Philosophy of physics

What are good theories of the world?

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Contents

  1. Theories of matter
    1. Ancient atomism
    2. Modern atomism
    3. Contemporary views of matter
  2. Classical physics
    1. Mechanics
    2. Electrodynamics
    3. Special relativity
  3. Statistical physics
    1. Introduction
    2. History
    3. Thermodynamics
    4. Canonical ensemble
    5. Phase translations
  4. Symmetry-first physics
    1. Curie’s principle
    2. Noether’s theorems
    3. Gauge principle
    4. Wigner-Stone theorems
  5. Quantum mechanics
    1. Introduction
    2. History
    3. Hydrogen atom
    4. Foundations of QM
    5. Secondary properties of QM
    6. Decoherence
    7. Quantum chemistry
    8. Quantum computing
  6. Quantum field theory
    1. Fields
    2. Symmetry
    3. Spin
    4. Scattering
    5. Path intergrals
    6. Renormalization
    7. Effective field theory
    8. Foundations of QFT
  7. Exotics in quantum field theory
    1. Higher gauge theory
    2. Non-perturbative features
    3. Supersymmetry
  8. Interpretations of quantum mechanics
    1. Measurement problem
    2. Copenhagen “interpretation”
    3. EPR paradox
    4. Bell’s theorem
    5. Bohmian mechanics
    6. Everettian interpretation
    7. Collapse interpretations
    8. Epistemic interpretations
    9. PBR theorem
    10. Other interpretations
    11. Bad takes
  9. The standard model of particle physics
    1. History of particle physics
    2. Mixing
    3. Higgs mechanism
    4. A model of leptons
    5. Quantum chromodynamics
    6. Three generations of fermions
    7. Experimental methods
  10. Beyond the standard model
    1. Neutrino masses
    2. Ad hoc structures
    3. Experimental anomalies
    4. Grand unification
    5. Baryogenesis
    6. Future colliders and criticisms
    7. Quantum gravity
  11. Gravity and cosmology
    1. General relativity
    2. Newtonian gravity
    3. Big bang model
    4. Spacetime
    5. Blackholes
    6. Gravitational waves
    7. Dark matter
    8. Inflation
    9. Alternative theories of gravity
  12. Fine-tuning
  13. Complexity and emergence
  14. Bracketing human experience
  15. My thoughts
  16. Annotated bibliography
    1. Einstein, A., Podolsky, B. & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?
    2. Anderson, P. (1972). More is different.
    3. Redhead, M. (1988). A philosopher looks at quantum field theory.
    4. Joos, E., Zeh, H.D., Kiefer, C., Kupsch, J., Stamatescu, I.O. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory.
    5. Pusey, M.F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state.
    6. More articles to do
  17. Links and encyclopedia articles
    1. SEP
    2. IEP
    3. Scholarpedia
    4. Wikipedia
    5. Others
    6. Videos
  18. References

Theories of matter

Ancient atomism

Discussion:

Modern atomism

Contemporary views of matter

See also:

Classical physics

Mechanics

History:

Lagrangian mechanics:

Pedagogy:

Dimensional analysis:

See also:

Electrodynamics

History:

Pedagogy:

Special relativity

History:

Stein:

And this is the crucial difference, as I see it, between Poincaré’s relation to the special theory of relativity and Einstein’s. Both of them discovered this theory—and did so independently. So far as its mathematical structure is concerned, Poincaré’s grasp of the theory was in some important respects superior to Einstein’s. But Einstein “took the theory seriously” in the sense that he looked to it for NEW INFORMATION about the physical world—that is, in Poincaré’s language, he regarded it as “fertile”: as a source of new “real generalizations”—of empirically testable consequences. And in doing so, Einstein attributed physical significance to the basic notions of the theory itself in a way that Poincaré did not.17

Pedagogy:

See also:

Statistical physics

Introduction

TODO:

History

Thermodynamics

Canonical ensemble

Phase translations

See also:

