# Timelessness Strictly inside the Quantum Realm

## Abstract

**:**

## 1. Classical World, CM

## 2. Quantum Realm, QM

## 3. Time Is Relational

## 4. Fundamental Directionality

## 5. Timelessness Strictly inside QM, Experiments with Slits

_{60}and C

_{82}[101,102].

## 6. Tunneling

## 7. The Mosaic

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Interpretations of Quantum Mechanics. Available online: https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (accessed on 15 July 2020).
- Zeilinger, A. On the Interpretation and Philosophical Foundation of Quantum Mechanics. In Vastakohtien todellisuus (Festschrift for K.V. Laurikainen); Ketvel, U., et al., Eds.; Helsinki University Press: Helsinki, Finland, 1996. [Google Scholar]
- Gell-Mann, M.; Hartle, J.B. Classical equations for quantum systems. Phys. Rev. D
**1993**, 47, 3345–3382. [Google Scholar] [CrossRef] [Green Version] - Jennings, D.; Leifer, M. No return to classical reality. Contemp. Phys.
**2016**, 57, 60–82. [Google Scholar] [CrossRef] [Green Version] - Zurek, W.H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys.
**2003**, 75, 715–775. [Google Scholar] [CrossRef] [Green Version] - Hagar, A. Decoherence: The view from the history and philosophy of science. Philos. Trans. R. Soc. A
**2012**, 370, 4594–4609. [Google Scholar] [CrossRef] - Zeh, H.D. On the interpretation of measurement in quantum theory. Found. Phys.
**1970**, 1, 69–76. [Google Scholar] [CrossRef] - Schlosshauer, M. Quantum decoherence. Phys. Rep.
**2019**, 831, 1–57. [Google Scholar] [CrossRef] [Green Version] - Novotny, J.; Alber, G.; Jex, I. Entanglement and Decoherence: Fragile and Robust Entanglement. Phys. Rev. Lett.
**2011**, 107, 090501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, Z.-C.; Gao, F.; Cao, T.-Q.; Qin, S.-J.; Wen, Q.-Y. Entanglement as a resource to distinguish orthogonal product states. Sci. Rep.
**2016**, 6, 30493. [Google Scholar] [CrossRef] [PubMed] - Lesovik, G.B.; Sadovskyy, I.A.; Lebedev, A.V.; Suslov, M.V.; Vinokur, V.M. Quantum H-theorem and irreversibility in quantum mechanics. arXiv
**2013**, arXiv:1312.7146. [Google Scholar] - Lesovik, G.B.; Sadovskyy, I.A.; Suslov, M.V.; Lebedev, A.V.; Vinokur, V.M. Arrow of time and its reversal on the IBM quantum computer. Sci. Rep.
**2019**, 9, 1–8. [Google Scholar] [CrossRef] [Green Version] - Gambini, R.; García-Pintos, L.P.; Pullin, J. Single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties. Phys. Rev. A
**2019**, 100, 012113. [Google Scholar] [CrossRef] [Green Version] - Penrose, R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravit.
**1996**, 28, 581–600. [Google Scholar] [CrossRef] - Jivulescu, M.A.; Lupa, N.; Nechita, I. Thresholds for reduction-related entanglement criteria in quantum information theory. Quantum Inf. Comput.
**2015**, 15, 1165–1184. [Google Scholar] - Javanmard, Y.; Trapin, D.; Bera, S.; Bardarson, J.H.; Heyl, M. Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain. New J. Phys.
**2018**, 20, 083032. [Google Scholar] [CrossRef] - Weilenmann, M.; Dive, B.; Trillo, D.; Aguilar, E.A.; Navascués, M. Entanglement Detection beyond Measuring Fidelities. Phys. Rev. Lett.
**2020**, 124, 200502. [Google Scholar] [CrossRef] - Frauchiger, D.; Renner, R. Quantum theory cannot consistently describe the use of itself. Nat. Commun.
**2018**, 9, 1–10. [Google Scholar] [CrossRef] - Thomsen, K. We just cannot have classical and quantum behavior at the same TIME. arXiv
**2018**, arXiv:1901.01841. [Google Scholar] - Laloë, F. Can quantum mechanics be considered consistent? A discussion of Frauchiger and Renner’s argument. arXiv
**2018**, arXiv:1802.06396v3. [Google Scholar] - Sudbery, A. Single-World Theory of the Extended Wigner’s Friend Experiment. Found. Phys.
