A shared set of stable question IDs, with space for assumptions, calculations, checks, and revised questions.
For a physicist entering another fieldSources checked 12 September 2026Editable working edition
80 questions · 16 chaptersChoose one question, make its assumptions explicit, and keep a record of what the answer changes.
These are entry points for an investigation. Calibration reproduces established results. A Diagnostic tests a specified model or inference. An Extension proposes bounded further work; it is not a promise of novelty or success. Read the linked chapter before treating a question as self-contained.
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QG-1 · Quantum gravityCalibration
Which gravitational phases are physically joint?
Do: Derive the determinant criterion above and compute each mass's reduced-state eigenvalues as functions of $\Phi$. Produce an entropy-versus-phase plot.
Check: Entropy vanishes at $\Phi=0,2\pi$ and is maximal at $\Phi=\pi$. Changing any local row or column phase leaves it unchanged.
Meaning: Establishes the precise witness that a proposed weak-field experiment must preserve. It is a known two-qubit result, not a new theory of gravity.
Do: For a background curvature radius $L$, estimate the ratio of $c_1R^2$ to the Einstein term using $R\sim L^{-2}$. Repeat after including a large dimensionless $c_1$.
Check: The ratio scales as $c_1/(M_{\rm P}L)^2$, up to geometric factors. Identify the actual breakdown scale rather than assuming it is always $M_{\rm P}$.
Meaning: Turns “low energy” into a condition on an observable regime and its coefficients.
Which correction is robust against unknown local interactions?
Do: In Donoghue's low-momentum scattering amplitude, separate polynomial terms from logarithms and other nonanalytic terms. Fourier-transform representative terms at nonzero separation.
Check: Contact terms and long-range tails must be distinguished; compare amplitudes or explicitly defined observables before comparing coordinate-dependent potentials.
Meaning: Produce a table of universal predictions and coefficients requiring measurement. This is a literature-guided calculation with established benchmarks.
Do: Apply independent dephasing channels to the two-path state. Calculate the negative eigenvalues, if any, of its partial transpose, obtained by transposing only one subsystem's indices.
Check: Recover the pure-state result at zero noise and a separable mixture at complete dephasing. Separate state entanglement from the sensitivity of a particular witness.
Meaning: Gives a quantitative noise budget within the model, not an apparatus design or a detection claim.
Does a proposed classical mediator actually satisfy its stated restrictions?
Do: Choose one published classical-channel model. Write its allowed operations and noise explicitly, then test the QG-1 preparation under that dynamics.
Check: Account for any hidden shared quantum resource, direct nonlocal interaction, or measurement feedback. Reproduce its published result first.
Meaning: A defensible output is an assumption-dependent distinction between model classes. Novelty requires checking the specific mediator literature; the general witness argument is established.
Why do independent Hawking-like pairs fail to purify radiation?
Do: Construct one, two, and three Bell pairs. Trace their partners and compute radiation entropy. Compare with arbitrary pure states on the same total qubits.
Check: Entropy is additive for independent pairs; a pure total state has equal entropies on complementary factors.
Meaning: Isolates the offending independence assumption in a solvable model. The Bell-pair construction approximates only part of the Hawking argument.
Does the entropy curve identify the radiation state?
Do: Construct different pure states with identical bipartite Schmidt coefficients, the nonnegative weights in a paired basis decomposition. Compare their local correlation functions.
Check: Entropies agree while a chosen observable differs. Report that observable and the measurement basis.
Meaning: Produces an explicit limit on what an island entropy calculation alone establishes about decoding or local measurements.
Do: Choose one two-dimensional evaporating model from the island review. Reproduce its no-island and island generalized entropies, including its matter state and regulator prescription.
Check: Verify the extremization before taking the minimum; track the domain of the semiclassical approximation.
Meaning: A successful output is a model-specific transition with assumptions, not an unqualified solution for every black hole.
How robust is the entropy transition to an imperfect radiation collector?
