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Quantum Discreteness is an Illusion

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Abstract

I review arguments demonstrating how the concept of “particle” numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number (“momentum”) characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines a non-degenerate “n-particle wave function”. Other discrete properties and phenomena (such as particle positions and “events”) can be understood by means of the fast but continuous process of decoherence: the irreversible dislocalization of superpositions. Any wave-particle dualism thus becomes obsolete. The observation of individual outcomes of this decoherence process in measurements requires either a subsequent collapse of the wave function or a “branching observer” in accordance with the Schrödinger equation—both possibilities applying clearly after the decoherence process. Any probability interpretation of the wave function in terms of local elements of reality, such as particles or other classical concepts, would open a Pandora’s box of paradoxes, as is illustrated by various misnomers that have become popular in quantum theory.

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References

  1. Mittelstaedt, P.: The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  2. Zeh, H.D.: On the interpretation of measurement in quantum theory. Found. Phys. 1, 69 (1970)

    Article  ADS  Google Scholar 

  3. Zurek, W.H.: Pointer basis of quantum apparatus: Into which mixture does the wave packet collapse? Phys. Rev. D 24, 1516 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  4. Joos, E., Zeh, H.D.: The emergence of classical properties through interaction with the environment. Z. Phys. B 59, 223 (1985)

    Article  ADS  Google Scholar 

  5. Schlosshauer, M.: Decoherence and the Quantum-to-Classical Transition. Springer, Berlin (2007)

    Google Scholar 

  6. Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J., Stamatescu, I.-O.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (2003)

    Google Scholar 

  7. Zeh, H.D.: Time in quantum theory. In: Greenberger, D., Hentschel, K., Weinert, F. (eds.) Compendium of Quantum Physics. Springer, Berlin (2009). http://arxiv.org/abs/0705.4638

    Google Scholar 

  8. Deléglise, S., Dotsenko, I., Sayrin, C., Bernu, J., Brune, M., Raimond, J.-M., Haroche, S.: Reconstruction of non-classical cavity fields with snapshots of their decoherence. Nature 455, 510 (2008)

    Article  ADS  Google Scholar 

  9. Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Nuovo Cimento B 37, 1 (1977)

    Article  ADS  Google Scholar 

  10. Kübler, O., Zeh, H.D.: Dynamics of quantum correlations. Ann. Phys. (N.Y.) 76, 405 (1973)

    Article  ADS  Google Scholar 

  11. Zeh, H.D.: There is no ‘first’ quantization. Phys. Lett. A 309, 329 (2003). http://arxiv.org/abs/quant-ph/0210098

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Ulfbeck, O., Bohr, A.: Genuine fortuitousness: where did that click come from? Found. Phys. 31, 757 (2001)

    Article  MathSciNet  Google Scholar 

  13. Schlosshauer, M., Camilleri, C.: The quantum-to-classical transition: Bohr’s doctrine of classical concepts, emergent classicality, and decoherence. http://arxiv.org/abs/0804.1609

  14. Zeh, H.D.: There are no quantum jumps, nor are there particles. Phys. Lett. A 172, 189 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  15. Giulini, D., Kiefer, C., Zeh, H.D.: Symmetries, superselection rules, and decoherence. Phys. Lett. A 199, 291 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. Zeh, H.D.: The Physical Basis of the Direction of Time, 5th edn. Springer, Berlin (2007), see www.time-direction.de

    MATH  Google Scholar 

  17. Tegmark, M.: Importance of quantum decoherence in brain processes. Phys. Rev. E 61, 4194 (2000). http://arxiv.org/abs/quant-ph/9907009

    Article  ADS  Google Scholar 

  18. Mott, N.F.: The wave mechanics of α-particle tracks. Proc. R. Soc. Lond. A 126, 79 (1929)

    Article  ADS  Google Scholar 

  19. Blood, C.: No evidence for particles. http://arxiv.org/abs/0807.3930v1

  20. Wilkinson, S.R., Barucha, C.F., Fischer, M.C., Madison, K.W., Morrow, P.R., Niu, Q., Sundaram, B., Raizen, M.G.: Experimental evidence for non-exponential decay in quantum tunnelling. Nature 387, 575 (1997)

    Article  ADS  Google Scholar 

  21. Sauter, Th., Neuhauser, W., Blatt, R., Toschek, P.E.: Observation of quantum jumps. Phys. Rev. Lett. 57, 1696 (1986)

    Article  ADS  Google Scholar 

  22. Garisto, R.: What is the speed of quantum information? http://arxiv.org/abs/quant-ph/0212078

  23. Salart, D., Baas, A., Branciard, C., Gisin, N., Zbinden, H.: Testing spooky action at a distance. Nature 454, 861 (2008). http://arxiv.org/abs/0808.3316

    Article  ADS  Google Scholar 

  24. Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  25. Bennett, C.H., Brassard, G., Crépau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Timpson, C.: The grammar of ‘teleportation’. Brit. J. Phil. Sci. 57, 587 (2006) http://arxiv.org/abs/quant-ph/0509048

    Article  MathSciNet  Google Scholar 

  27. Scully, M.O., Drühl, K.: Quantum eraser: a proposed photon correlation experiment concerning observation and ‘delayed choice’. Phys. Rev. A 25, 2208 (1982)

    Article  ADS  Google Scholar 

  28. Bennett, C.H.: Demons, engines, and the second law. Sci. Amer. 257(5), 88 (1987)

    Article  Google Scholar 

  29. Jaynes, E.T.: In: Barut, A. (ed.) Foundation of Radiation Theory and Quantum Electronics. Plenum, New York (1980)

    Google Scholar 

  30. Herbut, F.: On EPR-type entanglement in the experiments of Scully et al. I. The micromaser case and delayed choice quantum erasure, http://arxiv.org/abs/0808.3176v1

  31. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997). See Sect. 20.3

    Google Scholar 

  32. Kiefer, C.: Quantum Gravity, 2nd edn. Oxford Science Publications, Oxford (2007), p. 310 ff

    Book  MATH  Google Scholar 

  33. Kiefer, C., Lohmar, I., Polarski, D., Starobinski, A.A.: Pointer states for the primordial fluctuations in inflationary cosmology. Class. Quantum Gravity 24, 1699 (2007)

    Article  MATH  ADS  Google Scholar 

  34. Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

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  1. Universität Heidelberg, Heidelberg, Germany

    H. Dieter Zeh

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  1. H. Dieter Zeh
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Correspondence to H. Dieter Zeh.

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Zeh, H.D. Quantum Discreteness is an Illusion. Found Phys 40, 1476–1493 (2010). https://doi.org/10.1007/s10701-009-9383-9

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