**2017**, 47, 658–669. [Google Scholar] [CrossRef] [Green Version] - Lazarovici, D.; Hubert, M. How Quantum Mechanics can consistently describe the use of itself. Sci. Rep.
**2019**, 9, 1–8. [Google Scholar] [CrossRef] [Green Version] - Kastner, R.E. Unitary-Only Quantum Theory Cannot Consistently Describe the Use of Itself: On the Frauchiger–Renner Paradox. Found. Phys.
**2020**, 50, 441–456. [Google Scholar] [CrossRef] [Green Version] - Araújo, M. The Flaw in Frauchiger and Renner’s Argument. Available online: https://mateusaraujo.info/2018/10/24/the-flaw-in-frauchiger-and-renners-argument/ (accessed on 27 January 2021).
- Yan, B.; Sinitsyn, N.A. Recovery of Damaged Information and the Out-of-Time-Ordered Correlators. Phys. Rev. Lett.
**2020**, 125, 040605. [Google Scholar] [CrossRef] [PubMed] - Gisin, N. Stochastic quantum dynamics and relativity. Helv. Phys. Acta
**1989**, 62, 363–371. [Google Scholar] [CrossRef] - Page, D.; Wootters, W.K. Evolution without evolution: Dynamics described by stationary observables. Phys. Rev. D
**1983**, 27, 2885–2892. [Google Scholar] [CrossRef] - Schild, A. Time in quantum mechanics: A fresh look at the continuity equation. Phys. Rev. A
**2018**, 98, 052113. [Google Scholar] [CrossRef] [Green Version] - Maccone, L.; Sacha, K. Quantum Measurements of Time. Phys. Rev. Lett.
**2020**, 124, 110402. [Google Scholar] [CrossRef] [Green Version] - Unruh, W.G.; Wald, R.M. Time and the interpretation of canonical quantum gravity. Phys. Rev. D
**1989**, 40, 2598–2614. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zeilinger, A. A foundational principle for quantum mechanics. Found. Phys.
**1999**, 29, 631–643. [Google Scholar] [CrossRef] - Minkowski, H. Raum und Zeit. Phys. Z.
**1909**, 10, 104–111. [Google Scholar] - Rovelli, C. Forget time, ‘First Community Prize’ of the FQXi ‘The Nature of Time’ Essay Contest. arXiv
**2009**, arXiv:0903.3832. [Google Scholar] - Barbour, J. The End of Time: The Next Revolution in Our Understanding of the Universe; Oxford University Press: Oxford, UK, 1999. [Google Scholar]
- Alexander, H.G. The Leibniz-Clarke Correspondence: With Extracts from Newton’s ‘Principia’ and ‘Optiks’; Manchester University Press: Manchester, UK, 1956. [Google Scholar]
- Mach, E. Die Mechanik in Ihrer Entwicklung Historisch-Kritsch Dargestellt; Xenomoi Verlag: Leipzig, Germany, 1883. [Google Scholar]
- Einstein, A. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik
**1916**, 49, 769–822. [Google Scholar] [CrossRef] [Green Version] - Hecht, E. The physics of time and the arrow thereof. Eur. J. Phys.
**2017**, 39, 015801. [Google Scholar] [CrossRef] - Ranković, S.; Liang, Y.-C.; Renner, R. Quantum clocks and their synchronisation—The Alternate ticks Game. arXiv
**2015**, arXiv:1506.01373. [Google Scholar] - Woods, M.P. Autonomous Ticking Clocks from Axiomatic Principles. Quantum
**2021**, 5, 381. [Google Scholar] [CrossRef] - Anderson, E. Problem of time in quantum gravity. Ann. Phys.
**2012**, 524, 757–786. [Google Scholar] [CrossRef] [Green Version] - Fiscaletti, D. The Timeless Approach: Frontier Perspectives in 21st Century Physics; World Scientific: Singapore, 2016. [Google Scholar]
- Smolin, L. Temporal relationalism. In Beyond Spacetime; Huggett, N., Matsubara, K., Wuthrich, C., Eds.; Cambridge University Press: Cambridge, UK, 2018. [Google Scholar]
- Sears, A.P.; Petrenko, A.; Catelani, G.; Sun, L.; Paik, H.; Kirchmair, G.; Frunzio, L.; Glazman, L.I.; Girvin, S.M.; Schoelkopf, R.J. Photon shot noise dephasing in the strong-dispersive limit of circuit QED. Phys. Rev. B
