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Naturalness As a Reasonable Scientific Principle in Fundamental Physics

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Naturalness As a Reasonable Scientific Principle in Fundamental Physics Candidate: Casper Dani¨elDijkstra. Student Number: s2026104. Master's thesis for Philosophy of a Specific Discipline. Specialization: Natural Sciences. Naturalness as a reasonable scientific principle in fundamental physics Supervisor: Prof. Dr. Simon Friederich. Second examiner: Prof. Dr. Leah Henderson Third examiner: Prof. Dr. Frank Hindriks arXiv:1906.03036v1 [physics.hist-ph] 19 Apr 2019 Academic year: 2017/2018. Abstract Underdetermination by data hinders experimental physicists to test legions of fundamental theories in high energy physics, since these theories predict modifications of well-entrenched theories in the deep UV and these high energies cannot be probed in the near future. Several heuristics haven proven successful in order to assess models non-emperically and \naturalness" has become an oft-used heuristic since the late 1970s. The utility of naturalness is becoming pro- gressively more contested, for several reasons. The fact that many notions of the principle have been put forward in the literature (some of which are discordant) has obscured the physical content of the principle, causing confusion as to what naturalness actually imposes. Additionally, naturalness has been criticized to be a \sociological instrument" (Grinbaum 2007, p.18), an ill-defined dogma (e.g. by Hossenfelder (2018a, p.15)) and have an \aesthetic character" which is fundamentally different from other scientific principles (e.g. by Donoghue (2008, p.1)). I aim to clarify the physical content and significance of naturalness. Physicists' earliest understanding of natural- ness, as an autonomy of scales (AoS) requirement provides the most cogent definition of naturalness and I will assert that i) this provides a uniform notion which undergirds a myriad prominent naturalness conditions, ii) this is a reason- able criterion to impose on EFTs and iii) the successes and violations of naturalness are best understood when adhering to this notion of naturalness. I argue that this principle is neither an aesthetic nor a sociologically-influenced principle. I contend that naturalness may only be plausibly argued to be an aesthetic/sociological principle when formal measures of naturalness and their use in physics communities are conflated with the central dogma of naturalness - the former may indeed be argued to be sociologically-influenced and somewhat arbitrary - but these formal measures of naturalness are in fact less successful than AoS naturalness. I put forward arguments as to why AoS naturalness is well-defined and why it was reasonable for physicists to endorse this naturalness principle on both theoretical and empirical grounds. Two dire violations of naturalness - the Higgs mass and the cosmological constant - have already been discovered several decades, this fueled physicists' surmise that these problems can be rendered natural in more fundamental laws of nature. \If one has to summarise in one word what drove the efforts in physics beyond the Standard Model of the last several decades, the answer is naturalness" as was correctly pointed out by Giudice (2017, p.3). The surmise that these several parameters may actually be unnatural has recently gained credibility due to compelling anthropic arguments which entail that natural cosmological constant and Higgs vacuum expectation values would have led to life-hostile universes in which observers could not have emerged (Weinberg 1996, Donoghue 2007). Up to date, no compelling reasons have appeared as to why the laws of nature should generically decoupling into quasi-autonomous physical domains. Chaotic phenomena provide a clear exception to this rule within classical physics and we should take into account the possibility of violations of this dogma in quantum physics as well. A decoupling of scales in the quantum realm is often claimed to be entailed by the Decoupling Theorem (e.g. by Cao and Schweber (1993)), yet I will show that this theorem is too weak to underwrite quasi-autonomous physical domains in quantum field theories because one should additionally impose that parameters be natural. Violations of naturalness would then have ontological import - unnatural parameters would not be accurately described by effective field theories but rather by field theories exhibiting some kind of UV/IR interplay. Page 1 Contents Notation and conventions i 1 Introduction 1 1.1 Guiding principles for fundamental theoretical physics . 1 1.1.1 Symmetries, unification, renormalizability and unitarity . 2 1.1.2 Naturalness . 5 1.2 Outline of the thesis . 6 2 Motivating and defining naturalness 9 2.1 Effective field theories . 10 2.1.1 Why the Standard Model consists of effective field theories . 