Do: In that same model, first replace complete collection by a specified erasure channel in a finite-dimensional analogue. Vary collection efficiency and compute entropy and recoverable correlations separately.
Check: Recover full collection and total loss limits. Do not transplant the qubit channel into a gravitational bath without deriving the correspondence.
Meaning: Identifies an operationally precise modification worth comparing with existing partial-bath calculations; novelty remains to be checked.
DE-3 · Vacuum energy and cosmic accelerationDiagnostic
Does a proposed cancellation survive adding one heavy field?
Do: In a selected vacuum-energy proposal, integrate out a massive scalar and follow both its threshold correction and the adjustable constant term.
Check: Distinguish cancellation fixed by an identity or symmetry from a parameter chosen again after matching. Check renormalization-scale independence.
Meaning: Produce a stability audit with explicit assumptions. This is more decisive than comparing an arbitrary cutoff estimate with cosmological data.
DE-5 · Vacuum energy and cosmic accelerationExtension
Which additional observable breaks an expansion-history degeneracy?
Do: Construct two explicitly specified models with similar $H(a)$ over an observed interval. Compare their linear matter-growth equations and a lensing prediction.
Check: Match background parameters first and state which perturbation equations change. Test stability before fitting.
Meaning: The output is a discriminating observable in a restricted model pair. Check existing growth-versus-geometry tests before claiming novelty.
Do: Derive the density above and compare with a centrally concentrated luminous mass whose large-radius speed falls as $r^{-1/2}$.
Check: Keep units explicit and identify the spherical and equilibrium assumptions. A halo extending to infinity has infinite mass, so introduce a finite outer range.
Meaning: Clarifies the difference between a robust kinematic discrepancy and a unique microscopic interpretation.
Do: Integrate the abundance equation using an explicit equilibrium density and compare with the post-freeze-out solution above. Vary the annihilation strength.
Check: Test the early equilibrium and late constant-yield limits; tighten numerical tolerances near departure from equilibrium.
Meaning: Produces a relic-abundance mechanism you can explain quantitatively. It assumes the thermal and expansion history.
Can two production histories yield the same abundance?
Do: Tune one freeze-out and one simple decay-driven freeze-in model to the same final density. Compare the momentum distribution and a scattering observable.
Check: Verify that the freeze-in species never equilibrates and that both parameter choices satisfy their approximations.
Meaning: Shows why matching abundance is insufficient and identifies information needed to break the degeneracy.
Do: Derive the maximum elastic recoil energy $E_R^{\max}=2\mu_{\chi N}^2v^2/m_N$, with reduced mass $\mu_{\chi N}$ and nuclear mass $m_N$. Compare light and heavy particles.
Check: Fold a specified speed distribution, threshold, and efficiency into a rate before interpreting an event count.
Meaning: Separates particle physics, halo assumptions, and detector sensitivity. A high-energy event need not be compatible with every familiar dark-matter model.
Which halo uncertainty can a second target remove?
Do: Choose two nuclear targets and one interaction. Ask whether a cross-target rate ratio or common minimum-speed interval reduces sensitivity to the unknown speed distribution.
Check: Include nuclear response and threshold differences. Reproduce one existing halo-independent construction before modifying it.
Meaning: A bounded inference problem with established predecessors; a failure to remove the degeneracy is still an informative result.
Can you derive freezing without a horizon-crossing slogan?
Do: Differentiate the mode solution and verify its equation. Plot the physical amplitude as a function of $|k\eta|$.
Check: Recover the short-wavelength vacuum normalization and long-wavelength constant amplitude. Keep the test-field and exact-de-Sitter assumptions visible.
Meaning: Turns an often-used verbal mechanism into a controlled calculation.
Does the same scalar amplitude fix the inflationary scale?
Do: Hold $\mathcal P_\zeta$ fixed while varying $H$ and $\epsilon$ within slow roll. In the same canonical setup use the tensor ratio $r\simeq16\epsilon$.
Check: Verify that many pairs give the same scalar amplitude but different tensor power. The tensor relation inherits the model assumptions.