Symmetry-first physics

Curie’s principle

See also:

Noether’s theorems

Gauge principle

Weyl:

It seems to me that this new principle of gauge invariance, which follows not from speculation but from experiment, compellingly indicates that the electromagnetic field is a necessary accompanying phenomenon, not of gravitation, but of the material wave field represented by \(\psi\). Since gauge invariance includes an arbitrary function \(\lambda\) it has the character of “general” relativity and can naturally only be understood in that context.37

Wigner-Stone theorems

See also:

Quantum mechanics

Introduction

Feynman and Hibbs on wave-principle duality:

What is remarkable is that this dual use of wave and particle ideas does not lead to contradictions. This is so only if great care is taken as to what kind of statements one is permitted to make about the experimental situation.46

Feynman and Hibbs on the uncertainty principle:

Any determination of the alternative taken by a process capable of following more than one alternative destroys the interference between the alternatives.47

History

Figure 1: 1927 Solvay Conference on Quantum Mechanics (source: Wikimedia).

Hydrogen atom

Foundations of QM

\[ \hat{H} \: |n\rangle = E_{n} \: |n\rangle \]

\[ |\psi\rangle = \sum_{n} a_{n} \: |n\rangle \]

\[ P(n) = | \langle n | \psi \rangle |^{2} = |a_{n}|^{2} \]

The generators of the representation of a transformation in a Hilbert space are the operators representing the classical Noether charges that are conserved under that transformation.

\[ \hat{U}(x^{\mu}) = e^{ -i \, \hat{P}_\mu \, x^\mu } \]

Secondary properties of QM

\[ \langle x | n \rangle = \psi_{n}(x) \]

\[ i \hbar \: \partial_{t} \: |\psi\rangle = \hat{H} \: |\psi\rangle \]

\[ i \hbar \: \partial_{t} \: \hat{U}(t) \: |\psi\rangle = \hat{H} \: \hat{U}(t) \: |\psi\rangle \]

Schrödinger vs Heisenberg pictures is like Heraclitus vs Parmenides.

\[ \mathcal{H} = \mathcal{H}_\mathrm{S} \otimes \mathcal{H}_\mathrm{E} \]

\[ |\psi\rangle \otimes |\alpha\rangle \rightarrow |\psi; \alpha\rangle \otimes |\alpha\rangle \]

See Dutailly,54 for example, for a demonstration that the Schrödinger equation is derivable from Wigner’s theorem.

Decoherence

See also:

Quantum chemistry

Quantum computing

Quantum field theory

Fields

Introduction

Baez, Segal, & Zhou:

Quantum field theory is quintessentially the algebra and analysis of infinite-dimensional dynamical systems, as constrained by quantum phenomenology, causality, and symmetry. Although it has a clear-cut central goal, that of the realistic description of particle production and annihilation in terms of the localized interactions of fields in space-time, it is clear from this description that it is a multifaceted subject.69

Pedagogy

Symmetry

Introduction

See also:

Coleman-Mandula theorem

Wigner’s classification

CPT theorem

Spin

Introduction

Spinors

Michael Atiyah:

No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the “square root” of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors.87

Spin-statistics theorem

Scattering

Path intergrals

Renormalization

Effective field theory

Foundations of QFT

Introduction

Baez:

Nobody has found a fully rigorous formulation of QED, nor has anyone proved such a thing cannot be found.116

Baez:

In practice, quantum field theory is marvelously good for calculating answers to many physics questions. The answers involve approximations. These approximations seem to work very well: that is, the answers match experiments. Unfortunately we do not fully understand, in a mathematically rigorous way, what these approximations are supposed to be approximating.117

Wave-particle duality

Weinberg on wave-particle duality:

In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields. In a relativistic theory the wave function is a functional of these fields, not a function of particle coordinates. Quantum field theory hence led to a more unified view of nature than the old dualistic interpretation in terms of both fields and particles.119

Baez, Segal, & Zhou on wave-particle duality:

