Philosophy of physics
What are good theories of the world?
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Contents
- Theories of matter
- Classical physics
- Statistical physics
- Symmetry-first physics
- Quantum mechanics
- Quantum field theory
- Exotics in quantum field theory
- Interpretations of quantum mechanics
- The standard model of particle physics
- Beyond the standard model
- Gravity and cosmology
- Fine-tuning
- Complexity and emergence
- Bracketing human experience
- My thoughts
- Annotated bibliography
- Einstein, A., Podolsky, B. & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?
- Anderson, P. (1972). More is different.
- Redhead, M. (1988). A philosopher looks at quantum field theory.
- Joos, E., Zeh, H.D., Kiefer, C., Kupsch, J., Stamatescu, I.O. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory.
- Pusey, M.F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state.
- More articles to do
- Links and encyclopedia articles
- References
Theories of matter
Ancient atomism
- Kanada (c. 700-100 BCE)
- Empedocles (c. 494-434 BCE)
- theory of the four elements
- …
- Leucippus (fl. 5th century BCE)
- Democritus (c. 460-370 BCE)
- Epicurus (341-270 BCE)
- Lucretius (c. 99-55 BCE)
- De Rerum Natura translated by Esolen1
Discussion:
- Weinberg
- Nail
- Nail claims that Lecretius was not an atomist, and that translations of Lecretius are colored by readings of his teacher, Epicurus.2
- Crespo, H. (2018). Intro to book review of ontology of motion: On the subject of definitions.
Modern atomism
- Corpuscularianism
- Isaac Beeckman (1588-1637)
- René Descartes (1596-1650)
- Boyle, Newton, Locke, Dalton
- Yock, P. (2018). Newton’s hypotheses on the structure of matter.3
- …
- Boltzmann
- Johannes Diderik van der Waals (1837-1923)
- Modern Atomism
- Planck, J.J. Thomson, Rutherford
- Brownian motion
- Russell7
Contemporary views of matter
- Quantum field theory
- Statistical mechanics and condensed matter physics
- TODO: Brief nod to upcoming sections.
See also:
Classical physics
Mechanics
History:
- Isaac Newton (1642-1727)
- Edmond Halley (1656-1742)
- Gottfried Wilhelm Leibniz (1646-1716)
- Leonhard Euler (1707-1783)
- Joseph-Louis Lagrange (1736-1813)
- Pierre-Simon Laplace (1749-1827)
- Carl Friedrich Gauss (1777-1855)
- Joseph von Fraunhofer (1787-1826)
- Augustin-Louis Cauchy (1789-1857)
- William Rowan Hamilton (1805-1865)
- Emmy Noether (1882-1935)
Lagrangian mechanics:
- TODO: explain
- Complaint about explanations of the Lagrangian:
Howe, A.R. (2020). Why does the Lagrangian equal T-V? - Relationship to the path-intergral formulation of quantum mechanics.
Pedagogy:
- The Feynman Lectures on Physics8
- Holm’s Geometric Mechanics9
- ’t Hooft, G. How to become a GOOD Theoretical Physicist.
Dimensional analysis:
- Tao, T. (2012). A mathematical formalisation of dimensional analysis.
- Buckingham \(\pi\) theorem10
- physics.stackexchange.com: On the dot product of vectors in different vector spaces.
- Kasprzak, W., Lysik, B., & Rybaczuk, M. (1990). Dimensional Analysis in the Identification of Mathematical Models.11
- Duff, M.J., Okun, L.B., & Veneziano, G. (2001). Trialogue on the number of fundamental constants.12
- Janyska, J., Modugno, M., & Vitolo, R. (2007). Semi-vector spaces and units of measurement.13
- Zapata-Carratala, C. (2021). Dimensioned algebra: The mathematics of physical quantities.14
- TODO: Dimensional analysis can be formalized with each type of physical dimension having a corresponding vector space in a trivial vector bundle over a spacetime manifold, \(M\). Because the bundle projection, \(\pi\), is trivial, \(\pi: M \times \mathbb{R}^{n_1} \times \mathbb{R}^{n_2} \times \cdots \rightarrow M\), vectors in each vector space can be directly compared.
See also:
Electrodynamics
History:
- Michael Faraday (1791-1867)
- Invented the concept of a field
- James Clerk Maxwell (1831-1879)
- Josiah Willard Gibbs (1839-1903)
- Oliver Heaviside (1850-1925)
Pedagogy:
- TODO
Special relativity
History:
- Ernst Mach (1838-1916)
- Mach’s principle
- Hendrik Lorentz (1853-1928)
- Henri Poincaré (1854-1912)
- Hermann Minkowski (1864-1909)
- Albert Einstein (1879-1955)
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:
- Maudlin18
- Schroeder, D.V. (2022). Relativity in five lessons.
See also:
Statistical physics
Introduction
TODO:
- The goal of statistical mechanics.
- How statistical mechanics can be seen as pure mathematics.
- Statistical mechanics and thermodynamics
- Entropy
History
- James Clerk Maxwell (1831-1879)
- Josiah Willard Gibbs (1839-1903)
- Ludwig Boltzmann (1844-1906)
Thermodynamics
- Denker, J. (2021). Modern Thermodynamics.
- The 2nd Law of Thermodynamics said simply: Things tend to happen in ways for which there are many ways to happen like that.
Canonical ensemble
- Canonical ensemble
Phase translations
- Phase transitions
- Renormalization
- Universality
See also:
Symmetry-first physics
Curie’s principle
- Pierre Curie (1859-1906)
- “The symmetries of the causes are to be found in the effects.”
- Counting degrees of freedom
- Totalitarian principle: “Everything not forbidden is compulsory.” - Murray Gell-Mann
- Caulton, A. (2015). The role of symmetry in the interpretation of physical theories.20
- Caulton, A. & Butterfield, J. (2012). Symmetries and paraparticles as a motivation for structuralism.21
See also:
Noether’s theorems
- Principle of least action, Lagrangians
- Canonical dynamics
- Noether, E. (1918). Invariante variationsprobleme.22
- TODO: Noether’s first and second theorem.
- Wigner, E.P. (1954). Conservation laws in classical and quantum physics.23
- Brading, K.A. (2002). Which symmetry? Noether, Weyl, and conservation of electric charge.24
- Baez, J.C. (2018). Getting to the bottom of Noether’s theorem. Talk given at The Philosophy and Physics of Noether’s Theorems.25
- Goyal, P. (2020). Derivation of classical mechanics in an energetic framework via conservation and relativity.26
Gauge principle
- Weyl, H. (1918). Raum, Zeit, Materie.27
- Weyl, H. (1929). Elektron und gravitation.28
- Pauli, W. (1941). Relativistic field theories of elementary particles.29
- Yang C.N. & Mills R.L. (1954). Conservation of isotopic spin and isotopic gauge invariance.30
- ’t Hooft, G. (1994). Under the Spell of the Gauge Principle.31
- Teller, P. (2000). The gauge argument.32
- ’t Hooft, G. (2007). Lie groups in physics.33
- Afriat, A. (2013). Weyl’s gauge argument.34
- Schwichtenberg, J. (2015). Physics from Symmetry.35
- Dewar, N. (2019). Sophistication about symmetries.36
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
- Wigner, E.P. (1959). Group Theory and its Application to the Quantum Mechanics of Atomic Spectra.38
- Simon, B. (1976). Quantum dynamics: from automorphism to Hamiltonian.39
- Summers, S.J. (1999). On the Stone-von Neumann uniqueness theorem and its ramifications.40
- Keller, K.J., Papadopoulos, M.A., & Reyes-Lega, A.F. (2007). On the realization of symmetries in quantum mechanics.41
- Wigner-Stone theorems as cornerstones of QM (Ovrut)42
- Wigner’s classification
- See also: disucssuion of symmetry in the section on Fields
- Schweber, S.S. (1961). An Introduction to Relativistic Quantum Field Theory.43
- Schroeren, D. (2021). Symmetry fundamentalism in quantum mechanics.44
See also:
Quantum mechanics
Introduction
- Hilbert spaces. Wigner’s theorem. The Born rule.