Meaning: Identifies what a second observable adds and what an upper limit leaves degenerate.
What does a third-point correlation test that the power spectrum cannot?
Do: Follow the squeezed limit, with one wavelength much longer than the others, in Maldacena's single-field relation. Explain its connection to a long mode acting as a rescaling.
Check: List the attractor, initial-state, and single-clock assumptions; an attractor erases dependence on an independent background velocity.
Meaning: A failure can reject that class of models, not automatically all inflation. [16]
Which feature survives imperfect knowledge of the initial state?
Do: In the test-field model, mix positive and negative frequency solutions with explicitly normalized coefficients over a finite band. Track changes in two-point and selected higher correlations after adding a specified interaction.
Check: Bound the excitation energy so the test-field approximation survives, and recover the vacuum limit.
Meaning: A finite, testable robustness question; compare existing excited-initial-state studies before interpreting novelty.
Why does equilibrium obstruct the usual mechanism?
Do: Write forward and inverse reaction terms in a simple decay-plus-inverse-decay network. Derive the equilibrium cancellation with the required equilibrium distributions.
Check: Include every process needed at the chosen perturbative order and avoid counting an on-shell intermediate process twice.
Meaning: Identifies why a decay-rate asymmetry alone is not a consistent cosmological source.
When does the one-number washout description fail?
Do: Replace $Y_\Delta$ by a two-flavor vector and $W$ by a positive relaxation matrix. Rotate its weakly washed-out direction relative to the source and solve.
Check: Recover the one-flavor limit and verify that any apparent protection corresponds to a slow mode of the network.
Meaning: A tractable diagnostic for flavor effects, with established leptogenesis predecessors. A research extension must specify a new physical rate hierarchy.
Which extra observable narrows a degenerate mass mechanism?
Do: Choose a two-heavy-neutrino model and fix a compatible light mass matrix. Vary the remaining high-energy freedom and compute one specified heavy-light mixing or lepton-number-violating observable.
Check: Preserve the fitted low-energy matrix throughout; verify perturbativity and the validity of the heavy-mass expansion.
Meaning: Maps what one additional measurement could determine. Existing seesaw reconstruction literature is the novelty baseline.
HI-1 · The electroweak scale and flavorCalibration
What exactly fixes the symmetry-breaking scale?
Do: Minimize the scalar potential and expand around each stationary point. Identify stable minima, fluctuation masses, and the symmetric limit.
Check: Keep $\lambda>0$ for stability and distinguish the negative quadratic coefficient at the origin from a negative physical mass squared at a minimum.
Meaning: Separates the mechanism of symmetry breaking from the unexplained input scale.
HI-2 · The electroweak scale and flavorCalibration
Does a heavy particle decouple from every observable equally?
Do: Derive the threshold formula above and the leading $h^6$ coefficient from the same expansion.
Check: The scalar-mass shift grows with $M^2$ at fixed coupling, while higher-dimension terms carry inverse powers of $M$. Recover complete decoupling at zero portal coupling.
Meaning: Explains how effective-theory decoupling and mass sensitivity can coexist.
Which flavor predictions are independent of basis choices?
Do: Construct two small complex Yukawa matrices, whose entries couple the Higgs to fermions. Diagonalize them by unitary transformations and identify masses and relative left-handed rotations.
Check: Rotate both interaction bases and verify that singular values and observable mixing remain invariant. Zeros in a matrix need not be physical predictions.
Meaning: Establishes the correct objects for assessing a proposed flavor pattern before adding more parameters.
Does a claimed low-tuning region survive a change of matching scale?
Do: In the two-scalar model, match at nearby scales and evolve parameters consistently. Compare a physical low-energy prediction and the chosen sensitivity measure.
Check: Physical predictions agree to the retained order; residual differences quantify omitted terms. Report the independent-parameter convention behind the sensitivity measure.
Meaning: A reproducible robustness study. Novelty requires a particular model or inference issue beyond the textbook threshold calculation.