The treatment of the dynamics of quantum systems turns out to be naturally undertaken in terms of field rather than particle concepts, by virtue of the local character of relativistic interactions. In mathematical terms, the field is diagonalizcd in the functional integration representation, just as the particle numbers are diagonalized in the tensor product representation.121

Haag’s theorem

Quantization

Algebraic vs constructive QFT

Kastler:

Rudolf [Haag] is not satisfied by a notion of local observables relying plainly on space and time. Instead he wishes to base the theory on concepts related to individual processes. This attitude seems to me to move towards a basic “algebra of procedures,” pointing towards a theory of (non-commutative) space-time. I know that, coming from a very different angle, Alain Connes also believes the ultimate algebra of basic physics to be a discrete algebra of elements standing for experimental procedures—following the idea that the spatial notions man acquires in his cradle are less basic than his procedures at [particle] accelerators.143

Exotics in quantum field theory

Higher gauge theory

Aharanov-Bohm effect

Wikipedia discussion in the magnetic moment article:

A gauge theory like electromagnetism is defined by a gauge field, which associates a group element to each path in space time. For infinitesimal paths, the group element is close to the identity, while for longer paths the group element is the successive product of the infinitesimal group elements along the way.

In electrodynamics, the group is \(U(1)\), unit complex numbers under multiplication. For infinitesimal paths, the group element is \(1 + i\,A_\mu\,dx^\mu\) which implies that for finite paths parametrized by \(s\), the group element is:

\(\prod _{s}\left(1+i\,e\,A_\mu\,\frac{dx^\mu}{ds}\,ds\right) = \exp\left(i\,e\int A\cdot dx\right) \,.\)

The map from paths to group elements is called the Wilson loop or the holonomy, and for a \(U(1)\) gauge group it is the phase factor which the wavefunction of a charged particle acquires as it traverses the path. For a loop:

\(e\oint_{\partial D}A\cdot dx = e\int_{D}(\nabla \times A)\,dS = e\int_{D}B\,dS \,.\)

So that the phase a charged particle gets when going in a loop is the magnetic flux through the loop. When a small solenoid has a magnetic flux, there are interference fringes for charged particles which go around the solenoid, or around different sides of the solenoid, which reveal its presence.

Fiber bundles

Bundles are the global structure of physical fields and they are irrelevant only for the crude local and perturbative description of reality.149

Maudlin on fiber bundles:

If we adopt the metaphysics of the fiber bundle to represent chromodynamics, then we must reject the notion that quark color is a universal, or that there are color tropes which can be duplicates, or that quarks are parts of ‘natural sets’ which include all and only the quarks of the same color, for there is no fact about whether any two quarks are the same color or different. Further, we must reject the notion that there is any metaphysically pure relation of comparison between quarks at different points, since the only comparisons available are necessarily dependent on the existence of a continuous path in space-time connecting the points. So it seems that there are no color properties and no metaphysically pure internal relations between quarks.152

But if one asks whether, in this picture, the electromagnetic field is a substance or an instance of a universal or a trope, or some combination of these, none of the options seems very useful. If the electromagnetic field is a connection on a fiber bundle, then one understands what it is by studying fiber bundles directly, not by trying to translate modern mathematics into archaic philosophical terminology.153

See also:

Topological QFT

See also:

Non-perturbative features

Supersymmetry

Urs Schreiber:

not just that local spacetime supersymmetry is one possibility to have sensible particle content under Wigner classification, but that the class of (algebraic) super-groups precisely exhausts the moduli space of possible consistent local spacetime symmetry groups.163

See also:

Interpretations of quantum mechanics

The withdrawal of philosophy into a “professional” shell of its own has had disastrous consequences. The younger generation of physicists, the Feynmans, the Schwingers, etc., may be very bright; they may be more intelligent than their predecessors, than Bohr, Einstein, Schrödinger, Boltzmann, Mach and so on. But they are uncivilized savages, they lack in philosophical depth—and this is the fault of the very same idea of professionalism which you are now defending.

