# The Two-Time Interpretation and Macroscopic Time-Reversibility

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## Abstract

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## 1. Introduction

## 2. The Two-States-Vector Formalism

## 3. The Two-Time Interpretation

## 4. Measurement and State Reduction

## 5. Macroscopic World Also Decays

## 6. The Final Boundary Condition in the Forefront of Physics

## 7. Challenges and Horizons

- Long-lived universe—What happens when the BES occurs at a very late or even infinite time? Our answer is two-fold. First, it is not necessary to assume temporal endpoints in order to postulate forward and backward evolving states. In accordance with our proposal in [7,8] the BES can be replaced with a forward evolving “destiny” state, so even if the final projection never occurs, we can imagine another wavefunction describing the universe from its very beginning in addition to the ordinary one. Then, one may ask whether n can become comparable to N, thus threatening the above reasoning (see Equation (25)). We claim that it cannot; i.e., there is always a “macroscopic core” to every macroscopic object which initially contained N or more particles and undergone a partial collapse. It seems very plausible to assume that $\frac{dn}{dt}\le 0$ and also that $\frac{dn}{dt}\to 0$ for long enough times, assuming for example an exponential decay of the form:$$N\left(t\right)=N\left(0\right)exp(-t/T),$$
- Storage—in the TSVF, it is postulated that the final state of the Universe encodes the outcomes of all measurements performed during its lifetime. Performing one measurement, we entangle the particle with some degrees of freedom belonging to its environment, and having a specified classical state in the final boundary. More and more measurements amount to more and more entanglements, which mean more and more classical states encoded in the final boundary condition. Since the size of the final state is ultimately bounded, then so is its storage capacity. Accordingly, the number of measurements should also be bounded. Exceeding that bound would lead to a situation where the classical macroscopic state is not uniquely specified by the two-state. Moreover, imagine an experiment isolating a number of particles from the rest of the Universe. In that case, the subsequent number of measurements on the isolated system—and the time it takes to perform them—must become limited. These possibilities may suggest that the description is incomplete. Conceivably, there might be other bounds on the number of measurements which could possibly be performed in the course of the Universe’s lifetime. One such bound can be derived from the expansion of the Universe. It should significantly limit the locally available resources needed to perform measurements. Moreover, truly isolating a sub-system from the rest of the Universe to prevent decoherence, and performing measurements within it, is impossible. One reason is that there is no equivalence to a Faraday cage for gravitational waves; a second is the omnipresence of cosmic microwave background radiation. These will cause rapid decoherence to spread throughout the Universe.
- Tails—in the forgoing description of a measurement, we neglected a fractional part of the two-state in order to obtain a definite measurement outcome—the justification for which being the tiny square amplitude of the fractional part corresponding to a negligible probability. For all practical purposes, this minute probability does not play a role (and indeed, it is a common practice to omit such rare events when dealing with statistical mechanics of large systems). However, like the Ghirardi–Rimini–Weber theory (GRW) and many-worlds interpretations, the TTI is a psi-ontic interpretation (more accurately, a two-psi-ontic interpretation). Therefore, the two-state assumes a dual role—on the one hand, it represents the probabilities for measurement outcomes; on the other hand, it is in itself the outcomes: device, observer, and environment comprising a two-state taking on different forms. This leads to a difficulty, since the neglected fraction remains a physically meaningful part of reality despite having a damped amplitude. This is analogous to the so-called “problem of tails” in the GRW interpretation [30]. In GRW, macroscopic superpositions are supposed to be eliminated when the delocalized wavefunction is spontaneously multiplied by a localized Gaussian function. However, this elimination is incomplete, as it leaves behind small-amplituded terms that are structurally isomorphic to the main term of the wavefunction [30]. Since reality is not contingent upon the size of the amplitude, the macroscopic superposition persists, which also seems to be the case in TTI. To discard the tail, one of two paths can be chosen: we can define a cutoff amplitude which for some deeper reason is the smallest meaningful amplitude, or we can tune the final state such that it will not leave any tails. We consider the latter option more appealing, but it remains largely an open problem.
- The match between the FES and BES might seem conspirative—according to another line of objection, the correspondence between the FES and the BES is miraculous considering the fact that the two are independent [31]. We think that the Universe is in some way compelled to uphold classicality, so the two boundary conditions are linked by that principle.
- Can the TTI be applied to cyclic/ekpyrotic models of the universe? That is, can we accommodate a big bounce with our FES and BES states?

