Conceptual Challenges on the Road to the Multiverse
aa r X i v : . [ phy s i c s . h i s t - ph ] O c t Article
Conceptual challenges on the road to the multiverse
Ana Alonso-Serrano and Gil Jannes Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, D-14476 Golm,Germany; [email protected] Department of Financial and Actuarial Economics & Statistics, Universidad Complutense de Madrid,Campus Somosaguas s/n, 28223 Pozuelo de Alarcón (Madrid), Spain; [email protected] * Correspondence: [email protected]† The authors contributed equally to this work.Version October 17, 2019 submitted to Universe
Abstract:
The current debate about a possible change of paradigm from a single universe to amultiverse scenario could have deep implications on our view of cosmology and of science ingeneral. These implications therefore deserve to be analyzed from a fundamental conceptual level.We briefly review the different multiverse ideas, both historically and within contemporary physics.We then discuss several positions within philosophy of science with regard to scientific progress,and apply these to the multiverse debate. Finally, we construct some key concepts for a physicalmultiverse scenario and discuss the challenges this scenario has to deal with in order to provide asolid, testable theory.
Keywords:
Multiverse. Physical multiverse. Philosophy of science. Empirical testability.Falsifiability. Bayesian analysis. Fine-tuning
1. Introduction
Ideas related to what we nowadays call “the multiverse” have historically always attracted bothsupporters and detractors. The multiverse is not really a theory, but a scenario that arises in severaltheories and can be defined in different ways depending on the underlying theory. This apparentlyvague remark in fact has deep consequences on the discussion about the possible existence of otheruniverses and the associated change of the very definition of “the universe”, but also of what ascientific theory is or should be, and how it should be assessed. As we will discuss later in detail, thereis no standard or commonly agreed upon definition of universe, and therefore not for the multiverseeither. What seems clear along history is that the universe has been defined as the (connected) regionof space accessible to us. But this meaning has evolved depending upon the theory and observationsat our disposal.In the past few years, the amount of papers and ideas about the multiverse have increasedtremendously. The sometimes heated discussion about the viability of the multiverse and relatedideas [1–3] show that we are far from reaching an agreement in the scientific community. At this stagethere are, on the one hand, strong claims about what “could be one of the most important revolutionsin the history of cosmogonies”[4], which “changes the way we think about our place in the world” [5]and “if true - would force a profound change of our deep understanding of physics” [4]. On the otherhand, there is also a strong opposition to the very mention of the possibility of a multiverse scenarioand of the scientific significance of such mentions [6,7].We therefore believe that it is relevant to examine the fundamental questions that emerge inmultiverse ideas, and to emphasize some criteria that the multiverse should meet before beingmore widely acceptable as a viable scientific proposal. We therefore undertake an analysis basedon concepts from the philosophy of science related to the definition of the scientific method, an
Submitted to
Universe
Universe epistemological theory, and a scientific revolution implying a change of paradigm. This reflection willhelp us postulate some constraints that should be imposed on multiverse theories and the conceptualchallenges they will need to confront.
2. The multiverse: Nothing new under the suns?
The idea that there might be other worlds or universes beyond our own has been a recurrentconcept throughout history [8,9]. It followed naturally from the desire of knowing whether we areunique observers, and of the possibility of discovering worlds similar to ours. At the same time, it hasalways been accompanied by skepticism about the possibility of actually answering these questions.These issues are part of the most ancient and most essential philosophical and cosmologicalquestions. It should therefore come as no surprise that the first recorded notion of a multiverse inoccidental intellectual history dates back to the ancient Greeks. Anaximander, in the 6th Century BC,speculated about a plurality of worlds such as our cosmos, appearing and disappearing in an eternalmovement of generation and destruction. A few centuries later, Epicurus described how an unlimitednumber of worlds fills the infinite vacuum [10].In medieval times, Robert Grosseteste described the condensation of different universes from aninitial big-bang-like explosion [11]. Giordano Bruno proposed an infinite “cosmic pluralism” filledwith many inhabitable worlds as an alternative to the Copernican heliocentric model [12]. In the18th century, Emanuel Swedenborg conjectured a model of the evolution of our solar system and thefirmament we observe, based on theological and philosophical arguments. He postulated the possibleexistence of other celestial spheres in the firmament and argued that every of those world-systemswould follow the same principles. This argument can be interpreted as the first idea of a nebularhypothesis [13]. Thomas Wright was the first to interpret the astronomical observations of distantfaint nebulous structures as other galaxies, suggesting that they could have their own “externalcreation” [14]. This idea was later elaborated by Immanuel Kant, who popularized the idea of thepossible existence of habitable worlds around stars other than the Sun [15]. This theory was baptized“island universes” by von Humboldt a century later [16]. By 1920, as more observations becameavailable, the question led to the “Great Debate” between Shapley and Curtis about the scale of theUniverse. Shapley defended that our Milky Way constituted the entire universe and that the otherobserved nebulae were small entities on its outskirts, while in Curtis’ opinion, at least some of themwere in fact separate, distant galaxies [17]. It was not until Hubble’s decisive observational evidencea few years later that this battle of paradigms, originally started from purely philosophical principles,was finally settled.From a more metaphysical point of view, Leibniz argued that our universe was the best amongan infinity of possible universes [18]. According to Leibniz, logical constraints meant that (even)God could not have made our universe any better. This argument was later turned around bySchopenhauer, who argued that our world must be the worst of all possible worlds, because if it wereeven slightly worse in any respect, life could not continue to exist [19]. This argument is curiouslyreminiscent of recent fine-tuning arguments: a slight change in any of a number of basic constantswould have made complexity (and therefore life) impossible [20].Before turning to contemporary theories of the multiverse, it might be interesting to mentionthat there also exist (non-occidental) religious and mythological ideas related to the multiverse. Suchideas are implicit in Buddhism, with its cyclical view on the continuous destruction and recreation ofthe universe. They appear explicitly in Hinduism: “The golden egg that is this universe is wrappedin seven sheaths: the earth and the other elements, each casing being ten times as great as the oneit encases. There are millions upon millions of these in each universe. There are millions of suchuniverses. Lord, all these together are like a single atom upon your head! So, we call you Ananta,Infinite One.” [21]In Christianity, the multiverse idea is controversial, as it seems opposite to the uniqueness ideacommon to most monotheistic religions. However, Page has defended that the multiverse is not in ersion October 17, 2019 submitted to
Universe conflict with Christianity [22]. In this context, Page mentions a serious challenge to the multiverseconcept, namely the question of whether sinning civilizations in other universes have also beenredeemed by the death of Christ. To our great relief, Page himself answers this question: “we couldjust interpret the Bible to mean that Christ’s death here on earth is unique for our human civilization”,and so with peace in mind we will focus here on cosmological approaches of the multiverse and itsconceptual challenges.