**2012**, 86, 180504. [Google Scholar] [CrossRef] [Green Version] - Evans, D.J.; Searles, D.J. Equilibrium microstates which generate second law violating steady states. Phys. Rev. E
**1994**, 50, 1645–1648. [Google Scholar] [CrossRef] [Green Version] - Harrington, P.M.; Tan, D.; Naghiloo, M.; Murch, K.W. Characterizing a Statistical Arrow of Time in Quantum Measurement Dynamics. Phys. Rev. Lett.
**2019**, 123, 020502. [Google Scholar] [CrossRef] [Green Version] - Manikandan, S.K.; Elouard, C.; Jordan, A.N. Fluctuation theorems for continuous quantum measurements and absolute irreversibility. Phys. Rev. A
**2019**, 99, 022117. [Google Scholar] [CrossRef] [Green Version] - Linden, N.; Popescu, S.; Short, A.J.; Winter, A. Quantum evolution towards thermal equilibrium. Phys. Rev. E
**2009**, 79, 1–12. [Google Scholar] [CrossRef] [Green Version] - Malabarba, A.S.L.; García-Pintos, L.P.; Linden, N.; Farrelly, T.; Short, A.J. Quantum systems equilibrate rapidly for most observables. Phys. Rev. E
**2014**, 90, 012121. [Google Scholar] [CrossRef] [Green Version] - Landauer, R. Irreversibility and Heat Generation in the Computing Process. IBM J. Res. Dev.
**1961**, 5, 183–191. [Google Scholar] [CrossRef] - Landauer, R. Information is Physical. Phys. Today
**1991**, 44, 23–29. [Google Scholar] [CrossRef] - Yan, L.L.; Xiong, T.P.; Rehan, K.; Zhou, F.; Liang, D.F.; Chen, L.; Zhang, J.Q.; Yang, W.L.; Ma, Z.H.; Feng, M. Single-Atom Demonstration of the Quantum Landauer Principle. Phys. Rev. Lett.
**2018**, 120, 210601. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gaudenzi, R.; Burzurí, E.; Maegawa, S.; Van Der Zant, H.S.J.; Luis, F. Quantum Landauer erasure with a molecular nanomagnet. Nat. Phys.
**2018**, 14, 565–568. [Google Scholar] [CrossRef] [Green Version] - Bennett, C.H. Notes on Landauer’s principle, reversible computation, and Maxwell’s Demon. Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys.
**2003**, 34, 501–510. [Google Scholar] [CrossRef] [Green Version] - Vaccaro, J.A.; Barnett, S.M. Information erasure without an energy cost. Proc. R. Soc. A Math. Phys. Eng. Sci.
**2011**, 467, 1770–1778. [Google Scholar] [CrossRef] [Green Version] - Sagawa, T.; Ueda, M. Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure. Phys. Rev. Lett.
**2009**, 102, 250602. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Streltsov, A.; Singh, U.; Dhar, H.S.; Bera, M.N.; Adesso, G. Measuring Quantum Coherence with Entanglement. Phys. Rev. Lett.
**2015**, 115, 020403. [Google Scholar] [CrossRef] [Green Version] - Miller, H.J.D.; Guarnieri, G.; Mitchison, M.T.; Goold, J. Quantum Fluctuations Hinder Finite-Time Information Erasure near the Landuaer Limit. Phys. Rev. Lett.
**2020**, 125, 160602. [Google Scholar] [CrossRef] - Jacobs, K. Deriving Landauer’s erasure principle from statistical mechanics. arXiv
**2005**, arXiv:quant-ph/0512105. [Google Scholar] - Goold, J.; Paternostro, M.; Modi, K. A non-equilibrium quantum Landauer principle. arXiv
**2015**, arXiv:1402.4499. [Google Scholar] - Holevo, A. Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inf. Transm.
**1973**, 9, 3–11. [Google Scholar] - Plenio, M.B. The Holevo bound and Landauer’s principle. Phys. Lett. A
**1999**, 263, 281–284. [Google Scholar] [CrossRef] [Green Version] - Cramer, J.G. The transactional interpretation of quantum mechanics. Rev. Mod. Phys.
**1986**, 58, 647–687. [Google Scholar] [CrossRef] - Pfau, T.; Spälter, S.; Kurtsiefer, C.; Ekstrom, C.R.; Mlynek, J. Loss of Spatial Coherence by a Single Spontaneous Emission. Phys. Rev. Lett.
**1994**, 73, 1223–1226. [Google Scholar] [CrossRef] [Green Version] - Kokorowski, D.A.; Cronin, A.D.; Roberts, T.D.; Pritchard, D.E. From single- to multiple-photon decoherence in an atom interferometer. Phys. Rev. Lett.
**2001**, 86, 2191–2195. [Google Scholar] [CrossRef] [Green Version] - Drossel, B.; Ellis, F.R. Contextual wavefunction collapse: An integrated theory of quantum measurement. N. J. Phys.
