Projection Postulate and Atomic Quantum Zeno Effect

The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show analytically that for a wide range of parameters such a short laser pulse acts as an effective level measurement to which the usual projection postulate applies with high accuracy. The corrections to the ideal reductions and their accumulation over n pulses are calculated. Our conclusion is that the projection postulate is an excellent pragmatic tool for a quick and simple understanding of the slow-down of time evolution in experiments of this type. However, corrections have to be included, and an actual freezing does not seem possible because of the finite duration of measurements.Comment: 25 pages, LaTeX, no figures; to appear in Phys. Rev.

Emergence from irreversibility

The emergent nature of quantum mechanics is shown to follow from a precise correspondence with the classical theory of irreversible thermodynamics. Specifically, the linear (or Gaussian) regime of the latter can be put in a 1-to-1 map with the semiclassical approximation to quantum mechanics. The very possibility of reinterpreting quantum mechanics as a thermodynamics proves that the former is an emergent phenomenon. That is, quantum mechanics is a coarse-grained description of some underlying degrees of freedom. © Published under licence by IOP Publishing Ltd.Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Perea Córdoba, MH. (2013). Emergence from irreversibility. Journal of Physics: Conference Series. 442(012033). doi:10.1088/1742-6596/442/1/012033S442012033ACOSTA, D., FERNÁNDEZ DE CÓRDOBA, P., ISIDRO, J. M., & SANTANDER, J. L. G. (2012). AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS. International Journal of Geometric Methods in Modern Physics, 09(05), 1250048. doi:10.1142/s021988781250048xAcosta, D., Cordóba, P. F. de, Isidro, J. M., & Santander, J. L. G. (2012). A holographic map of action onto entropy. Journal of Physics: Conference Series, 361, 012027. doi:10.1088/1742-6596/361/1/012027Blasone, M., Jizba, P., & Vitiello, G. (2001). Dissipation and quantization. Physics Letters A, 287(3-4), 205-210. doi:10.1016/s0375-9601(01)00474-1Blasone, M., Jizba, P., & Vitiello, G. (2003). Dissipation, Emergent Quantization, and Quantum Fluctuations. Lecture Notes in Physics, 151-163. doi:10.1007/978-3-540-40968-7_12Blasone, M., Jizba, P., & Kleinert, H. (2005). Quantum behavior of deterministic systems with information loss: Path integral approach. Annals of Physics, 320(2), 468-486. doi:10.1016/j.aop.2005.09.001Blasone, M., Jizba, P., & Scardigli, F. (2009). Can quantum mechanics be an emergent phenomenon? Journal of Physics: Conference Series, 174, 012034. doi:10.1088/1742-6596/174/1/012034Blasone, M., Jizba, P., Scardigli, F., & Vitiello, G. (2009). Dissipation and quantization for composite systems. Physics Letters A, 373(45), 4106-4112. doi:10.1016/j.physleta.2009.09.016Carroll, R. (2010). On the Emergence Theme of Physics. doi:10.1142/7568ELZE, H.-T. (2009). THE ATTRACTOR AND THE QUANTUM STATES. International Journal of Quantum Information, 07(supp01), 83-96. doi:10.1142/s0219749909004700Elze, H.-T. (2009). Does quantum mechanics tell an atomistic spacetime? Journal of Physics: Conference Series, 174, 012009. doi:10.1088/1742-6596/174/1/012009Elze, H.-T. (2012). Linear dynamics of quantum-classical hybrids. Physical Review A, 85(5). doi:10.1103/physreva.85.052109Elze, H.-T. (2012). Four questions for quantum-classical hybrid theory. Journal of Physics: Conference Series, 361, 012004. doi:10.1088/1742-6596/361/1/012004Faraggi, A. E., & Matone, M. (1998). Equivalence principle, Planck length and quantum Hamilton–Jacobi equation. Physics Letters B, 445(1-2), 77-81. doi:10.1016/s0370-2693(98)01484-1Grössing, G., Fussy, S., Pascasio, J. M., & Schwabl, H. (2012). The Quantum as an Emergent System. Journal of Physics: Conference Series, 361, 012008. doi:10.1088/1742-6596/361/1/012008Hooft, G. ’t. (1999). Quantum gravity as a dissipative deterministic system. Classical and Quantum Gravity, 16(10), 3263-3279. doi:10.1088/0264-9381/16/10/316Hooft, G. ’t. (2012). Quantum Mechanics from Classical Logic. Journal of Physics: Conference Series, 361, 012024. doi:10.1088/1742-6596/361/1/012024HU, B. L. (2011). GRAVITY AND NONEQUILIBRIUM THERMODYNAMICS OF CLASSICAL MATTER. International Journal of Modern Physics D, 20(05), 697-716. doi:10.1142/s0218271811019049Hu, B. L. (2009). Emergent/quantum gravity: macro/micro structures of spacetime. Journal of Physics: Conference Series, 174, 012015. doi:10.1088/1742-6596/174/1/012015Kiefer, C. (2010). Can Quantum Theory be Applied to the Universe as a Whole? Foundations of Physics, 40(9-10), 1410-1418. doi:10.1007/s10701-010-9441-3Onsager, L., & Machlup, S. (1953). Fluctuations and Irreversible Processes. Physical Review, 91(6), 1505-1512. doi:10.1103/physrev.91.1505Penrose, R. (2009). Black holes, quantum theory and cosmology. Journal of Physics: Conference Series, 174, 012001. doi:10.1088/1742-6596/174/1/012001Sakellariadou, M., Stabile, A., & Vitiello, G. (2012). Noncommutative spectral geometry, dissipation and the origin of quantization. Journal of Physics: Conference Series, 361, 012025. doi:10.1088/1742-6596/361/1/012025Wetterich, C. (2009). Emergence of quantum mechanics from classical statistics. Journal of Physics: Conference Series, 174, 012008. doi:10.1088/1742-6596/174/1/01200

A holographic map of action onto entropy

We propose a holographic correspondence between the action integral I describing the mechanics of a finite number of degrees of freedom in the bulk, and the entropy S of the boundary (a holographic screen) enclosing that same volume. The action integral must be measured in units of (i times) Planck's constant, while the entropy must be measured in units of Boltzmann's constant. In this way we are led to an intriguing relation between the second law of thermodynamics and the uncertainty principle of quantum mechanics.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1107.189

An entropic picture of emergent quantum mechanics

Quantum mechanics emerges à la Verlinde from a foliation of 3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant k B. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on 3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. 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