3. Definition and classification of the multiverse
The epistemological extension from the universe to a multiverse is often compared to theCopernican revolution, as a further step in the gradual loss of importance of our own habitat(although there seems to be some disagreement about whether this would be the fourth [4,23]or fifth [24] Copernican revolution). However, from a physical point of view, the contemporarycosmological concept of multiverse arises not so much as a direct theory in itself, but as an indirectconsequence of problems mainly related to the current cosmological paradigm of an acceleratedlyexpanding universe governed by the laws of General Relativity . The multiverse is argued to bea natural extension of developments within string theory or early-universe cosmology (in particular,chaotic eternal inflation), and is invoked to solve a series of open problems in theoretical physics, suchas the problem of the beginning of the universe, the cosmic coincidence problem, or the smallnessof the cosmological constant, as well as the more general fine-tuning of physical constants [1]. Insome of those cases, the multiverse in itself only partially solves the problem, but mainly establishesa reformulation of the question. For example, related to the fine-tuning problem, the multiversesuggests a distribution of values of certain fundamental constants among the different possibleuniverses. The question why we live precisely in a universe with the observed values can then beanswered by some form of the anthropic principle. The new question which arises then is how likelythe values of the physical constants of our universe are across the probability distribution within themultiverse. In this context, Vilenkin introduced the mediocrity principle [27], which defends thatwe should be “typical” observers, and therefore a priori we are expected to live in one of the mostprobable universes among all those which allow for the existence of life. Ideally, this principle willbe testable by comparison with the probability distribution. We will come back to this issue later inSection 4.2.5. Let us first look at possible definitions of the multiverse.In general terms, a first attempt to define the concept of multiverse could be that the multiverseencompasses all the multiple possible universes predicted by an underlying theory insofar as theyare actually realized, i.e.: everything that physically exists, the totality of space and time and itsmaterial-energetic content. But this (intentionally vague) definition leads to an obvious questionfrom a semantic point of view. If we understand the Universe etymologically as the whole possibleentity, all of spacetime and its content, then there is no place for the multiverse. Perhaps one shouldthen redefine the universe itself, depending on concepts such as causal connection or variations ofphysical laws. The situation is reminiscent of the atom, originally meaning “indivisible”. Eventuallythe physical meaning was overcome even though the name stuck. In the case of the multiverse, thisapparently lexicological question bears a direct impact on physical issues. As is well-known, in the Even though Everett’s many-worlds interpretation of quantum mechanics is nowadays 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 historicalorigin purely within quantum mechanics. We will briefly mention this scenario again in Section 3.1 but otherwise focusmainly on cosmological multiverse scenarios. For the relationship between the anthropic principle and the multiverse, see e.g. [25]. We will not discuss the anthropicprinciple here because, first, as paraphrased in [25], “many commentators have already thrown much darkness on thissubject, and it is probable that, if they continue, we shall soon know nothing at all about it”; and second because, althoughthe anthropic principle has undoubtedly contributed much to conceptual thinking about the multiverse, it is not clearwhether it can also make any real contribution when it comes to empirical predictions, let alone–in spite of common claimsto the contrary–whether it has done this so far [26].ersion October 17, 2019 submitted to
Universe case of a single universe, the boundary conditions are crucial to determine the mathematically andphysically acceptable solutions (see the Hartle-Hawking no-boundary proposal [28] or Vilenkin’stunneling proposal [29]). Then in the case of a multiverse, the issue of the boundary conditionsbetween the various universes within the multiverse is probably equally important [30]. In fact,the issue is even more general, since the overall nature of the multiverse depends on the particulardefinition one uses of the constituent universes. It is possible to consider as universe, for instance, thehabitable region we live in (delimited by the Hubble sphere); a causal spacetime region; one of thequantum branches in the Everett interpretation of quantum mechanics; or simply one of the particularsolutions to the cosmological equations that appear in string theory.The best-known classification for the different multiverse hypotheses is due to Tegmark [31].Tegmark establishes a hierarchical classification, where each higher level includes the lower ones. Thelevel I multiverse consists of a variety of Hubble volumes, causally disconnected but all with the samephysical laws and constants. Level II allows for a variation of the physical constants, for example dueto bubble-breaking during the inflationary phase. Level III corresponds to quantum many-worldbranching. Finally, level IV is constituted by all the different possible mathematical structures, all ofwhich are assumed to represent physically real universes.A point which might be worth mentioning is that different physical multiverse models arenot always straightforward to classify in Tegmark’s (or some other) scheme. More generally, bothwhen defending or criticizing the multiverse, or when trying to elaborate on “the multiverse”, it isnot always clearly stipulated which kind of multiverse one is dealing with, and this can seriouslycomplicate the assessment of the arguments.In the following, we focus on the origin of the most common contemporary multiverse models.
The earliest multiverse model in modern physics comes from Everett’s many-worldsinterpretation of quantum mechanics [32]. This interpretation considers the multiverse as all thepossible histories from a quantum superposition, with one particular branch corresponding to ouruniverse. This configuration of the multiverse as a host of bifurcating quantum branches leads to acontinuous multiplication of parallel universes. Unsurprisingly, this interpretation has historicallybeen quite controversial.Inflation theory has led to a different multiverse notion. As a consequence of the quantum effectsin the early universe, it could be possible to create new universes by a mechanism of eternal chaoticinflation [33–35], in which the different regions of space can transform into macroscopic bubbleuniverses, which split off from a preceding universe and create a new one. In these multiversemodels, the fundamental laws of physics are the same in each universe, due to the fact that theywere originated in a common inflationary universe. The constants of nature, however, are allowed tohave different values, depending on the specific inflationary process of each particular universe.In the context of string theory, the idea of a multiverse stems from the pocket universesassociated to the colossal number of false vacua predicted by the theory, which conform the so-calledlandscape [35,36]. Each of the universes could have different dimensions, elementary particles orfundamental constants of nature. In this scenario, our universe emerges by a selection procedure,following an anthropic reasoning [36], or arguments from quantum cosmology [37]. This approachcan be related with the idea of bubble universes in the sense of the possibility of tunneling amongdifferent vacua, giving rise to an eternal inflation that populates the landscape.Recently, the idea that the landscape should be constrained by consistency conditions has gainedmomentum. The argument is that the vast range of solutions coming from the landscape arephysically restricted to those that give rise to effective field theories, surrounded by a swamplandof inconsistent solutions [38]. In this scenario, the huge amount of possible vacua from the stringlandscape is strongly restricted, possibly leading to a unique vacuum state and hence without roomfor a string multiverse, except perhaps in the form of a cyclic universe [39]. This idea is closely related ersion October 17, 2019 submitted to
Universe with other proposals about cyclic universes, where each end of a universe poses the initial conditionsfor a next one, thus leading to a conformal cyclic cosmology [40].There exists a larger variety of multiverse scenarios originating from other physical ideas andproposing different concrete schemes. We should stress that the different multiverse scenarios,although conceptually akin, are so far only vaguely related in terms of physical formulation. So anobvious challenge on the road to the multiverse is to clarify the physical and mathematical relationbetween the different multiverse scenarios. For example, the relation between inflation and stringtheory is a subject of ongoing research, and is in fact considered one of the major challenges withinstring theory research, see e.g. [41] and references therein. According to the present status of research,it seems that only certain very specific string theory scenarios might actually allow for inflation, andthe concrete details of the mechanism are only starting to be understood quantitatively. To illustratethis point, [41] states that “At present, we are led to inflation in string theory by a web of inference”and that a better understanding of “non-supersymmetric solutions of string theory, particularly deSitter solutions (. . . ) continues to be a zeroth-order challenge for deriving inflation from string theory”.Curiously, the fact that this embryonic understanding of the relation between inflation and stringtheory poses a major challenge for the multiverse idea and especially for the interpretation that acommon view should exist between string and inflationary multiverse scenarios is a question that (tothe best of our knowledge) is barely being addressed in current research. With respect to Everett’smany-worlds interpretation, the question is perhaps even less clear. In [42], an argument was madefor a relation between the many-worlds interpretation and the (inflationary) multiverse. But it isprobably only fair to say that the argument is mainly qualitative and much further work is requiredin this area to show whether the conjectured connections between the different types of multiversecan actually be described in a concrete and convincing way.A related point is that all of these multiverse scenarios currently face a series of unsolved issuesand require much more detailing before they can be considered mature physical theories. This,in combination with the simple fact that the multiverse can be argued to constitute a change ofparadigm, makes the multiverse subject to criticism. The strongest argument against the multiverseprobably lies in the fact that the multiverse is considered a speculative idea that cannot be falsified,perhaps not even in principle. Indeed, one could wonder what physical sense it makes to considerother different universes if these have no detectable effect whatsoever on our universe, possibly noteven in principle. Some scientists argue that, if this is indeed the case, then the multiverse cannotbe considered a scientific theory, but should at most be included in the field of metaphysics [1].Regardless of the defense that some authors have made of “non-empirical theory assessment” [43]and related concepts (see also our discussion in Section 4), it bears little doubt that multiversescenarios would gain strength if they would lead to new and preferably concrete predictions aboutthe properties of our universe [44]. Interesting examples are the prediction that some features of theCMB spectrum, such as the cold spot, could be due to entanglement with another universe in stringtheory [37,45,46], collisions with other bubble universes in the context of eternal inflation [47–49] orrecently topological defect nucleation in bubble universes [50]. From a philosophical point of view,as stressed by Popper [51], it is better to have concrete conjectures that can be tested and possiblyrefuted, rather than a very general scenario which cannot be confirmed nor refuted.Before discussing this philosophical question in more detail, let us already mention alesser-known multiverse scenario, which could alleviate some of the mentioned criticisms. In theproposal of a quantum multiverse [52–55], a quantum cosmology program is developed for themultiverse as a set of entangled universes. Two relevant characteristics of this scenario are thefollowing. First, it does not pre-suppose a specific model for the different universes to pop up.Second, the entanglement between universes could give rise to dynamical and observable effectson each universe due to its interaction with other universes [56–58]. We will come back to this idea inSection 6. ersion October 17, 2019 submitted to
Universe
As we have just argued, a question that naturally emerges when dealing with such physicaltheories that explore the limits of our knowledge concerns their scientific viability. In this context, letus take a look at the descriptions of scientific method, change of paradigm and related issues in thephilosophy of science.
