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:

More:

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.34

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.43

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.44

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,51 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.66

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.84

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.112

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.113

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.115

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.117

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.139

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.145

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.148

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.149

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.159

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.197

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.206

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).211

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;228 Peter Higgs;229 and Gerald Guralnik, Carl R. Hagen, and Tom Kibble,230 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 ATLAS233 and CMS234 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.285

See also:

Bracketing human experience

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

See also:

My thoughts

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.

SEP

IEP

Scholarpedia

Wikipedia

Others

Videos

References

Afriat, A. (2013). Weyl’s gauge argument. Foundations of Physics, 43, 699–705. http://philsci-archive.pitt.edu/9597/
Aharonov, Y. & Bohm, D. (1959). Significance of electromagnetic potentials in the quantum theory. Physical Review, 115, 485–491. https://journals.aps.org/pr/abstract/10.1103/PhysRev.115.485
Ahmed, A. & Caulton, A. (2014). Causal decision theory and EPR correlations. Synthese, 191, 4315–4352. http://philsci-archive.pitt.edu/10992/
Aime, C. (2022). Muon collider physics summary. https://arxiv.org/abs/2203.07256
Ananthaswamy, A. (2021). This simple experiment could challenge standard quantum theory. Scientific American. https://www.scientificamerican.com/article/this-simple-experiment-could-challenge-standard-quantum-theory/
Anderson, P. W. (1972). More is different. Science, 177, 393–396. http://science.sciencemag.org/content/177/4047/393
Arntzenius, F. (2012). Space, Time, and Stuff. Oxford University Press.
Arute, F. et al. (2019). Quantum supremacy using a programmable superconducting processor. Nature, 574, 505–510. https://www.nature.com/articles/s41586-019-1666-5
ATLAS Collaboration. (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Physics Letters B, 716, 1–29. https://arxiv.org/abs/1207.7214
Auyang, S. Y. (1995). How Is Quantum Field Theory Possible? Oxford University Press.
Bacciagaluppi, G. & Valentini, A. (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press. https://arxiv.org/abs/quant-ph/0609184
Baez, J. C. (2011). Division algebras and quantum theory. Foundations of Physics, 42, 819–855. https://arxiv.org/abs/1101.5690
———. (2016). Struggles with the continuum. https://arxiv.org/abs/1609.01421
———. (2018). Getting to the bottom of Noether’s theorem. Talk given at The Philosophy and Physics of Noether’s Theorems, University of Notre Dame, October 6, 2018. https://math.ucr.edu/home/baez/noether/noether_web.pdf
Baez, J. C. & Huerta, J. (2009a). Division algebras and supersymmetry I. https://arxiv.org/abs/0909.0551
———. (2009b). The algebra of grand unified theories. Bulletin of the American Mathematical Society, 47, 483–552. https://arxiv.org/abs/0904.1556
———. (2010). Division algebras and supersymmetry II. https://arxiv.org/abs/1003.3436
———. (2011). An invitation to higher gauge theory. General Relativity and Gravitation, 43, 2335–92. https://arxiv.org/abs/1003.4485
Baez, J. C. & Muniain, J. P. (1994). Gauge Fields, Knots and Gravity. World Scientific.
Baez, J. C. & Schreiber, U. (2005). Higher gauge theory. https://arxiv.org/abs/math/0511710
Baez, J. C., Segal, I., & Zhou, Z. (1992). Introduction to Algebraic and Constructive Quantum Field Theory. Princeton University Press. https://math.ucr.edu/home/baez/bsz.html
Baez, J. C. & Stay, M. (2009). Physics, topology, logic, and computation: A Rosetta Stone. https://arxiv.org/abs/0903.0340
Baggott, J. (2013). Farewell to Reality: How modern physics has betrayed the search for scientific truth. Pegasus Books.
Bahcall, N. A., Ostriker, J. P., Perlmutter, S., & Steinhardt, P. J. (1999). The cosmic triangle: Revealing the state of the universe. Science, 284, 1481–8. https://arxiv.org/abs/astro-ph/9906463
Bain, J. (2000). Against particle/field duality: Asymptotic particle states and interpolating fields in interacting QFT, or Who’s afraid of Haag’s theorem? Erkenntnis, 53, 375–406.
———. (2013a). Effective field theories. In R. Batterman (Ed.), The Oxford Handbook of Philosophy of Physics (pp. 224–254). Oxford University Press.
———. (2013b). Emergence in effective field theories. European Journal for Philosophy of Science, 3, 257–273.
Baker, D. J. (2009). Against field interpretations of quantum field theory. British Journal for the Philosophy of Science, 60, 585–609. http://philsci-archive.pitt.edu/4350/
Bargmann, V. & Wigner, E. P. (1948). Group theoretical discussion of relativistic wave equations. Proceedings of the National Academy of Sciences, 34, 211–223.
Barrett, J. A. (2011). Everett’s pure wave mechanics and the notion of worlds. European Journal for Philosophy of Science, 1, 277–302. https://link.springer.com/article/10.1007/s13194-011-0023-9
———. (2016). Quantum Worlds. Principia: An International Journal of Epistemology, 20, 45–60.
Batterman, R. W. (2003). Falling cats, parallel parking and polarized light. Studies in History and Philosophy of Modern Physics, 34, 527–557. http://philsci-archive.pitt.edu/794/
Becker, A. (2018). What is Real? The unfinished quest for the meaning of quantum physics. Basic Books.
Bedau, M. A. (1997). Weak emergence. Philosophical Perspectives, 11, 375–399.
Bell, J. S. (1955). Time reversal in field theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 231, 479–495.