**2018**, 20, 113025. [Google Scholar] [CrossRef] - Lucia, U.; Grisolia, G. Time: A Constructal viewpoint & its consequences. Sci. Rep.
**2019**, 9, 1–7. [Google Scholar] [CrossRef] [Green Version] - Bloch, F. Nuclear Induction. Phys. Rev.
**1946**, 70, 460–474. [Google Scholar] [CrossRef] - Fuchs, C.A. Information Gain vs. State Disturbance in Quantum Theory. Quantum Comput.
**2004**, 96, 229–259. [Google Scholar] [CrossRef] [Green Version] - Qing-Yu, C. Information Erasure and Recovery in Quantum Memory. Chin. Phys. Lett.
**2004**, 21, 1189–1190. [Google Scholar] [CrossRef] [Green Version] - Lin, Y.; Gaebler, J.; Reiter, F.; Tan, T.R.; Bowler, R.; Sørensen, A.S.; Leibfried, D.; Wineland, D.J. Dissipative production of a maximally entangled steady state of two quantum bits. Nat. Cell Biol.
**2013**, 504, 415–418. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Shankar, S.; Hatridge, M.; Leghtas, Z.; Sliwa, K.M.; Narla, A.; Vool, U.; Girvin, S.M.; Frunzio, L.; Mirrahimi, M.; Devoret, M.H. Autonomously stabilized entanglement between two superconducting quantum bits. Nat. Cell Biol.
**2013**, 504, 419–422. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nakajima, T.; Delbecq, M.R.; Otsuka, T.; Amaha, S.; Yoneda, J.; Noiri, A.; Takeda, K.; Allison, G.; Ludwig, A.; Wieck, A.D.; et al. Coherent transfer of electron spin correlations assisted by dephasing noise. Nat. Commun.
**2018**, 9, 2133. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Aharonov, Y.; Bergmann, P.G.; Lebowitz, J.L. Time Symmetry in the Quantum Process of Measurement. Phys. Rev.
**1964**, 134, B1410–B1416. [Google Scholar] [CrossRef] - Ellis, F.R.; Drossel, B. Emergence of time. Found. Phys.
**2020**, 50, 161–190. [Google Scholar] [CrossRef] [Green Version] - Zhou, Z.-Y.; Zhu, Z.-H.; Liu, S.-L.; Li, Y.-H.; Shi, S.; Ding, D.-S.; Chen, L.-X.; Gao, W.; Guo, G.-C.; Shi, B.-S. Quantum twisted double-slits experiments: Confirming wavefunctions’ physical reality. Sci. Bull.
**2017**, 62, 1185–1192. [Google Scholar] [CrossRef] [Green Version] - Lamb, W.E. An operational interpretation of nonrelativistic quantum mechanics. Phys. Today
**1969**, 22, 23–28. [Google Scholar] [CrossRef] - Pusey, M.; Barrett, J.; Rudolph, T. On the reality of the quantum state. Nat. Phys.
**2012**, 8, 475–478. [Google Scholar] [CrossRef] [Green Version] - Leifer, M.S. Is the Quantum State Real? An Extended Review of ψ-ontology Theorems. Quanta
**2014**, 3, 67. [Google Scholar] [CrossRef] - Fields, C. Decoherence as a sequence of entanglement swaps. Results Phys.
**2019**, 12, 1888–1892. [Google Scholar] [CrossRef] - Bohr, N. Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Phys. Rev.
**1935**, 48, 696–702. [Google Scholar] [CrossRef] - Wheeler, A. The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics; Davies, P.C.W., Brown, J.R., Eds.; Cambridge University Press: Cambridge, UK, 1993. [Google Scholar]
- Singh, T.P. The Problem of Time and the Problem of Quantum Measurement. arXiv
**2012**, arXiv:1210.8110. [Google Scholar] - Renninger, M. Messungen ohne Störung des Meßobjekts. Zeitschrift Physik
**1960**, 158, 417–421. [Google Scholar] [CrossRef] - Vaidman, L. The Meaning of the Interaction-Free Measurements. Found. Phys.
**2003**, 33, 491–510. [Google Scholar] [CrossRef] - Bohr, N. Quantum Physics and Philosophy: Causality and Complementarity. In Philosophy in Mid-Century: A Survey; Klibansky, R., Ed.; La Nuova Italia Editrice: Florence, Italy, 1963. [Google Scholar]
- Miller, W.A.; Wheeler, J.A. International Symposium on Foundations of Quantum Mechanics in the Light of New Technology; Physical Society: Tokyo, Japan, 1983. [Google Scholar]