Why is a quark mass phase part of the strong angle?
Do: For one massive quark, track a chiral field rotation through its mass term and the anomalous quantum measure. Identify the invariant angle in a declared sign convention.
Check: Repeating a field redefinition cannot change an observable. A total derivative must be treated with its boundary and topological information.
Meaning: Establishes which parameter needs explaining; setting the written gluonic coefficient to zero alone is insufficient.
How far does a small explicit breaking shift the axion minimum?
Do: Derive the shift above and compare with numerical minimization as $\varepsilon$ and $k$ vary.
Check: Recover zero shift at $\delta=0$ on the stable small-breaking branch; determine when the perturbative minimum ceases to describe the global minimum.
Meaning: A controlled robustness test with an exact numerical comparison.
Do: Write a linear response $d_n=c_\theta\bar\theta+\sum_jc_jg_j$ with hadronic coefficients and additional CP couplings $g_j$. Compare one-source and multi-source constraints.
Check: Propagate coefficient uncertainty and exhibit cancellations if several sources are allowed.
Meaning: Separates an experimental bound from the assumptions behind a strong-angle inference.
Which symmetry-breaking operators threaten a particular axion construction?
Do: Choose one explicit field content and symmetry assignment. Enumerate its lowest allowed breaking operators and map them to harmonics of the angular potential.
Check: Include radiatively generated terms and calculate their minimum shifts using CP-2. Verify the assumed suppression scale.
Meaning: Produces a finite operator audit. Its novelty depends on the construction; the quality problem itself is established.
Do: Draw a sequence of regulated theories with fixed physical volume and decreasing spacing, followed by increasing volume. Track dimensionless masses and physical correlation lengths.
Check: A nonzero mass in lattice units need not represent the desired continuum limit. State how the scale is set and which errors are controlled.
Meaning: Produces a precise distinction between numerical evidence and a constructive existence theorem.
Do: Use a two-state Hamiltonian mixing a linearly rising string energy with a nearly constant two-meson threshold. Diagonalize as a function of source separation.
Check: Recover a true crossing at zero mixing and an avoided crossing otherwise. Analyze the overlap of a string-like trial operator with the ground state.
Meaning: Explains why a poor operator basis can hide string breaking even when it occurs in the spectrum.
Which confinement diagnostic survives a controlled model deformation?
Do: Choose one finite lattice gauge model and add an explicitly specified dynamical matter field. Compare loop behavior, static-source energies, and a gauge-invariant correlation length.
Check: Benchmark the pure-gauge and decoupled-matter limits before extrapolating. Keep boundary and volume effects visible.
Meaning: Can separate diagnostics that coincide in a toy limit. Novelty needs a particular deformation; it is not a plan to prove the Clay problem by small-system numerics.
QM-2 · Quantum measurement and classical recordsCalibration
Can local measurements distinguish entanglement from ignorance?
Do: Compare the two-qubit Bell state with the equally weighted mixture of $|00\rangle$ and $|11\rangle$. Compute single-qubit states and the joint correlation $\langle X\otimes X\rangle$.
Check: Both local states equal the identity divided by two, while the correlation is one for the Bell state and zero for the mixture. $X$ flips $0$ and $1$.
Meaning: An exact example of why local diagonality does not identify the global physical state.
QM-4 · Quantum measurement and classical recordsDiagnostic
Which collapse effect is distinguishable from ordinary noise?
Do: Choose one published collapse model and one explicit environmental-noise model. Compare their predicted dependence on mass, separation, and interrogation time.
Check: Fix nuisance parameters using independent information. Agreement at one point does not establish agreement across a controlled scan.
Meaning: Produces a testable model comparison. This is a dynamics question, not a generic experiment deciding all interpretations.
QM-5 · Quantum measurement and classical recordsExtension
How much environmental access is needed to restore interference?
Do: In the independent-record model, reverse the interaction on only $k$ environment qubits. Compute the remaining visibility and compare with the best allowed joint measurement on the accessible part.