———. (1964). On the Einstein Podolsky Rosen Paradox. Physics, 1, 195–200. https://journals.aps.org/ppf/pdf/10.1103/PhysicsPhysiqueFizika.1.195
———. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447. http://fy.chalmers.se/~delsing/QI/Bell-RMP-66.pdf
———. (2004). Speakable and Unspeakable in Quantum Mechanics (2nd ed.). Cambridge University Press. (Originally published in 1987).
Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ’hidden’ variables, I and II. Physical Review, 85, 166–193.
———. (1953). Proof that probability density approaches \(|\psi|^2\) in causal interpretation of quantum theory. Physical Review, 89, 458–466.
Bohm, D. & Aharonov, Y. (1957). Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky. Physical Review, 108, 1070.
Bokulich, P. (2011). Hempel’s dilemma and domains of physics. Analysis, 71, 646–651.
Bong, K.W. et al. (2020). A strong no-go theorem on the Wigner’s friend paradox. Nature Physics, 16, 1199–1205. https://arxiv.org/abs/1907.05607
Borcherds, R. E. & Barnard, A. (2002). Lectures on quantum field theory. https://arxiv.org/abs/math-ph/0204014
Brading, K. A. (2002). Which symmetry? Noether, Weyl, and conservation of electric charge. Studies in History and Philosophy of Modern Physics, 33, 3–22. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.569.106&rep=rep1&type=pdf
Broughton, M. et al. (2020). TensorFlow Quantum: A software framework for quantum machine learning. https://arxiv.org/abs/2003.02989
Buchholz, D. (1998). Current trends in axiomatic quantum field theory. https://arxiv.org/abs/hep-th/9811233
Buckingham, E. (1914). On physically similar systems; Illustrations of the use of dimensional equations. Physical Review, 4, 345–376.
Bunge, M. (2001). Philosophy in Crisis: The Need for Reconstruction. Prometheus Books.
Butterfield, J. (2014). Reduction, emergence, and renormalization. The Journal of Philosophy, 111, 5–49. https://arxiv.org/abs/1406.4354v1
Butterfield, J. & Bouatta, N. (2015). Renormalization for philosophers. Metaphysics in Contemporary Physics, 104, 437–485. https://arxiv.org/abs/1406.4532
Cabibbo, N. (1963). Unitary symmetry and leptonic decays. Physical Review Letters, 10, 531–533. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.531
Candelas, P., Horowitz, G. T., Strominger, A., & Witten, E. (1985). Vacuum configurations for superstrings. Nuclear Physics B, 258, 46–74.
Cao, C., Hu, H., Li, J., & Schwarz, W. H. E. (2019). Physical origin of chemical periodicities in the system of elements. Pure and Applied Chemistry, 91, 1969–1999. https://www.degruyter.com/document/doi/10.1515/pac-2019-0901/html
Cao, T. Y. (1999). Conceptual Foundations of Quantum Field Theory. Cambridge University Press.
———. (2016). The Englert-Brout-Higgs mechanism: An unfinished project. International Journal of Modern Physics A, 31, 1630061.
Capdevilla, R., Curtin, D., Kahn, Y., & Krnjaic, G. (2021). A no-lose theorem for discovering the new physics of \((g−2)_\mu\) at muon colliders. https://arxiv.org/abs/2101.10334
Carroll, S. M. (2004). Spacetime and Geometry. Addison Wesley.
———. (2019). Something Deeply Hidden. Dutton.
Carroll, S. M. & Singh, A. (2019). Mad-Dog Everettianism: Quantum mechanics at its most minimal. In What is Fundamental? (pp. 95–104). Springer. https://arxiv.org/abs/1801.08132
Caulton, A. (2014). Physical entanglement in permutation-invariant quantum mechanics. https://arxiv.org/abs/1409.0246
———. (2015). The role of symmetry in the interpretation of physical theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 153–162. http://philsci-archive.pitt.edu/11571/
———. (2018). A persistent particle ontology for quantum field theory. Metascience, 27, 439–441.
Caulton, A. & Butterfield, J. (2012). Symmetries and paraparticles as a motivation for structuralism. British Journal for the Philosophy of Science, 63, 233–285. https://arxiv.org/abs/1002.3730
Caves, C. M., Fuchs, C. A., & Schack, R. (2001). Quantum probabilities as Bayesian probabilities. Physical Review A, 65, 022305. https://arxiv.org/abs/quant-ph/0106133
CDF Collaboration. (2022). High-precision measurement of the \(W\) boson mass with the CDF II detector. Science, 376, 170–176. https://www.science.org/doi/10.1126/science.abk1781
Chalmers, M. (2017). Model physicist. https://cerncourier.com/a/model-physicist/
Clauser, J., Horne, M., Shimony, A., & Holt, R. (1969). Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23, 880–884.
Clowe, D. et al. (2006). A direct empirical proof of the existence of dark matter. Astrophysical Journal Letters, 648, 109. https://arxiv.org/abs/astro-ph/0608407
CMS Collaboration. (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Physics Letters B, 716, 30–61. https://arxiv.org/abs/1207.7235
Coecke, B. & Kissinger, A. (2017). Picturing Quantum Processes: A first course in quantum theory and diagrammatic reasoning. Cambridge University Press.
Coleman, S. & Mandula, J. (1967). All possible symmetries of the \(S\) matrix. Physical Review, 159, 1251–1256.
Das, S. & Dürr, D. (2019). Arrival time distributions of spin-1/2 particles. Scientific Reports, 9, 2242. https://www.nature.com/articles/s41598-018-38261-4
Debono, I. & Smoot, G. F. (2016). General relativity and cosmology: Unsolved questions and future directions. Universe, 2, 23. https://arxiv.org/abs/1609.09781
Deutsch, D. (1985). Quantum theory as a universal physical theory. International Journal of Theoretical Physics, 24, 1–41.
Dewar, N. (2019). Sophistication about symmetries. British Journal for the Philosophy of Science, 70, 485–521.
DeWitt, B. S. (1970). Quantum mechanics and reality. Physics Today, 23, 30–35. https://physicstoday.scitation.org/doi/10.1063/1.3022331
DeWitt, B. S. & Graham, N. (1973). The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press.
Dimopoulos, S. & Georgi, H. (1981). Softly broken supersymmetry and SU(5). Nuclear Physics B, 193, 150–162.
Dine, M. & Kusenko, A. (2004). The origin of the matter-antimatter asymmetry. Reviews of Modern Physics, 76, 1–30. https://arxiv.org/abs/hep-ph/0303065
Drossel, B. (2015). On the relation between the second law of thermodynamics and classical and quantum mechanics. In B. Falkenburg & M. Morrison (Eds.), Why More is Different: Philosophical issues in condensed matter physics and complex systems (pp. 41–54). Springer.