4. Philosophical aspects
There are various reasons why it is relevant to look at philosophical aspects of the multiversequestion. Let us just mention two. First, as we already mentioned in the introduction, the genericidea of a multiverse is not really new, and so it might be interesting to look at what philosophers andhistorians of science have to say about this.Second, theories about the multiverse almost automatically lead to questions about how to assessthese theories. Notions such as theory confirmation, verification and viability then become important.These notions are rarely defined explicitly, but have acquired relatively well-developed meanings inthe philosophy of science. The following (basic) definitions might be useful to set the vocabulary.“Theory assessment” consists in submitting a given hypothesis to empirical data. As possibleoutcomes, “theory confirmation” consists in empirical evidence which supports a given hypothesis,in particular by being in agreement with a prediction from the hypothesis. “Falsification” obviouslyis the opposite case: empirical evidence which contradicts a given hypothesis. “Verification” is theideal case in which supporting evidence is so strong that the hypothesis can be considered to beconclusively confirmed. Finally, the “viability” of a theory could be paraphrased as its compatibilitywith already existing data, irrespectively of whether it has produced any new predictions whichcould be submitted to additional testing. We will not further discuss these concepts explicitly, butthe remainder of this section will make clear that their understanding has evolved over time, and thatthey are much more involved than the naive definitions just given might suggest, see e.g. [59].Our third, and most important argument, is that the idea of a multiverse clearly challengesthe epistemological boundaries of science, and so enters into the grey zone where physics meetsphilosophy. In fact, the multiverse is often presented as a change of paradigm which completely altersour understanding of cosmology, and perhaps even more: some physicists claim that the multiverserevolutionizes the way in which we should look at science itself, and the way in which we assessscientific theories. But these terms, “paradigm” and “scientific revolution” stem from the philosophyof science, where they have been studied in great detail. Claims about the character of science and itsmethodology transcend science itself, and would thus benefit from a broader philosophical context.The philosophical dispute about the multiverse has so far taken place almost exclusively betweenphysicists, with professional philosophers largely staying safely out of the ring. The argument hascentered on (naive interpretations of) Popper’s falsificationism criterion, with some recent attemptsto reframe the question in terms of Bayesianism. In the light of the philosophy of science of the pastcentury, this is a bit curious. To explain why, it might be useful to go through a crash course which willlead us from Popper to Bayesianism, and then see how these ideas can be interpreted in the contextof the multiverse.
We will limit ourselves to the key elements of Popper’s, Kuhn’s, Lakatos’ and Feyerabend’s ideaswith relation to the demarcation problem and the formal description of scientific progress, and howBayesianism can be situated in this context. The interested reader is referred to, e.g., [60] or [61] forgood introductions.Let us start by sketching the historical context in which Popper came to prominence. In theearly 20th Century, there was a generalized expectation that all of mathematics could be framed onsolid logical foundations. This expectation was epitomized by Russell and Whitehead’s “PrincipiaMathematica” [62] and Hilbert’s programme [63,64]. A related feeling existed in the philosophy ofscience: science should obey firm laws of logic, and scientific progress should be formally expressible ersion October 17, 2019 submitted to
Universe in terms of logical laws related to deduction and induction. The main discussion in the philosophyof science of the epoch was between proponents and opponents of logical positivism: the idea that(both in science and in philosophy) only verifiable claims about the empirically observable realityare meaningful. But even the opponents (including Popper) of logical positivism opposed only itspositivist part but had no doubt that scientific progress could be described as a cumulative logicalprocess. The Russell-Whitehead-Hilbert ambition was blown to pieces by Gödel’s incompletenesstheorems [65]. The demise of logic as the foundation of scientific knowledge took a bit longer, startingwith Kuhn. But we are running ahead of our argument.Karl Popper’s landmark “Logik der Forschung” [66] was an attempt to circumvent the problemof induction while retaining the logical mould into which the description of scientific process shouldbe cast. The problem of induction, in its simplest version, is the fact that inference from (no matterhow many) concrete observations or experiments can never lead to certain knowledge about a generaltheory. Popper’s replacement of induction as a scientific criterion by falsification, and by a process ofconjectures and refutations, is logically water-tight: in principle, a single counter-example suffices todemonstrate the falsity of a general conjecture. However, Popper’s programme failed in two senses.First, it failed as a demarcation criterion to distinguish science (which makes falsifiable conjectures)from non-science (which does not). Second, it failed as a description of how scientific progress reallyworks in practice. Enter Thomas Kuhn.Kuhn held a historical view of science, as opposed to Popper’s normative view. In [67], Kuhndefended that the advance of scientific knowledge is not linear and continuous, but proceeds byalternation between normal science and paradigm shifts or scientific revolutions. The paradigmis the basic set of concepts, beliefs and practices shared by a community of scientists. Duringthe normal science phase, scientists attempt to articulate this paradigm in more detail, makeempirical interpretations and predictions, but do not question the paradigm itself. The observationalinterpretations are always framed within the paradigm, and in particular: the further they are distantfrom direct sensory experiences, the more they depend on theoretical concepts characteristic of theparadigm, an issue called the “theory-ladenness of observations”.Through accumulation of anomalies, i.e.: conceptual or observational challenges that resisteasy solution within the paradigm, this paradigm can enter into a state of crisis, thus opening thepossibility for a paradigm shift or scientific revolution. Some scientists will swap allegiance to a newparadigm, others will stick to the old paradigm until they retire (or die). But generally speaking,scientists usually adhere quite strongly to the fundamental assumptions of their own paradigm,which are often not even formulated very explicitly, and use these to judge other paradigms. This lackof an explicit formulation of criteria within each paradigm makes it very hard for scientists belongingto different paradigms to converse rationally about the pros and cons of each approach, a problemcalled “incommensurability”. This is related to the well-known problem of underdetermination oftheory by evidence: the idea that the experimental and observational evidence available withina particular branch of science is (even in principle) insufficient to pick out a single “true” theoryin a uniquely determined way. Kuhn’s response to the problem of underdetermination is that“scientific truth” is not solely determined by objective facts but also by consensus within the scientificcommunity. In this sense, Kuhn was probably the first to emphasize the social aspect of science, anaspect which was later worked out in detail by authors such as Pickering [71]. This, in combinationwith the lack of a clear criterion for paradigm change, has led to criticisms on Kuhn as proposing arelativist, even irrational view on the progress of science. Kuhn defended himself by pointing out thatrational criteria for paradigm choice can indeed be identified, such as empirical accuracy, consistency, This issue becomes ever more acute in high-energy physics and cosmology, and is related to the question of non-empiricaltheory assessment that we have mentioned earlier [43]. See also [68–70] for contemporary views on this problem.ersion October 17, 2019 submitted to
Universe broad scope, simplicity, and fruitfulness. But these criteria are not sufficient, in Kuhn’s view: twoscientists might agree on the criteria but nevertheless make different paradigm choices.So who was right between Popper and Kuhn? There have been arguments in both directions.The two most influential reactions to the Popper versus Kuhn debate were embodied by Lakatos andFeyerabend, which we will briefly discuss in turn.Imre Lakatos [72] tried to reconcile Popper’s and Kuhn’s views. He replaced Kuhn’s “paradigm”by the concept of “research programme”, which consists of a hard core of fundamental assumptions,and a series of auxiliary hypotheses. These auxiliary hypotheses can serve to increase thepredictability of the research programme, or to save it from threats. If most auxiliary hypothesesbelong to the first category, and most of the novel predictions are confirmed, then the researchprogramme is in a progressive state. If most predictions of the theory are refuted, and auxiliaryhypotheses are invoked to save the research programme, then the latter is degenerative. Researchprogrammes are thus not falsified in Popper’s naive sense, but they should be abandoned if theyhave entered a degenerative state, and a progressive alternative is available which has a strongerempirical content. In this way, Lakatos tried to reframe Kuhn’s revolutions on a rational basis, bygiving concrete criteria for switching allegiance between research programmes, while updating theessence of Popper’s falsification idea.Feyerabend, on the other hand, dismissed both Popper and Kuhn’s views on science (andtherefore also Lakatos’ attempt at a compromise) [73]. According to Feyerabend’s “epistemologicalanarchism,” any standard of rationality or universal methodological rule would be too restrictive and,if really applied, in fact hinder science. Feyerabend concludes, based on a historical analysis, that allcommonly accepted rules of science are frequently violated, and that new theories are accepted notbecause of accord with some universal “scientific method”, but because its supporters made use ofany “trickery” – apart from rational argumentation, Feyerabend mentions propaganda, psychologicaltricks, and rhetoric, including jokes and non sequiturs – to advance their cause. Illustratively,Feyerabend disagreed with the commonly held negative attitude towards ad hoc hypotheses. InFeyerabend’s opinion, ad hoc hypotheses are often required to temporarily make things work untila better understanding is achieved. Furthermore, Feyerabend rejected consistency as a criterion fortheory-building, since new theories cannot be expected to be as consistent as the old theory theypurport to replace. Feyerabend also made controversial claims about the ideological totalitarianismof science, and its negative impact on (western) society. Few scientists and philosophers of sciencewould probably agree with Feyerabend’s most radically relativist claims. Nevertheless, the essenceof Feyerabend’s analysis has withstood criticisms. As a consequence of Feyerabend’s work, togetherwith a more general shift of focus within the philosophy of science, the goal of formulating a universallogical-methodological framework for science, or a single and absolute demarcation criterion betweenscience and non-science, has been mostly abandoned.However, one further attempt at formalizing the progress of science should be mentioned,namely Bayesian epistemology, or simply