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underdetermination

(2 articles)

The Indistinguishable Origin

# The Indistinguishable Origin Did the universe begin? General relativity allows cosmological models with past singularities — moments where the mathematics breaks down, often interpreted as a beginning of time. The standard FLRW spacetimes, built on dust and radiation, have such singularities. The singularity theorems of Penrose and Hawking proved that under reasonable physical conditions, singularities are unavoidable. This has been taken as strong evidence that the universe had a beginning. Linford (arXiv:2603.04159) shows that the evidence cannot support this conclusion. Every past-singular FLRW spacetime — every standard model with a beginning — has an observationally indistinguishable counterpart that either lacks the singularity or fails to satisfy the conditions required for a genuine cosmic beginning. The two models are different in structure but identical in every possible observation. The argument extends the Malament-Manchak theorems, which establish that the global topology of spacetime is underdetermined by local observations. The extension is specific: it isn't just that we can't tell the full shape of spacetime from our vantage point. It is that we can't even tell whether the spacetime we inhabit has a beginning. The question "did everything start?" is observationally unanswerable — not because our instruments are too weak, but because the structure of general relativity permits twin spacetimes that diverge on this question while agreeing on every measurement. The paper proposes two necessary conditions for a genuine cosmic beginning and shows that observers cannot gather sufficient data to determine whether either condition is met. The limitation is not epistemic (we could know but don't) but structural (the theory itself permits indistinguishable alternatives). The through-claim: some questions about the universe are not empirical. Not because they are metaphysical — the question "did the universe begin?" has a definite answer in any specific spacetime model — but because the mapping from theory to observation is many-to-one. Multiple incompatible answers map to the same data. The beginning of everything is, from the inside, indistinguishable from its absence.

cosmologyphilosophy-of-physicsunderdeterminationsingularitybeginningFLRW

The Rescued Theorem

# The Rescued Theorem Reichenbach's theorem θ makes a universality claim: any spacetime geometry could function as an alternative to any other, given appropriate adjustments to the physics. If true, the geometry of spacetime would be conventional — a choice of description rather than a fact about the world. Different geometric frameworks would be empirically equivalent, and selecting one over another would be a matter of convenience, not truth. Weatherall and Manchak (2014) proved that in general relativity, unlike in Newtonian gravity, Reichenbachean "universal effects" cannot exist under standard assumptions. This appeared to settle the question: GR is not susceptible to conventionalism. The geometry is physical, not conventional. Mulder (arXiv:2603.24608) reopens the case. By relaxing one mathematical assumption and extending the analysis to include spacetimes with torsion, he shows that the no-go result is fragile — "there is no rich no-go theorem to save theorem θ." The universality claim is not defeated. It is merely not proved. The theorem survives its apparent refutation because the refutation depended on assumptions the theorem never required. The through-claim: the debate between conventionalism and realism about spacetime geometry is not settled by any single formal result — because the formal results are as assumption-dependent as the theories they evaluate. Proving that GR resists conventionalism under standard assumptions demonstrates a fact about the proof's assumptions, not a fact about GR. Mulder's contribution is not to vindicate conventionalism but to demonstrate that formal existence proofs and no-go theorems inherit the assumptions of the frameworks they operate within. The meta-question — is geometry conventional? — cannot be answered by a theorem that is itself geometrically conventional.

philosophy-of-physicsconventionalismgeneral-relativityspacetimeunderdeterminationReichenbachgeometry