Duff, M. J., Okun, L. B., & Veneziano, G. (2001). Trialogue on the number of fundamental constants. https://arxiv.org/abs/physics/0110060
Duncan, A. (2012). Conceptual Framework of Quantum Field Theory. Oxford University Press.
Dutailly, J. C. (2014). Particles and Fields. https://hal.archives-ouvertes.fr/hal-00933043
Dürr, D., Goldstein, S., Tumulka, R., & Zanghì, N. (2004). Bohmian mechanics and quantum field theory. Physical Review Letters, 93, 090402. https://arxiv.org/abs/quant-ph/0303156
———. (2005). Bell-type quantum field theories. Journal of Physics A, 38, R1. https://arxiv.org/abs/quant-ph/0407116
Dürr, D., Goldstein, S., & Zanghì, N. (1995). Bohmian mechanics as the foundation of quantum mechanics. https://arxiv.org/abs/quant-ph/9511016
———. (2013). Quantum Physics Without Quantum Philosophy. Springer.
Dürr, D. & Lazarovici, D. (2020). Understanding Quantum Mechanics: The World According to Modern Quantum Foundations. Springer.
Dyson, F. J. (1949). The \(S\) matrix in quantum electrodynamics. Physical Review, 75, 1736.
———. (1952). Divergence of perturbation theory in quantum electrodynamics. Physical Review, 85, 631.
Earman, J. & Fraser, D. (2006). Haag’s theorem and its implications for the foundations of quantum field theory. Erkenntnis, 64, 305–344.
Einstein, A. (1905a). Ist die trägheit eines körpers von seinem energieinhalt abhängig? Annalen Der Physik, 323, 639–641. https://onlinelibrary.wiley.com/doi/10.1002/andp.19053231314
———. (1905b). Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Annalen Der Physik, 322, 549–560. https://onlinelibrary.wiley.com/doi/10.1002/andp.19053220806
———. (1905c). Über einen die erzeugung und verwandlung des lichtes betreffenden heuristischen gesichtspunkt. Annalen Der Physik, 322, 132–148. https://onlinelibrary.wiley.com/doi/10.1002/andp.19053220607
———. (1905d). Zur elektrodynamik bewegter körper. Annalen Der Physik, 322, 891–921. https://onlinelibrary.wiley.com/doi/10.1002/andp.19053221004
Einstein, A. & Grossmann, M. (1913). Entwurf einer verallgemeinerten relativitätstheorie und einer theorie der gravitation (Outline of a generalized theory of relativity and of a theory of gravitation). Zeitschrift für Mathematik Und Physik, 62, 225–261. http://www.icra.it/MG/doc/Einstein_Entwurf_1913.pdf
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780. https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777
Englert, F. & Brout, R. (1964). Broken symmetry and the mass of gauge vector mesons. Physical Review Letters, 13, 321–323. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.13.321
Everett, H. (1956). Theory of the Universal Wave Function. Princeton University. (Ph.D. thesis. Reprinted in Barrett & Byrne (2012).).
———. (1957). "Relative state" formulation of quantum mechanics. Reviews Modern Physics, 29, 454–462.
———. (2012). The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980 with Commentary. (J. A. Barrett & P. Byrne, Eds.). Princeton University Press.
Feynman, R. P. (1963). The Feynman Lectures on Physics, Volume I. California Institute of Technology. http://www.feynmanlectures.caltech.edu/I_03.html
———. (1965). The development of the space-time view of quantum electrodynamics. Nobel Lecture, December 11, 1965. https://www.nobelprize.org/prizes/physics/1965/feynman/lecture/
Feynman, R. P. & Hibbs, A. R. (1965). Quantum Mechanics and Path Integrals. Dover. Emended edition (2005).
Frankel, T. (2004). The Geometry of Physics (2nd ed.). Cambridge University Press.
Fraser, D. (2008). The fate of ’particles’ in quantum field theories with interactions. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 39, 841–859. http://philsci-archive.pitt.edu/4038/
———. (2011). How to take particle physics seriously: A further defence of axiomatic quantum field theory. Studies in History and Philosophy of Modern Physics, 42, 126–135.
Freedman, D. Z., Nieuwenhuizen, P. van, & Ferrara, S. (1976). Progress toward a theory of supergravity. Physical Review D, 13, 3214–3218.
Frè, P. G. (2013). Gravity, a Geometrical Course, Volume 2: Black Holes, Cosmology and Introduction to Supergravity. Springer.
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. Angewandte, 55, 5378–5392. https://onlinelibrary.wiley.com/doi/10.1002/anie.201509260
Fuchs, C. A. (2002). Quantum mechanics as quantum information (and only a little more). https://arxiv.org/abs/quant-ph/0205039
———. (2010). QBism, the perimeter of quantum Bayesianism. https://arxiv.org/abs/1003.5209
Fuchs, C. A., Mermin, N. D., & Schack, R. (2014). An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics, 82, 749–754. https://arxiv.org/abs/1311.5253
Fuchs, C. A. & Schack, R. (2013). Quantum-Bayesian coherence: The no-nonsense version. Reviews of Modern Physics, 85, 1693–1715. https://arxiv.org/abs/1301.3274
Fuchs, C. A. & Stacey, B. C. (2016). QBism: Quantum theory as a hero’s handbook. https://arxiv.org/abs/1612.07308
Georgi, H. (1999). Lie Algebras in Particle Physics (2nd ed.). Westview Press. (Originally published in 1982).
Georgi, H. & Glashow, S. L. (1974). Unity of all elementary-particle forces. Physical Review Letters, 32, 438–441. http://pcbat1.mi.infn.it/~battist/astrop/su5.pdf
Ghirardi, G. C., Rimini, A., & Weber, T. and. (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34, 470–491.
Gisin, N. (1991). Bell’s inequality holds for all non-product states. Physics Letters A, 154, 201–202.
———. (1999). Bell inequality for arbitrary many settings of the analyzers. Physics Letters A, 260, 1–3. https://arxiv.org/abs/quant-ph/9905062
Gisin, N. & Peres, A. (1992). Maximal violation of Bell’s inequality for arbitrarily large spin. Physics Letters A, 162, 15–17.
Glashow, S. (1961). Partial symmetries of weak interactions. Nuclear Physics, 22, 579–588.
Goldenfeld, N. (1992). Lectures on Phase Transitions and the Renormalization Group. Perseus Books.
Goyal, P. (2020). Derivation of classical mechanics in an energetic framework via conservation and relativity. Foundations of Physics, 50, 1426–1479.
Greaves, H. & Thomas, T. (2012). The CPT Theorem. https://arxiv.org/abs/1204.4674
Guralnik, G. S., Hagen, C. R., & Kibble, T. W. B. (1964). Global conservation laws and massless particles. Physical Review Letters, 13, 585–587. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.13.585
Haag, R. (1955). On quantum field theories. Matematisk-Fysiske Meddelelser, 29, 1–37. http://cds.cern.ch/record/212242