Bayesianism. Bayesianism relies on Bayesian inference,and especially its so-called “subjective” interpretation. This is historically prior to thePopper-Kuhn-Lakatos-Feyerabend discussion, but has become widely popular as an approach toscientific progress more recently, and in particular is often mentioned in the context of theoreticalphysics. Bayes’ famous formula which relates conditional probabilities can be written as P ( H | E ) = P ( E | H ) · P ( H ) P ( E ) (1) where, in this context, H represents a hypothesis and E the evidence, and probabilities are taken asexpressing a priori ( P ( H ) ) and a posteriori ( P ( H | E ) ) degrees of belief, and P ( E ) = ∑ P ( E | H i ) P ( H i ) the overall probability for the evidence E to actually occur. In practice, only a limited range ofhypotheses are summed over, and P ( E ) becomes a somewhat subjective assessment. The Bayesianists’claim is that Bayes’ formula provides a useful model for scientific progress in general [74]. This ersion October 17, 2019 submitted to Universe is certainly true within Kuhnian phases of “normal science”. Bayesian inference is commonly andsuccessfully used to assess, for instance, the significance level of the outcomes of particle detectorexperiments or of cosmological observations. When it comes to paradigm shifts, there is a certaindebate about Bayesianism [75]. The right-hand side in (1) contains the a priori or subjective belief P ( H ) in the hypothesis H . Then, no matter how rigorously one defines P ( E | H ) , and thus no matterhow rationally the belief in H is updated, the left-hand side will still be a subjective belief, not aproof for the validity or degree of probability for the truth of hypothesis H . However, two key pointsstressed by Bayesianists are the following. First, the subjectivity of the prior beliefs can be avoided byworking with Bayesian likelihood factors B = P ( H | E ) P ( H ) (cid:18) P ( H | E ) P ( H ) (cid:19) − , representing the relativesupport of evidence E for H with respect to H . These do indeed not depend on the prior beliefs P ( H i ) , although they still depend on the P ( E | H i ) , for which an agreement among defenders ofdifferent paradigms might be equally hard to achieve. Second, when there is a sufficient accumulationof evidence in favour of a particular hypothesis H , all rational observers will eventually agree on ahigh probability for H , regardless of their original degree of belief. Let us now see how all these general philosophical arguments relate to the multiverse.4.2.1. PopperFrom a Popperian point of view, “the multiverse” as a generic theory cannot be falsified, andthis probably forms the most frequently heard criticism on the multiverse. However, two nuances areimmediately in order.First, as indicated before, Popper’s falsificationist programme is no longer seriously upheldwithin the philosophy of science, certainly not in its naive form: falsification by itself is not the motorof scientific progress. This indicates that, within theoretical physics, we should overcome the verypopular discussions about the multiverse and the anthropic principles centred on falsificationism,with one side defending it [76] and the other side claiming that it is about time to throw itoverboard [77]. However, the question of falsifiability is not just about "scientific methodology".Popper’s insistence on the testing of theories is still as relevant as it was a hundred years ago. Youcan formulate theories about reality, but if reality disagrees, the only way for nature to “kick back”and tell us whether our theories are tentatively right or wrong is through empirical confrontationwith experiment and observation. Said in other words, a scientific theory should be able to makepredictions which are testable: it must be possible to formulate what should be the case empirically (atleast in principle) if the theory is true, and in which empirical case the theory should be considered asbeing in trouble. The idea that this combination of verification and falsification is an essential elementin the “scientific method” is still largely uncontroversial among the immense majority of scientistsand philosophers of science alike. Even [43], which advocates strongly for “non-empirical theoryassessment” based on the alleged success of string theory, admits that such non-empirical assessmentshould ideally be temporary and that “empirical testing must be the ultimate goal of natural science”.A second nuance is that, although the multiverse in general cannot be falsified, this does notmean that concrete multiverse scenarios cannot be falsified. In fact, in our opinion this is perhapsthe most crucial challenge for the multiverse in the near future: to work out concrete scenarios withconcrete predictions that could be tested, at least in principle. We will discuss this in more detail inSection 6.4.2.2. KuhnDoes the multiverse really represent a “paradigm change” or a “scientific revolution”, in Kuhn’svocabulary? This question is hard to answer for several reasons. One is that, historically speaking,such paradigm changes are usually not identified as and when they occur, but only a posteriori. Also, ersion October 17, 2019 submitted to
Universe
10 of 21 in spite of Kuhn’s insistence on the revolutionary character of such paradigm changes, the momentwhen this revolution has taken place is very hard to pinpoint exactly. The revolutionary processdepends on a confluence of several factors. That a single event and/or a single scientist is afterwardshighlighted has often more to do with good story-telling than with the real complicated process thathas taken place. Special Relativity is a good example. While often presented as Einstein’s first strokeof genius out of the blue, Einstein’s treatment was in fact the culmination of a long process withcrucial contributions from Lorentz and Poincaré.These observations are in stark contrast with some messages in the multiverse literature whichprophesy a revolution in our understanding of reality (see the examples [4,5,23,24] given earlier).In our opinion, one should be careful with this kind of claims. Announcing a scientific revolutionwhile it is supposedly taking place runs a serious risk of sounding hollow. We are not aware ofany research on the frequency of such claims in physics, but it might be interesting to note whatis happening in other areas of research. In medical research, for instance, it was found that thefrequency of announcements of “unprecedently innovative groundbreaking” ideas has increased upto 15000% over the past four decades [78]. The authors dryly remark that “whether this perceptionfits reality should be questioned”. The editorial [79] concludes that “it is time to acknowledge that themisrepresentation of research findings through exaggeration or hype is a grave matter for scientificintegrity”. In spite of Kuhn’s insistence on the social character of scientific truth-building, for ascientific revolution to take place, it is not sufficient that a particular scientific community claimsthat it is taking place. Similar feelings have often existed, even in the relatively recent past, andhave been proven to be wrong much more often than they were right. The development of quantummechanics is an interesting exception; Chew’s bootstrap model, early versions of supergravity andgeometrodynamics, and Euclidean quantum gravity are just a few confirming examples.A related question is: which paradigm is the multiverse supposed to be replacing? The paradigmof “the universe”? Or merely the standard Λ CDM model of cosmology? In the first case, it certainlyseems a bit early to argue that “the universe” is in a state of crisis. In the second case: it is truethat there are serious puzzles in cosmology, from the nature of dark matter and dark energy tothe connection between primordial fluctuations and large-scale structure formation, to name but afew. But these are challenges for any cosmological model rather than clear-cut problems with thecurrent Λ CDM paradigm. Λ CDM can be interpreted as the simplest cosmological model based onGeneral Relativity which is in agreement with the firmly established bulk of current observations, i.e.:a concordance model with much room for further modifications and extensions. There is at presentnot a single observation that points towards the assumption of a single universe as the crucial cause ofthese puzzles. Also, let us not forget that observational cosmology has grown in only a few decadesfrom a phenomenon almost on the margin of science to a blooming area of research, but is still inits infancy. Depending on how one wishes to look at it, one might therefore argue that the Λ CDMmodel is suffering from serious anomalies, or that it has so far been of an unprecedented success inthe history of cosmology. Either way, Λ CDM will undoubtedly require corrections, perhaps evenmajor revisions [80,81]. But from a purely observational point of view, the case for giving up tryingto explain cosmology within a single universe is currently rather thin.4.2.3. LakatosAccording to Lakatos’ criterion, a research programme should be abandoned when it enters intoa degenerative state, and at the same time a progressive alternative is available. Recall that a researchprogramme consists of a hard core, which is maintained unaltered until the research programme iscompletely abandoned, and a series of auxiliary hypotheses. A degenerative research programme ischaracterized by the formulation of auxiliary hypotheses in order to save it from failures to predict orexplain empirical observations, while a progressive one uses auxiliary hypotheses to strengthen itsempirical content. ersion October 17, 2019 submitted to
Universe
11 of 21
From this point of view, most approaches to the multiverse should probably not (yet) really beclassified as a research programme. Rather, in Lakatosian terms, the multiverse is in fact an auxiliaryhypothesis which has arisen within various existing research programmes (such as string theory andinflation theory) to justify their lack of empirical success, and more in general: the lack of empiricalsuccess of any approach to quantum gravity and/or Planckian physics. We do not wish here to jumpto the conclusion that these are all degenerative research programmes. But it might be relevant torealize that “the multiverse” in its current state does not fit the Lakatosian description of a (mature)research programme.Moreover, as we already indicated in the Kuhnian discussion above, there is no degenerativeresearch programme in need of replacement (yet). It is certainly true that there are many challengesfor the standard Λ CDM model of cosmology, in particular the cosmological constant problem. Butconcluding that Λ CDM is in a degenerative state would be a bit overhasty, and at present there isn’tany progressive alternative with a stronger and more successful empirical record available. Withregard to the cosmological constant problem (see also Section 5), the multiverse offers one type ofsolution, but there also exist several other categories of interesting ideas that do not require positinga multiverse [82], and it is probably fair to say that none of these proposals, neither universe normultiverse-related, are currently generally accepted as satisfactory.4.2.4. FeyerabendWithin Feyerabend’s vision, it is tempting to highlight that some scientists make use not onlyof rational argumentation, but also of the various types of “trickery” mentioned by Feyerabendto reinforce the impact of their model. There is a certain truth to this: the multiverse cause isomnipresent, especially in the popular scientific press, but also in the academic literature (with a highpublication rate of scientific articles). On the positive side, this illustrates that theoretical physicistsare no longer isolated in their academic ivory towers, but make an effort to reach out to the generalpublic and present current ideas about fundamental issues to a wider audience. On