- Wave-particle duality misconceptions. Fields are more fundamental than particles.
- Philosophy of QM traditionally focus on NRQM.45
- The measurement problem. Decoherence. The Born rule again.
- Uncertainty principle
- Decoherence brings quantum logic to classical logic?
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
- History of quantum mechanics
- Kelvin, L. (1901). Nineteenth century clouds over the dynamical theory of heat and light.48
- Hendrik Lorentz (1853-1928)
- Max Planck (1858-1947)
- Marie Curie (1867-1934)
- Albert Einstein (1879-1955)
- Max Born (1882-1970)
- Niels Bohr (1885-1962)
- Erwin Schrödinger (1887-1961)
- Louis de Broglie (1892-1987)
- Lawrence Bragg (1890-1971)
- Wolfgang Pauli (1900-1958)
- Werner Heisenberg (1901-1976)
- Paul Dirac (1902-1984)
- An introduction to the Solvay conferences on physics - Université PSL
- Bacciagaluppi, G. & Valentini, A. (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference.49
- Proceedings of the Solvay conferences on physics

- Pascual Jordan (1902-1980)
- Eugene Wigner (1902-1995)
- John von Neumann (1903-1957)
- J. Robert Oppenheimer (1904-1967)
- John Archibald Wheeler (1911-2008)
Hydrogen atom
- Factorizable in spherical coordinates, leading to solutions as a product of spherical harmonics in (\(\theta\), \(\phi\)) and Laguerre polynomials in \(r\).
- Fine structure
- Lamb shift
- Hyperfine structure
Foundations of QM
- Hilbert spaces:
\[ \hat{H} \: |n\rangle = E_{n} \: |n\rangle \]
- Superposition principle:
\[ |\psi\rangle = \sum_{n} a_{n} \: |n\rangle \]
- Born rule
\[ P(n) = | \langle n | \psi \rangle |^{2} = |a_{n}|^{2} \]
- Wigner’s theorem
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.
\[ \hat{U}(x^{\mu}) = e^{ -i \, \hat{P}_\mu \, x^\mu } \]
- Somehow, QM is about complex numbers:
- Jordan, P., von Neumann, J., & Wigner, E.P. (1934). On an algebraic generalization of the quantum mechanical formalism.52
- Baez, J.C. (2011). Division algebras and quantum theory.53
Secondary properties of QM
- Wave function:
\[ \langle x | n \rangle = \psi_{n}(x) \]
- Schrödinger equation:
\[ i \hbar \: \partial_{t} \: |\psi\rangle = \hat{H} \: |\psi\rangle \]
- Heisenberg picture:
\[ i \hbar \: \partial_{t} \: \hat{U}(t) \: |\psi\rangle = \hat{H} \: \hat{U}(t) \: |\psi\rangle \]
Schrödinger vs Heisenberg pictures is like Heraclitus vs Parmenides.
- Decoherence
\[ \mathcal{H} = \mathcal{H}_\mathrm{S} \otimes \mathcal{H}_\mathrm{E} \]
\[ |\psi\rangle \otimes |\alpha\rangle \rightarrow |\psi; \alpha\rangle \otimes |\alpha\rangle \]
See Dutailly,54 for example, for a demonstration that the Schrödinger equation is derivable from Wigner’s theorem.
Decoherence
- Zurek, W.H. (2003). Decoherence, einselection, and the quantum origins of the classical.55
- Decoherence and the Appearance of a Classical World in Quantum Theory56
- Decoherence times from various scatterings57
- Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics.58
- My quora answer: What is currently the best explanation for how and why the quantum wave function collapses?
- Decoherence and Everett’s interpretation
- Drossel, B. (2015). On the relation between the second law of thermodynamics and classical and quantum mechanics.59
- Zurek, W.H. (2022). Quantum theory of the classical: Einselection, envariance, quantum Darwinism and extantons.60
See also:
Quantum chemistry
- Friedrich, B. (2016). How did the tree of knowledge get its blossom? The rise of physical and theoretical chemistry, with an eye on Berlin and Leipzig.61
- Density functional theory
- Cao, C., Hu, H., Li, J., & Schwarz, W.H.E. (2019). Physical origin of chemical periodicities in the system of elements.62
- Cohen, M.L. (2015). Explaining and predicting the properties of materials using quantum theory.
Quantum computing
- Feynman
- Coecke, B. & Kissinger, A. (2017). Picturing Quantum Processes: A first course in quantum theory and diagrammatic reasoning.63
- Preskill, J. (2018). Quantum computing in the NISQ era and beyond.64
- Arute, F. et al. (2019). Quantum supremacy using a programmable superconducting processor.65
- Google AI Blog. (2019). Quantum supremacy using a programmable superconducting processor.
- Broughton, M. et al. (2020). TensorFlow Quantum: A software framework for quantum machine learning.66
- TensorFlow. (2020). tensorflow.org/quantum.
- TensorFlow. (2021). Quantum machine learning concepts.
Quantum field theory
Fields
Introduction
- Field definition - Faraday
- Richard Feynman (1918-1988)
- Julian Schwinger (1918-1994)
- Shin’ichirō Tomonaga (1906-1979)
- Feynman’s Nobel Lecture on QED67
- Weinberg’s folk theorem: QFT is the right way to combine Lorentz invariance, quantum mechanics, and the cluster decomposition principle.68
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
- Peskin and Schroeder70
- Zee71
- Schwartz72
- David Tong73
- Zeidler, vol 1,74 2,75 and 376
- Cao, T.Y. (1999). Conceptual Foundations of Quantum Field Theory.77
- ’t Hooft, G. (2005). The conceptual basis of quantum field theory.78
Symmetry
Introduction
- TODO
- Noether’s theorem, again
- Wigner-Stone theorems, again
See also:
Coleman-Mandula theorem
- Coleman-Mandula theorem79
Wigner’s classification
CPT theorem
- Bell, J.S. (1955). Time reversal in field theory.81
- Streater, R. & Wightman, A. (1964). PCT, spin and statistics, and all that.82
- Greaves, H. & Thomas, T. (2012). The CPT Theorem.83
Spin
Introduction
Spinors
- Spinor
- SU(2) double covers SO(3)
- Belt trick
- Orientation entanglement
- Spatial vectors alone are not sufficient to describe fully the properties of rotations in space.
- Penrose, R. & Weinstein, E. (2020). Video: Do we understand spinors?
- In some sense, a spinor is the square-root of a vector.