———. (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer.
Haag, R., Łopuszański, J. T., & Sohnius, M. (1975). All possible generators of supersymmetries of the S-matrix. Nuclear Physics B, 88, 257–274.
Hamamatsu. (2007). Photomultiplier Tubes: Basics and Applications (3rd ed.). Hamamatsu Photonics. https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/etd/PMT_handbook_v3aE.pdf
Harrigan, N. & Spekkens, R. W. (2010). Einstein, incompleteness, and the epistemic view of quantum states. Foundations of Physics, 40, 125–157. https://arxiv.org/abs/0706.2661
Healey, R. (2007). Gauging What’s Real. Oxford University Press.
Higgs, P. W. (1964). Broken symmetries, massless particles and gauge fields. Physics Letters, 13, 508–509. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.13.508
Holm, D. D. (2011a). Geometric Mechanics - Part I: Dynamics And Symmetry (2nd ed.). Imperial College Press.
———. (2011b). Geometric Mechanics - Part II: Rotating, Translating, and Rolling (2nd ed.). Imperial College Press.
Huggett, N. & Weingard, R. (1995). The renormalisation group and effective field theories. Synthese, 102, 171–194.
Jaeger, G. (2019). Are virtual particles less real? Entropy, 21, 141. https://www.mdpi.com/1099-4300/21/2/141
Janyska, J., Modugno, M., & Vitolo, R. (2007). Semi-vector spaces and units of measurement. https://arxiv.org/abs/0710.1313
Joos, E. et al. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory (2nd ed.). Springer. (Originally published in 1996).
Jordan, P., Neumann, J. von, & Wigner, E. P. (1934). On an algebraic generalization of the quantum mechanical formalism. Annals of Mathematics, 35, 29.
Kadanoff, L. P. (2013). Theories of matter: Infinities and renormalization. In R. Batterman (Ed.), The Oxford Handbook of Philosophy of Physics (pp. 109–141). Oxford University Press. https://arxiv.org/abs/1002.2985
Kasprzak, W., Lysik, B., & Rybaczuk, M. (1990). Dimensional Analysis in the Identification of Mathematical Models. World Scientific.
Kastler, D. (2003). Rudolf Haag—Eighty Years. Communications in Mathematical Physics, 237, 3–6.
Keller, K. J., Papadopoulos, M. A., & Reyes-Lega, A. F. (2007). On the realization of symmetries in quantum mechanics. https://arxiv.org/abs/0712.0997
Kelvin, L. (1901). Nineteenth century clouds over the dynamical theory of heat and light. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2, 1–40. https://www.equipes.lps.u-psud.fr/Montambaux/histoire-physique/Kelvin-1900.pdf
Klaczynski, L. (2016). Haag’s theorem in renormalised quantum field theories. https://arxiv.org/abs/1602.00662
Kochen, S. & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.
Kontsevich, M. & Segal, G. (2021). Wick rotation and the positivity of energy in quantum field theory. https://arxiv.org/abs/2105.10161
Lazarovici, D. (2018). Against fields. European Journal for Philosophy of Science, 8, 145–170. https://arxiv.org/abs/1809.00855
Lehmann, H., Symanzik, K., & Zimmermann, W. (1955). Zur formulierung quantisierter feldtheorien. Nuovo Cimento, 1, 205–225.
Leifer, M. S. & Spekkens, R. W. (2013). Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference. Physical Review A, 88, 052130. https://arxiv.org/abs/1107.5849
Lisi, A. G. (2007). An exceptionally simple theory of everything. https://arxiv.org/abs/0711.0770
———. (2017). Emergence. https://www.edge.org/response-detail/27149
LSND Collaboration. (1996). Evidence for neutrino oscillations from muon decay at rest. Physical Review C, 54, 2685–2708. https://arxiv.org/abs/nucl-ex/9605001
———. (2001). Evidence for neutrino oscillations from the observation of electron anti-neutrinos in a muon anti-neutrino beam. Physical Review D, 64, 112007. https://arxiv.org/abs/hep-ex/0104049
Lucretius. (1995). On the Nature of Things: De Rerum Natura. (A. M. Esolen, Trans.). Johns Hopkins University Press. (Originally written in the first century BCE).
Lyre, H. (2008). Does the Higgs mechanism exist? International Studies in the Philosophy of Science, 22, 119–133. https://arxiv.org/abs/0806.1359
Malament, D. B. (1996). In defence of dogma: Why there cannot be a relativistic quantum mechanics of (localizable) particles. In R. Clifton (Ed.), Perspectives on Quantum Reality (pp. 1–10). Springer.
Maldacena, J. M. (1998). The large \(N\) limit of superconformal field theories and supergravity. Advances in Theoretical and Mathematical Physics, 2, 231–252. https://arxiv.org/abs/hep-th/9711200
Martens, N. (2022). Dark matter realism. Foundations of Physics, 52, 1–19. https://link.springer.com/article/10.1007/s10701-021-00524-y
Martin, S. P. (2011). Phenomenology of particle physics. https://www.ippp.dur.ac.uk/~mspannow/files/Phenomenology_Particle_Physics_Martin.pdf
———. (2016). A supersymmetry primer. (First published in 1997). https://arxiv.org/abs/hep-ph/9709356
Maudlin, T. (1995). Three measurement problems. Topoi, 14, 7–15.
———. (2007). The Metaphysics Within Physics. Oxford University Press.
———. (2012). Philosophy of Physics: Space and Time. Princeton University Press.
———. (2014). What Bell did. Journal of Physics A: Mathematical and Theoretical, 47, 424010. https://iopscience.iop.org/article/10.1088/1751-8113/47/42/424010/pdf
———. (2018). Ontological clarity via canonical presentation: Electromagnetism and the Aharonov-Bohm effect. Entropy, 20, 465. https://www.mdpi.com/1099-4300/20/6/465
———. (2019). Philosophy of Physics: Quantum Theory. Princeton University Press.
McTaggart, J. E. (1908). The unreality of time. Mind, 17, 457–474. https://philarchive.org/archive/MCTTUO
Mermin, N. D. (1985). Is the moon there when nobody looks? Reality and the quantum theory. Physics Today, 38, 38–47.
———. (2022). A note on the quantum measurement problem. https://arxiv.org/abs/2206.10741
MicroBooNE Collaboration. (2021). Search for neutrino-induced neutral current \(\Delta\) radiative decay in MicroBooNE and a first test of the MiniBooNE low energy excess under a single-photon hypothesis. https://arxiv.org/abs/2110.00409
MiniBooNE Collaboration. (2018). Significant excess of electron-like events in the MiniBooNE short-baseline neutrino experiment. Physical Review Letters, 121, 221801. https://arxiv.org/abs/1805.12028
Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. Freeman and Co. (Reprinted by Princeton University Press (2017)).