the negativeside, in the absence of empirical testing, in spite of the robustness of the underlying theories, criticistsmight argue that the truth-claims of the multiverse rely mainly on a social consensus.There is a related point for which we will return to Lakatos’ terminology: research programmesdefine which paths to pursue (positive heuristic) but also which paths to avoid (negative heuristic).Is there a real risk that the increasing influence of multiverse ideas might lead to a gradual decline inexplorations of alternative approaches in cosmology and high-energy physics as has been argued inrelated contexts [83–85]? The current situation in cosmology does not seem so alarming. And in orderto raise a new issue it is necessary to explore its possibilities. We will therefore not further examinethis question here. It should be clear that we agree on the importance of empirical testing, and willtherefore insist that this should be crucial also within multiverse approaches.4.2.5. BayesianismThe main weakness, in our opinion, of a Bayesian defense of the multiverse, is the following.Bayesianism is very well-suited to formulate logically how the probability for the true occurrence ofa certain event should be updated in the light of observational evidence, but is more questionablewhen it comes to formalizing paradigm changes.We pointed out earlier–see Eq. (1)–that a sufficient accumulation of evidence in favour of aparticular hypothesis H will “force” all rational observers to assign a high degree of probability for H . But it is equally true that anybody who is strongly unconvinced a priori of the hypothesis H will (and, rationally speaking: should ) refuse to admit a strong probability for the truth of H untilthere really is overwhelming evidence. And such overwhelming evidence, in the opinion of the largemajority of scientists, should still come from the confrontation of the hypothesis with observation.Once such “traditional” scientific proof in the form of empirical verification becomes available, thenit is largely irrelevant whether one abides by Bayesian principles or not. It is therefore hard to see ersion October 17, 2019 submitted to Universe
12 of 21 how Bayesian inference could formalize scientific progress across the kind of paradigm shift whichis currently being defended by some proponents of the multiverse, namely one based largely ontheoretical arguments. More generally, in spite of the unquestionable value of Bayesian inference,the Bayesian view on scientific progress in general (including theoretical paradigm shifts) is a bitcurious, because it represents a return to an attempt at a logical formulation of the progress of science,disregarding the historical evolution from Popper to Feyerabend that we have tried to outline earlier.We will here briefly sketch three further problems related to Bayesianism.(1) The first problem is well known as the measure problem. Our universe provides us with asample of fixed size n =
1. This means that almost all statistical properties of the alleged multiversepopulation are ill-defined, unless one somehow defines a concept of measure across the multiversepopulation. This can be done essentially in two (interrelated) ways. The first way is to assume somesimple distribution, such as a uniform distribution of the possible cosmological constants [87] (or of asmall set of variables, for example the cosmological and gravitational constants). But apart from thefact that it is hard to justify a priori why precisely these variables should characterize the distribution,one should also realize that, with a uniform distribution, many statistical characteristics are essentiallydetermined by the limiting values. Just like in the famous German tank problem, estimating theselimiting values based on a single observation entails a very high degree of uncertainty. A secondmethod to define a measure is to assume some fundamental theory, typically string theory [36], anduse the theoretical knowledge obtained from this theory to derive a measure. But this has variousassociated risks. As pointed out by Ellis [85], “the statistical argument only applies if a multiverseexists; it is simply inapplicable if there is no multiverse: we cannot apply a probability argumentif there is no multiverse to apply the concept of probability to.” Even if the multiverse really doesexist, there is still a risk of circularity: to construct a measure from an empirically unverified theorybased on an n = n = n = n = − ( ) = Letus play the devil’s advocate and, for the mere sake of the argument, defend the creationist view ofintelligent design in biology. State any four gaps in the evolutionary picture of life and humanity.The Polchinski-Bayesian conclusion would be that there is a 93.75% probability that the universe wasliterally created by God in seven days. If this argument sounds too far-fetched, let us insist on the keypoint: the current lack of explanation for any scientific challenge within conventional single-universe In reality Polchinski’s four questions are not independent, so the numerical estimate is incorrect even from a purelyprobabilistic point of view. But since Polchinski himself states that the number itself is not important, we will not furtherdissect this issue.ersion October 17, 2019 submitted to
Universe
13 of 21 relativistic cosmology in itself is not a sufficient support for an anthropic or multiverse argument. Wewill come back to this question in Section 4.3.(3) The third problem is closely related to the previous one, namely the risk of acceptingBayesianism in combination with purely theoretical arguments as a substitute for empirical testing.This is best illustrated by an example. According to a Bayesian reasoning with purely theoreticalarguments, there should have been almost 100% certainty in favour of the Georgi-Glashow SU(5)model [90]: this was closely based on some of the best physical theories that mankind has everproduced, it was mathematically elegant and favoured by a large proportion of theoretical physicists,and no alternatives even closely as appealing were available at the time. Yet, proton decay was notobserved and so the Georgi-Glashow SU(5) unification model turned out to be wrong. This againillustrates our continuous insistence on empirical assessment.
In the previous section, we have insisted on empirical theory assessment. Within the multiversecontext, some authors propose to diminish the importance thereof, and to replace it (partially) bypurely theoretical criteria. This is another line of thought where the philosophy and history of sciencecan be relevant.The idea that theoretical arguments, for example criteria of mathematical consistency andelegance, can illuminate the path towards a correct “fundamental” theory, is not new. On the contrary,this is closely related to Platonism, one of the oldest branches of western philosophy. It has resurgedin theoretical physics repeatedly, especially in the past century or so [91]. The common pattern isstriking: a scientist or group of scientists believes in the fundamentality and finality of the theory theyare working on, based on the past success of the building blocks of this theory and the elegance oftheir construction. Empirical predictivity is either looked down upon, or the lack of empirical successis simply disregarded. Eventually, so far at least, the theory turns out to be either completely wrong or,in the best of cases, simply void of empirical content. The best-known example is perhaps Descartes’vortex theory, abandoned in favour of Newton’s empirically much more successful laws of motion.But more recent examples also abound. A ring-vortex theory, highly popular in late 19th centuryBritain, was developed in quite some mathematical detail by such famous contributors as William“Lord Kelvin” Thomson and FitzGerald. Although it never managed any level of empirical success, itcontinued to be defended by many scientists for several decades because of its elegance. As anotherexample, Eddington developed a fundamental “Relativity Theory of Protons and Electrons” basedon the construction of a series of fundamental constants which were supposed to relate microphysicsand cosmology. In Eddington’s view, the truth of his theory followed from purely epistemologicalconsiderations. Empirical confirmation was completely secondary, and even though he did in factmake quite a few observational predictions, he would simply disregard any disagreement with actualobservations rather than let them ruin his beautiful theory. Many more historic and contemporaryexamples are discussed in detail in the excellent [91].While [91] cautiously avoids extracting any explicit conclusions with regard to the currentsituation, authors such as [92,93] have argued that a blind quest for mathematical beauty has indeedled contemporary fundamental physics astray. So does history simply repeat itself? Let us examinesome reasons to believe that the case of the multiverse might be different. From a social point of view,the current state with respect to various approaches in quantum gravity represents the first timethat a large and international scientific community defend a common idea based on such theoreticalcriteria. The previous occurrences were mainly of single scientists (including such prestigious ones asEddington and his “Fundamental Theory” or even Einstein and his “Unified Field Theory”), or hadat most “national” success (the late 19th-century vortex theory, which has been called a “Victoriantheory of everything” by Kragh [94], was very popular in the UK but had limited resonance in therest of the world). With respect to scientific content, the key argument in string theory and somemultiverse-related approaches is that the theoretical “gap” to be bridged is shallow, in other words: ersion October 17, 2019 submitted to
Universe
14 of 21 that the multiverse is a natural continuation of our best theories, general relativity and quantumfield theory; that we are indeed close to finding such a “final theory”, and that consistency, eleganceand uniqueness should therefore be sufficient arguments to solve the remaining problems (until thesolution is eventually confirmed empirically). In this context, there is a statement by Popper thatcomes to mind: “Whenever a theory appears to you as the only possible one, take this as a sign thatyou have neither understood the theory nor the problem which it was intended to solve.” [95].But let us try to make a more precise counter-argument.First of all, it is true of course that unification has been an important motor in the history ofscience. However, unification and uniqueness are two different concepts. Their apparent relationfinds its origin in the reductionist idea that gradual unification will lead to a unique theory ofeverything, at the top of a pyramid of theories. This idea has been strongly criticized by somephysicists [96] and philosophers [97] alike, see also [98], who argue that the major advances infundamental physics in the recent past have relied on a combination of unification and emergence.Second, it is an interesting question whether the current state of physics, and in particular generalrelativity and quantum field theory (the precursors of the multiverse), could have been achievedthrough arguments of consistency, elegance and uniqueness. For general relativity, such argumentshave certainly been crucial in Einstein’s reasoning, and so one might be tempted to answer “yes”. Butfor quantum field theory, and its application to particle physics, although we cannot repeat history toanswer the hypothetical question, the historical answer is a definite “no”, as described in detail forthe case of quarks in [71].Third, the final unification is believed to take place at the Planck scale, and so the “dreams of afinal theory” [99] are related to the idea that we are close to uncovering Planckian physics. This thirdpoint deserves a more detailed analysis, which we will undertake in the next section.