– from a letter in Appendix B of Feyerabend’s Against Method

Measurement problem

Copenhagen “interpretation”

Figure 2: Interpretations of quantum mechanics (philosophy-in-figures.tumblr.com).

EPR paradox

Bell’s theorem

Bohmian mechanics

Everettian interpretation

A theory containing many ad hoc constants and restrictions, or many independent hypotheses, in no way impresses us as much as one which is largely free of arbitrariness.202

It is therefore improper to attribute any less validity or “reality” to any element of a superposition than any other element, due to this ever present possibility of obtaining interference effects between the elements. All elements of a superposition must be regarded as simultaneously existing.211

A way out of this dilemma [the measurement problem] within quantum mechanical concepts requires one of two possibilities: a modification of the Schrödinger equation that explicitly describes a collapse (also called “spontaneous localization”), or an Everett type interpretation, in which all measurement outcomes are assumed to exist in one formal superposition, but to be perceived separately as a consequence of their dynamical autonomy resulting from decoherence. While this latter suggestion has been called “extravagant” (as it requires myriads of co-existing quasi-classical “worlds”), it is similar in prin- ciple to the conventional (though nontrivial) assumption, made tacitly in all classical descriptions of observation, that consciousness is localized in certain semi-stable and sufficiently complex subsystems (such as human brains or parts thereof) of a much larger external world. Occam’s razor, often applied to the “other worlds,” is a dangerous instrument: philosophers of the past used it to deny the existence of the interior of stars or of the back side of the moon, for example. So it appears worth mentioning at this point that environmental decoherence, derived by tracing out unobserved variables from a universal wave function, readily describes precisely the apparently observed “quantum jumps” or “collapse events” (as will be discussed in great detail in various parts of this book).216

See also:

Collapse interpretations

Epistemic interpretations

PBR theorem

Other interpretations

Bad takes

The standard model of particle physics

History of particle physics

Mixing

Higgs mechanism

In 1964, three groups: Robert Brout and Francois Englert;236 Peter Higgs;237 and Gerald Guralnik, Carl R. Hagen, and Tom Kibble,238 independently demonstrated an exception to Goldstone’s theorem, showing that Goldstone bosons do not occur when a spontaneously broken symmetry is local. Instead, the Goldstone mode provides the third polarization of a massive vector field, resulting in massive gauge bosons. The other mode of the original scalar doublet remains as a massive spin-zero particle, the Higgs boson. This is the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, or Higgs mechanism. In the Standard Model, the Higgs boson also couples to the fermions, generating their bare masses.

On July 4 of 2012, the ATLAS241 and CMS242 experiments both announced discovering a new particle consistent with the long-sought-after Higgs boson, a key to explaining electroweak symmetry breaking in the Standard Model of particle physics.

A model of leptons

Quantum chromodynamics

Three generations of fermions

Figure 3: The total action of the physics of the standard model together with general relativity as presented by Sean Carroll on his blog. In this all encompassing equation, fermions are the quanta of the \psi fields and bosons are the quanta of the g, A, and \Phi fields.

More:

Experimental methods

Beyond the standard model

Neutrino masses

Ad hoc structures

See also:

Experimental anomalies

Grand unification

Figure 4: Two-loop renormalization group evolution of the inverse gauge couplings, \alpha^{-1}, in the Standard Model (dashed lines) and the MSSM (solid lines). In the MSSM case, the sparticle masses are treated as a common threshold varied between 750 GeV (blue) and 2.5 TeV (red).

See also:

Baryogenesis

Future colliders and criticisms

Quantum gravity

Gravity and cosmology

General relativity

Newtonian gravity

Big bang model

Spacetime

Blackholes

Gravitational waves

Dark matter

Inflation

Figure 5: How the \Lambda-CDM concordance model of cosmology was developed.

Alternative theories of gravity

Fine-tuning

Complexity and emergence

Anderson:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.295

See also:

Bracketing human experience

Figure 6: Sean Carroll on the entailment of everyday life by physics.

