# Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability

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## Abstract

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## 1. Introduction

#### 1.1. Scientific Method

#### 1.2. Cosmology as an Experimental Science

#### 1.3. Physical Laws and Constants

#### 1.4. What Is the Multiverse?

## 2. Some History and Remarks on Varying Constants

## 3. Theories Incorporating Varying Constants

#### 3.1. Formulations

#### 3.1.1. Varying Gravitational Constant G

#### 3.1.2. Varying Fine Structure Constant $\alpha $ or the Electric Charge e

#### 3.1.3. Varying Speed of Light c

#### 3.2. Bounds on Variability of Fundamental Constants

#### 3.2.1. Varying G

#### 3.2.2. Varying $\alpha $

#### 3.2.3. Varying c

#### 3.3. Varying Constants as the Path to the Multiverse

## 4. Varying Constants and Anthropic Principles

#### 4.1. Coincidences

#### 4.2. Anthropic Principles (AP)

#### 4.2.1. Weak Anthropic Principle (WAP)

#### 4.2.2. Strong Anthropic Principle (SAP)

- Interpretation A says that “there exists only one possible Universe designed with the goal of generating and sustaining observers” [62]. In fact, it is very teleological, and this is why it sometimes is also called “An Intelligent Project” interpretation.
- Interpretation C says that “the whole ensemble of other and different universes is necessary for the existence of our Universe” [62]. The best-known, though most controversial version of this interpretation is the many-worlds theory of Everett [71,72] having recently some strong support from superstring theory [73].

#### 4.2.3. Final Anthropic Principle (FAP)

#### 4.2.4. Minimalistic Anthropic Principle (MAP)

#### 4.2.5. Going Beyond

## 5. The Multiverse and Its Testability

#### 5.1. Multiverse Hierarchy

- Level I obeys the pieces of our universe which are outside the cosmic horizon (behind our reach due to finite speed of information transmission by the speed of light), it presumably allows the same laws of physics, though different initial conditions.
- Level II are the other bubbles (universes) created during the process of eternal cosmic inflation which allows the same laws of physics but the different values of physical constants and different dimensionality of space. Our universe (set of constants) is likely as one of the many options.
- Level III is what is essentially the many-wolds of quantum physics proposed by Everett. It is the same as the level II but with some quantum curiosities such as superpositions of “alive” and “dead” cats, etc. The main issue is that there is no collapse of the total wave function of the Universe so that the decoherence (appearance of a classical world) happens only for a branching piece of the whole multiverse.
- Level IV is very extreme since it contains “any mathematical structure which is realised somewhere in the multiverse and it is fully materialisable”. Within this multiverse, one can have different physical constants, different laws of physics, dimensionality, etc. Since on this level we can make an equality between “mathematical existence” and “physical existence”, then we can answer the famous Wheeler and Hawking question: “why these equations (laws of physics), and not others?

