Abstract
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”.
Similar content being viewed by others
References
Zeilinger, A.: A foundational principle for quantum mechanics. Found. Phys. 29, 631 (1999)
Brukner, C., Zeilinger, A.: Operationally invariant information in quantum measurements. Phys. Rev. Lett. 83, 3354 (1999)
Fuchs, C.: Quantum mechanics as quantum information, mostly. J. Mod. Opt. 50, 987 (2003)
Caves, C.M., Fuchs, C.A., Schack, R.: Subjective probability and quantum certainty. Stud. Hist. Philos. Sci. B 38, 255 (2007)
Goyal, P.: Information-geometric reconstruction of quantum theory. Phys. Rev. A 78, 052120 (2008)
Lee, J.-W.: Quantum mechanics emerges from information theory applied to causal horizons. Found. Phys. 41, 744 (2011)
Leifer, M.S., Spekkens, R.W.: Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference. Phys. Rev. A 88, 052130 (2013)
Resch, K.J., Lundeen, J.S., Steinberg, A.M.: Experimental realization of the quantum box problem. Phys. Lett. A 324, 125 (2004)
Jordan, A.N., Korotkov, A.N., Büttiker, M.: Leggett–Garg inequality with a kicked quantum pump. Phys. Rev. Lett. 97, 026805 (2006)
Lundeen, J.S., Steinberg, A.M.: Experimental joint weak measurement on a photon pair as a probe of Hardy’s paradox. Phys. Rev. Lett. 102, 020404 (2009)
Yokota, K., Yamamoto, T., Koashi, M., Imoto, N.: Direct observation of Hardy’s paradox by joint weak measurement with an entangled photon pair. New J. Phys. 11, 033011 (2009)
Goggin, M.E., Almeida, M.P., Barbieri, M., Lanyon, B.P., O’Brien, J.L., White, A.G., Pryde, G.J.: Violation of the Leggett–Garg inequality with weak measurements of photons. Proc. Natl. Acad. Sci. USA. 108, 1256 (2011)
Suzuki, Y., Iinuma, M., Hofmann, H.F.: Violation of Leggett–Garg inequalities in quantum measurements with variable resolution and back-action. New J. Phys. 14, 103022 (2012)
Denkmayr, T., Geppert, H., Sponar, S., Lemmel, H., Matzkin, A., Tollaksen, J., Hasegawa, Y.: Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment. Nat. Commun. 5, 4492 (2014)
Okamoto, R., Takeuchi, S.: Experimental demonstration of a quantum shutter closing two slits simultaneously. Sci. Rep. 6, 35161 (2016)
Minev, Z., Mundhada, S., Shankar, S., Reinhold, P., Gutierrez-Jauregui, R., Schoelkopf, R.J., Mirrahimi, M., Carmichael, H.J., Devoret, M.H.: To catch and reverse a quantum jump mid-flight. Nature 570, 200 (2019)
Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)
Wiseman, H.M.: Weak values, quantum trajectories, and the cavity-QED experiment on wave-particle correlation. Phys. Rev. A 65, 032111 (2002)
Hofmann, H.F.: Complete characterization of post-selected quantum statistics using weak measurement tomography. Phys. Rev. A 81, 012103 (2010)
Hofmann, H.F.: Quasi-determinism of weak measurement statistics: Laplace’s demon’s quantum cousin, e-print arXiv:1005.0654 (2010)
Hosoya, A., Shikano, Y.: Strange weak values. J. Phys. A 43, 385307 (2010)
Bednorz, A., Belzig, W.: Quasiprobabilistic interpretation of weak measurements in mesoscopic junctions. Phys. Rev. Lett. 105, 106803 (2010)
Lundeen, J.S., Sutherland, B., Patel, A., Stewart, C., Bamber, C.: Direct measurement of the quantum wavefunction. Nature 474, 188 (2011)
Hofmann, H.F.: On the role of complex phases in the quantum statistics of weak measurements. New J. Phys. 13, 103009 (2011)
Lundeen, J.S., Bamber, C.: Procedure for direct measurement of general quantum states using weak measurement. Phys. Rev. Lett. 108, 070402 (2012)
Hofmann, H.F.: Complex joint probabilities as expressions of reversible transformations in quantum mechanics. New J. Phys. 14, 043031 (2012)
Morita, T., Sasaki, T., Tsutsui, I.: Complex probability measure and Aharonov’s weak value. Progress of Theoretical and Experimental Physics (2013)
Das, D.: Estimation of quantum states by weak and projective measurements. Phys. Rev. A 89, 062121 (2014)
Dressel, J.: Weak values as interference phenomena. Phys. Rev. A 91, 032116 (2014)
Hofmann, H.F.: How weak values emerge in joint measurements on cloned quantum systems. Phys. Rev. Lett. 109, 020408 (2012)
Bednorz, A., Franke, K., Belzig, W.: Noninvasiveness and time symmetry of weak measurements. New J. Phys. 15, 023043 (2013)
Maccone, L., Rusconi, C.C.: State estimation: a comparison between direct state measurement and tomography. Phys. Rev. A 89, 022122 (2014)
Mochizuki, R.: Weak value as an indicator of back-action. Progress of Theoretical and Experimental Physics (2014)
Ipsen, A.C.: Disturbance in weak measurements and the difference between quantum and classical weak values. Phys. Rev. A 91, 062120 (2014)
Cohen, E., Pollak, E.: Determination of weak values of quantum operators using only strong measurements. Phys. Rev. A 98, 042112 (2018)
Matzkin, A.: Weak values and quantum properties. Found. Phys. 49, 298 (2019)
Hofmann, H.F.: Derivation of quantum mechanics from a single fundamental modification of the relations between physical properties. Phys. Rev. A 89, 042115 (2014)
Hofmann, H.F.: On the fundamental role of dynamics in quantum physics. Eur. Phys. J 70, 118 (2016)
Hibino, K., Fujiwara, K., Wu, J.-Y., Iinuma, M., Hofmann, H.F.: Derivation of quantum statistics from the action of unitary dynamics. Eur. Phys. J. 133, 118 (2018)
Patekar, K., Hofmann, H.F.: The role of system-meter entanglement in controlling the resolution and decoherence of quantum measurements. New J. Phys. 21, 103006 (2019)
Hartle, J.B.: Quantum mechanics with extended probabilities. Phys. Rev. A 78, 012108 (2008)
Dressel, J., Bliokh, K.Y., Nori, F.: Classical Field Approach to Quantum Weak Measurements. Phys. Rev. Lett. 112, 110407 (2014)
Hofmann, H.F.: Quantum paradoxes originating from the nonclassical statistics of physical properties related to each other by half-periodic transformations. Phys. Rev. A 91, 062123 (2015)
Hofmann, H.F.: Quantum interference of position and momentum: a particle propagation paradox. Phys. Rev. A 96, 020101(R) (2017)
Hofmann, H.F.: Control of particle propagation beyond the uncertainty limit by interference between position and momentum. Phys. Rev. A 98, 052104 (2018)
Hofmann, H.F.: A quantum magic bullet: hitting two targets without a clear line-of-sight, e-print arXiv:1909.09259 (2019)
Acknowledgements
This work has been supported by JST-CREST (JPMJCR1674), Japan Science and Technology Agency.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hofmann, H.F. Quantum Causality Relations and the Emergence of Reality from Coherent Superpositions. Found Phys 50, 1809–1823 (2020). https://doi.org/10.1007/s10701-020-00346-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-020-00346-4