# Conceptual Challenges on the Road to the Multiverse

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## Abstract

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## 1. Introduction

## 2. The Multiverse: Nothing New under the Suns?

## 3. Definition and Classification of the Multiverse

#### 3.1. Physically Motivated Multiverse Scenarios

## 4. Philosophical Aspects

#### 4.1. Philosophy of Science and the Description of Scientific Progress

#### 4.2. Application to the Multiverse

#### 4.2.1. Popper

#### 4.2.2. Kuhn

#### 4.2.3. Lakatos

#### 4.2.4. Feyerabend

#### 4.2.5. Bayesianism

#### 4.3. Consistency and Uniqueness Claims

## 5. Fine-Tuning and the Multiverse… or Is It Really a Tale of Scales?

## 6. Physical Multiverse and Testability

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1. | Even though Everett’s many-worlds interpretation of quantum mechanics is presently considered a multiverse scenario (see Tegmark’s classification below), it really stands a bit apart for a variety of reasons, the first one being its historical origin purely within quantum mechanics. We will briefly mention this scenario again in Section 3.1 but otherwise focus mainly on cosmological multiverse scenarios. |

2. | For the relationship between the anthropic principle and the multiverse, see e.g., [25]. We will not discuss the anthropic principle here because, first, as paraphrased in [25], “many commentators have already thrown much darkness on this subject, and it is probable that, if they continue, we shall soon know nothing at all about it”; and second because, although the anthropic principle has undoubtedly contributed much to conceptual thinking about the multiverse, it is not clear whether it can also make any real contribution when it comes to empirical predictions, let alone—despite common claims to the contrary—whether it has done this so far [26]. |

3. | |

4. | In reality Polchinski’s four questions are not independent, so the numerical estimate is incorrect even from a purely probabilistic point of view. However, since Polchinski himself states that the number itself is not important, we will not further dissect this issue. |

5. | Just in case some reader might benefit from a reminder, the theoretical estimate comes essentially from assuming that the cosmological constant represents the vacuum energy ${E}_{\mathrm{vac}}$, imposing a cut-off ${k}_{c}$ to the theory and calculating ${E}_{\mathrm{vac}}$ by integrating over all degrees of freedom up to ${k}_{c}$, which gives ${E}_{\mathrm{vac}}=\hslash {k}_{c}^{4}$ (a result which is consistent with a straightforward dimensional analysis [102]). Assuming ${k}_{c}={E}_{\mathrm{Planck}}$ immediately leads to the undesired result, while even ${k}_{c}={E}_{\mathrm{EW}}$, with ${E}_{\mathrm{EW}}$ the electroweak scale, still leads to a discrepancy of some 50 orders of magnitude. It might be worth insisting that it is essential to insert a cut-off in the calculation in order to avoid an even more unpleasant prediction for the vacuum energy, namely infinity. Note that the observational energy scale associated with dark energy is in fact small, and might therefore be due to quantum field effects potentially accessible to near-future observations. However, this would still leave the cosmological coincidence problem unexplained, namely why the matter energy density and the dark energy density have the same order of magnitude in the present epoch. |

6. | The only well-developed bottom-up approach to “quantum gravity phenomenology” is the ongoing search for Lorentz Invariance Violations [104,105]. However, it might be useful to stress that neither string theory nor loop quantum gravity make clear and unambiguous predictions about Lorentz Invariance, not even at a qualitative level. |

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Alonso-Serrano, A.; Jannes, G.
Conceptual Challenges on the Road to the Multiverse. *Universe* **2019**, *5*, 212.
https://doi.org/10.3390/universe5100212

**AMA Style**

Alonso-Serrano A, Jannes G.
Conceptual Challenges on the Road to the Multiverse. *Universe*. 2019; 5(10):212.
https://doi.org/10.3390/universe5100212

**Chicago/Turabian Style**

Alonso-Serrano, Ana, and Gil Jannes.
2019. "Conceptual Challenges on the Road to the Multiverse" *Universe* 5, no. 10: 212.
https://doi.org/10.3390/universe5100212