#### 5.2. Multiverse and Our Vision of Life

#### 5.3. Falsifying the Multiverse

#### 5.4. How Many Universes?

#### 5.5. Falsifying due to Quantum Entanglement

#### 5.6. Redundant or Necessary?

## 6. Afterword

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Popper, K. The Logic of Scientific Discovery; Routledge-Taylor & Francis: Abingdon, UK, 2002. [Google Scholar]
- Hubble, E. A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae. Proc. Natl. Acad. Sci. USA
**1929**, 15, 168. [Google Scholar] [CrossRef] [PubMed] - Penzias, A.A.; Wilson, R.W. A Measurement of Excess Antenna Temperature at 4080 Mc/s. Astrophys. J. Lett.
**1965**, 142, 419–421. [Google Scholar] [CrossRef] - Ade, P.A.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C. Planck 2015 results-xiii. cosmological parameters. Astron. Astrophys.
**2016**, 594, A13. [Google Scholar] - Spergel, D.N.; Bean, R.; Doré, O.; Nolta, M.R.; Bennett, C.L.; Dunkley, J. Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Implications for cosmology. Astrophys. J. Suppl. Ser.
**2007**, 170, 377. [Google Scholar] [CrossRef] - Ade, P.A.R.; Akiba, Y.; Anthony, A.E.; Arnold, K.; Atlas, M.; Barron, D. Measurement of the cosmic microwave background polarization lensing power spectrum with the POLARBEAR experiment. Phys. Rev. Lett.
**2014**, 113, 021301. [Google Scholar] [CrossRef] - Ellis, G.F.R. On the philosophy of cosmology. Studi. Philos. Mod. Phys.
**2014**, 46, 5–23. [Google Scholar] [CrossRef] - Ellis, G.F.R. The Domain of Cosmology and the Testing of Cosmological Theories. In The Philosophy of Cosmology; Chamcham, K., Silk, J., Barrow, J.D., Saunders, S., Eds.; Cambridge University Press: Cambridge, UK, 2017; pp. 3–39. [Google Scholar] [Green Version]
- James, W. Is Life Worth Living? Int. J. Ethics
**1895**, 6, 1–24. [Google Scholar] [CrossRef] [Green Version] - Duff, M.J.; Okun, L.B.; Veneziano, G. Trialogue on the number of fundamental constants. J. High Energy Phys.
**2002**, 2002, 023. [Google Scholar] [CrossRef] - Okun, L.B. The fundamental constants of physics. Sov. Phys. Usp.
**1991**, 34, 818. [Google Scholar] [CrossRef] - Levy-Leblond, J.M. The Importance of Being (a) Constant. In Proceedings of the Problems in the Foundations of Physics, Varenna, Italy, 25 July–6 August 1977. [Google Scholar]
- Uzan, J.-P. Varying constants, gravitation and cosmology. Living Rev. Relat.
**2011**, 14, 2. [Google Scholar] [CrossRef] - Cavendish, H. XXI. Experiments to determine the density of the earth. Philos. Trans. R. Soc. Lond.
**1798**, 88, 469–526. [Google Scholar] [Green Version] - Johnstone-Stoney, G. LII. On the physical units of nature. Philos. Mag.
**1881**, 5, 381–390. [Google Scholar] [CrossRef] - Uzan, J.-P. The fundamental constants and their variation: Observational and theoretical status. Rev. Mod. Phys.
**2003**, 75, 403. [Google Scholar] [CrossRef] - Weyl, H. Eine neue erweiterung der relativitaetstheorie. Annalen der Physik
**1919**, 59, 101–133. [Google Scholar] [CrossRef] - Eddington, A.S. New Pathways in Science; Cambridge University Press: Cambridge, UK, 1934. [Google Scholar]
- Dirac, P.A.M. A new basis for cosmology. Proc. R Soc. A
**1938**, 165, 199–208. [Google Scholar] [CrossRef] [Green Version] - Jordan, P. The present state of Dirac’s cosmological hypothesis. Z. Phys.
**1959**, 157, 112–121. [Google Scholar] [CrossRef] - Brans, C.; Dicke, R.H. Mach’s principle and a relativistic theory of gravitation. Phys. Rev.
**1961**, 124, 925. [Google Scholar] - Gasperini, M.; Veneziano, G. The pre-big bang scenario in string cosmology. Phys. Rep.
**2003**, 373, 1–212. [Google Scholar] [CrossRef] [Green Version] - Khoury, J.; Steinhardt, P.; Turok, N. Inflation versus cyclic predictions for spectral tilt. Phys. Rev. Lett.
**2003**, 91, 161301. [Google Scholar] [CrossRef] - Barrow, J.D. The Constants of Nature; Vintage Books: London, UK, 2002. [Google Scholar]
- Barrow, J.D. Varying alpha. Annalen der Physik
**2010**, 19, 202–210. [Google Scholar] [CrossRef] [Green Version] - Albrecht, A.; Magueijo, J. Time varying speed of light as a solution to cosmological puzzles. Phys. Rev. D
**1999**, 59, 043516. [Google Scholar] [CrossRef] [Green Version] - Sandvik, J.H.B.; Barrow, J.D.; Magueijo, J. A Simple Cosmology with a Varying Fine Structure Constant. Phys. Rev. Lett.
**2002**, 88, 031302. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Teller, E. On the change of physical constants. Phys. Rev.
**1948**, 73, 801. [Google Scholar] [CrossRef] - Gamow, G. Electricity, gravity, and cosmology. Phys. Rev. Lett.
**1967**, 19, 759. [Google Scholar] [CrossRef] - Dirac, P.A.M. The cosmological constants. Nature
**1937**, 139, 323. [Google Scholar] [CrossRef] - Bekenstein, J.D. Fine-structure constant: Is it really a constant? Phys. Rev. D
**1982**, 25, 1527. [Google Scholar] [CrossRef] - Barrow, J.D.; Magueijo, J. Solutions to the quasi-flatness and quasi-lambda Problems. Phys. Lett. B
**1999**, 447, 246–250. [Google Scholar] [CrossRef] - Petit, J.