- Aspect, A. Bell’s inequality test: More ideal than ever. Nat. Cell Biol.
**1999**, 398, 189–190. [Google Scholar] [CrossRef] - Clemente, L.; Kofler, J. Necessary and sufficient conditions for macroscopic realism from quantum mechanics. Phys. Rev. A
**2015**, 91, 062103. [Google Scholar] [CrossRef] [Green Version] - Gomes, H. Timeless Configuration Space and the Emergence of Classical Behavior. Found. Phys.
**2018**, 48, 668–715. [Google Scholar] [CrossRef] [Green Version] - Pauli, W. The General Principles of Quantum Mechanics; Springer Verlag: Berlin/Heidelberg, Germany, 1980. [Google Scholar]
- Kullie, O. Tunneling time in attosecond experiments and the time-energy uncertainty relation. Phys. Rev. A
**2015**, 92, 052118. [Google Scholar] [CrossRef] [Green Version] - Kullie, O. Time Operator, Real Tunneling Time in Strong Field Interaction and the Attoclock. Quantum Rep.
**2020**, 2, 233–252. [Google Scholar] [CrossRef] [Green Version] - Bender, C.M.; Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT-symmetry. Phys. Rev. Lett.
**1998**, 80, 5243–5246. [Google Scholar] [CrossRef] [Green Version] - Klauck, F.; Teuber, L.; Ornigotti, M.; Heinrich, M.; Scheel, S.; Szameit, A. Observation of PT-symmetric quantum interference. Nat. Photonics
**2019**, 13, 883–887. [Google Scholar] [CrossRef] [Green Version] - Graefe, E.-M. PT symmetry dips into two-photon interference. Nat. Photonics
**2019**, 13, 822–823. [Google Scholar] [CrossRef] - Li, J.; Wang, T.; Luo, L. Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions. arXiv
**2020**, arXiv:2004.01364. [Google Scholar] - Riek, R. A Derivation of a Microscopic Entropy and Time Irreversibility from the Discreteness of Time. Entropy
**2014**, 16, 3149–3172. [Google Scholar] [CrossRef] [Green Version] - Elitzur, A.C.; Dolev, S. Quantum Phenomena Within a New Theory of Time. In Quo Vadis Quantum Mechanics? Elitzur, A.C., Dolev, S., Kolenda, N., Eds.; Springer: Berlin, Germany, 2005. [Google Scholar]
- Merli, P.G.; Missiroli, G.F.; Pozzi, G. On the statistical aspect of electron interference phenomena. Am. J. Phys.
**1976**, 44, 306–307. [Google Scholar] [CrossRef] [Green Version] - Arndt, M.; Nairz, O.; Vos-Andreae, J.; Keller, C.; Van Der Zouw, G.; Zeilinger, A. Wave–particle duality of C60 molecules. Nat. Cell Biol.
**1999**, 401, 680–682. [Google Scholar] [CrossRef] - Nairz, O.; Arndt, M.; Zeilinger, A. Quantum interference experiments with large molecules. Am. J. Phys.
**2003**, 71, 319–325. [Google Scholar] [CrossRef] [Green Version] - Sawant, R.; Samuel, J.; Sinha, A.; Sinha, S.; Sinha, U. Nonclassical Paths in Quantum Interference Experiments. Phys. Rev. Lett.
**2014**, 113, 120406. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sinha, A.; Vijay, A.H.; Sinha, U. On the superposition principle in interference experiments. Sci. Rep.
**2015**, 5, 10304. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sorkin, R.D. Quantum mechanics as quantum measure theory. Mod. Phys. Lett. A
**1994**, 9, 3119–3127. [Google Scholar] [CrossRef] [Green Version] - Rengaraj, G.; Prathwiraj, U.; Sahoo, S.N.; Somashekhar, R.; Sinha, U. Measuring the deviation from the superposition principle in interference experiments. New J. Phys.
**2018**, 20, 063049. [Google Scholar] [CrossRef] - Magana-Loaiza, O.S.; De Leon, I.; Mirhosseini, M.; Fickler, R.; Safari, A.; Mick, U.; McIntyre, B.; Banzer, P.; Rodenburg, B.; Leuchs, G.; et al. Exotic looped trajectories of photons in three-slit interference. Nat. Commun.
**2016**, 7, 13987. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Da Paz, I.G.; Vieira, C.; Ducharme, R.; Cabral, L.; Alexander, H.; Sampaio, M.D.R. Gouy phase in nonclassical paths in a triple-slit interference experiment. Phys. Rev. A
**2016**, 93, 033621. [Google Scholar] [CrossRef] [Green Version] - Hackermüller, L.; Hornberger, K.; Brezger, B.; Zeilinger, A.; Arndt, M. Decoherence of matter waves by thermal emission of radiation. Nat. Cell Biol.