Murayama, H. (2000). Supersymmetry phenomenology. https://arxiv.org/abs/hep-ph/0002232
Myrvold, W. C. (2015). What is a wavefunction? Synthese, 192, 3247–3274. http://philsci-archive.pitt.edu/11117/
Nail, T. (2018). Lucretius I: An Ontology of Motion. Edinburgh University Press.
Ney, A. (2021). From quantum entanglement to spatiotemporal distance. In Christian Wüthrich Baptiste Le Bihan & N. Huggett (Eds.), Philosophy Beyond Spacetime. Oxford University Press.
Ney, A. & Albert, D. Z. (2013). The Wave Function: Essays on the metaphysics of quantum mechanics. Oxford University Press.
Nguyen, T. (2016). The perturbative approach to path integrals: A succinct mathematical treatment. Journal of Mathematical Physics, 57, 092301. https://arxiv.org/abs/1505.04809
Nigg, D. et al. (2015). Can different quantum state vectors correspond to the same physical state? An experimental test. New Journal of Physics, 18, 013007. https://arxiv.org/abs/1211.0942
nLab authors. (2021). Fiber bundles in physics. http://ncatlab.org/nlab/show/fiber%20bundles%20in%20physics
Noether, E. (1918). Invariante variationsprobleme. Nachrichten von Der Gesellschaft Der Wissenschaften Zu Göttingen, Mathematisch-Physikalische Klasse, 235.
Ohanian, H. C. (1986). What is spin? American Journal of Physics, 54, 500.
Pati, J. C. & Salam, A. (1974). Lepton number as the fourth color. Physical Review D, 10, 275–289. https://pdfs.semanticscholar.org/21fb/f9d49acf3e3f07098ca686ae4058c38dbd03.pdf
Patterson, G. (2007). Jean Perrin and the triumph of the atomic doctrine. Endeavour, 31, 50–53.
Penington, G. (2019). Entanglement wedge reconstruction and the information paradox. https://arxiv.org/abs/1905.08255
Perrin, J. (1913). Les Atomes. Paris: Libraire Felix Alcan.
Peskin, M. E. (1994). Spin, mass, and symmetry. https://arxiv.org/abs/hep-ph/9405255
Peskin, M. E. & Schroeder, D. V. (1995). An Introduction to Quantum Field Theory. Westview Press.
Pessa, E. (2009). The concept of particle in quantum field theory. https://arxiv.org/abs/0907.0178
Pierre Auger Collaboration. (2007). Correlation of the highest-energy cosmic rays with nearby extragalactic objects. Science, 318, 938–943.
———. (2010). Measurement of the depth of maximum of extensive air showers above \(10^{18}\) eV. Physical Review Letters, 104, 091101.
———. (2020a). Features of the energy spectrum of cosmic rays above \(2.5 \times 10^{18}\) eV using the Pierre Auger Observatory. Physical Review Letters, 125, 121106. https://arxiv.org/abs/2008.06488
———. (2020b). Measurement of the cosmic ray energy spectrum above \(2.5 \times 10^{18}\) eV using the Pierre Auger Observatory. Physical Review D, 102, 062005. https://arxiv.org/abs/2008.06486
Preskill, J. (2013). We are all Wilsonians now. https://quantumfrontiers.com/2013/06/18/we-are-all-wilsonians-now/
———. (2018). Quantum computing in the NISQ era and beyond. https://arxiv.org/abs/1801.00862
Proietti, M. et al. (2019). Experimental test of local observer independence. Science Advances, 5, 9832. https://arxiv.org/abs/1902.05080
Pusey, M. F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state. Nature Physics, 8, 476. https://arxiv.org/abs/1111.3328
Redhead, M. (1982). Quantum field theory for philosophers. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1982, 57–99.
———. (1988). A philosopher looks at quantum field theory. In H. R. Brown & R. Harré (Eds.), Philosophical Foundations of Quantum Field Theory (pp. 9–24). Oxford University Press.
Reece, R. (2007). Quantum field theory: An introduction. http://rreece.github.io/publications/pdf/2007.Reece.Quantum-Field-Theory-An-Introduction.pdf
Romero, G. E. (2015). On the ontology of spacetime: Substantivalism, relationism, eternalism, and emergence. Foundations of Science, 22, 141–159.
Rosaler, J. (2022). Dogmas of effective field theory: Scheme dependence, fundamental parameters, and the many faces of the Higgs naturalness principle. Foundations of Physics, 52, 1–32. https://link.springer.com/article/10.1007/s10701-021-00510-4
Rubbia, C. (1984). Experimental observation of the intermediate vector bosons \(W^{+}\), \(W^{-}\), and \(Z^{0}\). Nobel lecture, December 8, 1984. https://www.nobelprize.org/uploads/2018/06/rubbia-lecture.pdf
Ruetsche, L. (2002). Interpreting quantum field theory. Philosophy of Science, 69, 348–378.
Russell, B. (1992). The Analysis of Matter. Routledge. (Originally published in 1927).
Ryden, B. (2003). Introduction to Cosmology. Addison Wesley.
Salam, A. & Ward, J. C. (1964a). Electromagnetic and weak interactions. Physics Letters, 13, 168–171.
———. (1964b). Gauge theory of elementary interactions. Physical Review, 136, 763–768.
Schlosshauer, M. (2005). Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern Physics, 76, 1267–1305. https://arxiv.org/abs/quant-ph/0312059
Schlosshauer, M. & Fine, A. (2012). Implications of the Pusey-Barrett-Rudolph quantum no-go theorem. Physical Review Letters, 108, 260404. https://arxiv.org/abs/1203.4779
Schreiber, U. (2016). Learn about supersymmetry and Deligne’s theorem. https://www.physicsforums.com/insights/supersymmetry-delignes-theorem/
———. (2020). Differential cohomology in a cohesive \(\infty\)-topos. https://ncatlab.org/schreiber/show/differential+cohomology+in+a+cohesive+topos
Schroeren, D. (2021). Symmetry fundamentalism in quantum mechanics. Philosophical Studies. https://link.springer.com/article/10.1007%2Fs11098-021-01634-z
Schwartz, M. D. (2014). Quantum Field Theory and the Standard Model. Cambridge University Press.
Schweber, S. S. (1961). An Introduction to Relativistic Quantum Field Theory. Harper & Row.
Schwichtenberg, J. (2015). Physics from Symmetry. Springer.
Sebens, C. T. (2019). How electrons spin. Studies in History and Philosophy of Science Part B, 68, 40–50. https://arxiv.org/abs/1806.01121
Shifman, M. (2012). Advanced Topics in Quantum Field Theory: A lecture course. Cambridge University Press.
Simon, B. (1976). Quantum dynamics: From automorphism to Hamiltonian. In E. H. Lieb (Ed.), Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann (pp. 327–350). Princeton University Press. http://www.math.caltech.edu/SimonPapers/R12.pdf
Slansky, R. (1981). Group theory for unified model building. Physics Reports, 79, 1–128. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.126.1581&rep=rep1&type=pdf
