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the claim

The undecidability of the spectral gap implies fundamental limits on predicting macroscopic quantum phenomena

the verdict
SUPPORTED
the evidence backs this
Recorded sources
5 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that the undecidability of the spectral gap implies fundamental limits on predicting macroscopic quantum phenomena?

Yes. Recent findings in quantum many-body physics confirm that fundamental properties like the spectral gap, phase diagrams, and thermalization are undecidable or uncomputable, establishing deep limitations on predicting macroscopic quantum phenomena.

Verdict: SUPPORTED · 5 sources for, 0 against · Last checked

The analysis

The claim connects the undecidability of the spectral gap and related quantum undecidability results to fundamental predictive limits on macroscopic quantum systems. Papers [0], [1], [2], [5], and [6] all directly support this by demonstrating that properties such as thermalization, renormalization group flows, phase diagrams, and thermodynamic limit observables are uncomputable or undecidable. There are no papers contradicting this claim, making the verdict SUPPORTED.

Evidence for · 5
Undecidability in quantum thermalization.
2021
Demonstrates that determining thermalization in many-body quantum systems is undecidable, preventing general predictive procedures.
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N, S. & K, M. (2021). Undecidability in quantum thermalization.. doi.org. https://doi.org/10.1038/s41467-021-25053-0

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More for · 4
Uncomputably complex renormalisation group flows.
2022
Shows that key physical properties such as renormalization group flows can be uncomputable, introducing severe limits on prediction.
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JD, W., E, O., & TS, C. (2022). Uncomputably complex renormalisation group flows.. doi.org. https://doi.org/10.1038/s41467-022-35179-4

Uncomputability of phase diagrams.
2021
Proves that determining the phase diagram of many-body quantum systems is uncomputable, aligning with spectral gap undecidability.
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J, B., TS, C., & JD, W. (2021). Uncomputability of phase diagrams.. doi.org. https://doi.org/10.1038/s41467-020-20504-6

Size-driven quantum phase transitions.
2018
Proves that certain quantum phase transitions driven by system size can lead to completely misleading results when extrapolated from finite cases.
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J, B., TS, C., A, L., D, P., & MM, W. (2018). Size-driven quantum phase transitions.. doi.org. https://doi.org/10.1073/pnas.1705042114

Certified algorithms for equilibrium states of local quantum Hamiltonians.
2024
Notes that mathematical formulations of predicting observables in equilibrium states in the thermodynamic limit result in undecidable problems.
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H, F., O, F., & SO, S. (2024). Certified algorithms for equilibrium states of local quantum Hamiltonians.. doi.org. https://doi.org/10.1038/s41467-024-51592-3

Receipt History
first checked04 Aug 2026
judged → SUPPORTED · 8004 Aug 2026
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