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The Role of Quantum Jumps in Quantum Ontology

Journal for General Philosophy of Science (2023)Cite this article

Abstract

Quantum theory determines the evolution of quantum states between quantum jumps. Quantum theory also allows us to calculate rates of quantum jumps and, on a probabilistic level, the outcomes of those quantum jumps. Both quantum jumps and the continuous evolution of quantum states are important in the time evolution of quantum systems, and the scattering matrix ties those seemingly disparate concepts together. Indeed, quantum jumps are so essential in quantum dynamics that we should refocus discussion of a quantum ontology on the power and principal limitations of our knowledge about quantum jumps as encoded in the scattering matrix. On the one hand, one might argue that the lack of a dynamical resolution of quantum jumps indicates an inherent incompleteness of the theory. However, we would rather submit that quantum theory is complete and that the observations indicate a principal limitation to the description of the universe as a smoothly evolving dynamical system. The modern understanding of quantum jumps therefore calls for updates to the Copenhagen interpretation instead of modifications of quantum theory.

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Notes

  1. On the other hand, spreadings of electron wave functions from millimetre-aperture electron guns or of neutron wave functions from centimetre-aperture neutron guides are completely negligible on the time scales of lab experiments, even without any environmental stabilization.

  2. We will define the notion of a “traditional Copenhagen interpretation”in Sect. 2.

  3. This distinguishes decoherence theory from dynamical collapse theories which modify the quantum evolution equations (Ghirardi et al. 1986) or use gravitational contributions to the evolution equations to generate collapse (Károlyházy 1966; Diósi 1989; Penrose 1996; Bassi et al. 2017).

  4. We denote a signal in a particle detector as “pointlike” if the resolution of the spatial location of a single-particle signal is only determined by the spatial resolution of the detector, but not by the wave function of the incident particle that is observed. High-energy physics allows to calculate limits on elementary particle radii from the agreement of observed properties of charged particles with radiative corrections which are calculated under the assumption of point particles. This leads e.g. to a limit \(R<4\times 10^{-19}\) m for the electron radius from the comparison of high-precision measurements with high-precision calculations for the fine structure constant (Morel et al. 2020). A limit of \(R<2\times 10^{-20}\) m has been inferred from the absence of non-renormalizable contact interactions of the electron in measurements at the LEP collider (Bourilkov 2001). However, these theoretical limits on a possible electron radius are model dependent with respect to how substructure of an electron should relate to its anomalous magnetic moment and to non-renormalizable couplings, respectively, and they do not constitute position measurements. Nevertheless, it is noteworthy that all observations to date are compatible with a point particle interpretation of the electron. However, the point about pointlike signals concerns the observation that single-particle position signals in diffraction experiments are determined by detector resolution and are much smaller than the widths of the wave functions.

  5. Fock space is a priori a representation space for the Schrödinger picture quantum fields and the freely evolving quantum fields of the Dirac picture. The transformation from the Dirac picture fields into the Heisenberg picture fields is defined through a similarity transformation which involves the interaction terms of the theory expressed through the Dirac picture fields. As such, the transformation into the Heisenberg picture is singular since it generates the same self-energy effects that affect higher orders in the scattering matrix. The expression of time-evolved quantum states through Heisenberg picture quantum fields therefore always comes with the cautionary remark that renormalization is required if we apply higher powers of interaction terms on quantum states. We will not go deeper into the renormalization program, since wave-particle duality, quantum jumps, and the ontic-epistemic boundary in Fock space all show up already in first order.

  6. We recall that a pointlike signal is a signal for which the spatial resolution is only determined by the resolution of the detector.

  7. The non-local relation of the relativistic particle creation operators in position space to the full quantum fields had caused a lot of confusion about the concept of relativistic wave functions in position space. However, the position space operators allow for the formulation of local energy-momentum densities, \({\mathcal {P}}_\mu ({\varvec{x}},t)=-\,\mathrm {i}\hbar \sum _s\varPsi ^+_s({\varvec{x}},t)\partial _\mu \varPsi _s({\varvec{x}},t)\), and local charge densities, \(\varrho ({\varvec{x}},t)=q\sum _s\varPsi ^+_s({\varvec{x}},t)\varPsi _s({\varvec{x}},t)\), which after integration yield the same results as the full interaction picture quantum fields after neglecting the anti-particle contributions. It is clear from the observation of relativistic electron and meson tracks, and from the creation and observation of single-photon states (Kuhn et al. 2002; Eisaman et al. 2011; Rueckner and Peidle 2013; Aspden et al. 2016; Aharonovich et al. 2016), that position space wave functions and their corresponding operators must exist. The reason why we cannot observe photon tracks is that photons are annihilated in interactions and therefore cannot participate in consecutive interactions. Furthermore, the differential cross section for elastic photon scattering off electrons, \(d\sigma /d\varOmega =(\alpha _S\hbar /m_ec)^2(1+\cos ^2\theta )/2\), implies that emitted photons from scattering have the same emission probability in forward and backward direction relative to the incident photon. Sequences of photons from scattering of a single incident photon cannot even yield the illusion of a photon track. Light rays in a transparent medium arise through interference from coherent scattering of many incident photons off many scattering centers in the medium, i.e. we cannot interprete them as manifestations of photon tracks.