Stein, H. (2021). Physics and philosophy meet: The strange case of Poincaré. Foundations of Physics, 51, 1–24.
Stopp, F., Ortiz-Gutiérrez, L., Lehec, H., & Schmidt-Kaler, F. (2021). Single ion thermal wave packet analyzed via time-of-flight detection. New Journal of Physics, 23, 063002. https://iopscience.iop.org/article/10.1088/1367-2630/abffc0
Streater, R. & Wightman, A. (1964). PCT, spin and statistics, and all that. New York: Benjamin.
Summers, S. J. (1999). On the Stone-von Neumann uniqueness theorem and its ramifications. In John von Neumann and the Foundations of Quantum Physics (pp. 135–152). Budapest: Kluwer.
’t Hooft, G. (1971). Renormalizable Lagrangians for massive Yang-Mills fields. Nuclear Physics B, 35, 167–188.
———. (1978). Extended objects in gauge field theories. In D. H. Bod & A. N. Kamal (Eds.), Particles and Fields (pp. 165–198). New York: Plenum.
———. (1994). Under the Spell of the Gauge Principle. World Scientific.
———. (1999). A confrontation with infinity. Nobel Lecture, December 8, 1999. https://www.nobelprize.org/prizes/physics/1999/thooft/lecture/
———. (2005). The conceptual basis of quantum field theory. https://dspace.library.uu.nl/bitstream/handle/1874/22670/hooft_05_conceptualbasisofquantumfieldtheory.pdf
———. (2007). Lie groups in physics. http://www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
———. (2021). An unorthodox view on quantum mechanics. https://arxiv.org/abs/2104.03179
Tegmark, M. (1993). Apparent wave function collapse caused by scattering. Foundations of Physics Letters, 6, 571–590. https://arxiv.org/abs/gr-qc/9310032
Teller, P. (1997). An Interpretive Introduction to Quantum Field Theory. Princeton University Press.
———. (2000). The gauge argument. Philosophy of Science, 67, 466–481.
Tong, D. (2006). Lectures on Quantum Field Theory. https://www.damtp.cam.ac.uk/user/tong/qft.html
———. (2022). Lectures on Supersymmetric Field Theory. https://www.damtp.cam.ac.uk/user/tong/susy.html
Tumulka, R. (2017). Bohmian mechanics. https://arxiv.org/abs/1704.08017
van Hove, L. (1958). Von Neumann’s contributions to quantum theory. Bulletin of the American Mathematical Society, 64, 95–100. https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-64/issue-3.P2/Von-Neumanns-contributions-to-quantum-theory/bams/1183522374.full
van Nieuwenhuizen, P. (1981). Supergravity. Physics Reports, 68, 189–398.
Vákár, M. (2011). Principal bundles and gauge theories. https://arxiv.org/abs/2110.06334
Vitagliano, E., Tamborra, I., & Raffelt, G. (2020). Grand unified neutrino spectrum at Earth: Sources and spectral components. Reviews of Modern Physics, 92, 045006. https://arxiv.org/abs/1910.11878
von Neumann, J. (1955). The Mathematical Foundations of Quantum Mechanics. (R. T. Beyer, Trans.). Princeton University Press. (Originally published in German in 1932).
Wallace, D. (2011). Taking particle physics seriously: A critique of the algebraic approach to quantum field theory. Studies in History and Philosophy of Modern Physics, 42, 116–125.
———. (2012). The Emergent Multiverse. Oxford University Press.
Way, R. (2010). Introduction to connections on principal fibre bundles. http://personal.maths.surrey.ac.uk/T.Bridges/GEOMETRIC-PHASE/Connections_intro.pdf
Weinberg, S. (1964a). Feynman rules for any spin. Physical Review, 133, B1318.
———. (1964b). Feynman rules for any spin II: Massless particles. Physical Review, 134, B882.
———. (1967). A model of leptons. Physical Review Letters, 19, 1264–1266. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.19.1264
———. (1977). The First Three Minutes. Basic Books.
———. (1979). Conceptual foundations of the unified theory of weak and electromagnetic interactions. Nobel lecture, December 8, 1979. https://www.nobelprize.org/uploads/2018/06/weinberg-lecture.pdf
———. (1997a). What is an elementary particle? Beam Line, 27, 17–21. https://www.slac.stanford.edu/pubs/beamline/27/1/27-1-weinberg.pdf
———. (1997b). What is quantum field theory, and what did we think it is? Conceptual Foundations of Quantum Field Theory: Proceedings, Symposium and Workshop, Boston, USA, March 1-3, 1996. http://arxiv.org/abs/hep-th/9702027
Weyl, H. (1929). Elektron und gravitation. Zeitschrift für Physik, 56, 330–352.
Wheeler, J. A. (1957). Assessment of Everett’s "relative state" formulation of quantum theory. Reviews of Modern Physics, 29, 46–465.
Wigner, E. P. (1939). On unitary representations of the inhomogeneous Lorentz group. Annals of Mathematics, 40, 149–204.
———. (1954). Conservation laws in classical and quantum physics. Progress of Theoretical Physics, 11, 437–440. https://academic.oup.com/ptp/article/11/4-5/437/1831457
———. (1959). Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Academic Press. (Originally published in German in 1931).
Wilhelm, I. (2022). Centering the Everett interpretation. https://philpapers.org/rec/WILCTE-4
Williams, P. (2019). Scientific realism made effective. British Journal for the Philosophy of Science, 70, 209–237. https://www.journals.uchicago.edu/doi/full/10.1093/bjps/axx043
Wilson, K. (1974). The renormalization group and the \(\varepsilon\) expansion. Physics Reports, 12, 75–199.
Witten, E. (1998). Anti-de Sitter space and holography. Advances in Theoretical and Mathematical Physics, 2, 253–291. https://arxiv.org/abs/hep-th/9802150
Yock, P. (2018). Newton’s hypotheses on the structure of matter. https://arxiv.org/abs/1807.05486
Zapata-Carratala, C. (2021). Dimensioned algebra: The mathematics of physical quantities. https://arxiv.org/abs/2108.08703
Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press.
Zeidler, E. (2007). Quantum Field Theory I: Basics in mathematics and physics, Vol. 1. Springer.
———. (2008). Quantum Field Theory II: Quantum electrodynamics, Vol. 2. Springer.
———. (2011). Quantum Field Theory III: Gauge theory, Vol. 3. Springer.
Zurek, W. H. (2003). Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75, 715–775. https://arxiv.org/abs/quant-ph/0105127
———. (2022). Quantum theory of the classical: Einselection, envariance, quantum Darwinism and extantons. https://arxiv.org/abs/2208.09019
Zyla, P.A. et al. (Particle Data Group). (2021). Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2020, 083C01. (and 2021 update). https://pdg.lbl.gov/2021/reviews/contents_sports.html