-P. Cosmological model with variable light velocity: The interpretation of red shifts. Mod. Phys. Lett. A
**1988**, 3, 1733–1744. [Google Scholar] [CrossRef] - Moffat, J.W. Quantum gravity, the origin of time and time’s arrow. Found. Phys.
**1993**, 23, 411–437. [Google Scholar] [CrossRef] - Moffat, J.W. Variable speed of light cosmology, primordial fluctuations and gravitational waves. Eur. Phys. J. C
**2016**, 76, 130. [Google Scholar] [CrossRef] - Clayton, M.A.; Moffat, J.W. A scalar-tensor cosmological model with dynamical light velocity. Phys. Lett. B
**2001**, 506, 177–186. [Google Scholar] [CrossRef] [Green Version] - Magueijo, J.; Smolin, L. Gravity’s rainbow. Class. Quantum Gravity
**2004**, 21, 1725. [Google Scholar] [CrossRef] - Ivanchik, A.; Rodriguez, E.; Petitjean, P.; Yarshalovich, D. Do the fundamental constants vary in the course of cosmological evolution? Astron. Lett.
**2002**, 28, 423–427. [Google Scholar] [CrossRef] [Green Version] - Moeller, J.; Biskupek, L. Variations of the gravitational constant from lunar laser ranging data. Class. Quantum Gravity
**2007**, 24, 4533. [Google Scholar] [CrossRef] - Kaspi, V.M.; Taylor, J.H.; Riba, M.F. High-precision timing of millisecond pulsars. 3: Long-term monitoring of PSRs B1855+ 09 and B1937+ 21. Astrophys. J.
**1994**, 428, 713–728. [Google Scholar] [CrossRef] - Shlyakhter, A.I. Direct test of the constancy of fundamental nuclear constants. Nature
**1976**, 264, 340. [Google Scholar] [CrossRef] - Petrov, Y.V.; Nazarov, A.I.; Onegin, M.S.; Petrov, V.Y.; Sakhnovsky, E.G. Natural nuclear reactor at Oklo and variation of fundamental constants: Computation of neutronics of a fresh core. Phys. Rev. C
**2006**, 74, 064610. [Google Scholar] [CrossRef] [Green Version] - Fujii, Y.; Iwamoto, A.; Fukahori, T.; Ohnuki, T.; Nakagawa, M.; Hidaka, H.; Oura, Y.; Moeller, P. The nuclear interaction at Oklo 2 billion years ago. Nucl. Phys. B
**2000**, 573, 377–401. [Google Scholar] [CrossRef] [Green Version] - Wilczynska, M.R.; Webb, J.K.; King, J.A.; Murphy, M.T.; Bainbridge, M.B.; Flambaum, V.V. A new analysis of fine-structure constant measurements and modelling errors from quasar absorption lines. Mon. Not. R. Astron. Soc.
**2015**, 454, 3082–3093. [Google Scholar] [CrossRef] - Levshakov, S.A.; Centurion, M.; Molaro, P. Most precise single redshift bound to. Astron. Astrophys.
**2006**, 449, 879–889. [Google Scholar] [CrossRef] - Resolution 2 of the 15th CGPM (1975). Available online: http://www.bipm.org/en/CGPM/db/15/2/ (accessed on 13 July 2019).
- Evenson, K.M.; Wells, J.S.; Petersen, F.R.; Danielson, B.L.; Day, G.W.; Barger, R.L.; Hall, J.L. Speed of light from direct frequency and wavelength measurements of the methane-stabilized laser. Phys. Rev. Lett.
**1972**, 29, 1346. [Google Scholar] [CrossRef] - Salzano, V.; Da̧browski, M.P.; Lazkoz, R. Measuring the speed of light with Baryon Acoustic Oscillations. Phys. Rev. Lett.
**2015**, 114, 101304. [Google Scholar] [CrossRef] [PubMed] - Salzano, V.; Da̧browski, M.P. Statistical hierarchy of varying speed of light cosmologies. Astrophys. J.
**2017**, 851, 97. [Google Scholar] [CrossRef] - Cao, S.; Biesiada, M.; Jackson, J.; Zheng, X.; Zhao, Y.; Zhu, Z.-H. A new test of f(R) gravity with the cosmological standard rulers in radio quasars. J. Cosmol. Astropart. Phys.
**2017**, 2017, 012. [Google Scholar] [CrossRef] - Barrow, J.D. Cosmologies with varying light speed. Phys. Rev. D
**1999**, 59, 043515. [Google Scholar] [CrossRef] [Green Version] - Barrow, J.D.; Magueijo, J. Solving the flatness and quasi-flatness problems in Brans-Dicke cosmologies with a varying light speed. Class. Quantum Gravity
**1999**, 16, 1435. [Google Scholar] [CrossRef] - Balcerzak, A. Non-minimally coupled varying constants quantum cosmologies. J. Cosmol. Astropart. Phys.
**2015**, 4, 019. [Google Scholar] [CrossRef] - Barrow, J.D.; Magueijo, J.; Sandvik, H.B. A cosmological tale of two varying constants. Phys. Lett. B
**2002**, 541, 201–210. [Google Scholar] [CrossRef] [Green Version] - Ellis, G.F.R.; Kirchner, U.; Stoeger, W.R. Multiverses and physical cosmology. Mon. Not. R. Astron. Soc.
**2004**, 347, 921–936. [Google Scholar] [CrossRef] [Green Version] - Schutz, B.F. A First Course in General Relativity; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Tessarotto, M.; Cremaschini, C. Theory of non-local point transformations-Part 1: Representation of Teleparallel Gravity. arXiv
**2016**, arXiv:1601.03940. [Google Scholar] - Magueijo, J. New varying speed of light theories. Rep. Prog. Phys.
**2003**, 66, 2025. [Google Scholar] [CrossRef] - Landau, L.D.; Lifschitz, E.M. The Classical Theory of Fields; Addison-Wesley: Boston, MA, USA, 1957. [Google Scholar]
- Magueijo, J. Covariant and locally lorentz-invariant varying speed of light theories. Phys. Rev. D
