# Philosophy of physics

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## Issues and positions

### Symmetry-first physics

• Principle of least action
• Canonical dynamics
• Curie’s principle
• Noether’s theorem
• group theory1
• Physics from Symmetry2

### Statistical physics

• Entropy
• Statistical mechanics and thermodynamics
• Boltzmann, Ludwig (1844-1906)
• The 2nd Law of Thermodynamics said simply: Things tend to happen in ways for which there are many ways to happen like that.

### Emergence

Thermodynamics, statistical mechanics, renormalization.

• More is different3
• Emergence4
• Bain

### Quantum mechanics

• Hilbert spaces. Wigner’s theorem. The Born rule.
• Wave-particle duality misconceptions. Fields are more fundamental than particles.
• The measurement problem. Decoherence. The Born rule again.
• Decoherence brings quantum logic to classical logic.
• Bell’s inequality
• PBR theorem. 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.
• Gisin’s Theorem

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

#### 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.

$\hat{U}(x^{\mu}) = e^{ -i \: \hat{P}_\mu \: x^\mu }$

#### Secondary properties of QM:

• Wave function:

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

• Schrödinger Equation

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

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

• Decoherence

$\mathcal{H} = \mathcal{H}_\mathrm{S} \otimes \mathcal{H}_\mathrm{E}$

$|\alpha\rangle \otimes |\psi\rangle \rightarrow |\alpha\rangle \otimes |\psi; \alpha\rangle$

#### “Atom” (2009) BBC documentary

Jim Al-Khalili tells the story of the greatest scientific discovery ever - that everything is made of atoms.

### Quantum field theory

#### Fields

• Field definition
• Coleman-Mandula theorem6
• Fiber bundles in physics
• Fiber bundles embody two central principles of modern physics:
1. the principle of locality
2. the gauge principle.
• Healey on the Aharonov-Bohm effect7
• 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.8

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.9

#### Foundations

• Peskin and Schroeder
• David Tong
• Weinberg
• No “2nd quantization”
• AQFT vs LQFT

#### Spin-statistics theorem

• Spin-statistics theorem - Pauli

#### Scattering

• Interaction picture
• Correlation AKA Green’s functions
• Wick’s theorem
• Vaccuum bubble cancelation
• Dyson series
• LSZ reduction formula12
• Feynman diagrams and Feynman rules

#### Renormalization

• Wilson
• Huggett and Weingard13
• Butterfield14
• Butterfield15

#### Effective field theory

• Huggett and Weingard, again16
• Weinberg17
• Bain18

#### Haag’s theorem

• Haag’s theorem19
• Malament20
• Bain21
• Earman and Fraser’s analysis22
• Klaczynski’s analysis23

### Interpretations of quantum mechanics

• Copenhagen
• de Broglie-Bohm
• Everett
• others

### Beyond the standard model

• Neutrino masses and mixings
• Running of the couplings
• Grand unification
• Supersymmetry
• Strong $$CP$$ problem
• Quantum gravity

### Cosmology

• Big bang
• Dark matter
• Bullet Cluster
• “A direct empirical proof of the existence of dark matter” astro-ph/0608407
• Inflation
• $$\Lambda$$+CMD Cosmological Standard Model

## My thoughts

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• gravity: from aether to not to fabric
• Sean Carroll QM: what there is, is more than we can see.

## Annotated bibliography

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

• Einstein, Podolsky, & Rosen (1935)

• TODO.

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

• Anderson (1972)

• TODO.

• TODO.

### Giulini, D., E. Joos, C. Kiefer, J. Kupsch, I.O. Stamatescu, & H. Zeh (1996). Decoherence and the Appearance of a Classical World in Quantum Theory.

• Giulini, D. et al. (1996)

• TODO.

• TODO.

## References

Anderson, P. W. (1972). More is different. Science, 177, 393–396. http://science.sciencemag.org/content/177/4047/393

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.

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

Coleman, S. & Mandula, J. (1967). All possible symmetries of the S matrix. Physical Review, 159, 1251–1256.

Earman, J. & Fraser, D. (2006). Haag’s theorem and its implications for the foundations of quantum field theory. Erkenntnis, 64, 305–344.

Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780.

Giulini, D. et al. (1996). Decoherence and the Appearance of a Classical World in Quantum Theory. Springer.

Haag, R. (1955). On quantum field theories. Det Kongelige Danske Videnskabernes Selakab, 29.

Haag, R., Łopuszański, J. T., & Sohnius, M. (1975). All possible generators of supersymmetries of the S-matrix. Nuclear Physics B, 88, 257–274.

Healey, R. (2007). Gauging What’s Real. Oxford University Press.

Huggett, N. & Weingard, R. (1995). The renormalisation group and effective field theories. Synthese, 102, 171–194.

Klaczynski, L. (2016). Haag’s theorem in renormalised quantum field theories. https://arxiv.org/abs/1602.00662

Lehmann, H., Symanzik, K., & Zimmermann, W. (1955). Zur formulierung quantisierter feldtheorien. Nuovo Cimento, 1, 205–225.

Lisi, A. G. (2017). Emergence. https://www.edge.org/response-detail/27149

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.

Maudlin, T. (2007). The Metaphysics Within Physics. Oxford University Press.

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. Brown & R. Harré (Eds.), Philosophical Foundations of Quantum Field Theory (pp. 9–24).

Schwichtenberg, J. (2015). Physics from Symmetry. Springer.

’t Hooft, G. (2007). Lie Groups in Physics. http://www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf

Weinberg, S. (1996). 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

1. ’t Hooft (2007).

2. Schwichtenberg (2015).

3. Anderson (1972).

4. Lisi (2017).

5. Giulini, D. et al. (1996).

6. Coleman & Mandula (1967).

7. Healey (2007), ch. 2-4.

8. Maudlin (2007), p. 96.

9. Maudlin (2007), p. 101.

12. Lehmann, Symanzik, & Zimmermann (1955).

13. Huggett & Weingard (1995).

14. Butterfield (2014).

15. Butterfield & Bouatta (2015).

16. Huggett & Weingard (1995).

17. Weinberg (1996).

18. Bain (2013a) and Bain (2013b).

19. Haag (1955).

20. Malament (1996).

21. Bain (2000).

22. Earman & Fraser (2006).

23. Klaczynski (2016).

24. Haag, Łopuszański, & Sohnius (1975).