  8. This can obviously be a transient notion. Protons were considered elementary particles in the 1940s.

  9. Equation (17) provides the \({\mathcal {O}}(\alpha _S)\) probability amplitude for the electron-electron scattering between initial and final normalized wave packets in \({\varvec{k}}\)-space.

  10. The term on the right hand side of Eq. (33) satisfies the consistency condition \({\varvec{\nabla }}\cdot {\varvec{J}}=0\) as a consequence of the local charge conservation law that follows from Eq. (31). We also note that the driving terms on the right hand side of Eq. (33) show that there is no continuous wave-like photon emission from energy eigenstates in the first-quantized theory: substition of wave functions of energy eigenstates of Eq. (31) with \({\varvec{A}}=0\), \(\varphi _{a,s,n}({\varvec{x}},t)=\varphi _{a,s,n}({\varvec{x}})\exp (-\,\mathrm {i}E_n t/\hbar )\), \(\varphi _{a,s,n}({\varvec{x}})\in {\mathbb {R}}\), for the Schrödinger operators \(\varPsi _{a,s}({\varvec{x}},t)\) yields \({\varvec{A}}=0\) as a solution Eq. (33).

  11. The scattering matrix element for photon emission is proportional to \(1/\sqrt{\alpha _S}\) although the photon interaction term is proportional to \(\sqrt{\alpha _S}\). This is because the matrix element \(\langle 1,0,0|z|2,1,0\rangle\) of the hydrogen states is proportional to \(a=\hbar /\alpha _S\mu c\).

  12. We would be remiss to not acknowledge the fact that the question for the correct formulation of quantum field theory as a basis for quantum ontology itself is subject to philosophical debate (Wallace 2006; MacKinnon 2008; Fraser 2009; Ruetsche 2011; Myrvold 2015).

References

  • Aharonovich, I., D. Englund, and M. Toth. 2016. Solid-state single-photon emitters. Nature Photonics 10: 631–641.

    Article  Google Scholar 

  • Aspden, R.S., M.J. Padgett, and G.C. Spalding. 2016. Video recording true single-photon double-slit interference. American Journal of Physics 84: 671–677.

    Article  Google Scholar 

  • Ballentine, L.E. 1970. The statistical interpretation of quantum mechanics. Reviews of Modern Physics 42: 358–381.

    Article  Google Scholar 

  • Ballentine, L.E. 1998. Quantum Mechanics: A Modern Development. Singapore: World Scientific.

    Book  Google Scholar 

  • Barton, P.A., C.J.S. Donald, D.M. Lucas, D.A. Stevens, A.M. Steane, and D.N. Stacey. 2000. Measurement of the lifetime of the \(3d^2 D_{5/2}\) state in \({}^{40}Ca^+\). Physical Review A 62: 032503.

    Article  Google Scholar 

  • Bassi, A., A. Großardt, and H. Ulbricht. 2017. Gravitational decoherence. Classical and Quantum Gravity 34: 193002.

    Article  Google Scholar 

  • Bohm, D. 1952. A suggested interpretation of the quantum theory in terms of “hidden’’ variables. I. Physical Review 85: 166–179.

    Article  Google Scholar 

  • Bohm, D. 1952. A suggested interpretation of the quantum theory in terms of “hidden’’ variables. II. Physical Review 85: 180–193.

    Article  Google Scholar 

  • Bohr, N. 1928. Das Quantenpostulat und die neuere Entwicklung der Atomistik. Naturwissenschaften 16: 245–257.

    Article  Google Scholar 

  • Bohr, N. 1929. Wirkungsquantum und Naturbeschreibung. Naturwissenschaften 17: 483–486.

    Article  Google Scholar 

  • Bourilkov, D. 2001. Hint for axial-vector contact interactions in the data on \(e^+ e^-\rightarrow e^+ e^-(\gamma )\) at center-of-mass energies 192–208 GeV. Physical Review D 64: 071701.