**2000**, 62, 103521. [Google Scholar] [CrossRef] - Mattingly, D. Modern tests of Lorentz invariance. Living Rev. Relat.
**2005**, 8, 5. [Google Scholar] [CrossRef] [PubMed] - Barrow, J.D.; Tipler, F.J. The Anthropic Cosmological Principle; Oxford University Press: Oxford, UK, 1986. [Google Scholar]
- Laskar, J.; Robutel, P. The chaotic obliquity of the planets. Nature
**1993**, 361, 608. [Google Scholar] [CrossRef] - Tegmark, M. Parallel universes. Sci. Am.
**2003**, 288, 40–51. [Google Scholar] [CrossRef] [PubMed] - Tegmark, M. Science and Ultimate Reality; Barrow, J.D., Davies, P.C.W., Harper, C.L., Eds.; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Carter, B. Large Number Coincidences and the Anthropic Principle in Cosmology. In Confrontation of Cosmological Theories with Observation, (IAU Symposium No 63); Longair, M., Ed.; Reidel: Dordrecht, The Netherlands, 1974; pp. 291–298. [Google Scholar]
- Carter, B. The anthropic Principle and its Implication for Biological Evolution. Philos. Trans. R. Soc. Lond. A
**1983**, 310, 347. [Google Scholar] [CrossRef] - Lee, P. Bayesian Statistics: An Introduction; Wiley: Hoboken, NJ, USA, 2012. [Google Scholar]
- Sahlén, B. On Probability and Cosmology: Inference Beyond Data. In The Philosophy of Cosmology; Chamcham, K., Silk, J., Barrow, J.D., Saunders, S., Eds.; Cambridge University Press: Cambridge, UK, 2017; pp. 429–446. [Google Scholar]
- Rees, M.J. Cosmological significance of e
^{2}/Gm^{2}and related ”large numbers”. Comments Astrophys. Space Phys.**1972**, 4, 179. [Google Scholar] - Everett, H. Relative state formulation of quantum mechanics. Rev. Mod. Phys.
**1957**, 29, 454. [Google Scholar] [CrossRef] - DeWitt, B.; Graham, R.N. (eds.) The Many Worlds Interpretation of Quantum Mechanics; Princeton University Press: Princeton, NJ, USA, 1973. [Google Scholar]
- Polchinski, J. String Theory; Cambridge University Press: Cambridge, UK, 1998. [Google Scholar]
- Douglas, M.R. The Statistics of string/M-theory vacua. J. High Energy Phys.
**2003**, 2003, 046. [Google Scholar] [CrossRef] - Vafa, C. The string landscape and the swampland. arXiv
**2005**, arXiv:hep-th/0509212. [Google Scholar] - Susskind, L. The anthropic landscape of string theory. arXiv
**2003**, arXiv:hep-th/0302219. [Google Scholar] - Douglas, M.R. The string theory landscape. Universe
**2019**. submitted. [Google Scholar] - Pogosian, L.; Vilenkin, A.; Tegmark, M. Anthropic Predictions for Vacuum Energy and Neutrino Masses. J. Cosmol. Astropart. Phys.
**2004**, 2004, 005. [Google Scholar] [CrossRef] - Heller, M. Multiverse – too much or not enough? Universe
**2019**, 5, 113. [Google Scholar] [CrossRef] - Guth, A.H. Inflationary universe. A possible solution to the horizon and flatness problem. Phys. Rev. D
**1981**, 23, 347. [Google Scholar] [CrossRef] - Linde, A.D. A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B
**1982**, 108, 389. [Google Scholar] [CrossRef] - Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K. Quantum entanglement. Rev. Mod. Phys.
**2009**, 81, 865. [Google Scholar] [CrossRef] - Harnik, R.; Kribs, G.D.; Perez, G. A universe without weak interactions. Phys. Rev. D
**2006**, 74, 035006. [Google Scholar] [CrossRef] [Green Version] - Gauthier, Y. A general no-cloning theorem for an infinite multiverse. Rep. Math. Phys.
**2013**, 72, 191–199. [Google Scholar] [CrossRef] - Hilbert, D. On the Infinite. Philosophy of Mathematics; Benacerraf, P., Putnam, H., Eds.; Prentice Hall: Englewood Cliffs, NJ, USA, 1964; pp. 134–151. [Google Scholar]
- Davies, P.C.W.; (Beyond Center, Arizona State University, Tempe, AZ, USA). Personal communication, 2019.
- Robles-Perez, S. Time reversal symmetry in cosmology and the creation of a universe-antiuniverse pair. Universe
**2019**, 5, 150. [Google Scholar] [CrossRef] - Mersini-Houghton, L.; Holman, R. ‘Tilting’ the Universe with the Landscape Multiverse: The ‘Dark’ Flow. J. Cosmol. Astropart. Phys.
**2009**, 2009, 006. [Google Scholar] [CrossRef] - di Valentino, E.; Mersini-Houghton, L. Testing Predictions of the Quantum Landscape Multiverse 1: The Starobinsky Inflationary Potential. J. Cosmol. Astropart. Phys.
**2017**, 2017, 002. [Google Scholar] [CrossRef] - di Valentino, E.; Mersini-Houghton, L. Testing predictions of the quantum landscape multiverse 2: The exponential inflationary potential. J. Cosmol. Astropart. Phys.
**2017**, 2017, 020. [Google Scholar] [CrossRef] - Kinney, W.H. Limits on Entanglement Effects in the String Landscape from Planck and BICEP/Keck Data. J. Cosmol. Astropart. Phys.
**2016**, 2016, 013. [Google Scholar] [CrossRef] - Robles-Perez, S.; Balcerzak, A.; Da̧browski, M.P.; Krämer, M. Interuniversal entanglement in a cyclic multiverse. Phys. Rev. D
**2017**, 95, 083505. [Google Scholar] [CrossRef] [Green Version]