11 2.1.2 The assumed decoupling of vastly separated energy scales . 12 2.1.2.1 The Decoupling Theorem . 14 2.1.2.2 A pragmatic motivation for effective field theories . 15 2.2 Naturalness as autonomy of scales . 15 2.2.1 How to recognize natural and unnatural theories? . 15 2.2.1.1 A natural theory: m M ............................. 16 2.2.1.2 An unnatural theory: m M ........................... 16 2.2.2 Naturalness implies a prohibition of correlations among widely separated scales . 18 2.3 Absolute naturalness and technical naturalness . 18 2.3.1 Absolute naturalness . 18 2.3.1.1 Why O(1) parameters may imply a prohibition of widely separated correlations 20 2.3.1.2 Failures of absolute naturalness . 23 2.3.2 Technical naturalness . 24 2.3.2.1 Why technical naturalness reproduces the central dogma of autonomy of scales naturalness . 24 2.3.2.2 Successes of technical naturalness . 25 2.3.2.3 Violations of technical naturalness . 26 2.3.2.4 Technical naturalness is too restrictive . 27 2.3.3 Concluding remarks . 28 2.4 Naturalness as a prohibition of fine-tuning . 28 2.4.1 cn 6= O(1) implies fine-tuning . 28 2.4.2 Fine-tuning problems can be devalued to pseudo-problems . 29 2.4.3 The Barbieri-Giudice measure . 30 2.4.3.1 Why Barbieri-Giudice naturalness does not formalize naturalness as autonomy of scales . 31 2.4.3.2 Failure of the Barbieri-Giudice measure: the proton mass . 32 2.5 A Bayesian notion of naturalness: landscape naturalness . 32 2.5.1 The Anderson-Casta~nolandscape . 32 2.5.2 The multiverse . 33 3 Defending autonomy of scales naturalness 36 3.1 Naturalness and aesthetics . 36 3.1.1 Aesthetics in physics . 37 3.1.1.1 Defending aesthetics . 38 3.1.1.2 Criticizing aeshetics . 38 3.1.1.3 Dirac's Large Number Hypothesis . 39 3.1.1.4 Implications for naturalness . 40 3.1.2 Naturalness problems are not aesthetic pseudoproblems . 42 3.2 Why autonomy of scales naturalness is not ill-defined . 44 4 Assessing the utility of naturalness 46 4.1 Successes of the naturalness criterion . 46 4.1.1 The charm quark . 46 4.1.2 A posteriori successes . 47 4.1.2.1 Electron mass . 47 4.1.2.2 Pion mass difference . 48 4.2 Violations of naturalness . 49 4.2.1 The Higgs mass . 49 4.2.2 The cosmological constant . 51 4.3 The current role of naturalness in theory choice . 53 4.3.1 Little Higgs models . 53 4.3.2 Supersymmetry . 54 4.3.3 Concluding remarks . 55 4.4 Can we do without naturalness? . 57 4.4.1 Selection criteria in the multiverse . 57 4.4.2 The Decoupling Theorem is not necessarily satisfied . 63 4.4.3 UV/IR mixing . 65 5 Conclusions 68 References 70 CONTENTS Notation and conventions Natural units Natural units simplify particle physics considerably in relativistic quantum mechanics, since quantum mechan- ics introduces factors of ~ and special relativity introduces factors of c which obfuscate equations. We can bypass this by using natural units where ~ = h=2π = 1 (turns Joule into inverse seconds) and c = 1 (turns meters into seconds). This makes all quantities have dimensions of energy (or mass, using E = mc2) to some power. Quantities with positive mass dimension, (e.g. momentum p and @µ) can be thought of as energies and quantities with negative mass dimension (e.g. position x and time t) can be thought of as lengths. Denoting the dimensionality of ` ···0 by [··· ], some examples are: [@µ] = [pµ] = [kµ] = [m] = M; (1a) [velocity] = [x]=[t] = M 0; (1b) [dx] = [x] = [t] = M −1; (1c) d4x = M −4: (1d) The fact that the action [S] = R d4x L = 0 is a dimensionless quantity implies that the Lagrangian density has dimensionality energy to the power four, i.e. [L] = M 4.1 It is worth mentioning the exact expressions of several important constants in natural units. The Einstein equation in general relativity (GR) is given by 1 R − Rg = κτ ; (2) µν 2 µν µν where τµν is the energy-momentum tensor and κ is the constant which guarantees that Newtonian mechanics is recovered for low energies. Its expression is well-known in SI units, namely: κ = 8πG=c4 and this thus reduces to 8πG in natural units. It is often desirable to display the Planck mass (which sets the scale where gravitational quantum effects become important) instead of κ in gravitational equations, let us therefore mathematically relate these quantities. The Planck mass is defined as r c m := ~ ' 1:2 · 1019 GeV (3a) pl G −2 and since ~ = c = 1 in natural units we can relate κ and mp (κ = 8πmpl ), which can be written more conveniently after introducing the reduced Planck mass which already contains the requisite factor of 8π: r c M := ~ ' 2:4 · 1019 GeV: (3b) P 8πG Dimensional analysis Free massive spin-0 particles are described by the Klein-Gordon equation 1 L = @ φ∂µφ − m2φ2 (4) free 2 µ 1This only holds true for field theories in four dimensions but the dimensional analysis can easily be generalized. One obtains [L] = M D in D spacetime dimensions (e.g.
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