5. Fine-tuning & the multiverse... or is it really a tale of scales?
One of the strongest arguments in favour of the multiverse is the cosmological constant problem.Since the observed value of Λ is some 120 orders of magnitude smaller than the straightforwardtheoretical estimation , and any value of Λ very different from the actually observed one wouldprobably make life in the universe impossible, it is argued that “the only known way to address [thisproblem] without invoking incredible fine-tuning [is] related to the anthropic principle, and, therefore,to the theory of the multiverse”[5].Let us jump back to the Planck-scale unification argument of Section 4.3 for a moment. Somescientists working in quantum gravity believe that we are close to uncovering Planck-scale physics,and that consistency and perhaps uniqueness arguments should therefore be sufficient to bridge theremaining gap towards a final theory [43,88,99], possibly a multiverse theory.The highest-energy physics that we actively control is the energy produced at the LHC. This iscurrently on the order of 10 TeV, i.e. 10 GeV. Compare this to the Planck scale, 10 GeV, the scaleat which quantum gravity supposedly take place. There is a difference of 15 orders of magnitude.Even high-energy cosmic ray detection rarely exceeds 10 TeV, still 13 orders of magnitude below thePlanck scale. This problem is of course well-known among high-energy physicists, but there seemsnevertheless to exist an optimistic view on bridging this gap [88]. However, two simple comparisons Just in case some reader might benefit from a reminder, the theoretical estimate comes essentially from assuming thatthe cosmological constant represents the vacuum energy E vac , imposing a cut-off k c to the theory and calculating E vac byintegrating over all degrees of freedom up to k c , which gives E vac = ¯ hk c (a result which is consistent with a straightforwarddimensional analysis [100]). Assuming k c = E Planck immediately leads to the undesired result, while even k c = E EW , with E EW the electroweak scale, still leads to a discrepancy of some 50 orders of magnitude. It might be worth insisting thatit is essential to insert a cut-off in the calculation in order to avoid an even more unpleasant prediction for the vacuumenergy, namely infinity. Note that the observational energy scale associated to dark energy is in fact small, and mighttherefore be due to quantum field effects potentially accessible to near-future observations. However, this would still leavethe cosmological coincidence problem unexplained, namely why the matter energy density and the dark energy densityhave the same order of magnitude in the present epoch.ersion October 17, 2019 submitted to Universe
15 of 21 might serve as a cold shower. The extrapolation from the highest-energy physics that we controlempirically to the physical theories which justify the idea of a multiverse is (literally) still severalorders of magnitude stronger than the extrapolation from a grain of salt (size 10 − m) to the sizeof the moon (diameter 10 m). To put another example: imagine that a biologist would claim that,by studying the macroscopic properties of the largest living beings on earth, blue whales, he couldinfer the biological structure of the smallest known bacterial cells, with sizes 0.1 µ m. The mere scaledifference of 10 is peanuts in comparison with the jump from the LHC to the Planck scale.There are strong theoretical reasons to believe that the cosmological constant is related toPlanck-scale physics. In fact, the argument in favour of the landscape of string theory rests preciselyon Planck-scale arguments. Therefore, because of the energy gap just described, perhaps weshould simply admit that the “worst theoretical prediction in the history of physics” is due to our(unsurprising) ignorance of physics at the Planck scale, that we are currently exploring many ideas,but that all of these (including the multiverse) are so far still in an embryonic state.It is tempting to put the blame on the lack of empirical data [43]. It is of course true that thereis no empirical data available for physics at the Planck scale. But two interpretations are possible.One could say that experimentalists have not been able to keep up with theorists. Perhaps a fairerinterpretation is that, after the enormous success of quantum field theory and the standard modelof particle physics, theorists have run ahead, jumping several scales and constructing theories wellabove current experimental possibilities. As we have defended above, scientific progress typicallyrests on a complex interplay between theory and observation, and this might be even more importantas we move further and further away from direct sensory experience. Bottom-up and top-downapproaches in fundamental physics should be complementary [101]. Nowadays the equilibrium inthe search for quantum gravity is a bit distorted. Near-future observational surveys with respectto the “dark sector” of the universe such as DESI and EUCLID are promising. But because of thescale problem that we have just stressed, the key message should probably be one of patience and ofanticipating slow and indirect progress, rather than immediate spectacular advances.
6. Physical multiverse and testability
The previous discussion leads to the following general issue: How could the overallconceptual challenge be met of converting the multiverse from a speculative (or even metaphysical)consideration into a physical theory? The multiverse currently provides an interesting framework tounderstand reality, but it should also be followed by testable predictions. To come back to the relationbetween the multiverse idea as an epistemological extension of the Copernican revolution that wementioned at the beginning of Section 3: Humanity has gradually realized its loss of importance as thecenter of existence when science has been able to look further and realize that those observed objectswere in fact other structures similar to ours: other planets, other stars, other galaxies. The possibleextension to the multiverse is not accompanied by any such direct observation, and is thereforeof a different speculative order. Ultimately, the multiverse question comes down to determiningwhether, in order to confront the observational challenges and anomalies of cosmology, it is sufficientto consider a single universe, or whether we need a multiverse scenario. The main element in theeffort to answer this question consists in setting up multiverse scenarios and looking for empiricalpredictions which can be tested. Depending on the type of multiverse scenario, this can be very hard,perhaps even impossible. For instance, in a multiverse scenario where the different universes possessdifferent physical laws or mathematical structures, it is hard to see how to look for interactions with The only well-developed bottom-up approach to “quantum gravity phenomenology” is the ongoing search for LorentzInvariance Violations [102,103]. However, it might be useful to stress that neither string theory nor loop quantum gravitymake clear and unambiguous predictions about Lorentz Invariance, not even at a qualitative level.ersion October 17, 2019 submitted to
Universe
16 of 21 our universe. Alternative ways of assessment might then still lead to a certain degree of confidence,but always provided that other parts of the theory can be tested empirically.In this section, we want to sketch a possible way of approaching the empirical multiversequestion, i.e.: to establish empirical predictions in the traditional physical sense, limited to ouruniverse but nevertheless allowing us to find some hint of interactions with other universes. Inorder to describe such “physical multiverse” scenarios, no specific multiverse model is required. It issufficient to impose certain minimal requirements on the multiverse scenario.The first of these requirements is the classical independence of the spacetimes of each composinguniverse, at the level of the standard phenomena in General Relativity. This degree of independenceis essential in order to consider each universe as a separate and differentiable entity. In the oppositecase, it would be possible to define the different components as different regions of a single universe.If we understand as standard spacetime connections the ones allowed by General Relativity (withoutintroducing exotic issues such as closed timelike curves) we assume that such causally completelydetermined relations do not exist between the spacetimes of the different universes that composethe multiverse. Note that the existence of non-standard (classical or quantum) connections is notprohibited by this definition. On the contrary, these are essential in order to have some possibility ofinteraction among universes and therefore some empirical imprint to look for.The second requirement is that each of the universes must be potentially observable, by director indirect measures, from some other universe. In this way, physical predictions in our universecan be established as a consequence of the physics of the whole multiverse. This shows that theindependence among universes works only at the (classical) level of the spacetimes per se, not of allits components. There must exist some degree of interaction among them.Finally, we also impose that, if the constants of nature are allowed to vary from one universe toanother, then the values of these constants must be linked through the physical laws governing theoverall multiverse. In other words, these physical constants cannot emerge independently but mustbe correlated, for instance, through quantum entanglement effects between universes.One could paraphrase these three conditions by saying that the different universes in themultiverse should have causally independent spacetimes but with correlations among them. Theserequirements do not impose any specific physical scenario, but are sufficient to define testableconsequences of any multiverse scenario which obeys them.In order to clarify this concept one can consider a classification of these correlations in termsof their classical or quantum nature. The classical correlations could be given, for instance, byconsidering the multiverse as a multiply connected spacetime, where each universe is connected withother by means of Lorentzian tunnels [104,105]. It is important to note that, from the first conditiongiven above, there cannot exist causal relations among the different universes. The existence of causalrelations would entail the existence of a common time between both universes which could then notbe considered independent. The connections could therefore be formed by wormholes convertedinto time machines, providing closed timelike curves in the interior of the tunnel [106]. Potentialobservable effects of wormholes have been studied in several papers [107–112]. The current challengein the multiverse context is the search of an unequivocal observable effect of such a wormholeconnection with another universe [113].Quantum correlations could come from the quantum entanglement between universes.According to the first physical multiverse requirement, the spacetimes of each component universemust be classically differentiable. But in this scenario they would not be quantum separable, givingrise to an entangled multiverse [114]. In this context, one could determine the effects on our universethat show up as a consequence of these inter-universe quantum correlations. In the absence of aclassical channel, these correlations cannot be directly detected. But the influence of such correlationscan be examined, for example on the value of the cosmological constant. It might be hard to imaginesuch an indirect effect which could not equally be explained within a single-universe scenario.However, the study of the different schemes of interaction among universes and the development of ersion October 17, 2019 submitted to
Universe
17 of 21 a toy-model catalogue of observable effects and predictions allows an important progress towardsmultiverse phenomenology and of the types of effects that could be expected in more detailedscenarios [56–58,114,115]. The investigation of these quantum correlations is complicated by thelack of a quantum theory describing our universe, and most current models therefore focus onqualitative approximations to the collective phenomena that can arise in the consideration of aquantum multiverse. Alternatively, an exhaustive description of the spacetimes in the framework ofquantum mechanics could be attempted. This allows a more rigorous description of the interactions,but at the cost of a great technical complexity which limits the conception of different universes [116].We are still very far from having a complete theory that would allow us to settle the presentdiscussion, or a fully systematic way of deriving empirical consequences from concrete multiversescenarios. Nonetheless, the physical multiverse ideas just described show that, at least for certainclasses of multiverse models, it should be possible to extract empirical predictions based on relativelygeneral considerations. So it is interesting to keep them in mind when dealing with these issues.Also, if such inter-universe correlations as just described really exist, then this would indicate thenecessity of considering the multiverse as an indivisible framework. This in itself should be sufficientmotivation to construct such generic physical multiverse models and study their possible empiricaleffects.