Check: Recover full reversal at $k=N$ and ordinary reduced visibility at $k=0$. State which operations and records are available.
Meaning: A tractable access-dependent question. The simple model is established; a worthwhile extension needs a specified correlated environment or operational restriction.
TH-3 · Thermalization and the arrow of timeDiagnostic
Does breaking integrability make the chosen observable thermal?
Do: Compare $g_z=0$ with a generic nonzero value at matched energy density. Plot diagonal matrix elements of a local observable against energy, resolving symmetries.
Check: Use several sizes and the same energy window. Smoothness alone is not enough if the initial energy distribution is broad.
Meaning: Produces a scoped eigenstate-thermalization diagnostic, not a universal law.
TH-5 · Thermalization and the arrow of timeExtension
Which observable forgets the initial state last?
Do: In one chain family, compare local magnetization, a two-point correlation, and a subsystem entropy after matched-energy quenches. A quench is a specified sudden parameter change.
Check: Define a relaxation tolerance and time window before inspecting results. Test sizes and initial states to distinguish slow dynamics from finite-size recurrences.
Meaning: A useful model-specific hierarchy of memory; novelty requires comparison with known conserved and nearly conserved modes.
TU-1 · Turbulence and anomalous dissipationCalibration
Can dissipation survive a coefficient tending to zero?
Do: Verify the shock solution and evaluate the dissipation integral analytically and numerically for several viscosities.
Check: Increase spatial resolution as the width decreases and include boundary energy flux. The integral tends to $2U^3/3$ without inventing a forcing term.
Meaning: A complete controlled example of a singular dissipation limit.
TU-2 · Turbulence and anomalous dissipationCalibration
What assumptions go into the minus-five-thirds spectrum?
Do: Derive the spectrum from units and its normalization. Then allow an outer length or a fluctuating local transfer rate as an extra input.
Check: Distinguish dimensional consistency from a uniqueness theorem. Define the scale interval in which forcing and viscosity are both negligible in the balance.
Meaning: Reveals exactly what the scaling argument explains and leaves undetermined.
TU-3 · Turbulence and anomalous dissipationDiagnostic
Can a measured structure function test the energy flux?
Do: In a homogeneous, isotropic, statistically stationary three-dimensional dataset, compare the longitudinal third-order velocity increment with the inertial-range prediction $\langle(\delta u_L)^3\rangle=-4\varepsilon r/5$. Here $\delta u_L=[\mathbf u(\mathbf x+\mathbf r)-\mathbf u(\mathbf x)]\cdot\hat{\mathbf r}$ is the velocity difference projected along the separation.
Check: Account for finite-viscosity, forcing, anisotropy, and finite-sampling corrections before declaring a violation.
Meaning: Tests a constrained flux relation rather than merely fitting a spectral slope. Its assumptions and limiting range are essential. [35]
TU-4 · Turbulence and anomalous dissipationDiagnostic
Which rare events dominate high moments?
Do: For a specified velocity dataset or synthetic model, compare $\langle|\delta u|^p\rangle$ for several orders $p$, including sensitivity to removing a small extreme tail.
Check: Use independent samples and convergence checks. A high-order moment with no stable estimate is not a measured exponent.
Meaning: Quantifies intermittency and distinguishes statistical uncertainty from failure of simple scaling.
TU-5 · Turbulence and anomalous dissipationExtension
Which coarse-graining scale reveals a stable energy flux?
Do: Filter one resolved velocity field at several lengths and derive the sub-filter transfer from the filtered equation. Compare it with the dissipation estimate.
Check: The filter definition and boundaries must be explicit; verify the resolved-plus-unresolved energy balance and vary the filter shape.
Meaning: A bounded robustness study of scale transfer. Existing coarse-graining theory is the starting benchmark, not a novelty claim.
SM-3 · Strange metals and electrical resistanceDiagnostic
Which step makes disorder essential in a solvable strange-metal model?
Do: Follow the cited random-interaction model through its conductivity calculation. Identify the term that relaxes current and compare with a spatially uniform coupling.
