A working library of theoretical physics
A pedagogical research companion: understand the theory, isolate a mechanism, and choose a calculation that changes what you understand.
An open problem becomes useful when we can say what an explanation must reproduce, which assumptions a proposed mechanism needs, and what a smaller calculation would teach us. The aim of this collection is to build that understanding. A successful investigation may end with a derivation, a counterexample, a controlled comparison, or a better question. It need not produce a new theory.
The first edition has 16 chapters and 80 questions. Each chapter develops the physical problem, separates established results from unsettled explanations, works through a concrete model, and ends with a sequence of questions. Start with a chapter's guiding question, read its worked example, then choose one question whose output you can describe before calculating.
The intended reader knows basic quantum mechanics, classical mechanics, and some field theory, but need not know every subfield. Symbols are defined where introduced. The concepts and notation companion explains recurring terms and unit conventions. The investigation guide explains how to distinguish a learning calculation from a potential research extension.
What counts as progress? “In model $M$, observable $X$ changes this way when ingredient $Y$ is removed. This means $Y$ is necessary for this effect within the tested regime, while the connection to the physical system still requires check $Z$.” A precise negative answer is often as useful as a positive one.
This is a broad, expandable selection rather than a ranking of all important questions. The last chapter is deliberately different: the type-III structure of local algebras is established in broad classes of QFT; its consequences under finite operational constraints provide the open research direction.
No matches. Try a broader term or clear a filter.
Known / open: Low-energy quantum gravity is predictive; a microscopic completion is not experimentally selected.
Which low-energy observations require a quantum mediator, and which would distinguish different microscopic theories of spacetime?
Known / open: Unitary entropy behavior is reproduced in specified models; full operational and spacetime-wide accounts remain incomplete.
Which correlations or changes in subsystem assignment make unitary evaporation compatible with the semiclassical near-horizon description?
Known / open: Acceleration is well supported within the standard framework; its source and vacuum-energy stability remain unsettled.
Can we separate the mechanism driving late-time acceleration from the problem of making its energy scale stable under quantum corrections?
Known / open: Independent gravitational observations motivate an unseen component; its microscopic identity is unconfirmed.
Which properties of the unseen component are required by independent observations, and which production or interaction mechanisms can satisfy them together?
Known / open: Primordial correlations are measured; their generating field and pre-hot-universe history remain undetermined.
Which observable correlations can distinguish mechanisms that produce almost the same primordial two-point spectrum?
Known / open: The matter excess is inferred; a mechanism generating and preserving it is not established.
What creates a particle–antiparticle excess, and what prevents the same interactions from erasing it?
Known / open: Mass differences and mixing are established; absolute masses, identity, and origin remain incompletely known.
Which measurements distinguish a small Dirac mass from lepton-number-violating mass generation, and how much of the underlying theory can they reconstruct?
Known / open: The Higgs mechanism is established; scale stability and the flavor pattern lack a selected explanation.
Which small masses are protected by symmetries, and which remain sensitive to physically heavy thresholds in a specified extension?
Known / open: Strong CP violation is tightly constrained; an axion or another suppression mechanism is unconfirmed.
What makes the physically observable strong-interaction CP angle small, and which assumptions keep that mechanism stable?
Known / open: QCD has major quantitative successes; continuum Yang–Mills existence and mass-gap proof remain open.
Which controlled mechanisms explain confinement diagnostics, and which parts of that explanation survive the continuum limit of four-dimensional Yang–Mills theory?
Known / open: Measurement statistics and decoherence are well tested; the account of definite outcomes remains disputed.
Which part of a measurement can unitary system–apparatus–environment dynamics explain, and which additional claims lead to experimentally distinct predictions?
Known / open: Thermalization occurs in many systems; its general conditions, limits, and relation to a low-entropy past need separate explanations.
For which observables, initial states, and time scales does an isolated quantum system behave thermally, and what assumptions supply the time direction?
Known / open: Energy balances and controlled limits are known; full turbulent statistics and the stated 3D regularity problem remain unresolved.
Which properties of nonlinear transfer across scales survive as viscosity decreases, and which turbulent statistics require information beyond dimensional scaling?
Known / open: Several models produce unusual transport; selecting a complete material mechanism remains difficult.
Which microscopic interactions relax electric current at the observed rate, and why do several independent transport and thermodynamic observables agree or disagree with the same mechanism?
Known / open: Pairing mechanisms and model benchmarks exist; a complete transferable cuprate explanation remains unsettled.
Which ingredients produce a robust superconducting state in a controlled model, and which evidence is needed to transfer that mechanism to a particular material?
Known / open: Local type-III structure is established in broad QFT classes; resource-limited operational consequences are an active question.
What experimentally or computationally meaningful distinction remains between continuum local field algebras and finite quantum subsystems after energy, resolution, and access are constrained?
Begin with AQ-1: coupled oscillators and QM-2: identical local states, different global states. Continue to BH-3: what entropy does not identify. The connecting question is what information belongs to a state, what belongs to a chosen algebra of observables, and what a restricted observer can access. Then QG-1 asks what a joint gravitational phase could reveal.
Start with DM-2: freeze-out and BA-1: survival against washout. Both teach how competition between reaction and expansion leaves a relic. Add NU-2: seesaw masses to understand one possible connection between neutrinos and the matter excess. These mechanisms can be studied separately before assuming they explain the same universe.
Compare HI-2: a heavy threshold, CP-2: a shifted axion minimum, and DE-3: vacuum-energy stability. Each asks whether a desired small number remains small after a permitted change. The useful unifying idea is to test the protecting mechanism, not merely display the small number.
Begin with SC-1: superexchange, SM-1: current and conserved momentum, and TH-1: dephasing. Add TU-1: finite dissipation in a singular limit. These examples teach distinct routes by which many degrees of freedom defeat a naive extrapolation from one particle or one scale.
The question bank and notebook gathers all 80 questions and filters them by topic, type, or your progress. Each has a stable ID, such as BH-3 or SC-1, so later work can refer to a precise question. Keep the ID when refining a question and record what changed. If a new question replaces the original one, retain the old conclusion and state why the replacement is better posed.
“Answered” in your notebook means answered in the recorded setting. It does not promote a toy-model result to an explanation of nature. Export the notebook to keep the investigation record outside the browser.
The original cuprate text is included unchanged as the project's precedent. The superconductivity companion connects it to this broader map and distinguishes local pairing evidence from long-distance coherent order. The original's 32 questions are not included in the count of 80 new questions.
Further chapters could give dedicated treatment to flavor, finite-density QCD and neutron-star matter, quantum criticality and topological phases, the cosmological initial condition, or specific expansion and structure-growth tensions. The current chapters provide bridges into several of these subjects without claiming exhaustive coverage. A new chapter should earn its place by supplying a clear physical puzzle and at least one informative calculation we can actually complete.