1. | A famous example of a quantity which is frame-dependent in general relativity is the gravitational energy represented by a pseudotensor [59]. |

**Figure 1.**Bronshtein-Zelmanov-Okun cube, or the cube of the physical theories [11]. Three orthonormal axes are marked by $1/c$, h and G. The vertex $(0,0,0)$ corresponds to non-relativistic mechanics; ($c,0,,0$) to special relativity; ($0,h,0$) to non relativistic quantum mechanics; ($c,,h,0$) to quantum field theory; ($c,0,G$) to general relativity, ($c,h,G$) to relativistic quantum gravity.

**Figure 2.**Fine-tuning of the parameters $\alpha $ and ${\alpha}_{s}$. Life-permitting parameter zone of these constants is marked in red [65].

Inhabitable | Uninhabitable | |
---|---|---|

our life | I, OUL | UI, OUL |

other life | I, OTL | UI, OTL |

Inhabitable | Uninhabitable | |
---|---|---|

our set of laws | I, OUS | UI, OUS |

other set of laws | I, OTS | UI, OTS |

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**MDPI and ACS Style**

Da̧browski, M.P.
Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability. *Universe* **2019**, *5*, 172.
https://doi.org/10.3390/universe5070172

**AMA Style**

Da̧browski MP.
Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability. *Universe*. 2019; 5(7):172.
https://doi.org/10.3390/universe5070172

**Chicago/Turabian Style**

Da̧browski, Mariusz P.
2019. "Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability" *Universe* 5, no. 7: 172.
https://doi.org/10.3390/universe5070172