Check: Include the corrections required by charge conservation when relating self-energy to conductivity. Recover the stated clean-limit behavior.
Meaning: Determines necessity or sufficiency only within the specified model, not for every strange metal. [36]
SM-4 · Strange metals and electrical resistanceDiagnostic
Can one mechanism explain transport and thermodynamics together?
Do: For a single chosen parameter set, compare the predicted temperature dependence of resistivity, optical conductivity, and specific heat, the derivative of energy with temperature.
Check: Use one parameter set and one regime. Record which observable is fitted and which is then predicted.
Meaning: A mechanism becomes informative when agreement with one measurement constrains another; a separate fit for every curve weakens the test.
SM-5 · Strange metals and electrical resistanceExtension
Which disorder dependence separates two plausible mechanisms?
Do: Choose a conventional momentum-relaxation model and one critical-interaction model. Vary only a specified disorder parameter and compare residual resistance and temperature slope.
Check: Determine whether disorder also changes carrier density, pairing, or the critical point. Hold those fixed only when the model permits it.
Meaning: Produces an experimentally motivated comparison with explicit nuisance effects. Novelty depends on the selected pair and observable.
Does a small-cluster binding energy predict long-distance order?
Do: Compare a defined pair-binding energy with pair-correlation decay across a sequence of small clusters or ladders using the same Hamiltonian.
Check: Fix boundary conditions and particle-number conventions. Pair binding on one cluster is neither necessary nor sufficient evidence for a two-dimensional condensate.
Meaning: Locates the inferential gap between local energetics and a thermodynamic superconducting phase.
Is phase stiffness a ceiling or the actual limiting scale?
Do: In a chosen two-dimensional model, compute or use benchmark values of temperature-dependent stiffness and pairing amplitude. Compare the stiffness transition criterion with the pairing scale.
Check: Use renormalized stiffness near the transition, not only its zero-temperature value. State dimensional and interaction assumptions.
Meaning: Determines the bottleneck in that regime; an upper bound alone cannot establish it. [38]
Which conclusion survives changing the microscopic reduction?
Do: Match a small multi-orbital cluster to a one-band model using low-energy levels. Compare one additional pair or spin observable not used in matching.
Check: Transform observables as well as the Hamiltonian and identify the energy window where discarded states remain separated.
Meaning: Tests transfer of a mechanism across a reduction. It is a bounded continuation of the original cuprate program, with novelty requiring a specific regime and comparison.
AQ-3 · Local quantum fields and operational accessDiagnostic
What changes when a boundary is given a finite buffer?
Do: On a massive free-field lattice, compare adjacent regions with regions separated by a fixed physical gap. Refine the spacing while keeping region and buffer sizes physical.
Check: Separate ultraviolet, volume, and mass effects. For mutual information, compute the entropy combination in a common regulator before extrapolating.
Meaning: Tests the value of separation for a specified information quantity. A numerical limit is evidence in this model, not a proof of the split property.
AQ-4 · Local quantum fields and operational accessDiagnostic
What is the operational cost of a local postselection?
Do: In a finite entangled-chain analogue, choose a local measurement outcome intended to prepare a distant target. Track conditional fidelity, success probability, and energy change together.
Check: Average over all local outcomes and verify no change in the distant reduced state. High conditional fidelity must not hide vanishing success.
Meaning: Makes the resource issue behind remote-preparation statements concrete without equating the chain with continuum QFT.
AQ-5 · Local quantum fields and operational accessExtension
Which continuum distinction remains after an energy budget is imposed?
Do: Specify one local discrimination or preparation task, two state families, a spatial buffer, and a bound on injected energy. Compare a free-field continuum prediction with convergent lattice approximations.
Check: Hold physical budgets fixed as the cutoff changes; inspect whether the claimed advantage requires energy or operator norms to diverge.
Meaning: A focused bridge between algebraic structure and operations. Its novelty must be checked against energy-constrained and split-inclusion literature before a research claim.