## 8. Summary

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Zurek, W.H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys.
**2003**, 75, 715. [Google Scholar] [CrossRef] - Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys.
**2005**, 76, 1267–1305. [Google Scholar] [CrossRef] - Aharonov, Y.; Bergmann, P.G.; Lebowitz, J.L. Time symmetry in the quantum process of measurement. Phys. Rev. B
**1964**, 134, 1410–1416. [Google Scholar] [CrossRef] - Aharonov, Y.; Vaidman, L. The two-state vector formalism of quantum mechanics. In Time in Quantum Mechanics; Muga, J.G., Sala Mayato, R., Egusquiza, I.L., Eds.; Springer: Berlin/Heidelberg, Germany, 2002; pp. 369–412. [Google Scholar]
- Aharonov, Y.; Reznik, B. How macroscopic properties dictate microscopic probabilities. Phys. Rev. A
**2002**, 65, 052116. [Google Scholar] [CrossRef] - Aharonov, Y.; Rohrlich, D. Quantum Paradoxes: Quantum Theory for the Perplexed; Wiley: New York, NY, USA, 2005; pp. 16–18. [Google Scholar]
- Aharonov, Y.; Gruss, E.Y. Two time interpretation of quantum mechanics. arXiv
**2005**. [Google Scholar] - Aharonov, Y.; Cohen, E.; Gruss, E.; Landsberger, T. Measurement and collapse within the two-state-vector formalism. Quantum Stud. Math. Found.
**2014**, 1, 133–146. [Google Scholar] [CrossRef] - Aharonov, Y.; Cohen, E.; Elitzur, A.C. Can a future choice affect a past measurement’s outcome? Ann. Phys.
**2015**, 355, 258–268. [Google Scholar] [CrossRef] - Aharonov, Y.; Cohen, E.; Shushi, T. Accommodating retrocausality with free will. Quanta
**2016**, 5, 53–60. [Google Scholar] [CrossRef] - Cohen, E.; Aharonov, Y. Quantum to classical transitions via weak measurements and postselection. In Quantum Structural Studies: Classical Emergence from the Quantum Level; Kastner, R., Jeknic-Dugic, J., Jaroszkiewicz, G., Eds.; World Scientific: Singapore, 2016. [Google Scholar]
- Aharonov, Y.; Albert, D.Z.; Vaidman, L. How the result of a measurement of a component of a spin 1/2 particle can turn out to be 100? Phys. Rev. Lett.
**1988**, 60, 1351–1354. [Google Scholar] [CrossRef] [PubMed] - Aharonov, Y.; Cohen, E.; Elitzur, A.C. Foundations and applications of weak quantum measurements. Phys. Rev. A
**2014**, 89, 052105. [Google Scholar] [CrossRef] - Aharonov, Y.; Landsberger, T.; Cohen, E. A nonlocal ontology underlying the time-symmetric Heisenberg representation. arXiv
**2016**. [Google Scholar] - Aharonov, Y.; Colombo, F.; Cohen, E.; Landsberger, T.; Sabadini, I.; Struppa, D.C.; Tollaksen, J. Finally making sense of the double-slit experiment: A quantum particle is never a wave. P. Natl. Acad. Sci. USA
**2017**, in press. [Google Scholar] - Stoica, O.C. Smooth quantum mechanics. Philsci Arch.
**2008**. [Google Scholar] - Stoica, O.C. The universe remembers no wavefunction collapse. arXiv
**2016**. [Google Scholar] - Sutherland, R.I. Causally symmetric Bohm model. Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Mod. Phys.
**2008**, 39, 782–805. [Google Scholar] [CrossRef] - Bedingham, D.J.; Maroney, O.J.E. Time symmetry in wave function collapse. arXiv
**2016**. [Google Scholar] - Aaronson, S. Quantum computing, postselection, and probabilistic polynomial-time. Proc. R. Soc. A Math. Phy. Eng. Sci.
**2005**, 461, 3473–3482. [Google Scholar] [CrossRef] - Weng, G.F.; Yu, Y. Playing quantum games by a scheme with pre-and post-selection. Quantum Inf. Process.
**2016**, 15, 147–165. [Google Scholar] [CrossRef] - Lloyd, S.; Maccone, L.; Garcia-Patron, R.; Giovannetti, V.; Shikano, Y. Quantum mechanics of time travel through post-selected teleportation. Phys. Rev. D
**2011**, 84, 025007. [Google Scholar] [CrossRef] - Davies, P. Quantum weak measurements and cosmology. arXiv
**2013**. [Google Scholar] - Bopp, F.W. Time symmetric quantum mechanics and causal classical physics. arXiv
**2016**. [Google Scholar] - Horowitz, G.T.; Maldacena, J.M. The black hole final state. J. High Energy Phys.
**2004**, 2004, 8. [Google Scholar] [CrossRef] - Gottesman, D.; Preskill, J. Comment on “The black hole final state”. J. High Energy Phys.
**2004**, 2004, 26. [Google Scholar] [CrossRef] - Lloyd, S.; Preskill, J. Unitarity of black hole evaporation in final-state projection models. J. High Energy Phys.
**2014**, 2014, 126. [Google Scholar] [CrossRef] - Hawking, S.W. Breakdown of predictability in gravitational collapse. Phys. Rev. D
**1976**, 14, 2460–2473. [Google Scholar] [CrossRef] - Maldacena, J. The large-N limit of superconformal field theories and supergravity. Int. J. Theor. Phys.
**1999**, 38, 1113–1133. [Google Scholar] [CrossRef][Green Version] - McQueen, K.J. Four tails problems for dynamical collapse theories. Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Mod. Phys.
**2015**, 49, 10–18. [Google Scholar] [CrossRef] - Vaidman, L. Time symmetry and the many-worlds interpretation. In Many Worlds? Everett, Realism and Quantum Mechanics; Saunders, S., Barrett, J., Kent, A., Wallacepage, D., Eds.; Oxford University Press: Oxford, UK, 2010; pp. 582–586. [Google Scholar]

**Figure 1.**The universal wavefunction according to (

**a**) the many worlds interpretation (MWI) and (

**b**) the two-state vector-formalism (TSVF).

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Aharonov, Y.; Cohen, E.; Landsberger, T. The Two-Time Interpretation and Macroscopic Time-Reversibility. *Entropy* **2017**, *19*, 111.
https://doi.org/10.3390/e19030111

**AMA Style**

Aharonov Y, Cohen E, Landsberger T. The Two-Time Interpretation and Macroscopic Time-Reversibility. *Entropy*. 2017; 19(3):111.
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**Chicago/Turabian Style**

Aharonov, Yakir, Eliahu Cohen, and Tomer Landsberger. 2017. "The Two-Time Interpretation and Macroscopic Time-Reversibility" *Entropy* 19, no. 3: 111.
https://doi.org/10.3390/e19030111