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
- Spin-statistics theorem - Pauli
Scattering
- Interaction picture
- Correlation AKA Green’s functions
- Wick’s theorem
- Kontsevich, M. & Segal, G. (2021). Wick rotation and the positivity of energy in quantum field theory.88
- Vaccuum bubble cancelation
- Dyson series
- LSZ reduction formula91
- Haag-Ruelle scattering theory
- Feynman diagrams and Feynman rules
- Weinberg, S. (1964). Feynman rules for any spin.92
- Martin, S.P. (2011). Phenomenology of particle physics.93
- My notes: Reece, R. (2007). Quantum field theory: An introduction.94
- Jaeger, G. (2019). Are virtual particles less real?95
Path intergrals
- Feynman
- Feynman and Hibbs (1965)96
- Partition functions and generating functionals
- Show this way of deriving the Feynman rules
- Nguyen97
Renormalization
- Dyson
- Dirac, P.A.M. (1963). The evolution of the physicist’s picture of nature.98
- ’t Hooft, G. (1971). Renormalizable Lagrangians for massive Yang-Mills fields.99
- Wilson, K. (1974). The renormalization group and the \(\varepsilon\) expansion.100
- Goldenfeld, N. (1992). Lectures on Phase Transitions and the Renormalization Group.101
- Butterfield, J. (2014). Reduction, emergence, and renormalization.102
- Butterfield, J. & Bouatta, N. (2015). Renormalization for philosophers.103
- Universality is multiple realizability
- ’t Hooft, G. (1994). Under the Spell of the Gauge Principle. (again)104
- ’t Hooft, G. (1999). A confrontation with infinity (Nobel lecture).105
- The “renormalization group” isn’t a group; it’s actually a semigroup. The reason that renormalization produces a semigroup is that a block transformation loses information.106
- Borcherds, R.E. & Barnard, A. (2002). Lectures on quantum field theory.107
- Video: Moving Naturalism Forward, Day 1, Afternoon, 2nd Session: Simon DeDeo on renormalization.
Effective field theory
- Effective field theory (EFT)
- Huggett, N., & Weingard, R. (1995). The renormalisation group and effective field theories.108
- Weinberg, S. (1997). What is quantum field theory, and what did we think it is?.109
- Bain, J. (2013). Effective field theories.110
- Preskill, J. (2013). We are all Wilsonians now.111
- Williams, P. (2019). Scientific realism made effective.112
- Rosaler, J. (2022). Dogmas of effective field theory: Scheme dependence, fundamental parameters, and the many faces of the Higgs naturalness principle.113
Foundations of QFT
Introduction
- Weinberg
- Struggles with the continuum114
- Reeh-Schlieder theorem
- Taj Mahal principle
- Auyang, S.Y. (1995). How Is Quantum Field Theory Possible?115
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
- Einstein, A. (1905). On a heuristic point of view about the creation and conversion of light.118
- Wolchover, N. (2020). What is a particle?
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
- Weinberg, S. (1997). What is an elementary particle?120
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
- Fraser, D. (2008). The fate of ‘particles’ in quantum field theories with interactions.122
- Pessa, E. (2009). The concept of particle in quantum field theory.123
- Duncan, A. (2012). The Conceptual Framework of Quantum Field Theory.124
- Myrvold, W.C. (2015). What is a wavefunction?125
- Lazarovici, D. (2018). Against fields.126
- Baker, D.J. (2009). Against field interpretations of quantum field theory.127
- Caulton, A. (2018). A persistent particle ontology for quantum field theory.128
Haag’s theorem
- Haag’s theorem129
- The interaction picture does not exist in interacting relativistic QFT.
- States in the free theory are unitarily inequivalent to those in interacting relativistic QFT.
- Discussion:
- Resolution:
I have really fallen into a rabbit hole over Haag's theorem. #HaagsTheorem #philsci #philqft pic.twitter.com/6DhBpnWPKQ
— Ryan Reece (&commm;RyanDavidReece) September 13, 2017
You all weren't much help on Haag's theorem.
— Ryan Reece (&commm;RyanDavidReece) September 21, 2017
Duncan, A. (2012). Conceptual Framework of QFT. Oxford. p. 359. pic.twitter.com/NIHgfNh7s6
Quantization
- Canonical quantization
- Path integral quantization
- No “2nd quantization”
- Redhead137
- Redhead138
- Instead of quantizing classical theories, should we be finding the classical limit of quantum theories?
- Geometric 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
- Aharonov, Y. & Bohm, D. (1959). Significance of electromagnetic potentials in quantum theory.144
- Healey on the Aharonov-Bohm effect145
- Holonomy
- Batterman, R. (2003). Falling cats, parallel parking and polarized light.146
- Maudlin, T. (2018). Ontological clarity via canonical presentation: Electromagnetism and the Aharonov-Bohm effect.147
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
- Fiber bundles in physics - nLab
- Fiber bundles embody two central principles of modern physics:
- the principle of locality
- the gauge principle.
- Fiber bundles embody two central principles of modern physics:
- Vector bundle
- Frankel, T. (2004). The Geometry of Physics.148
Bundles are the global structure of physical fields and they are irrelevant only for the crude local and perturbative description of reality.149
- Higher gauge field - nLab
- An ordinary gauge field is a field which is locally represented by a differential 1-form, the gauge potential, and whose field strength is locally a differential 2-form.
- Principal bundle
- Ehresmann connection
- Way, R. (2010). Introduction to connections on principal fibre bundles.150
- Vákár, M. (2011). Principal bundles and gauge theories.151
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
- Baez, J.C. & Muniain, J.P. (1994). Gauge Fields, Knots and Gravity.154
- Baez, J.C. & Schreiber, U. (2005). Higher gauge theory.155
- Baez, J.C. & Huerta, J. (2011). An invitation to higher gauge theory.156
See also:
- Differential geometry in the Outline on mathematics.
Topological QFT
- Topological QFT (TQFT)
- Simon Donaldson and Edward Witten
- Chern-Simons theory
- Cobordism hypothesis - nLab
- Schreiber, U. (2020). Differential cohomology in a cohesive \(\infty\)-topos.157
- Baez, J.C. & Stay, M. (2009). Physics, topology, logic, and computation: A Rosetta Stone.158
See also:
- Category theory in the Outline on mathematics.
- Differential geometry in the Outline on mathematics.
Non-perturbative features
Supersymmetry
- Graded Lie algebras
- \(\mathbb{Z}/2\mathbb{Z}\)
- The supersymmetry algebra is a graded Lie algebra which closes under a combination of commutation and anti-commutation relations.
- Haag-Łopuszański-Sohnius theorem162
- The unique loop-hole in the Coleman-Mandula theorem
- Deligne’s theorem on tensor categories
- Deligne’s theorem - physicsforums.com
- Deligne’s theorem on tensor categories - nLab
- Supersymmetry - nLab
- Superalgebra
- Non-commutative geometry
- Connes, A. (1985).
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
- Minimal Supersymmetric Standard Model (MSSM)
- Dimopoulos, S. & Georgi, H. (1981). Softly broken supersymmetry and SU(5).164
- Murayama, H. (2000). Supersymmetry_phenomenology.165
- SUSY GUTs
- Supersymmetry allows unification of the couplings at the GUT scale.
- Supergravity
- Pedagogy
- Martin, S.P. (2016). A supersymmetry primer.169
- Ellis, J. (2020). The Higgs, supersymmetry and all that. CERN Courier. January 10, 2020.