**2004**, 427, 711–714. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hornberger, K.; Uttenthaler, S.; Brezger, B.; Hackermüller, L.; Arndt, M.; Zeilinger, A. Collisional Decoherence Observed in Matter Wave Interferometry. Phys. Rev. Lett.
**2003**, 90, 160401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Coles, P.J.; Kaniewski, J.; Wehner, S. Equivalence of wave–particle duality to entropic uncertainty. Nat. Commun.
**2014**, 5, 5814. [Google Scholar] [CrossRef] [Green Version] - Barbieri, M.; Goggin, M.E.; de Almeida, M.P.; Lanyon, B.P.; White, A.G. Complementarity in variable strength quantum non-demolition measurements. New J. Phys.
**2009**, 11, 093012. [Google Scholar] [CrossRef] - Kolenderski, P.; Scarcella, C.; Johnsen, K.D.; Hamel, D.R.; Holloway, C.; Shalm, L.K.; Tisa, S.; Tosi, A.; Resch, K.J.; Jennewein, T. Time-resolved double-slit interference pattern measurement with entangled photons. Sci. Rep.
**2014**, 4, 4685. [Google Scholar] [CrossRef] - Kocsis, S.; Braverman, B.; Ravets, S.; Stevens, M.J.; Mirin, R.P.; Shalm, L.K.; Steinberg, A.M. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer. Conf. Lasers Electro-Opt.
**2011**, 332, 1170–1173. [Google Scholar] [CrossRef] - Xiao, Y.; Wiseman, H.M.; Xu, J.-S.; Kedem, Y.; Li, C.-F.; Guo, G.-C. Observing momentum disturbance in double-slit «which-way» measurements. Sci. Adv.
**2019**, 5, eaav:9547. [Google Scholar] [CrossRef] [Green Version] - Mahler, D.H.; Rozema, L.; Fisher, K.; Vermeyden, L.; Resch, K.J.; Wiseman, H.M.; Steinberg, A. Experimental nonlocal and surreal Bohmian trajectories. Sci. Adv.
**2016**, 2, e1501466. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wheeler, A. Mathematical Foundations of Quantum Theory; Marlow, A.R., Ed.; Academic Press: Cambridge, MA, USA, 1978. [Google Scholar]
- Jacques, V.; Wu, E.; Grosshans, F.; Treussart, F.; Grangier, P.; Aspect, A.; Roch, J.-F. Experimental Realization of Wheeler’s Delayed-Choice Gedanken Experiment. Science
**2007**, 315, 966–968. [Google Scholar] [CrossRef] [Green Version] - Manning, A.G.; Khakimov, R.I.; Dall, R.G.; Truscott, A.G. Wheeler’s delaced-choice gedanken experiment with a single atom. Nat. Phys.
**2015**, 11, 539–544. [Google Scholar] [CrossRef] - Leung, C.; Brown, A.; Nguyen, H.; Friedman, A.; Kaiser, D.I.; Gallicchio, J. Astronomical random numbers for quantum foundations experiments. Phys. Rev. A
**2018**, 97, 042120. [Google Scholar] [CrossRef] [Green Version] - Afshar, S.S.; Flores, E.; McDonald, K.F.; Knoesel, E. Paradox in Wave-Particle Duality. Found. Phys.
**2007**, 37, 295–305. [Google Scholar] [CrossRef] [Green Version] - Jacques, V.; Lai, N.D.; Dréau, A.; Zheng, D.; Chauvat, D.; Treussart, F.; Grangier, P.; Roch, J.-F. Illustration of quantum complementarity using single photons interfering on a grating. New J. Phys.
**2008**, 10, 123009. [Google Scholar] [CrossRef] - Horsman, D.; Heunen, C.; Pusey, M.; Barrett, J.; Spekkens, R.W. Can a quantum state over time resemble a quantum state at a single time? Proc. R. Soc. A Math. Phys. Eng. Sci.
**2017**, 473, 20170395. [Google Scholar] [CrossRef] - Masanes, L.; Galley, T.D.; Müller, M.P. The measurement postulates of quantum mechanics are operationally redundant. Nat. Commun.
**2019**, 10, 1–6. [Google Scholar] [CrossRef] [Green Version] - Khrennikov, A. Born’s rule from measurements of classical signals by threshold detectors which are properly calibrated. J. Mod. Opt.