  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. McTaggart (1908).↩︎

  20. Caulton (2015).↩︎

  21. Caulton & Butterfield (2012).↩︎

  22. Noether (1918).↩︎

  23. Wigner (1954).↩︎

  24. Brading (2002).↩︎

  25. Baez (2018).↩︎

  26. Goyal (2020).↩︎

  27. Weyl (1929).↩︎

  28. ’t Hooft (1994).↩︎

  29. Teller (2000).↩︎

  30. ’t Hooft (2007).↩︎

  31. Afriat (2013).↩︎

  32. Schwichtenberg (2015).↩︎

  33. Dewar (2019).↩︎

  34. Weyl (1929), p. TODO.↩︎

  35. Wigner (1959).↩︎

  36. Simon (1976).↩︎

  37. Summers (1999).↩︎

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

  39. Reece (2007), p. X.↩︎

  40. Schweber (1961), p. TODO.↩︎

  41. Schroeren (2021).↩︎

  42. Ney & Albert (2013).↩︎

  43. Feynman & Hibbs (1965), p. 6.↩︎

  44. Feynman & Hibbs (1965), p. 9.↩︎

  45. Kelvin (1901).↩︎

  46. Bacciagaluppi & Valentini (2009).↩︎

  47. von Neumann (1955).↩︎

  48. van Hove (1958).↩︎

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

  50. Baez (2011).↩︎

  51. Dutailly (2014), p. 11–13.↩︎

  52. Zurek (2003).↩︎

  53. Joos, E. et al. (2003).↩︎

  54. Tegmark (1993).↩︎

  55. Schlosshauer (2005).↩︎

  56. Drossel (2015), p. 51–2.↩︎

  57. Zurek (2022).↩︎

  58. Friedrich (2016).↩︎

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

  60. Coecke & Kissinger (2017).↩︎

  61. Preskill (2018).↩︎

  62. Arute, F. et al. (2019).↩︎

  63. Broughton, M. et al. (2020).↩︎

  64. Feynman (1965).↩︎

  65. Weinberg (1997b), p. 8.↩︎

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

  67. Peskin & Schroeder (1995).↩︎

  68. Zee (2003).↩︎

  69. Schwartz (2014).↩︎

  70. Tong (2006).↩︎

  71. Zeidler (2007).↩︎

  72. Zeidler (2008).↩︎

  73. Zeidler (2011).↩︎

  74. T. Y. Cao (1999).↩︎

  75. ’t Hooft (2005).↩︎

  76. Coleman & Mandula (1967).↩︎

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

  78. Bell (1955).↩︎

  79. Streater & Wightman (1964).↩︎

  80. Greaves & Thomas (2012).↩︎

  81. Ohanian (1986).↩︎

  82. Peskin (1994).↩︎

  83. Sebens (2019).↩︎

  84. Dutailly (2014), p. 37.↩︎

  85. Kontsevich & Segal (2021).↩︎

  86. Dyson (1949).↩︎

  87. Dyson (1952).↩︎

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

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

  90. Martin (2011).↩︎

  91. Reece (2007).↩︎

  92. Jaeger (2019).↩︎

  93. Feynman & Hibbs (1965).↩︎

  94. Nguyen (2016).↩︎

  95. ’t Hooft (1971).↩︎

  96. Wilson (1974).↩︎

  97. Goldenfeld (1992).↩︎

  98. Butterfield (2014).↩︎

  99. Butterfield & Bouatta (2015).↩︎

  100. ’t Hooft (1994).↩︎

  101. ’t Hooft (1999).↩︎

  102. Kadanoff (2013), p. 50.↩︎

  103. Borcherds & Barnard (2002).↩︎

  104. Huggett & Weingard (1995).↩︎

  105. Weinberg (1997b).↩︎

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

  107. Preskill (2013).↩︎

  108. Williams (2019).↩︎

  109. Rosaler (2022).↩︎

  110. Baez (2016).↩︎

  111. Auyang (1995).↩︎

  112. Baez (2016), p. 17.↩︎

  113. Baez (2016), p. 18.↩︎

  114. Einstein (1905c).↩︎

  115. Weinberg (1997b), p. 2.↩︎

  116. Weinberg (1997a).↩︎

  117. Baez et al. (1992), p. 59.↩︎

  118. Fraser (2008).↩︎

  119. Pessa (2009).↩︎

  120. Duncan (2012), p. 163–4.↩︎

  121. Myrvold (2015).↩︎

  122. Lazarovici (2018).↩︎

  123. Baker (2009).↩︎

  124. Caulton (2018).↩︎

  125. Haag (1955).↩︎

  126. Malament (1996).↩︎

  127. Teller (1997), p. 115.↩︎

  128. Earman & Fraser (2006).↩︎

  129. Klaczynski (2016).↩︎

  130. Ruetsche (2002).↩︎

  131. Bain (2000).↩︎

  132. Duncan (2012).↩︎

  133. Redhead (1982).↩︎

  134. Redhead (1988).↩︎

  135. Haag (1992).↩︎

  136. Wallace (2011).↩︎

  137. Fraser (2011).↩︎

  138. Buchholz (1998).↩︎

  139. Kastler (2003), p. 6.↩︎

  140. Aharonov & Bohm (1959).↩︎

  141. Healey (2007), ch. 2-4.↩︎

  142. Batterman (2003).↩︎

  143. Maudlin (2018).↩︎

  144. Frankel (2004).↩︎

  145. nLab authors (2021).↩︎

  146. Way (2010).↩︎

  147. Vákár (2011).↩︎

  148. Maudlin (2007), p. 96.↩︎

  149. Maudlin (2007), p. 101.↩︎

  150. Baez & Muniain (1994).↩︎

  151. Baez & Schreiber (2005).↩︎

  152. Baez & Huerta (2011).↩︎

  153. Schreiber (2020).↩︎

  154. Baez & Stay (2009).↩︎

  155. ’t Hooft (1978).↩︎

  156. ’t Hooft (1994).↩︎

  157. Shifman (2012).↩︎

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

  159. Schreiber (2016).↩︎

  160. Dimopoulos & Georgi (1981).↩︎

