Did the universe have a beginning? The question seems empirical — look at the data, apply the singularity theorems, trace backward. But Linford demonstrates that in almost all classical spacetimes, observers cannot collect sufficient data to answer it.
The argument extends the Malament-Manchak theorems, which establish that local observations cannot uniquely determine global spacetime structure. Linford shows three specific limitations: observers cannot determine whether the conditions of the singularity theorems actually hold, whether the proposed necessary conditions for a cosmic beginning are satisfied, and whether the required time ordering for a genuine beginning is present.
The key construction: singular dust FLRW spacetimes — the standard Big Bang models — possess observationally indistinguishable counterparts that share every local observable property but either lack a past singularity entirely or fail to satisfy the temporal ordering that would constitute a “beginning.” Two observers in these different spacetimes would make identical measurements, see identical cosmic microwave backgrounds, reconstruct identical expansion histories, and draw opposite conclusions about whether their universe had a beginning.
This is not an in-principle limitation of current technology. It is a structural feature of general relativity. The global topology of spacetime is underdetermined by any finite collection of local observations, and “having a beginning” is a global property.
The structural point: some questions about the universe are observationally irresolvable not because we lack instruments but because the answer lives in a part of the mathematical structure that no instrument can access. The beginning of the universe is a claim about global topology, and local physics — which is all physics can ever be — cannot determine it.