Foundations and Reality: Research Directions

Foundations research is strongest when a precise question connects mathematical assumptions to an operational or explanatory consequence. This chapter helps choose between experiments that constrain modified dynamics, theorems that constrain model classes, and studies of how classical records emerge. Reviewed 11 October 2026; each linked dossier states its own cited evidence horizon.

Helpful background. The Foundations volume owns established arguments and interpretations. Begin with its research bridge when the distinction between a theorem, an experimental inference, and an interpretation is unfamiliar.

Enter this chapter

Your question	Research dossier	A tractable first result
What does a measurement model explain about outcomes?	Measurement problem	Compare reduced states with globally recoverable coherence.
Which local models do correlations exclude?	Bell tests	Validate an inference procedure under drift and optional stopping.
Which nonclassical feature helps a specified task?	Contextuality	Derive a witness robust to measured calibration errors.
Which large-scale coherence is actually certified?	Macroscopic superpositions	Reconstruct a coherence witness and its nuisance parameters.
Which modified dynamics is excluded?	Collapse tests	Reproduce one geometry-dependent exclusion.
Which assumptions conflict in extended-observer scenarios?	Wigner’s friend	Reconstruct a finite inequality with an explicit record model.
What can interventions identify?	Quantum causal structure	Distinguish direct and common causes with limited instruments.
What can uncharacterized devices certify?	Device-independent foundations	Compute a valid finite-data guarantee.
How do several observers obtain compatible records?	Classical emergence	Compare redundancy with accessible information.
What is excluded by a state-ontology theorem?	Probability and ontology	Build a noise-tolerant assumption map.

Choose the kind of contribution first

A theorem project needs a defined model class, hypotheses, and a verifiable proof or counterexample. A numerical project needs a physical or logical question, convergence checks, and a comparison that could falsify the proposed interpretation of the data. An experimental project needs a forward signal model and a defensible noise budget. A conceptual project needs a precise claim whose consistency or explanatory relation can be assessed.

These are not ranks of scientific worth. They are different evidence contracts. For example, a loophole-controlled Bell violation can reject a factorized local model under its assumptions without selecting among all interpretations that reproduce quantum statistics. A rigorous decoherence calculation can explain suppression of local interference without stipulating a unique global outcome.

The source literature illustrates this division: Brunner and colleagues organize correlation-based tests; Budroni and colleagues distinguish contextuality frameworks; Bassi and colleagues connect modified dynamics to experimental constraints. Use the relevant framework before importing a slogan from another.

Match the first question to available resources

Probability and optimization, with a laptop. The Bell and device-independent dossiers are suitable if you can work with conditional probability and adversarial models. The first artifact is a reproduced finite-data bound, including a null case that never yields positive certification. The risk is proof mismatch: a formula derived for independent rounds does not certify a device with memory. An improvement must preserve the adversary, failure probability, input model, and trial-selection rules.

Linear algebra and small-system simulation. The measurement and classical-emergence dossiers supply exact reduced-state and fragment-discrimination benchmarks. Begin with systems small enough to verify every partial trace. The risk is an inaccessible observable: a global coherence or information measure may be unavailable to every observer permitted by the experiment. An extension should change an explicit control, geometry, or noise restriction and compare an operational quantity.

Access to an experimental group or a published calibration model. Collapse and macroscopic-superposition projects require exposure, geometry, preparation, readout, and nuisance information. The first artifact is a reproduced likelihood or exclusion at fixed model parameters. A larger mass or a smaller residual alone is not a research result. If signal and nuisance effects have the same dependence on all available settings, obtain another setting or calibration before proposing a stronger limit.

Interest in ontology and conceptual analysis. The probability and Wigner’s-friend dossiers are suitable if you enjoy proofs and exact model comparison. Begin by reproducing one exclusion theorem and one model outside its hypotheses. The risk is changing the meaning of a premise midway through the argument. A new conclusion should follow from a clearly weaker assumption, a sharper quantitative tradeoff, or an explicit counterexample to a published inference.

These profiles are entry routes, not rigid career categories. Causal inference and contextuality connect several of them: a proposed witness may be mathematically valid while the required interventions or operational equivalences are unavailable. The decisive feasibility check is whether the group can establish those conditions, not whether it can run the optimizer.

A proposal that can survive its first month

Write down one target statement and one established baseline. Name the assumptions that would make the statement false, the resources you can access, and the result you can obtain even if the ambitious hypothesis fails.

Use a four-week feasibility pass with a result that remains useful if the proposed extension fails:

1. Specify. Select one paper, its precise claim, and one figure, inequality, or model table to reproduce. Record required data and trusted inputs. If an essential calibration or theorem assumption is unavailable, choose a different baseline now.
2. Reproduce. Check an analytic limiting case and recover the selected result within a stated numerical or statistical tolerance. Save the source version, units, conventions, and executable notebook or proof notes.
3. Perturb. Change one limitation, such as setting bias, finite records, an intervention restriction, or preparation dependence. Include the null model and a deliberately adverse case. Find where the claim ceases to hold.
4. Decide. Deliver a short report with the baseline, changed assumption, surviving bound, resource estimate, and nearest competing result. Continue only if the proposed increment is distinguishable from existing work and the group’s available methods can resolve it.

For example, a proposed “improved collapse limit” should first reproduce the published likelihood at a fixed localization length. If a common environmental rate and a collapse rate cannot be separated with one setting, the immediate research question becomes which additional observable breaks that degeneracy. The macroscopic-superposition dossier works through this identifiability issue. Reporting the degeneracy is already a defensible first-month outcome; presenting a bound obtained by fixing an unconstrained nuisance is not.

Stop and reformulate if the proposed discriminator is operationally inaccessible, if two compared theories make identical predictions for the allowed experiment, or if the result disappears when its stated nuisance parameters are included. These are scientifically useful diagnoses, not reasons to conceal a negative result.

Read an evidence update at the level of its claim

A review date marks when this assessment was checked; it does not mean every dossier surveys literature through that date. The macroscopic-superposition dossier includes a January 2026 nanoparticle-interference report and separates the mass range with quantum-discriminating evidence from larger interference patterns compatible with a classical model. The Wigner’s-friend dossier includes a 2024 analysis of additional memory assumptions. Neither update establishes a general resolution of the measurement problem.

Before choosing a thesis topic, search forward citations of the baseline paper, recent reviews, and the precise inequality, protocol, or noise model being extended. Record whether a candidate improvement has already been proved under equivalent assumptions. An older theorem can remain the right starting point while its proposed numerical extension has become routine.

Interfaces and limits

Quantum-gravity interfaces require additional care about subsystem partitions, mediator assumptions, and spacetime. Rigorous frontiers addresses operator domains, infinite systems, and proof questions. Neither interface licenses treating a suggestive analogy as empirical evidence.

This chapter offers bounded entry projects and explicit update triggers. It does not promise that any suggested extension is novel; establish that through a focused literature search and specialist discussion before committing a thesis.

References

• A. Bassi, M. Dorato, and H. Ulbricht, “Collapse Models: A Theoretical, Experimental and Philosophical Review,” Entropy 25, 645 (2023). Review.
• N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics 86, 419–478 (2014). Review.
• C. Budroni, A. Cabello, O. Gühne, M. Kleinmann, and J.-Å. Larsson, “Kochen–Specker contextuality,” Reviews of Modern Physics 94, 045007 (2022). Review.

Entry points

Use Choosing a research direction to turn one row of the table into a proposal, then read the selected dossier’s primary source and reproduce its baseline.