  161. Murayama (2000).↩︎

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

  163. van Nieuwenhuizen (1981).↩︎

  164. Frè (2013), ch. 6.↩︎

  165. Martin (2016).↩︎

  166. Tong (2022).↩︎

  167. Maudlin (2019), p. TODO.↩︎

  168. Maudlin (1995).↩︎

  169. Dürr & Lazarovici (2020).↩︎

  170. Mermin (2022).↩︎

  171. Becker (2018).↩︎

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

  173. Bohm & Aharonov (1957).↩︎

  174. Mermin (1985).↩︎

  175. Caulton (2014).↩︎

  176. Bell (1964).↩︎

  177. Bell (1966).↩︎

  178. Kochen & Specker (1967).↩︎

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

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

  181. Bell (2004), pp. 232–248.↩︎

  182. Maudlin (2014).↩︎

  183. Ahmed & Caulton (2014).↩︎

  184. Deutsch (1985).↩︎

  185. Bong, K.W. et al. (2020).↩︎

  186. Bohm (1952).↩︎

  187. Bohm (1953).↩︎

  188. Bell (2004).↩︎

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

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

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

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

  193. Tumulka (2017).↩︎

  194. Das & Dürr (2019).↩︎

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

  196. Ananthaswamy (2021).↩︎

  197. Everett (2012), p. 171.↩︎

  198. Everett (1956).↩︎

  199. Everett (1957).↩︎

  200. Wheeler (1957).↩︎

  201. Everett (2012).↩︎

  202. DeWitt (1970).↩︎

  203. DeWitt & Graham (1973).↩︎

  204. Barrett (2011).↩︎

  205. Barrett (2016).↩︎

  206. Everett (2012), p. 150.↩︎

  207. Wallace (2012).↩︎

  208. Carroll & Singh (2019).↩︎

  209. Carroll (2019).↩︎

  210. Wilhelm (2022).↩︎

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

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

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

  214. Fuchs (2002).↩︎

  215. Fuchs (2010).↩︎

  216. Fuchs & Schack (2013).↩︎

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

  218. Fuchs & Stacey (2016).↩︎

  219. Harrigan & Spekkens (2010).↩︎

  220. Leifer & Spekkens (2013).↩︎

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

  222. Schlosshauer & Fine (2012).↩︎

  223. Nigg, D. et al. (2015).↩︎

  224. ’t Hooft (2021).↩︎

  225. Proietti, M. et al. (2019).↩︎

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

  227. Cabibbo (1963).↩︎

  228. Englert & Brout (1964).↩︎

  229. Higgs (1964).↩︎

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

  231. Georgi (1999), p. 280.↩︎

  232. Lyre (2008).↩︎

  233. ATLAS Collaboration (2012).↩︎

  234. CMS Collaboration (2012).↩︎

  235. T. Y. Cao (2016).↩︎

  236. Glashow (1961).↩︎

  237. Weinberg (1967).↩︎

  238. Salam & Ward (1964b).↩︎

  239. Salam & Ward (1964a).↩︎

  240. Weinberg (1979).↩︎

  241. Rubbia (1984).↩︎

  242. Chalmers (2017).↩︎

  243. Hamamatsu (2007).↩︎

  244. LSND Collaboration (1996).↩︎

  245. LSND Collaboration (2001).↩︎

  246. MiniBooNE Collaboration (2018).↩︎

  247. MicroBooNE Collaboration (2021).↩︎

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

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

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

  251. Aime (2022).↩︎

  252. CDF Collaboration (2022).↩︎

  253. Baez & Huerta (2009a).↩︎

  254. Baez & Huerta (2010).↩︎

  255. Pati & Salam (1974).↩︎

  256. Georgi & Glashow (1974).↩︎

  257. Slansky (1981).↩︎

  258. Georgi (1999).↩︎

  259. Baez & Huerta (2009b).↩︎

  260. Lisi (2007).↩︎

  261. Martin (2016), p. 66.↩︎

  262. Dine & Kusenko (2004).↩︎

  263. Baggott (2013).↩︎

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

  265. Maldacena (1998).↩︎

  266. Witten (1998).↩︎

  267. Ney (2021).↩︎

  268. Einstein & Grossmann (1913).↩︎

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

  270. Carroll (2004).↩︎

  271. Arntzenius (2012).↩︎

  272. Frè (2013), ch. 4.↩︎

  273. Weinberg (1977).↩︎

  274. Ryden (2003).↩︎

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

  276. Romero (2015).↩︎

  277. Penington (2019).↩︎

  278. Clowe, D. et al. (2006).↩︎

  279. Martens (2022).↩︎

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

  281. Anderson (1972).↩︎

  282. Bedau (1997).↩︎

  283. Bunge (2001), p. 72.↩︎

  284. Lisi (2017).↩︎

  285. Anderson (1972), p. 393.↩︎

  286. Bokulich (2011).↩︎