- Tong, D. (2022). Lectures on Supersymmetric Field Theory.170
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
- TODO: Maudlin171
Measurement problem
- Maudlin, T. (1995). Three measurement problems.172
- Schrödinger’s cat
- Video: Veritasium. (2020). Parallel worlds probably exist. Here’s why.
- Penrose: \(U\) and \(R\) operators
- Dürr, D. & Lazarovici, D. (2020). Understanding Quantum Mechanics: The World According to Modern Quantum Foundations.173
- Mermin, N.D. (2022). A note on the quantum measurement problem.174
Copenhagen “interpretation”
- Niels Bohr (1885-1962)
- Complementarity
- Becker, A. (2018). What is Real?175

EPR paradox
- Einstein, A., Podolsky, B. & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?176
- Bohm, D. & Aharonov, Y. (1957). Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky.177
- Mermin, N.D. (1985). Is the moon there when nobody looks?178
- Caulton, A. (2014). Physical entanglement in permutation-invariant quantum mechanics.179
Bell’s theorem
- Bell, J.S. (1964). On the Einstein Podolsky Rosen Paradox.180
- Bell, J.S. (1966). On the problem of hidden variables in quantum mechanics.181
- Kochen, S. & Specker, E.P. (1967). The problem of hidden variables in quantum mechanics.182
- Clauser, J., Horne, M., Shimony, A., & Holt, R. (1969). Proposed experiment to test local hidden-variable theories.183
- Epistemological Letters
- Aspect experiments (1982)
- Gisin’s theorem184
- La Nouvelle Cuisine185
- Maudlin, T. (2014). What Bell did.186
- Ahmed, A., & Caulton, A. (2014). Causal decision theory and EPR correlations.187
- Wigner’s friend
- Deutsch, D. (1985). Quantum theory as a universal physical theory.188
- Bong, K.W. et al. (2020). A strong no-go theorem on the Wigner’s friend paradox.189
Bohmian mechanics
- de Broglie-Bohm theory
- version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952.
- Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ‘hidden’ variables, I and II.190
- Bohm, D. (1953). Proof that probability density approaches \(|\psi|^2\) in causal interpretation of quantum theory.191
- Schönberg, M. (1954). On the hydrodynamical model of the quantum mechanics.192
- Bell, J.S. (1987). Speakable and Unspeakable in Quantum Mechanics.193
- Dürr, D., Goldstein, S., & Zanghì, N. (1995). Bohmian mechanics as the foundation of quantum mechanics194
- Dürr, D., Goldstein, S., Tumulka, R., & Zanghì, N. (2004). Bohmian mechanics and quantum field theory.195
- Dürr, D., Goldstein, S., Tumulka, R., & Zanghì, N. (2005). Bell-type quantum field theories.196
- Dürr, D., Goldstein, S., & Zanghì, N. (2013). Quantum Physics Without Quantum Philosophy. Springer.197
- Tumulka, R. (2017). Bohmian_mechanics.198
- Das, S. & Dürr, D. (2019). Arrival time distributions of spin-1/2 particles.199
- Stopp, F., Ortiz-Gutiérrez, L., Lehec, H., & Schmidt-Kaler, F. (2021). Single ion thermal wave packet analyzed via time-of-flight detection.200
- Ananthaswamy, A. (2021). This simple experiment could challenge standard quantum theory.201
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
- Schrödinger himself suggested in 1952 that the different terms of a superposition evolving under the Schrödinger equation are “not alternatives but all really happen simultaneously” (Wikipedia)
- Hugh Everett, III
- Everett, H. (1956). Theory of the Universal Wave Function. Ph.D. thesis.203
- Everett, H. (1957). “Relative state” formulation of quantum mechanics.204
- Wheeler, J.A. (1957). Assessment of Everett’s “relative state” formulation of quantum theory.205
- Everett’s collected works206
- Shikhovtsev, E. (2003). Biographical sketch of Hugh Everett, III.
- DeWitt, B.S. (1970). Quantum mechanics and reality.207
- DeWitt, B.S. & Graham, N. (1973). The Many-Worlds Interpretation of Quantum Mechanics.208
- Barrett, J.A. (2011). Everett’s pure wave mechanics and the notion of worlds.209
- Barrett, J.A. (2016). Quantum worlds.210
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
- Wallace, D. (2012). The Emergent Multiverse.212
- Carroll’s mad-dog Everettianism213
- Carroll, S.M. (2019). Something Deeply Hidden.214
- Everett’s later influence on the theory of decoherence
- Wilhelm, I. (2022). Centering the Everett interpretation.215
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
- Ghirardi-Rimini-Weber theory (GRW)217
- TODO: find ref that GRW is empirical
- Putnam, H. (1965). A philosopher looks at quantum mechanics.218
- Putnam, H. (2005). A philosopher looks at quantum mechanics (again).219
- Wuthrich, C. (2014). Putnam looks at quantum mechanics (again and again).220
Epistemic interpretations
- \(\psi\)-epistemic interpretations
- Quantum Bayesianism (QBism)
- Caves, C.M., Fuchs, C.A., & Schack, R. (2001). Quantum probabilities as Bayesian probabilities.221
- Fuchs, C.A. (2002). Quantum mechanics as quantum information (and only a little more).222
- Fuchs, C.A. (2010). QBism, the perimeter of quantum Bayesianism.223
- Fuchs, C.A. & Schack, R. (2013). Quantum-Bayesian coherence: The no-nonsense version.224
- Fuchs, C.A., Mermin, N.D., & Schack, R. (2014). An introduction to QBism with an application to the locality of quantum mechanics.225
- Fuchs, C.A. & Stacey, B.C. (2016). QBism: Quantum theory as a hero’s handbook.226
- Harrigan, N., & Spekkens, R.W. (2010). Einstein, incompleteness, and the epistemic view of quantum states.227
- Leifer, M.S. & Spekkens, R.W. (2013). Towards a formulation of quantum theory as a causally neutral theory of bayesian inference.228
PBR theorem
- Pusey, M.F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state.229
- Wikipedia: Either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance.
- Leifer, M.S. (2011). Can the quantum state be interpreted statistically?
- Schlosshauer, M. & Fine, A. (2012). Implications of the Pusey-Barrett-Rudolph quantum no-go theorem.230
- Nigg, D. et al. (2015). Can different quantum state vectors correspond to the same physical state? An experimental test.231
- Ontological vs nomological interpretations of wavefunctions
Other interpretations
- Relational quantum mechanics
- Transactional quantum mechanics
- ’t Hooft, G. (2021). An unorthodox view on quantum mechanics.232
- Chen, E.K. (2022). The quantum wave function isn’t real.
Bad takes
- MIT Technology Review. (2019). A quantum experiment suggests there’s no such thing as objective reality.
- Proietti233
- Weinberg, J. et al. (2019). Philosophers on a physics experiment that “suggests there’s no such thing as objective reality”. Daily Nous. March 21, 2019.
The standard model of particle physics
History of particle physics
- Ernest Rutherford (1871-1937)
- Rolf Widerøe (1902-1996)
- Ernest Lawrence (1901-1958)
- Particle accelerator
- Particle physics
- Brookhaven National Laboratory
- Luis Walter Alvarez (1911-1988)
- SLAC National Accelerator Laboratory
- \(J/\psi\) meson - “November Revolution” in particle physics (1974)
- European Organization for Nuclear Research (CERN)
- Carlo Rubbia (b. 1934)
- Fermilab
- Review of Particle Physics234
- Physics Problems for the Next Millennium
Mixing
- Cabibbo angle (1963)235
- CP violation
- CKM matrix
- Kaons
- B-mesons
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.