See also:

My thoughts

Annotated bibliography

Click to show annotated bibliography

Einstein, A., Podolsky, B. & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?

  • Einstein et al. (1935)

My thoughts

  • TODO.

Anderson, P. (1972). More is different.

  • Anderson (1972)

My thoughts

  • TODO.

Redhead, M. (1988). A philosopher looks at quantum field theory.

  • Redhead (1988)

My thoughts

  • TODO.

Joos, E., Zeh, H.D., Kiefer, C., Kupsch, J., Stamatescu, I.O. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory.

  • Joos, E. et al. (2003).

My thoughts

  • TODO.

Pusey, M.F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state.

My thoughts

  • TODO.
Click to show links

SEP

IEP

Scholarpedia

Wikipedia

Others

Videos

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Wheeler, J. A. (1957). Assessment of Everett’s "relative state" formulation of quantum theory. Reviews of Modern Physics, 29, 46–465.
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  1. Lucretius (1995), p. TODO.↩︎

  2. Nail (2018).↩︎

  3. Yock (2018).↩︎

  4. Einstein (1905b).↩︎

  5. Perrin (1913).↩︎

  6. Patterson (2007).↩︎

  7. Russell (1992).↩︎

  8. Feynman (1963).↩︎

  9. Holm (2011a) and Holm (2011b).↩︎

  10. Buckingham (1914).↩︎

  11. Kasprzak, Lysik, & Rybaczuk (1990).↩︎

  12. Duff, Okun, & Veneziano (2001).↩︎

  13. Janyska, Modugno, & Vitolo (2007).↩︎

  14. Zapata-Carratala (2021).↩︎

  15. Einstein (1905d).↩︎

  16. Einstein (1905a).↩︎

  17. Stein (2021), p. 69.↩︎

  18. Maudlin (2012), p. TODO.↩︎

  19. Wu (2021).↩︎

  20. Caulton (2015).↩︎

  21. Caulton & Butterfield (2012).↩︎

  22. Noether (1918).↩︎

  23. Wigner (1954).↩︎

  24. Brading (2002).↩︎

  25. Baez (2018).↩︎

  26. Goyal (2020).↩︎

  27. Weyl (1918).↩︎

  28. Weyl (1929).↩︎

  29. Pauli (1941).↩︎

  30. Yang & Mills (1954).↩︎

  31. ’t Hooft (1994).↩︎

  32. Teller (2000).↩︎

  33. ’t Hooft (2007).↩︎

  34. Afriat (2013).↩︎

  35. Schwichtenberg (2015).↩︎

  36. Dewar (2019).↩︎

  37. Weyl (1929), p. TODO.↩︎

  38. Wigner (1959).↩︎

  39. Simon (1976).↩︎

  40. Summers (1999).↩︎

  41. Keller, Papadopoulos, & Reyes-Lega (2007).↩︎

  42. Reece (2007), p. X.↩︎

  43. Schweber (1961), p. TODO.↩︎

  44. Schroeren (2021).↩︎

  45. Ney & Albert (2013).↩︎

  46. Feynman & Hibbs (1965), p. 6.↩︎

  47. Feynman & Hibbs (1965), p. 9.↩︎

  48. Kelvin (1901).↩︎

  49. Bacciagaluppi & Valentini (2009).↩︎

  50. von Neumann (1955).↩︎

  51. van Hove (1958).↩︎

  52. Jordan, Neumann, & Wigner (1934).↩︎

  53. Baez (2011).↩︎

  54. Dutailly (2014), p. 11–13.↩︎