7. Conclusion
In our view, it is not so important to determine whether speculations about “the multiverse” arepart of science or not. Only time will tell. But certainly multiverse scenarios should be recognizedfor what they (still) are: an embryonic framework which can be useful to understand and formulatecertain problems related to cosmology, but which is still far away from being testable in any generalphysical sense. Care should perhaps be taken with claims that “multiverse theories are utterlyconventionally scientific” [117], or that Bayesian arguments show that, by a “conservative” estimate,“the likelihood that the multiverse exists [is] 94%” and that “those who find this calculation amusing(...) should be a bit more humble” [88]. Such claims might be more counter-productive than anythingelse. Indeed, they do not fairly reflect the current scientific status of the field, nor do they agree withhistorical and philosophical analyses and in particular the importance of empirical content and of thecomplex interplay between theory-building and observation required for scientific progress.Vice versa, in spite of all the warnings that we have formulated, it is certainly not our intentionto dismiss the general idea of a multiverse as a developing physical theory. This would imply closingthe door to a whole range of ideas and techniques that are currently being developed, and some ofwhich could indeed turn out to be fundamental in our understanding of the nature of spacetime. Butempirical testing should always remain the central aim of science, even (or perhaps: especially) inthe multiverse epoch. In that sense, the general framework for a physical multiverse that we havediscussed could be useful as a guide for the development of empirical multiverse scenarios, andmore generally: to discriminate emergent ideas and to look for the possible testability of differentcosmological scenarios involving either a single universe or a multiverse in any of the variousmultiverse definitions.
Acknowledgments:
A. A-S. wants to acknowledge the memory of Pedro Félix González-Díaz as a source ofinspiration for her research and for originating the discussion about the physical multiverse. The authorsacknowledge Project No. FIS2017-86497-C2-2-P (A. A-S.) and FIS2017-86497-C2-1 (G. J.) from the SpanishMineco.
Author Contributions:
Both authors contributed equally to this work
Conflicts of Interest:
The authors declare no conflict of interest.
References
1. Carr, B. (ed.), Universe or Multiverse? Cambridge University Press (2007) ersion October 17, 2019 submitted to
Universe
18 of 21
2. Chamcham, K.; Silk, J.; Barrow, J. D. and Saunders, S. (eds.), The Philosophy of Cosmology. CambridgeUniversity Press (2017)3. Dardashti, R. ; Dawid, R. and Thébault, K. (eds.), Epistemology of Fundamental Physics: Why Trust aTheory? Cambridge University Press (2019)4. Barrau, A. Physics in the multiverse: an introductory review. CERN Courier 47, 13-17 (2007)5. Linde, A. A brief history of the multiverse. Rep. Prog. Phys. 80, 022001 (2017)6. Ellis, G. and Silk, J. Scientific method: Defend the integrity of physics. Nature 516, 321–323 (2014)7. Ellis, G. Does the Multiverse Really Exist? Scientific American, August 2011, 38-438. Kragh, H. Contemporary History of Cosmology and the Controversy over the Multiverse, Annals ofScience, 66:4, 529-551 (2009)9. Bettini, S. A Cosmic Archipelago: Multiverse Scenarios in the History of Modern Cosmology.arXiv:physics/0510111 (2005).10. Rioja, A.; Ordoñez, J. Teorías del universo. Síntesis, Madrid, Spain, 200611. Bower, R. G.; McLeish, T. C. B.; Tanner, B. K.; Smithson, H. E.; Panti, C.; Lewis, N. and Gasper, G. E. M.A medieval multiverse?: Mathematical modelling of the thirteenth century universe of Robert Grosseteste,Proc. Roy. Soc. Lond. A (2014) 2014002512. Bruno, G. De la causa, principio et Uno (1584). For a modern translation, see Bruno, G. Cause, Principleand Unity. Translated and edited by De Lucca, R. Cambridge University Press, Cambridge, UK (1998).13. Swedenborg, E. Principia Rerum Naturalium (1734). Translated by J. R. Rendell and I. Tansley as: ThePrincipia Or The First Principles Of Natural Things. The Swedenborg Society, London (1912)14. Wright, T. An Original Theory or new Hypothesis of the Universe, Founded upon the Laws of Nature.London (1750). Modern edition: Cambridge University Press (2014).15. Kant, I. Universal natural history and theory of the heavens, 1755. Cambridge University Press, Cambridge,UK, 2012.16. Von Humboldt, A. Cosmos: A sketch of a physical description of the universe, 1845-1862. CambridgeUniversity Press, Cambridge, UK, 2011.17. Shapley, H.; Curtis, H. D. The scale of the universe. Bulletin of the National Research Council. 2 (Part 3,Issue 11): 171–217 (1921).18. Leibniz, G.W. Essais de Théodicée sur la bonté de Dieu, la liberté de l’homme et l’origine du mal.Amsterdam (1710). For a modern translation, see e.g. Leibniz, G. W. Theodicy: Essays on the Goodness ofGod, the Freedom of Man, and the Origin of Evil. Translated by E. M. Huggard. Lasalle, IL: Open Court,198519. Schopenhauer, A. Von der Nichtigkeit und dem Leiden des Lebens. Chapter 46 in: Die Welt als Willeund Vorstellung, first included in the 2nd expanded edition (1844). For a modern translation, see e.g.Schopenhauer, A. On the Vanity and Suffering of Life. Chapter 46 in: The World as Will and Representation,Translated by E.F.J. Payne, Dover (1969).20. Rees, M. Just Six Numbers: The Deep Forces that Shape the Universe. Weidenfeld & Nicolson, London(1999)21. ´Sr¯ımad-Bh¯agavatam (Bh¯agavata Pur¯ana) 6.16.37. The translation is taken from Ramesh Menon, BhagavataPurana, The Holy Book of Vishnu (2 vols.), Vedic Books, Delhi (2007).22. Page, D. Does God So Love the Multiverse? In: Stewart, M. Y. (ed.), Science and Religion in Dialogue.Blackwell Publishing (2010)23. Rees, M. On the future - Prospects for humanity. Princeton University Press (2018)24. Livio, M. and Rees, M. Fine-Tuning, Complexity, and Life in the Multiverse. arXiv:1801.06944. To appearin: Consolidation of Fine Tuning (forthcoming)25. Vilenkin, A. Many Worlds in One: The Search for Other Universes. Hill and Wang (2007)26. Kragh, H. An anthropic myth: Fred Hoyle’s carbon-12 resonance level. Arch. Hist. Exact Sci. (2010) 64: 72127. Vilenkin, A. The principle of mediocrity, in: Astronomy and geophysics. National meeting of the RoyalAstronomical Society. Blackwell Publishing Ltd, Oxford, UK, 2011.28. Hartle, J. B. and Hawking, S. W. Wave function of the Universe, Phys. Rev. D 28, 2960 (1983).29. Vilenkin, A. Boundary conditions in quantum cosmology, Phys. Rev. D 33 , 3560 (1986).30. Gott, J. R. III and Li, L. X. Can the universe create itself?, Phys. Rev. D , 023501 (1998)31. Tegmark, M. The multiverse hierarchy. In: [1] ersion October 17, 2019 submitted to Universe