**2012**, 59, 667–678. [Google Scholar] [CrossRef] [Green Version] - La Cour, B.R.; Williamson, M.C. Emergence of the Born rule in quantum optics. Quantum
**2020**, 4, 350. [Google Scholar] [CrossRef] - Riek, R. On the nature of the Born rule. arXiv
**2019**, arXiv:1901.03663. [Google Scholar] - Lindgren, J.; Liukkonen, J. Quantum Mechanics can be understood through stochastic optimization on spacetimes. Sci. Rep.
**2019**, 9, 1–8. [Google Scholar] [CrossRef] - Barbour, J.; Koslowski, T.; Mercati, F. Identification of a Gravitational Arrow of Time. Phys. Rev. Lett.
**2014**, 113, 181101. [Google Scholar] [CrossRef] [Green Version] - Anderson, E. Records Theory. Int. J. Mod. Phys. D
**2009**, 18, 635–667. [Google Scholar] [CrossRef] [Green Version] - Zurek, W.H. Quantum Darwinism, classical reality, and the randomness of quantum jumps. Phys. Today
**2014**, 67, 44–50. [Google Scholar] [CrossRef] [Green Version] - Riedel, C.J.; Zurek, W.H.; Zwolak, M. Objective past of a quantum universe: Redundant records of consistent histories. Phys. Rev. A
**2016**, 93, 032126. [Google Scholar] [CrossRef] [Green Version] - Winful, H.G. Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox. Phys. Rep.
**2006**, 436, 1–69. [Google Scholar] [CrossRef] - Raciti, F.; Salesi, G. Complex-barrier tunnelling times. J. Phys. I
**1994**, 4, 1783–1789. [Google Scholar] [CrossRef] [Green Version] - Nimtz, G.; Spieker, H.; Brodowsky, H.M. Tunneling with dissipation. J. Phys. I
**1994**, 4, 1379–1382. [Google Scholar] [CrossRef] - Torlina, L.; Morales, F.; Kaushal, J.; Ivanov, I.; Kheifets, A.; Zielinski, A.; Scrinzi, A.; Muller, H.G.; Sukiasyan, S.; Ivanov, M.; et al. Interpreting attoclock measurements of tunnelling times. Nat. Phys.
**2015**, 11, 503–508. [Google Scholar] [CrossRef] [Green Version] - Sainadh, U.S.; Xu, H.; Wang, X.; Atia-Tul-Noor, A.; Wallace, W.C.; Douguet, N.; Bray, A.; Ivanov, I.; Bartschat, K.; Kheifets, A.; et al. Attosecond angular streaking and tunnelling time in atomic hydrogen. Nat. Cell Biol.
**2019**, 568, 75–77. [Google Scholar] [CrossRef] [Green Version] - Mandelstam, L.; Tamm, I. The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics. Phaenomenologica
**1991**, 9, 115–123. [Google Scholar] [CrossRef] - Urbanowski, K. Remarks on the uncertainty relations. Mod. Phys. Lett. A
**2020**, 35, 2050219. [Google Scholar] [CrossRef] - Quiao, C.; Ren, Z.-Z. Uncertainty in Larmor clock. Chin. Phys. C
**2011**, 35, 992–996. [Google Scholar] [CrossRef] - Spierings, D.C.; Steinberg, A.M. Tunneling takes less time when it’s less probable. arXiv
**2021**, arXiv:2101.12309v1. [Google Scholar] - Busch, P. The Time-Energy Uncertainty Relation. Lect. Notes. Phys.
**2008**, 734, 73–105. [Google Scholar] - Dumont, R.S.; Rivlin, T.; Pollak, E. The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling. New J. Phys.
**2020**, 22, 093060. [Google Scholar] [CrossRef] - Capellmann, H. Space-Time in Quantum Theory. Found. Phys.
**2021**, 51, 1–34. [Google Scholar] [CrossRef] - Ren, C.; Hofmann, H.F. Analysis of the time-energy entanglement of down-converted photon pairs by correlated single-photon interference. Phys. Rev. A
**2012**, 86, 04823. [Google Scholar] [CrossRef] [Green Version] - Hatridge, M.; Shankar, S.; Mirrahimi, M.; Schackert, F.; Geerlings, K.; Brecht, T.; Sliwa, K.M.; Abdo, B.; Frunzio, L.; Girvin, S.M.; et al. Quantum Back-Action of an Individual Variable-Strength Measurement. Science
**2013**, 339, 178–181. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lüders, G. Über die Zustandsänderung durch den Meßprozeß. Annalen Physik Berlin
**1950**, 443, 322–328. [Google Scholar] [CrossRef] - Minev, Z.K.; Mundhada, S.O.; Shankar, S.; Reinhold, P.; Gutiérrez-Jáuregui, R.; Schoelkopf, R.J.; Mirrahimi, M.; Carmichael, H.J.; Devoret, M.H. To catch and reverse a quantum jump mid-flight. Nature
**2019**, 570, 200–204. [Google Scholar] [CrossRef] [Green Version] - Pokorny, F.; Zhang, C.; Higgins, G.; Cabello, A.; Kleinmann, M.; Hennrich, M. Tracking the Dynamics of an Ideal Quantum Measurement. Phys. Rev. Lett.
