Paper III — Physics
36 QUESTIONS
Paper III covers physics from its foundations to its frontiers. Quantum theory is examined at the point of its unresolved business — the measurement problem, Bell’s theorem and what it does not rule out, decoherence and its residue, the reversibility of the Schrödinger equation against the definiteness of outcomes. Statistical and thermal physics are set through the second law, equipartition, fluctuation–dissipation, phase transitions, and the Landauer bound on computation. Field theory and gravitation appear as gauge redundancy, spontaneous symmetry breaking, the Higgs mechanism, renormalisation, the cosmological constant, black-hole thermodynamics and the information paradox, and holography. Condensed matter, astrophysics and turbulence are each represented, and four later questions treat the acoustics of a struck string and of a radiating body, the seismological case for a liquid outer core, and the aperiodicity of geomagnetic reversals.
The knowledge base is the standard graduate curriculum, but the examination is of physical understanding rather than of formalism. Derivations are demanded where a derivation settles the matter — the Chandrasekhar mass from first principles, the Landauer bound, a conserved quantity from Noether’s theorem — and elsewhere the candidate is asked to say what a piece of mathematics is physically doing: what renormalisation removes, why spin is not rotation, why entanglement carries no signal. Several questions turn on the distinction between a symmetry of the laws and a symmetry of a state, or between what a theory explains and what it merely accommodates. The paper closes its original sequence by asking which single experiment would most sharply discriminate between interpretations of quantum mechanics, and expects the answer to be feasible in principle and decisive in fact.
Conduct of the response
Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page.
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1.
State the quantum measurement problem precisely and say what a solution would have to deliver.
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2.
Prove that the Yang–Mills mass gap, if it exists, cannot be seen perturbatively; explain the difficulty of establishing it rigorously.
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3.
What is renormalisation actually doing, physically?
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4.
Derive the equipartition theorem and state exactly where it fails.
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5.
Why does the cosmological constant problem count as a problem?
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6.
Explain gauge invariance as redundancy of description, not as symmetry of nature.
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7.
What does Bell's theorem rule out, and what does it not rule out?
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8.
Reconstruct the second law from a microscopic, reversible dynamics — where does irreversibility enter?
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9.
What is the black-hole information paradox, and what would resolve it?
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10.
Explain why the electron's spin is not literal rotation.
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11.
Give the physical meaning of the action principle.
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12.
What is spontaneously broken symmetry, and how does a Goldstone mode arise?
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13.
Why is there an arrow of time if the microphysics is time-symmetric?
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14.
Explain the significance of the Higgs mechanism for mass.
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15.
What distinguishes a phase transition from a crossover, precisely?
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16.
State Noether's theorem and apply it to a non-obvious conserved quantity.
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17.
What does decoherence explain, and what does it leave unexplained?
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18.
Why can't information travel faster than light even though entanglement is "instantaneous"?
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19.
Explain the physical content of the fluctuation–dissipation theorem.
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20.
What is a topological phase of matter, and how is it robust?
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21.
Estimate the Chandrasekhar mass from first principles.
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22.
What is the status of the fine-structure constant — computed, measured, or explained?
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23.
Why is turbulence hard, as physics rather than as mathematics?
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24.
Give the Landauer bound and explain what it says about computation.
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25.
What is the difference between a symmetry of the laws and a symmetry of a state?
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26.
Explain why general relativity resists quantisation by the usual recipe.
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27.
What does the holographic principle claim, and what evidence bears on it?
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28.
Reconcile the reversibility of the Schrödinger equation with the definiteness of measurement outcomes.
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29.
Why is temperature well-defined for a black hole?
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30.
Which single experiment, feasible or not, would most sharply discriminate between interpretations of quantum mechanics?
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31.
Is time an emergent phenomenon?
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32.
Why does a struck piano string not sound the harmonic series it is drawn to sound? Quantify the inharmonicity contributed by bending stiffness, and say what stretched tuning is for.
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33.
A violin and a loudspeaker radiating the same spectrum do not sound alike in a room. Account for the difference from the directivity of the source, and say what a measurement at one microphone position cannot capture.
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34.
How do we know the Earth has a liquid outer core? Argue from the S-wave shadow zone, and quantify what the observation constrains.
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35.
The geodynamo has reversed the field hundreds of times without periodicity. State what a working dynamo requires, and say why the reversal statistics resist prediction rather than merely resisting measurement.
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36.
What would happen if we added one electron to every atom in the universe?
Question 31 was added by Examination Amendment v2.1. Questions 1–30 stand verbatim as fixed at expansion v2.0.
Questions added by Examination Expansion v5.0, which extended the examination to music and geography. All earlier questions stand verbatim and unrenumbered.
Question 36 was added by Examination Amendment v5.3. All earlier questions stand verbatim and unrenumbered.