19 of 21
32. Everett, H. Relative state formulation of quantum mechanics.
Rev. Mod. Phys. , , 454.33. Linde, A. D. Eternal chaotic inflation. Mod. Phys. Lett. A , , 81.34. Linde, A. D. Eternally existing selfreproducing chaotic inflationary Universe. Phys. Lett. B , , , 395.35. Linde, A.; Vanchurin, V. How many universes are in the multiverse?. Phys. Rev. D , , 083525.36. Susskind, L. The anthropic landscape of string theory. In: [1].37. Holman, R.; Mersini-Houghton, L.; Takahashi, T. Cosmological avatars of the landscape. II. CMB and LSSsignatures. Phys. Rev. D , , 063511.38. Vafa, C. The String landscape and the swampland, hep-th/0509212.39. Johnson, M. C. and Lehners, J. L. Cycles in the Multiverse, Phys. Rev. D (2012) 10350940. Penrose, R. Before the Big Bang: An outrageous new perspective and its implications for particle physics. Conf. Proc. C060626 , 2759.41. Baumann, D; McAllister,L. Inflation and String Theory. Cambridge Monographs on Mathematical Physics,Cambridge University Press (2015)42. Bousso, R; Susskind, L. The Multiverse Interpretation of Quantum Mechanics, Phys. Rev. D 85, 045007,2012.43. Dawid, R. String Theory and the Scientific Method. Cambridge University Press (2013)44. Rees, M. J. Cosmology and the multiverse. In: [1].45. Di Valentino, E.; Mersini-Houghton, L. Testing Predictions of the Quantum Landscape Multiverse 1: TheStarobinsky Inflationary Potential. JCAP (2017) no.03, 002.46. Kinney, W. H. Limits on Entanglement Effects in the String Landscape from Planck and BICEP/Keck Data.JCAP (2016) no.11, 013.47. Aguirre, A.; Johnson, M. C.; Shomer, A. Towards observable signatures of other bubble universes. Phys.Rev. D , (2007) 063509.48. Wainwright, C. L.; Johnson, M. C.; Aguirre, A.; Peiris, H. V. Simulating the universe(s) II: phenomenologyof cosmic bubble collisions in full General Relativity. JCAP (2014) no.10, 024.49. Zhang, P.; Johnson, M. C. Testing eternal inflation with the kinetic Sunyaev Zel’dovich effect. JCAP (2015) no.06, 046.50. Zhang, J.; Blanco-Pillado, J. J.; Garriga, J.; Vilenkin, A. Topological Defects from the Multiverse. JCAP (2015) no.05, 059.51. Popper, K. R. Conjectures and Refutations: The Growth of Scientific Knowledge. Routledge (1963).52. Robles-Perez, S. and Gonzalez-Diaz, P. F. Quantum state of the multiverse, Phys. Rev. D (2010) 083529.53. Robles-Perez, S. and Gonzalez-Diaz, P. F. Quantum entanglement in the multiverse, J. Exp. Theor. Phys. (2014) 34.54. Kanno, S.; Shock, J. P. and Soda, J. Entanglement negativity in the multiverse, JCAP (2015) 015.55. Kanno, S. Quantum Entanglement in the Multiverse, Universe (2017) no.2, 28.56. Robles-Perez, S.; Alonso-Serrano, A. and Gonzalez-Diaz, P. F. Decoherence in an accelerated universe, Phys.Rev. D (2012) 063511.57. Alonso-Serrano, A.; Bastos, C.; Bertolami, O. and Robles-Perez, S. Interacting universes and thecosmological constant, Phys. Lett. B (2013) 200.58. Robles-Pérez, S.; Alonso-Serrano, A.; Bastos, C. and Bertolami, O. Vacuum decay in an interactingmultiverse, Phys. Lett. B (2016) 328.59. Hacking, I. Representing and Intervening: Introductory topics in the philosophy of natural science.Cambridge University Press (1983)60. Okasha, S. Philosophy of Science: A Very Short Introduction, Oxford University Press, 2002.61. Chalmers, A. What is this thing called science? Queensland University Press, 4th ed., 2013.62. Whitehead, A. N. and Russell, B. Principia Mathematica (3 vols.) Cambridge University Press (1910-1913).63. Hilbert, D. Mathematische Probleme. Nachrichten von der Königlichen Gesellschaft der Wissenschaftenzu Göttingen, Math.-Phys. Klasse, 253-297. Based on a lecture given at the International Congress ofMathematicians, Paris, 1900.64. Hilbert, D. Grundlagen der Mathematik. Vorlesung, Winter-Semester 1921/22. Lecture notes by PaulBernays, Universität Göttingen65. Gödel, K. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.Monatshefte für Mathematik 38, 173-198 (1931) ersion October 17, 2019 submitted to Universe
20 of 21
66. Popper, K.R. Logik der Forschung. Zur Erkenntnistheorie der modernen Naturwissenschaft. Springer(1934). Extended English version: K.R. Popper, The Logic of Scientific Discovery, Hutchison (1959)67. Kuhn, T. The Structure of Scientific Revolutions. University of Chicago Press (1962).68. Dardashti, R. Physics without Experiments? In: [3]69. Oriti, D. No alternative to proliferation. In: [3]70. Sahlén, M. On Probability and Cosmology: Inference Beyond Data? In: [2]71. Pickering, A. Constructing Quarks: A Sociological History of Particle Physics. Edinburgh University Press(1984)72. Lakatos, I. Falsification and the Methodology of Scientific research programmes. In: In Lakatos, I. andMusgrave, A. (eds.), Criticism and the Growth of Knowledge. Cambridge University Press (1970)73. Feyerabend, P. Against Method: Outline of an Anarchistic Theory of Knowledge. New Left Books, London(1975)74. Howson, C. and Urbach, P. Scientific Reasoning: The Bayesian Approach. Open Court, La Salle, IL. (1989)75. Ortovela, P. Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News. AmericanEconomic Review 2012, 102(6): 2410–243676. Smolin, L. Scientific alternatives to the anthropic principle. In: [1]77. Susskind, L. The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. Little Brown &co (2005)78. Vinkers, C.; Tijdink, J.; Otte W. Use of positive and negative words in scientific PubMed abstracts between1974 and 2014: retrospective analysis. BMJ 351:h6467 (2015).79. Scott, S. L. and Jones, C. W. Superlative Scientific Writing. ACS Catal. 7, 3, 2218-2219 (2017).80. Silk, J. Towards the limits of cosmology. Found. Phys. 48.10, 1305-1332 (2018)81. Turner, M. S. Λ CDM: Much More Than We Expected, but Now Less Than What We Want. Found. Phys. 48,1261–1278 (2018)82. S. Nobbenhuis, Categorizing different approaches to the cosmological constant problem, Found. Phys. ,613 (2006)83. Woit, P. Not Even Wrong: : The Failure of String Theory and the Search for Unity in Physical Law. BasicBooks (2006)84. Smolin, L. The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What ComesNext. Houghton Mifflin Harcourt (2006)85. Ellis, G. Multiverses, Science, and Ultimate Causation. In: R.D. Holder and S. Mitton (eds.), GeorgesLemaître: Life, Science and Legacy. Springer Verlag, Berlin (2012)86. Barnes, L. A. et al. Galaxy formation efficiency and the multiverse explanation of the cosmological constantwith EAGLE simulations. Monthly Notices of the Royal Astronomical Society 477 (2018) 3727.87. Weinberg, S. Anthropic Bound on the Cosmological Constant. Phys. Rev. Lett. 59, 2607 (1987)88. Polchinski, J. String Theory to the Rescue (2015). In: [3].89. Polchinski, J. Why trust a theory? Some further remarks (part 1) (2016). In: [3].90. Georgi, H.; Glashow, S. Unity of All Elementary-Particle Forces. Phys. Rev. Lett. 32 (8): 438 (1974)91. Kragh, H. Higher Speculations: Grand Theories and Failed Revolutions in Physics and Cosmology. OxfordUniversity Press (2011)92. Baggott, J. Farewell to Reality. Constable(2013)93. Hossenfelder, S. Lost in Math. Basic Books (2018)94. Kragh, H. The Vortex Atom: A Victorian Theory of Everything. Centaurus 44, 32 - 114 (2003)95. Popper, K.R. Objective Knowledge: An Evolutionary Approach. Oxford University Press (1972)96. Anderson, P.W. More Is Different. Science 177, 393-396 (1972)97. Battermnan, R.W. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, andEmergence. Oxford University Press (2001)98. Jannes, G. Some comments on “The Mathematical Universe”. Found. Phys. 39: 397-406 (2009)99. Weinberg, S. Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature. Vintage(1992)100. Carroll, S. M. The Cosmological Constant. Living Rev. Relativ. 4, 1 (2001). ersion October 17, 2019 submitted to Universe
21 of 21