**2020**, 124, 080401. [Google Scholar] [CrossRef] [Green Version] - Guryanova, Y.; Friis, N.; Huber, M. Ideal Projective Measurements Have Infinite Resource Costs. Quantum
**2020**, 4, 222. [Google Scholar] [CrossRef] [Green Version] - Fields, C. Some Consequences of the Thermodynamic Cost of System Identification. Entropy
**2018**, 20, 797. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Del Santo, F.; Gisin, N. Physics without determinism: Alternative interpretations of classical physics. Phys. Rev. A
**2019**, 100, 062107. [Google Scholar] [CrossRef] [Green Version] - Boekholt, T.C.N.; Zwart, S.F.P.; Valtonen, M. Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length. Mon. Not. R. Astron. Soc.
**2020**, 493, 3932–3937. [Google Scholar] [CrossRef] - Riek, R. Entropy Derived from Causality. Entropy
**2020**, 22, 647. [Google Scholar] [CrossRef] - Smolin, L. Beyond weird. New Sci.
**2019**, 24, 35–37. [Google Scholar] [CrossRef] - Ried, K.; MacLean, J.-P.W.; Spekkens, R.W.; Resch, K.J. Quantum to classical transitions in causal relations. Phys. Rev. A
**2017**, 95, 062102. [Google Scholar] [CrossRef] [Green Version] - Quantum causality. Nat. Phys.
**2014**, 10, 259–263. [CrossRef] - Procopio, L.M.; Moqanaki, A.; Araújo, M.; Costa, F.; Calafell, I.A.; Dowd, E.G.; Hamel, D.R.; Rozema, L.A.; Brukner, Č.; Walther, P. Experimental superposition of orders of quantum gates. Nat. Commun.
**2015**, 6, 7913. [Google Scholar] [CrossRef] [Green Version] - Oreshkov, O.; Costa, F.; Brukner, Č. Quantum correlations with no causal order. Nat. Commun.
**2012**, 3, 1092. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ellis, G.F.R. The evolving block universe and the meshing together of times. Ann. N. Y. Acad. Sci.
**2014**, 1326, 26–41. [Google Scholar] [CrossRef] [Green Version] - Drossel, B. What condensed matter physics and statistical physics teach us about the limits of unitary time evolution. Quantum Stud. Math. Found.
**2019**, 7, 217–231. [Google Scholar] [CrossRef] [Green Version] - Anderson, P.W. More is different, Broken symmetry and the nature of the hierarchical structure of science. Science
**1972**, 177, 393–396. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hartmann, N. Die Erkenntnis im Lichte der Ontologie, mit einer Einführung von Josef Stallmach; Felix Meiner Verlag: Hamburg, Germany, 1982. [Google Scholar]
- Haken, H. Synergetics, An Introduction: Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology, 3rd ed.; Springer: New York, NY, USA, 1983. [Google Scholar]
- Pearson, A.N.; Guryanova, Y.; Erker, P.; Laird, E.A.; Briggs, G.A.D.; Huber, M.; Ares, N. Measuring the Thermodynamic Cost of Timekeeping. Phys. Rev. X
**2021**, 11, 021029. [Google Scholar] [CrossRef] - Kiefer, C. Space, Time, Matter in Quantum Gravity. arXiv
**2009**, arXiv:0909.3767. [Google Scholar] - Verlinde, E.P. On the origin of gravity and the laws of Newton. J. High Energy Phys.
**2011**, 29, 1–27. [Google Scholar] [CrossRef] [Green Version] - Freidel, L.; Leigh, R.G.; Minic, D. Modular Spacetime and Metastring Theory. J. Phys. Conf. Ser.
**2017**, 804, 012032. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Thomsen, K.
Timelessness Strictly inside the Quantum Realm. *Entropy* **2021**, *23*, 772.
https://doi.org/10.3390/e23060772

**AMA Style**

Thomsen K.
Timelessness Strictly inside the Quantum Realm. *Entropy*. 2021; 23(6):772.
https://doi.org/10.3390/e23060772

**Chicago/Turabian Style**

Thomsen, Knud.
2021. "Timelessness Strictly inside the Quantum Realm" *Entropy* 23, no. 6: 772.
https://doi.org/10.3390/e23060772