  55. Zurek (2003).↩︎

  56. Joos, E. et al. (2003).↩︎

  57. Tegmark (1993).↩︎

  58. Schlosshauer (2005).↩︎

  59. Drossel (2015), p. 51–2.↩︎

  60. Zurek (2022).↩︎

  61. Friedrich (2016).↩︎

  62. C. Cao, Hu, Li, & Schwarz (2019).↩︎

  63. Coecke & Kissinger (2017).↩︎

  64. Preskill (2018).↩︎

  65. Arute, F. et al. (2019).↩︎

  66. Broughton, M. et al. (2020).↩︎

  67. Feynman (1965).↩︎

  68. Weinberg (1997b), p. 8.↩︎

  69. Baez, Segal, & Zhou (1992), p. 1.↩︎

  70. Peskin & Schroeder (1995).↩︎

  71. Zee (2003).↩︎

  72. Schwartz (2014).↩︎

  73. Tong (2006).↩︎

  74. Zeidler (2007).↩︎

  75. Zeidler (2008).↩︎

  76. Zeidler (2011).↩︎

  77. T. Y. Cao (1999).↩︎

  78. ’t Hooft (2005).↩︎

  79. Coleman & Mandula (1967).↩︎

  80. Wigner (1939) and Bargmann & Wigner (1948).↩︎

  81. Bell (1955).↩︎

  82. Streater & Wightman (1964).↩︎

  83. Greaves & Thomas (2012).↩︎

  84. Ohanian (1986).↩︎

  85. Peskin (1994).↩︎

  86. Sebens (2019).↩︎

  87. Dutailly (2014), p. 37.↩︎

  88. Kontsevich & Segal (2021).↩︎

  89. Dyson (1949).↩︎

  90. Dyson (1952).↩︎

  91. Lehmann, Symanzik, & Zimmermann (1955).↩︎

  92. Weinberg (1964a) and Weinberg (1964b).↩︎

  93. Martin (2011).↩︎

  94. Reece (2007).↩︎

  95. Jaeger (2019).↩︎

  96. Feynman & Hibbs (1965).↩︎

  97. Nguyen (2016).↩︎

  98. Dirac (1963).↩︎

  99. ’t Hooft (1971).↩︎

  100. Wilson (1974).↩︎

  101. Goldenfeld (1992).↩︎

  102. Butterfield (2014).↩︎

  103. Butterfield & Bouatta (2015).↩︎

  104. ’t Hooft (1994).↩︎

  105. ’t Hooft (1999).↩︎

  106. Kadanoff (2013), p. 50.↩︎

  107. Borcherds & Barnard (2002).↩︎

  108. Huggett & Weingard (1995).↩︎

  109. Weinberg (1997b).↩︎

  110. Bain (2013a) and Bain (2013b).↩︎

  111. Preskill (2013).↩︎

  112. Williams (2019).↩︎

  113. Rosaler (2022).↩︎

  114. Baez (2016).↩︎

  115. Auyang (1995).↩︎

  116. Baez (2016), p. 17.↩︎

  117. Baez (2016), p. 18.↩︎

  118. Einstein (1905c).↩︎

  119. Weinberg (1997b), p. 2.↩︎

  120. Weinberg (1997a).↩︎

  121. Baez et al. (1992), p. 59.↩︎

  122. Fraser (2008).↩︎

  123. Pessa (2009).↩︎

  124. Duncan (2012), p. 163–4.↩︎

  125. Myrvold (2015).↩︎

  126. Lazarovici (2018).↩︎

  127. Baker (2009).↩︎

  128. Caulton (2018).↩︎

  129. Haag (1955).↩︎

  130. Malament (1996).↩︎

  131. Teller (1997), p. 115.↩︎

  132. Earman & Fraser (2006).↩︎

  133. Klaczynski (2016).↩︎

  134. Ruetsche (2002).↩︎

  135. Bain (2000).↩︎

  136. Duncan (2012).↩︎

  137. Redhead (1982).↩︎

  138. Redhead (1988).↩︎

  139. Haag (1992).↩︎

  140. Wallace (2011).↩︎

  141. Fraser (2011).↩︎