- Georgi: Is the Higgs real?239
- Lyre, H. (2008). Does the Higgs mechanism exist?240
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.
- Cao, T.Y. (2016). The Englert-Brout-Higgs mechanism: An unfinished project.243
- ’t Hooft, G. (2022). A triumph for theory.
A model of leptons
- Glashow, S. (1961). Partial symmetries of weak interactions.244
- Weinberg, S. (1967). A model of leptons.245
- Salam, A. & Ward, J.C. (1964). Gauge theory of elementary interactions.246
- Salam, A. & Ward, J.C. (1964). Electromagnetic and weak interactions.247
- GWS electroweak theory: SU(2) \(\times\) U(1)
- Weinberg, S. (1979). Conceptual foundations of the unified theory of weak and electromagnetic interactions. Nobel Lecture, December 8, 1979.248
- UA1 and UA2 Collaborations discovered the \(W\) and \(Z\) bosons in 1983.
- Rubbia, C. (1984). Experimental observation of the intermediate vector bosons \(W^{+}\), \(W^{-}\), and \(Z^{0}\). Nobel lecture, December 8, 1984.249
- Weinberg - Model physicst250
- Woit, P. (2022). Glashow interview.
Quantum chromodynamics
- QCD: SU(3)
- SU(3) \(\times\) SU(2) \(\times\) U(1)
- Asymptotic freedom
Three generations of fermions
- Discovery of charm: “November revolution” at SLAC and BNL (1974)
- Discovery of tau at SLAC + LBL (1975)
- Discovery of bottom at Fermilab (1977)
- Discovery of three neutrino generations from the \(Z\) width at LEP (1989)
- Discovery of top at Fermilab (1995)

More:
- Nima Arkani-Hamed doing particle physics a priori: “Why is there a Macroscopic Universe?”
- Nima Arkani-Hamed on Collider Physics from the Bottom Up
Experimental methods
- Hamamatsu. (2007). Photomultiplier Tubes: Basics and Applications.251
Beyond the standard model
- Beyond the standard model (BSM)
Neutrino masses
- Neutrino masses and mixings
- PMNS matrix and CP-violation
- Are neutrinos Marojana or Dirac fermions?
- Solar neutrino problem
- LSND anomaly
- Vitagliano, E., Tamborra, I., & Raffelt, G. (2020). Grand unified neutrino spectrum at Earth: Sources and spectral components.256
Ad hoc structures
- Why SU(3) \(\times\) SU(2) \(\times\) U(1)?
- Strong \(CP\) problem
- Axions
- Matter-antimatter asymmetry
- 3 generations
- Hierarchy problem(s)
- Dark matter and dark energy
See also:
Experimental anomalies
- Ultra-high-energy cosmic rays
- Greisen-Zatsepin-Kuzmin (GZK) limit
- Pierre Auger Collaboration257
- LSND anomaly, again
- PRL. (2016). Theorists react to the CERN 750 GeV diphoton data.
- Garisto, D. (2018). The era of anomalies.
- Lepton universality at LHCb
- LHCb Collaboration. (2021). Test of lepton universality in beauty-quark decays.
- LHCb Collaboration. (2021). Tests of lepton universality using \(B^{0}\rightarrow{}K^{0}_{S}\ell^{+}\ell^{-}\) and \(B^{+}\rightarrow{}K^{*+}\ell^{+}\ell^{-}\) decays.
- Muon \(g-2\)
- A no-lose theorem for discovering the new physics of \((g-2)_\mu\) at muon colliders258
- Muon collider physics summary259
- \(W\) mass
Grand unification
- Running of the couplings
- Supersymmetry
- Baez, J.C. & Huerta, J. (2009). Division algebras and supersymmetry I.261
- Baez, J.C. & Huerta, J. (2010). Division algebras and supersymmetry II.262
- Grand Unified Theories (GUTs)
- Pati & Salam263
- Georgi & Glashow264
- Slansky265
- Georgi, H. (1982). Lie Algebras in Particle Physics.266
- Baez, J.C. & Huerta, J. (2009). The algebra of grand unified theories.267
- Lisi, A.G. (2007). An exceptionally simple theory of everything.268

See also:
Baryogenesis
- Matter-antimatter asymmetry
- Dine, M. & Kusenko, A. (2004). The origin of the matter-antimatter asymmetry.270
Future colliders and criticisms
- Baggot, J. (2013). Farewell to Reality.271
- CERN. (2020). Press Release: Particle physicists update strategy for the future of the field in Europe. (“FCC”)
- Hossenfelder, S. (2020). The world doesn’t need a new gigantic particle collider.
Quantum gravity
- Start of string phenomenology272
- Maldacena, J.M. (1998). The large \(N\) limit of superconformal field theories and supergravity.273
- Witten, E. (1998). Anti-de Sitter space and holography.274
- Ney, A. (2021). From quantum entanglement to spatiotemporal distance.275
Gravity and cosmology
General relativity
- Recall Special relativity.
- Bernhard Riemann (1826-1866)
- Einstein, A. & Grossmann, M. (1913). Outline of a generalized theory of relativity and of a theory of gravitation.276
- Misner, C.W., Thorne, K.S., & Wheeler, J.A. (1973). Gravitation.277
- Carroll, S.M. (2004). Spacetime and Geometry.278
- Arntzenius, F. (2012). Space, Time, and Stuff.279
- Diffeomorphism invariance, background independence
Newtonian gravity
- History of Newton and calculus.
- Newtonian gravity is the right law to conserve gravitational force flux in three dimensions.
- Derive Newtonian gravity as the low-velocity, low-curavature limit of GR.
Big bang model
- Alexander Friedmann solves the Einstein field equations for an expanding universe in 1922.
- Edwin Hubble discovered that our galaxy is one of many in 1923.
- Georges Lemaître independently solved the Einstein field equations in 1927.
- Edwin Hubble observationally confirmed the expansion of the universe in 1929.
- Arno Penzias and Robert Wilson discovered the cosmic background radiation (CMB) in 1964.
- See history reviewed by Frè280
- The First Three Minutes281
- Ryden, B. (2003). Introduction to Cosmology.282
- Big Bang Nucleosynthesis (BBN)
- Bahcall, N.A., Ostriker, J.P., Perlmutter, S., & Steinhardt, P.J. (1999). The cosmic triangle: Revealing the state of the universe.283
Spacetime
- Substantivalism vs relationism
- Leibniz, Mach, Barbour
- Romero, G.E. (2015). On the ontology of spacetime: Substantivalism, relationism, eternalism, and emergence.284
- Video: A mock debate on time with Julian Barbour and Tim Maudlin (2011).
Blackholes
- Penington, G. (2019). Entanglement wedge reconstruction and the information paradox.285
Gravitational waves
- Poincaré
- Einstein
- Hulse–Taylor binary pulsar
- LIGO
- Multi-messenger astronomy
Dark matter
- Bullet Cluster
- “A direct empirical proof of the existence of dark matter”286
- Galaxy formation
- Millennium Simulation
- WIMP Miracle
- Disfavored by LHC thus far.
