# Fundamental Irreversibility: Planckian or Schrödinger–Newton?

## Abstract

**:**

## 1. Introduction

## 2. Irreversibility at Planck Scale

## 3. Irreversibility in the Schrödinger–Newton Context

## 4. Planck Scale or Schrödinger–Newton Context?

## 5. Concluding Remarks

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

11^{10}Aharonov: His office and desk are almost empty, no personal library, no paper piles. He is at most 50 or so. He sits behind the desk, smokes a long fat cigar, makes a phone call, and asks that I take a seat.We await David Bohm, who I will also be introduced to. Until then, I can unfold my quantum-gravity idée fix. David Bohm arrives. He is at least in his 60s, but could be 70. I am listening as Aharonov explains the superstring to Bohm who is repeatedly asking questions. Finally, I also communicate my layman’s views; Bohm’s criticism is also akin. Aharonov allows me to speak, but first tells Bohm with hellish intensively what he could not have heard. Aharonov dislikes gravitational noise; he prefers dynamics. However, at the end, my master equation and the pure state representation may have caught him a bit. He understood everything very well, he spoke steadily, with real firmness and organization.He got two offprints (localization + orthog.)Peres will send money for me.13^{30}We say goodbye.Left margin: Bohm looked at the master equation intently! Immediately, he also knew that decoherence ≠ reduction.

## References

- Bronstein, M. Quantentheorie schwacher Gravitationsfelder. Phys. Z. Sowjetunion
**1936**, 9, 140–157. (In German) [Google Scholar] - Bronstein, M.P. Kvantovanie gravitatsionnykh voln. Zh. Eksp. Theor. Fiz.
**1936**, 6, 195–236. (In Russian) [Google Scholar] - Gorelik, G.M. Matvei Bronstein and quantum gravity: 70th anniversary of the unsolved problem. Usp. Fiz. Nauk
**2005**, 48, 1039–1053. [Google Scholar] [CrossRef] - Wheeler, J.A. Geometrodynamics; Academic Press: New York, NY, USA, 1962. [Google Scholar]
- Bekenstein, J.D. Black holes and entropy. Phys. Rev. D
**1973**, 7, 2333. [Google Scholar] [CrossRef] - Hawking, S.W. Particle creation by black holes. Commun. Math. Phys.
**1975**, 43, 199–220. [Google Scholar] [CrossRef] - Hawking, S.W. The unpredictability of quantum gravity. Commun. Math. Phys.
**1982**, 87, 395–415. [Google Scholar] [CrossRef] - Ellis, J.; Hagelin, S.; Nanopoulos, D.V.; Srednicki, M. Search for violations of quantum mechanics. Nucl. Phys. B
**1984**, 241, 381–405. [Google Scholar] [CrossRef] [Green Version] - Banks, T.; Susskind, L.; Peskin, M.E. Difficulties for the evolution of pure states into mixed states. Nucl. Phys. B
**1984**, 244, 125–134. [Google Scholar] [CrossRef] - Bohm, D.; Bub, J. A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory. Rev. Mod. Phys.
**1966**, 38, 453–469. [Google Scholar] [CrossRef] - Karolyhazy, F. Gravitation and quantum mechanics of macroscopic objects. Nuovo Cim.
**1966**, 42, 390–402. [Google Scholar] [CrossRef] - Diósi, L. Gravitation and quantum-mechanical localization of macro-objects. Phys. Lett. A
**1984**, 105, 199–202. [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] - Diósi, L. A universal master equation for the gravitational violation of quantum mechanics. Phys. Lett. A
**1987**, 120, 377–381. [Google Scholar] [CrossRef] - Unruh, W.G. Steps towards a quantum theory of gravity. In Quantum Theory of Gravity; Christensen, S.M., Ed.; Adam Hilger Ltd.: Bristol, UK, 1984; pp. 234–242. [Google Scholar]
- Tilloy, A.; Diósi, L. Principle of least decoherence for Newtonian semi-classical gravity. Phys. Rev. D
**2017**, 96, 104045. [Google Scholar] [CrossRef]

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Diósi, L.
Fundamental Irreversibility: Planckian or Schrödinger–Newton? *Entropy* **2018**, *20*, 496.
https://doi.org/10.3390/e20070496

**AMA Style**

Diósi L.
Fundamental Irreversibility: Planckian or Schrödinger–Newton? *Entropy*. 2018; 20(7):496.
https://doi.org/10.3390/e20070496

**Chicago/Turabian Style**

Diósi, Lajos.
2018. "Fundamental Irreversibility: Planckian or Schrödinger–Newton?" *Entropy* 20, no. 7: 496.
https://doi.org/10.3390/e20070496