    Article  Google Scholar 

  • DeBrota, J.B., C.A. Fuchs, and R. Schack. 2020. Respecting one’s fellow: QBism’s analysis of Wigner’s friend. Foundations of Physics 50: 1859–1874.

    Article  Google Scholar 

  • Dick, R. 2017. Quantum jumps, superpositions, and the continuous evolution of quantum states. Studies in History and Philosophy of Modern Physics 57: 115–125.

    Article  Google Scholar 

  • Dick, R. 2020. Advanced Quantum Mechanics: Materials and Photons, 3rd ed. Cham: Springer-Nature.

    Book  Google Scholar 

  • Diósi, L. 1989. Models for universal reduction of macroscopic quantum fluctuations. Physical Review A 40: 1165–1174.

    Article  Google Scholar 

  • Earman, J. 2019. Quantum Bayesianism assessed. The Monist 102: 403–423.

    Article  Google Scholar 

  • Eisaman, M.D., J. Fan, A. Migdall, and S.V. Polyakov. 2011. Invited review article: single-photon sources and detectors. Reviews of Scientific Instruments 82: 071101.

    Article  Google Scholar 

  • Esfeld, M., D. Lazarovici, M. Hubert, and D. Dürr. 2014. The ontology of Bohmian mechanics. The British Journal for the Philosophy of Science 65: 773–796.

    Article  Google Scholar 

  • Falkenburg, B. 2007. Particle Metaphysics: A Critical Account of Subatomic Reality. Berlin: Springer.

    Google Scholar 

  • Fraser, D. 2009. Quantum field theory: underdetermination, inconsistency, and idealization. Philosophy of Science 76: 536–567.

    Article  Google Scholar 

  • Fuchs, C.A., N.D. Mermin, and R. Schack. 2014. An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics 82: 749–754.

    Article  Google Scholar 

  • Ghirardi, G.C., A. Rimini, and T. Weber. 1986. Unified dynamics for microscopic and macroscopic systems. Physical Review D 34: 470–491.

    Article  Google Scholar 

  • Heisenberg, W. 1927. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43: 172–198.

    Article  Google Scholar 

  • Heisenberg, W. 1930. The Physical Principles of the Quantum Theory. New York: Dover Publications.

    Google Scholar 

  • Heisenberg, W. 1955. The Development of the Interpretation of Quantum Theory. In Niels Bohr and the Development of Physics, ed. W. Pauli, 12–29. London: Pergamon Press.

    Google Scholar 

  • Joos, E., and H.D. Zeh. 1985. The emergence of classical properties through interaction with the environment. Zeitschrift für Physik B 59: 223–243.

    Article  Google Scholar 

  • Károlyházy, F. 1966. Gravitation and quantum mechanics of macroscopic objects. Nuovo Cimento A 42: 390–402.

    Article  Google Scholar 

  • Kramers, H.A., and W. Heisenberg. 1925. Über die Streuung von Strahlung durch Atome. Zeitschrift für Physik 31: 681–708.

    Article  Google Scholar 

  • Kuhn, A., M. Hennrich, and G. Rempe. 2002. Deterministic single-photon source for distributed quantum networking. Physical Review Letters 89: 067901.

    Article  Google Scholar 

  • MacKinnon, E. 2008. The standard model as a philosophical challenge. Philosophy of Science 75: 447–457.

    Article  Google Scholar 

  • Merli, P.G., G.F. Missiroli, and G. Pozzi. 1976. On the statistical aspect of electron interference phenomena. American Journal of Physics 44: 306–307.

    Article  Google Scholar 

  • Mittleman, R.K., I.I. Ioannou, H.G. Dehmelt, and N. Russell. 1999. Bound on CPT and Lorentz symmetry with a trapped electron. Physical Review Letters 83: 2116–2119.

    Article  Google Scholar 

  • Morel, L., Z. Yao, P. Cladé, and S. Guellati-Khélifa. 2020. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature 588: 61–65.

    Article  Google Scholar 

  • Myrvold, W.C. 2015. What is a wavefunction? Synthese 192: 3247–3274.

    Article  Google Scholar 

  • Nagourney, W., J. Sandberg, and H. Dehmelt. 1986. Shelved optical electron amplifier: observation of quantum jumps. Physical Review Letters 56: 2797–2799.

    Article  Google Scholar 

  • Odom, B., D. Hanneke, B. D’Urso, and G. Gabrielse. 2006. New measurement of the electron magnetic moment using a one-electron quantum cyclotron. Physical Review Letters 97: 030801.