- Bahcall, N.A. (2015). Dark matter universe.287
- Howe, A.R. (2019). The dark matter flowchart, annotated.
- Arbey, A. & Mahmoudi, F. (2021). Dark matter and the early Universe: a review.288
- Martens, N. (2022). Dark matter realism.289
Inflation
- Proposed by Alan Guth in 1979.
- Dark energy
- Vaccuum energy
- Inflaton field and slow-roll inflation
- \(\Lambda\)-CDM Cosmological Standard Model

Alternative theories of gravity
- Einstein-Cartan theory
- Modified Newtonian dynamics (MOND)
- TODO: Sabine Hossenfelder
- Entropic gravity
Fine-tuning
- Fine-tuning and naturalness
- Anthropic principle
- TODO: Find Weinberg on AP and naturalness
- Relationship to evolution
- Richard Dawkins and Steven Weinberg discuss science and religion
- Meta-stability of the Higgs vaccuum in \(m_t\) vs \(m_H\)
Complexity and emergence
- nonlinear systems
- chaos
- Universality
- Thermodynamics, statistical mechanics, renormalization.
- Anderson, P.W. (1972). More is different.291
- Bedau, M.A. (1997). Weak emergence.292
- Bunge, M. (2001). Philosophy in Crisis: The Need for Reconstruction.
- Emergence293
- DeDeo, S. (2012). Video: Lecture 1: Coarse-graining, renormalization & universality.
- Lisi, A.G. (2017). Emergence.294
- Bain
- TODO
- Jardón, R. (2020). Emergence.
- Views on reductionism
- Video: Closer To Truth: What’s Strong Emergence?
- George F. R. Ellis vs Barry Loewer
- John, Y.J. (2020). An emergence reading list.
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
- entailment, reductionism
- crossing symmetry in QFT
- Bokulich, P. (2011). Hempel’s dilemma and domains of physics.296
- Carroll, S. (2013). Talk: Poetic Naturalism.
- Carroll, S. (2014). Talk: Has science refuted religion? Acceptance speech for the FFRF’s the emperor has no clothes award.
- Carroll, S. (2015). Quantum field theory and the limits of knowledge.
- Carroll, S. & Wallace, A. (2017). Talk: The Nature of Reality: A Dialogue Between a Buddhist Scholar and a Theoretical Physicist.
- Carroll, S. (2021). The quantum field theory on which the everyday world supervenes.

See also:
- Physicalism in the Outline on naturalism
My thoughts
- Sean Carroll QM: what there is, is more than we can see.
- Reece, R. (2017). Quora: What is currently the best explanation for how and why the quantum wave function collapses?
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.
- Pusey et al. (2012)
- arxiv:1111.3328
My thoughts
- TODO.
More articles to do
Links and encyclopedia articles
SEP
- Being and Becoming in Modern Physics
- Bell’s Theorem
- Bohmian Mechanics
- Boltzmann’s Work in Statistical Physics
- Chaos
- Collapse Theories
- Computer Simulations in Science
- Copenhagen Interpretation of Quantum Mechanics
- Decoherence
- Emergent Properties
- Everett’s Relative-State Formulation of Quantum Mechanics
- Fine-tuning
- General relativity, Early philosophical interpretations of
- Holism and Nonseparability in Physics
- Identity and Individuality in Quantum Theory
- Identity of Indiscernibles
- Kochen-Specker Theorem
- Many-Worlds Interpretation of Quantum Mechanics
- Modal Interpretations of Quantum Mechanics
- Measurement in Quantum Theory
- Philosophical Issues in Quantum Theory
- Poincaré, Henri (1854-1912)
- Quantum-Bayesian and Pragmatist Views of Quantum Theory
- Quantum Entanglement and Information
- Quantum Field Theory
- Quantum Field Theory, History of
- Quantum Gravity
- Quantum Logic and Probability Theory
- Quantum Mechanics
- Quantum Theory: von Neumann vs Dirac
- Relational Quantum Mechanics
- Statistical mechanics, Philosophy of
- Supertasks
- Symmetry and Symmetry Breaking
- Time
- Weyl, Hermann (1885-1955)
IEP
- Einstein-Podolsky-Rosen Argument and the Bell Inequalities
- Emergence
- Interpretations of Quantum Mechanics
- Laws of nature
- What Else Science Requires of Time
Scholarpedia
- Algebraic renormalization
- ATLAS experiment
- Bjorken scaling
- Coleman-Mandula theorem
- Coleman-Weinberg mechanism
- CP violation in electroweak interactions
- Critical Phenomena: field theoretical approach
- Daya Bay Experiment
- Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism
- Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism (history)
- Faddeev-Popov ghosts
- Gauge invariance
- Gauge theories
- Glashow-Iliopoulos-Maiani mechanism
- Grand unification
- Lagrangian formalism for fields
- Lattice gauge theories
- Lattice quantum field theory
- Leptogenesis
- Local operator
- MS-bar definition of parton distribution functions
- Multiloop Feynman integrals
- Operator product expansion
- Parton shower Monte Carlo event generators
- Path integral
- Path integral: mathematical aspects
- Principle of least action
- QCD evolution equations for parton densities
- Second quantization
- Symmetry breaking in classical systems
- Wightman quantum field_theory
Wikipedia
- AdS/CFT correspondence
- Aharonov-Bohm effect
- Ampère, André-Marie (1775-1836)
- Atomism
- Background independence
- Bargmann, Valentine (1908-1989)
- Bargmann-Wigner equations
- Beeckman, Isaac (1588-1637)
- Bell’s theorem
- Bekenstein bound
- Black hole information paradox
- Bohm, David (1917-1992)
- Bohr, Niels (1885-1962)
- Bohr-Einstein debates
- Born rule
- Bullet Cluster
- C*-algebra
- Casimir effect
- Cauchy, Augustin-Louis (1789-1857)
- Causal Processes
- Causal perturbation theory
- Central limit theorem
- Causality
- CHSH inequality
- Chronology of the universe
- Church-Turing-Deutsch principle
- Church-Turing thesis
- Clinamen
- Complexity
- Constructor theory
- Corpuscularianism
- CP violation
- Curie’s Principle
