# Philosophy of physics

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## Issues and positions

TODO.

### Statistical physics

TODO.

• 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 different1
• Emergence2

### 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

#### 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:

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

• Schrodinger 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.

TODO.

### Beyond the standard model

• Supersymmetry.
• Running of the couplings.
• Grand unification.
• TODO.

### Cosmology

TODO.

Big bang. $$\Lambda$$+CMD Cosmological Standard Model. Inflation.

Reductionism.

TODO.

## 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

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### Redhead, M. (1988). A Philosopher Looks at Quantum Field Theory.

In the collection: Brown, H. and R. Harré, Eds. (1988). Philosophical Foundations of Quantum Field Theory.

TODO.

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## References

Anderson, P. W. (1972). More Is Different. Science, 177, 393–396.

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

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

1. Anderson (1972).

2. Lisi (2017).