    Article  Google Scholar 

  • Penrose, R. 1996. On gravity’s role in quantum state reduction. General Relativity and Gravitation 28: 581–600.

    Article  Google Scholar 

  • Pozzi, G. 2016. Particles and Waves in Electron Optics and Microscopy. Cambridge: Academic Press.

    Google Scholar 

  • Rueckner, W., and J. Peidle. 2013. Young’s double-slit experiment with single photons and quantum eraser. American Journal of Physics 81: 951–958.

    Article  Google Scholar 

  • Ruetsche, L. 2011. Interpreting Quantum Theories. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Sakurai, J.J. 1967. Advanced Quantum Mechanics. Reading: Addison-Wesley.

    Google Scholar 

  • Sauter, Th., W. Neuhauser, R. Blatt, and P.E. Toschek. 1986. Observation of quantum jumps. Physical Review Letters 57: 1696–1698.

    Article  Google Scholar 

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

    Google Scholar 

  • Schrödinger, E. 1926a. Quantisierung als Eigenwertproblem (Erste Mitteilung). Annalen der Physik 384: 361–376.

    Article  Google Scholar 

  • Schrödinger, E. 1926b. Quantisierung als Eigenwertproblem (Vierte Mitteilung). Annalen der Physik 386: 109–139.

    Article  Google Scholar 

  • Schrödinger, E. 1952. Are there quantum jumps? Part I. The British Journal for the Philosophy of Science 3: 109–123.

    Article  Google Scholar 

  • Schrödinger, E. 1952. Are there quantum jumps? Part II. The British Journal for the Philosophy of Science 3: 233–242.

    Article  Google Scholar 

  • Spekkens, R.W. 2007. Evidence for the epistemic view of quantum states: a toy theory. Physical Review A 75: 032110.

    Article  Google Scholar 

  • Steiner, M., H.M. Meyer, C. Deutsch, J. Reichel, and M. Köhl. 2013. Single ion coupled to an optical fiber cavity. Physical Review Letters 110: 043003.

    Article  Google Scholar 

  • Tonomura, A., J. Endo, T. Matsuda, T. Kawasaski, and H. Ezawa. 1989. Demonstration of single-electron buildup of an interference pattern. American Journal of Physics 57: 117–120.

    Article  Google Scholar 

  • von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. New edition of R.T. Beyer’s English translation by N.A. Wheeler: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 2018).

  • Wallace, D. 2006. In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory. Synthese 151: 33–80.

    Article  Google Scholar 

  • Wheeler, J.A. 1983. Law without law. In Quantum Theory and Measurement, ed. J.A. Wheeler and W.H. Zurek, 182–213. Princeton: Princeton University Press.

    Chapter  Google Scholar 

  • Wineland, D.J. 2013. Nobel lecture: superposition, entanglement, and raising Schrödinger’s cat. Reviews of Modern Physics 85: 1103–1114.

    Article  Google Scholar 

  • Zeh, H.D. 1970. On the interpretation of measurement in quantum theory. Foundations of Physics 1: 69–76.

    Article  Google Scholar 

  • Zeh, H.D. 1993. There are no quantum jumps, nor are there particles! Physics Letters A 172: 189–192.

    Article  Google Scholar 

  • Zeh, H.D. 2004. The wave function: It or bit? In Science and Ultimate Reality, ed. J.D. Barrow, P.C.W. Davies, and C.L. Harper Jr., 103–120. Cambridge: Cambridge University Press. See also arXiv:quant-ph/0204088v2.

  • Zurek, W.H. 1981. Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? Physical Review D 24: 1516–1525.

    Article  Google Scholar 

  • Zurek, W.H. 1982. Environment-induced superselection rules. Physical Review D 26: 1862–1880.

    Article  Google Scholar 

  • Zurek, W.H., S. Habib, and J.P. Paz. 1993. Coherent states via decoherence. Physical Review Letters 70: 1187–1190.

    Article  Google Scholar 

  • Zyla, P.A., (Particle Data Group), et al. 2020. Review of Particle Physics. Progress of Theoretical and Experimental Physics 2020: 083C01.

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  1. Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, SK, S7N 5E2, Canada

    Rainer Dick

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Dick, R. The Role of Quantum Jumps in Quantum Ontology. J Gen Philos Sci (2023). https://doi.org/10.1007/s10838-022-09635-0

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Keywords

  • Quantum ontology
  • Copenhagen interpretation
  • Ontic states
  • Epistemic states