Unphysical

In the philosophy of physics, the term unphysical means a prediction of a physical theory that is in contradiction to existing broad understanding of the physical world. In his Oxford Handbook of Philosophy of Physics the philosopher Robert W. Batterman uses the term "defying our antecedent expectations as to what ought to happen". ^[1]

The concept has been used in discussions of issues in many areas of physics, including equations with singularities, ^{[2] [3]} physical quantities with infinite values, events with negative probabilities or infinite probabilities, ^[4] states with energies less than the ground state ^[5] and predictions which violate conservation laws. The mathematical description of a physical system may have multiple solutions, with some being physically realizable and others unphysical. ^[6] Green's functions and proper vertices have been given as examples of entities which can suffer from unphysicality. ^{[6] [7] [8]}

Norton's taxonomy

In a 2006 paper, the philosopher of physics John D. Norton has examined the concept of what it means for something to be unphysical. ^[9] Norton states that the term means "cannot obtain in the real world", listing the following possibilities: ^[9]

• Unphysical as gauge (over-description), in which "a theory admits more structures than are in the world for descriptive convenience"

• Unphysical as objectively false, in which "a theory makes a prediction that turns out to be false and quite far from approximations to the actual"

• Unphysical as pathological, in which "a physical theory is used to generate conclusions that turn out to contradict the original theory"
• Unphysical through under-description, in which "a theory may under describe or under constrain a system’s properties, with the outcome that the theory admits solutions that do not apply to the system"

See also

• Absurdity
• Ghost (physics)
• Naked singularity
• Non-physical entity
• Physicalism
• Unobservable

References

1. Batterman, Robert (2013-03-14). The Oxford Handbook of Philosophy of Physics. OUP USA. p. 130. ISBN   978-0-19-539204-3.
2. Shikhmurzaev, Y. D. "Singularities in Mathematical Models". web.mat.bham.ac.uk. Retrieved 2025-12-18.
3. Richens, P J (1983-12-01). "Unphysical singularities in semiclassical level density expansions for polygon billiards". Journal of Physics A: Mathematical and General. 16 (17): 3961–3970. doi:10.1088/0305-4470/16/17/013. ISSN   0305-4470.
4. Carcassi, Gabriele; Calderon, Francisco; Aidala, Christine A. (2024-12-22), The unphysicality of Hilbert spaces, arXiv, doi:10.48550/arXiv.2308.06669, arXiv:2308.06669, retrieved 2025-12-18
5. Adams, William H. (1992). "The problem of unphysical states in the theory of intermolecular interactions". Journal of Mathematical Chemistry. 10 (1): 1–23. doi:10.1007/BF01169168. ISSN   0259-9791.
6. Stan, Adrian; Romaniello, Pina; Rigamonti, Santiago; Reining, Lucia; Berger, J A (2015-09-25). "Unphysical and physical solutions in many-body theories: from weak to strong correlation". New Journal of Physics. 17 (9) 093045. doi:10.1088/1367-2630/17/9/093045. ISSN   1367-2630.
7. Stevenson, P. M. (2022-03-21). Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity. World Scientific. p. 26. ISBN   978-981-12-5570-0.
8. Mikhailov, Andrei (Nov 2012). "Cornering the unphysical vertex". Journal of High Energy Physics. 2012 (11). doi:10.1007/JHEP11(2012)082. ISSN   1029-8479.
9. Norton, John D. (December 2008). "The Dome: An Unexpectedly Simple Failure of Determinism" (PDF). Philosophy of Science. 75 (5): 786–798. doi:10.1086/594524. ISSN   0031-8248.