Particulate exotica

TL;DR

The paper explores the potential implications of exotic smooth structures in four-dimensional spacetime on physical theories, suggesting that such exotica could introduce fundamental uncertainties in microscopic physics models.

Contribution

It offers a speculative discussion on how exotic smoothness in 4D spacetime might impact particle physics models and the transfer of physical information.

Findings

Exotic smooth structures could cause pathologies in standard physical theories.

Re-examining particle models through the lens of exotica may provide new insights.

Mathematical tools for this analysis are still in early development.

Abstract

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, consisting merely of conjectures, because the necessary mathematical tools have only just began to be developed.