- de Broglie, Louis (1892-1987)
- De Broglie-Bohm theory
- Democritus (c. 460-370 BCE)
- Descartes, René (1596-1650)
- Determinism
- Digital philosophy
- Digital physics
- Effective field theory
- Einselection
- Equivalence principle
- Emergence
- Entropic gravity
- Entropy
- Entropy, Introduction to
- Epicurus (341-270 BCE)
- Equipartition theorem
- Erlangen program
- Eternalism (philosophy of time)
- Franklin, Benjamin (1706-1790)
- Fraunhofer, Joseph von (1787-1826)
- Four-dimensionalism
- Field
- Firewall
- Gauss, Carl Friedrich (1777-1855)
- Gelfand-Naimark theorem
- Gelfand-Naimark-Segal construction
- General relativity
- Ghirardi-Rimini-Weber theory
- Gibbs, Josiah Willard (1839-1903)
- Grand Unified Theory
- Haag, Rudolf (1922-2016)
- Haag-Łopuszański-Sohnius theorem
- Haag’s theorem
- Hidden variable theory
- Hierarchy problem
- Hilbert, David (1862-1943)
- Hilbert space
- Holographic principle
- Holomovement
- Holonomy
- Kaluza-Klein theory
- Kanada (c. 600-100 BCE)
- Kochen-Specker Theorem
- Lambda-CDM model
- Landau pole
- Leucippus (fl. 5th century BCE)
- Little hierarchy problem
- Locality, Principle of
- Local hidden variable theory
- Local (algebraic) quantum field theory
- Loopholes in Bell test experiments
- Lucretius (c. 99-55 BCE)
- Mach’s principle
- Measurement in quantum mechanics
- Measurement problem
- M-theory
- M-theory, Introduction to
- Mu problem
- No-cloning theorem
- Noether, Emmy (1882-1935)
- Noether’s theorem
- Objective collapse theory
- Particle physics
- Particle physics and representation theory
- PBR theorem
- Physical cosmology
- Physicalism
- Physics, Philosophy of
- Poincaré, Henri (1854-1912)
- Poincaré group
- Quantization
- Quantization, Canonical
- Quantization, Geometric
- Quantum decoherence
- Quantum entanglement
- Quantum field theory
- Quantum gravity
- Quantum mechanics
- Quantum mechanics, Mathematical formulation of
- Quantum triviality
- Reeh-Schlieder theorem
- Regularization
- Relational quantum mechanics
- Relativity
- Relativity, General
- Relativity, Introduction to General
- Renormalization
- Renormalization group
- Representation theory
- Rietdijk-Putnam argument
- Shape dynamics
- Standard Model
- Standard Model (mathematical formulation)
- Statistical mechanics
- Stone-von Neumann theorem
- String theory
- Strong CP problem
- Supertask
- Supergravity
- Supersymmetry
- Thermal and statistical physics, Philosophy of
- Timeline of cosmological theories
- Timeline of particle physics
- Timeline of particle physics technology
- Timeline of quantum mechanics
- Topological order
- Ultraviolet catastrophe
- Universality
- Unruh effect
- Unsolved problems in physics, List of
- van der Waals, Johannes Diderik (1837-1923)
- Volta, Alessandro (1745-1827)
- von Neumann, John (1903-1957)
- Wave function
- Wave function collapse
- Wave-particle duality
- Weinberg-Witten theorem
- Weyl, Hermann (1885-1955)
- Wightman axioms
- Wigner, Eugene (1902-1995)
- Wigner’s classification
- Wigner’s theorem
- Wigner-Eckart theorem
Others
- bohmianmechanics.org
- Can the quantum state be interpreted statistically? - Matt Leifer
- Can we trivialize the equivalence between canonical quantization of fields and second quantization of particles? - physics.stackexchange
- Could one argue that \(h\) (Planck constant) and \(\hbar/2\) (Dirac constant) are in fact independant constants? - physics.stackexchange
- Effective field theory - nlab
- Emergence - RationalWiki.org
- Fiber bundles in physics - nlab
- Intuitively, why are bundles so important in Physics? - nlab
- Is a third quantization possible? - physics.stackexchange
- Kochen-Specker theorem
- lqp2.org - serving several papers on AQFT
- Philosophy of general relativity - Jonathan Bain
- Philosophy of quantum mechanics - Jonathan Bain
- Quantization - nLab
- What is a gauge? - Terence Tao
- Struggles With the Continuum - John Baez
- Kelvin’s “Clouds” Speech
Videos
- Al-Khalili, J. (2009). “Atom” BBC documentary (3 episodes)
- Carroll, S. (2013). Particles, Fields and The Future of Physics.
- Carroll, S. (2019). Something Deeply Hidden - talk at Google.
- Kuhn, R.L. (2020). Closer To Truth: What’s Strong Emergence?
- Maudlin, T. (2018). Ontological clarity, electromagnetism, Aharanov-Bohm effect.
- Tong, D. (2017). Quantum Fields: The Real Building Blocks of the Universe.
References
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Nail (2018).↩︎
Yock (2018).↩︎
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Holm (2011a) and Holm (2011b).↩︎
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Kasprzak, Lysik, & Rybaczuk (1990).↩︎
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Janyska, Modugno, & Vitolo (2007).↩︎
Zapata-Carratala (2021).↩︎
Einstein (1905d).↩︎
Einstein (1905a).↩︎
Stein (2021), p. 69.↩︎
Maudlin (2012), p. TODO.↩︎
Wu (2021).↩︎
Caulton (2015).↩︎
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Noether (1918).↩︎
Wigner (1954).↩︎
Brading (2002).↩︎
Baez (2018).↩︎
Goyal (2020).↩︎
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’t Hooft (2007).↩︎
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Schroeren (2021).↩︎
Ney & Albert (2013).↩︎
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Feynman & Hibbs (1965), p. 9.↩︎
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van Hove (1958).↩︎
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Drossel (2015), p. 51–2.↩︎
Zurek (2022).↩︎
Friedrich (2016).↩︎
C. Cao, Hu, Li, & Schwarz (2019).↩︎
Coecke & Kissinger (2017).↩︎
Preskill (2018).↩︎
Arute, F. et al. (2019).↩︎
Broughton, M. et al. (2020).↩︎