  142. Buchholz (1998).↩︎

  143. Kastler (2003), p. 6.↩︎

  144. Aharonov & Bohm (1959).↩︎

  145. Healey (2007), ch. 2-4.↩︎

  146. Batterman (2003).↩︎

  147. Maudlin (2018).↩︎

  148. Frankel (2004).↩︎

  149. nLab authors (2021).↩︎

  150. Way (2010).↩︎

  151. Vákár (2011).↩︎

  152. Maudlin (2007), p. 96.↩︎

  153. Maudlin (2007), p. 101.↩︎

  154. Baez & Muniain (1994).↩︎

  155. Baez & Schreiber (2005).↩︎

  156. Baez & Huerta (2011).↩︎

  157. Schreiber (2020).↩︎

  158. Baez & Stay (2009).↩︎

  159. ’t Hooft (1978).↩︎

  160. ’t Hooft (1994).↩︎

  161. Shifman (2012).↩︎

  162. Haag, Łopuszański, & Sohnius (1975).↩︎

  163. Schreiber (2016).↩︎

  164. Dimopoulos & Georgi (1981).↩︎

  165. Murayama (2000).↩︎

  166. Freedman, Nieuwenhuizen, & Ferrara (1976).↩︎

  167. van Nieuwenhuizen (1981).↩︎

  168. Frè (2013), ch. 6.↩︎

  169. Martin (2016).↩︎

  170. Tong (2022).↩︎

  171. Maudlin (2019), p. TODO.↩︎

  172. Maudlin (1995).↩︎

  173. Dürr & Lazarovici (2020).↩︎

  174. Mermin (2022).↩︎

  175. Becker (2018).↩︎

  176. Einstein, Podolsky, & Rosen (1935).↩︎

  177. Bohm & Aharonov (1957).↩︎

  178. Mermin (1985).↩︎

  179. Caulton (2014).↩︎

  180. Bell (1964).↩︎

  181. Bell (1966).↩︎

  182. Kochen & Specker (1967).↩︎

  183. Clauser, Horne, Shimony, & Holt (1969).↩︎

  184. Gisin (1991), Gisin & Peres (1992), and Gisin (1999).↩︎

  185. Bell (2004), pp. 232–248.↩︎

  186. Maudlin (2014).↩︎

  187. Ahmed & Caulton (2014).↩︎

  188. Deutsch (1985).↩︎

  189. Bong, K.W. et al. (2020).↩︎

  190. Bohm (1952).↩︎

  191. Bohm (1953).↩︎

  192. Schönberg (1954).↩︎

  193. Bell (2004).↩︎

  194. Dürr, Goldstein, & Zanghì (1995).↩︎

  195. Dürr, Goldstein, Tumulka, & Zanghì (2004).↩︎

  196. Dürr, Goldstein, Tumulka, & Zanghì (2005).↩︎

  197. Dürr, Goldstein, & Zanghì (2013).↩︎

  198. Tumulka (2017).↩︎

  199. Das & Dürr (2019).↩︎

  200. Stopp, Ortiz-Gutiérrez, Lehec, & Schmidt-Kaler (2021).↩︎

  201. Ananthaswamy (2021).↩︎

  202. Everett (2012), p. 171.↩︎

  203. Everett (1956).↩︎

  204. Everett (1957).↩︎

  205. Wheeler (1957).↩︎

  206. Everett (2012).↩︎

  207. DeWitt (1970).↩︎

  208. DeWitt & Graham (1973).↩︎

  209. Barrett (2011).↩︎

  210. Barrett (2016).↩︎

  211. Everett (2012), p. 150.↩︎

  212. Wallace (2012).↩︎

  213. Carroll & Singh (2019).↩︎

  214. Carroll (2019).↩︎

  215. Wilhelm (2022).↩︎

  216. Joos, E. et al. (2003), p. 22.↩︎

  217. Ghirardi, Rimini, & Weber (1986).↩︎

  218. Putnam (1975).↩︎

  219. Putnam (2005).↩︎

  220. Wuthrich (2014).↩︎

  221. Caves, Fuchs, & Schack (2001).↩︎

  222. Fuchs (2002).↩︎