Feynman (1965).↩︎
Weinberg (1997b), p. 8.↩︎
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Peskin & Schroeder (1995).↩︎
Zee (2003).↩︎
Schwartz (2014).↩︎
Tong (2006).↩︎
Zeidler (2007).↩︎
Zeidler (2008).↩︎
Zeidler (2011).↩︎
T. Y. Cao (1999).↩︎
’t Hooft (2005).↩︎
Coleman & Mandula (1967).↩︎
Wigner (1939) and Bargmann & Wigner (1948).↩︎
Bell (1955).↩︎
Streater & Wightman (1964).↩︎
Greaves & Thomas (2012).↩︎
Ohanian (1986).↩︎
Peskin (1994).↩︎
Sebens (2019).↩︎
Dutailly (2014), p. 37.↩︎
Kontsevich & Segal (2021).↩︎
Dyson (1949).↩︎
Dyson (1952).↩︎
Lehmann, Symanzik, & Zimmermann (1955).↩︎
Weinberg (1964a) and Weinberg (1964b).↩︎
Martin (2011).↩︎
Reece (2007).↩︎
Jaeger (2019).↩︎
Feynman & Hibbs (1965).↩︎
Nguyen (2016).↩︎
Dirac (1963).↩︎
’t Hooft (1971).↩︎
Wilson (1974).↩︎
Goldenfeld (1992).↩︎
Butterfield (2014).↩︎
Butterfield & Bouatta (2015).↩︎
’t Hooft (1994).↩︎
’t Hooft (1999).↩︎
Kadanoff (2013), p. 50.↩︎
Borcherds & Barnard (2002).↩︎
Huggett & Weingard (1995).↩︎
Weinberg (1997b).↩︎
Bain (2013a) and Bain (2013b).↩︎
Preskill (2013).↩︎
Williams (2019).↩︎
Rosaler (2022).↩︎
Baez (2016).↩︎
Auyang (1995).↩︎
Baez (2016), p. 17.↩︎
Baez (2016), p. 18.↩︎
Einstein (1905c).↩︎
Weinberg (1997b), p. 2.↩︎
Weinberg (1997a).↩︎
Baez et al. (1992), p. 59.↩︎
Fraser (2008).↩︎
Pessa (2009).↩︎
Duncan (2012), p. 163–4.↩︎
Myrvold (2015).↩︎
Lazarovici (2018).↩︎
Baker (2009).↩︎
Caulton (2018).↩︎
Haag (1955).↩︎
Malament (1996).↩︎
Teller (1997), p. 115.↩︎
Earman & Fraser (2006).↩︎
Klaczynski (2016).↩︎
Ruetsche (2002).↩︎
Bain (2000).↩︎
Duncan (2012).↩︎
Redhead (1982).↩︎
Redhead (1988).↩︎
Haag (1992).↩︎
Wallace (2011).↩︎
Fraser (2011).↩︎
Buchholz (1998).↩︎
Kastler (2003), p. 6.↩︎
Aharonov & Bohm (1959).↩︎
Healey (2007), ch. 2-4.↩︎
Batterman (2003).↩︎
Maudlin (2018).↩︎
Frankel (2004).↩︎
nLab authors (2021).↩︎
Way (2010).↩︎
Vákár (2011).↩︎
Maudlin (2007), p. 96.↩︎
Maudlin (2007), p. 101.↩︎
Baez & Muniain (1994).↩︎
Baez & Schreiber (2005).↩︎
Baez & Huerta (2011).↩︎
Schreiber (2020).↩︎
Baez & Stay (2009).↩︎
’t Hooft (1978).↩︎
’t Hooft (1994).↩︎
Shifman (2012).↩︎
Haag, Łopuszański, & Sohnius (1975).↩︎
Schreiber (2016).↩︎
Dimopoulos & Georgi (1981).↩︎
Murayama (2000).↩︎
Freedman, Nieuwenhuizen, & Ferrara (1976).↩︎
van Nieuwenhuizen (1981).↩︎
Frè (2013), ch. 6.↩︎
Martin (2016).↩︎
Tong (2022).↩︎
Maudlin (2019), p. TODO.↩︎
Maudlin (1995).↩︎
Dürr & Lazarovici (2020).↩︎
Mermin (2022).↩︎
Becker (2018).↩︎
Einstein, Podolsky, & Rosen (1935).↩︎
Bohm & Aharonov (1957).↩︎
Mermin (1985).↩︎
Caulton (2014).↩︎
Bell (1964).↩︎
Bell (1966).↩︎
Kochen & Specker (1967).↩︎
Clauser, Horne, Shimony, & Holt (1969).↩︎
Gisin (1991), Gisin & Peres (1992), and Gisin (1999).↩︎
Bell (2004), pp. 232–248.↩︎
Maudlin (2014).↩︎
Ahmed & Caulton (2014).↩︎
Deutsch (1985).↩︎
Bong, K.W. et al. (2020).↩︎
Bohm (1952).↩︎
Bohm (1953).↩︎
Schönberg (1954).↩︎
Bell (2004).↩︎
Dürr, Goldstein, & Zanghì (1995).↩︎
Dürr, Goldstein, Tumulka, & Zanghì (2004).↩︎
Dürr, Goldstein, Tumulka, & Zanghì (2005).↩︎
Dürr, Goldstein, & Zanghì (2013).↩︎
Tumulka (2017).↩︎
Das & Dürr (2019).↩︎
Stopp, Ortiz-Gutiérrez, Lehec, & Schmidt-Kaler (2021).↩︎
Ananthaswamy (2021).↩︎
Everett (2012), p. 171.↩︎
Everett (1956).↩︎
Everett (1957).↩︎
Wheeler (1957).↩︎
Everett (2012).↩︎
DeWitt (1970).↩︎
DeWitt & Graham (1973).↩︎
Barrett (2011).↩︎
Barrett (2016).↩︎
Everett (2012), p. 150.↩︎
Wallace (2012).↩︎
Carroll & Singh (2019).↩︎
Carroll (2019).↩︎
Wilhelm (2022).↩︎
Joos, E. et al. (2003), p. 22.↩︎
Ghirardi, Rimini, & Weber (1986).↩︎
Putnam (1975).↩︎
Putnam (2005).↩︎
Wuthrich (2014).↩︎
Caves, Fuchs, & Schack (2001).↩︎
Fuchs (2002).↩︎
Fuchs (2010).↩︎
Fuchs & Schack (2013).↩︎
Fuchs, Mermin, & Schack (2014).↩︎
Fuchs & Stacey (2016).↩︎
Harrigan & Spekkens (2010).↩︎
Leifer & Spekkens (2013).↩︎
Pusey, Barrett, & Rudolph (2012).↩︎
Schlosshauer & Fine (2012).↩︎
Nigg, D. et al. (2015).↩︎
’t Hooft (2021).↩︎
Proietti, M. et al. (2019).↩︎
Zyla, P.A. et al. (Particle Data Group) (2021).↩︎
Cabibbo (1963).↩︎
Englert & Brout (1964).↩︎
Higgs (1964).↩︎
Guralnik, Hagen, & Kibble (1964).↩︎
Georgi (1999), p. 280.↩︎
Lyre (2008).↩︎
ATLAS Collaboration (2012).↩︎
CMS Collaboration (2012).↩︎
T. Y. Cao (2016).↩︎
Glashow (1961).↩︎
Weinberg (1967).↩︎
Salam & Ward (1964b).↩︎
Salam & Ward (1964a).↩︎
Weinberg (1979).↩︎
Rubbia (1984).↩︎
Chalmers (2017).↩︎
Hamamatsu (2007).↩︎
LSND Collaboration (1996).↩︎
LSND Collaboration (2001).↩︎
MiniBooNE Collaboration (2018).↩︎
MicroBooNE Collaboration (2021).↩︎
Vitagliano, Tamborra, & Raffelt (2020).↩︎
TODO: Pierre Auger Collaboration (2007), Pierre Auger Collaboration (2010), Pierre Auger Collaboration (2020a), and Pierre Auger Collaboration (2020b).↩︎
Capdevilla, Curtin, Kahn, & Krnjaic (2021).↩︎
Aime (2022).↩︎
CDF Collaboration (2022).↩︎
Baez & Huerta (2009a).↩︎
Baez & Huerta (2010).↩︎
Pati & Salam (1974).↩︎
Georgi & Glashow (1974).↩︎
Slansky (1981).↩︎
Georgi (1999).↩︎
Baez & Huerta (2009b).↩︎
Lisi (2007).↩︎
Martin (2016), p. 66.↩︎
Dine & Kusenko (2004).↩︎
Baggott (2013).↩︎
Candelas, Horowitz, Strominger, & Witten (1985).↩︎
Maldacena (1998).↩︎
Witten (1998).↩︎
Ney (2021).↩︎
Einstein & Grossmann (1913).↩︎
Misner, Thorne, & Wheeler (1973).↩︎
Carroll (2004).↩︎
Arntzenius (2012).↩︎
Frè (2013), ch. 4.↩︎
Weinberg (1977).↩︎
Ryden (2003).↩︎
Bahcall, Ostriker, Perlmutter, & Steinhardt (1999).↩︎
Romero (2015).↩︎
Penington (2019).↩︎
Clowe, D. et al. (2006).↩︎
Bahcall (2015).↩︎
Arbey & Mahmoudi (2021).↩︎
Martens (2022).↩︎
Debono & Smoot (2016), figure 4.↩︎
Anderson (1972).↩︎
Bedau (1997).↩︎
Bunge (2001), p. 72.↩︎
Lisi (2017).↩︎
Anderson (1972), p. 393.↩︎
Bokulich (2011).↩︎