  223. Fuchs (2010).↩︎

  224. Fuchs & Schack (2013).↩︎

  225. Fuchs, Mermin, & Schack (2014).↩︎

  226. Fuchs & Stacey (2016).↩︎

  227. Harrigan & Spekkens (2010).↩︎

  228. Leifer & Spekkens (2013).↩︎

  229. Pusey, Barrett, & Rudolph (2012).↩︎

  230. Schlosshauer & Fine (2012).↩︎

  231. Nigg, D. et al. (2015).↩︎

  232. ’t Hooft (2021).↩︎

  233. Proietti, M. et al. (2019).↩︎

  234. Zyla, P.A. et al. (Particle Data Group) (2021).↩︎

  235. Cabibbo (1963).↩︎

  236. Englert & Brout (1964).↩︎

  237. Higgs (1964).↩︎

  238. Guralnik, Hagen, & Kibble (1964).↩︎

  239. Georgi (1999), p. 280.↩︎

  240. Lyre (2008).↩︎

  241. ATLAS Collaboration (2012).↩︎

  242. CMS Collaboration (2012).↩︎

  243. T. Y. Cao (2016).↩︎

  244. Glashow (1961).↩︎

  245. Weinberg (1967).↩︎

  246. Salam & Ward (1964b).↩︎

  247. Salam & Ward (1964a).↩︎

  248. Weinberg (1979).↩︎

  249. Rubbia (1984).↩︎

  250. Chalmers (2017).↩︎

  251. Hamamatsu (2007).↩︎

  252. LSND Collaboration (1996).↩︎

  253. LSND Collaboration (2001).↩︎

  254. MiniBooNE Collaboration (2018).↩︎

  255. MicroBooNE Collaboration (2021).↩︎

  256. Vitagliano, Tamborra, & Raffelt (2020).↩︎

  257. TODO: Pierre Auger Collaboration (2007), Pierre Auger Collaboration (2010), Pierre Auger Collaboration (2020a), and Pierre Auger Collaboration (2020b).↩︎

  258. Capdevilla, Curtin, Kahn, & Krnjaic (2021).↩︎

  259. Aime (2022).↩︎

  260. CDF Collaboration (2022).↩︎

  261. Baez & Huerta (2009a).↩︎

  262. Baez & Huerta (2010).↩︎

  263. Pati & Salam (1974).↩︎

  264. Georgi & Glashow (1974).↩︎

  265. Slansky (1981).↩︎

  266. Georgi (1999).↩︎

  267. Baez & Huerta (2009b).↩︎

  268. Lisi (2007).↩︎

  269. Martin (2016), p. 66.↩︎

  270. Dine & Kusenko (2004).↩︎

  271. Baggott (2013).↩︎

  272. Candelas, Horowitz, Strominger, & Witten (1985).↩︎

  273. Maldacena (1998).↩︎

  274. Witten (1998).↩︎

  275. Ney (2021).↩︎

  276. Einstein & Grossmann (1913).↩︎

  277. Misner, Thorne, & Wheeler (1973).↩︎

  278. Carroll (2004).↩︎

  279. Arntzenius (2012).↩︎

  280. Frè (2013), ch. 4.↩︎

  281. Weinberg (1977).↩︎

  282. Ryden (2003).↩︎

  283. Bahcall, Ostriker, Perlmutter, & Steinhardt (1999).↩︎

  284. Romero (2015).↩︎

  285. Penington (2019).↩︎

  286. Clowe, D. et al. (2006).↩︎

  287. Bahcall (2015).↩︎

  288. Arbey & Mahmoudi (2021).↩︎

  289. Martens (2022).↩︎

  290. Debono & Smoot (2016), figure 4.↩︎

  291. Anderson (1972).↩︎

  292. Bedau (1997).↩︎

  293. Bunge (2001), p. 72.↩︎

  294. Lisi (2017).↩︎

  295. Anderson (1972), p. 393.↩︎

  296. Bokulich (2011).↩︎