Physics is often imagined as the discipline that, more than any other, promises global coherence. Its aspiration is universal law: equations that apply everywhere, explanations that close, models that scale without remainder.
And yet, some of the most persistent and troubling features of modern physics appear precisely where this aspiration is most strongly asserted.
Singularities.
Points where quantities diverge, predictions fail, and models are said to “break down”. These are typically treated as sites where reality itself outruns our theoretical grasp.
But this diagnosis deserves scrutiny.
Nothing Locally Goes Wrong
At a singularity, the mathematics does not suddenly become incoherent. The equations continue to follow their rules. The derivations remain valid. The formalism behaves exactly as specified.
What fails is not local lawfulness.
What fails is the attempt to extend that lawfulness beyond its legitimate domain — the demand that a locally successful model must also be globally world-forming.
Seen this way, a singularity is not evidence of disorder in nature. It is evidence of over-extension in our expectations.
The Hidden Assumption of Universality
To call a singularity a “breakdown” is already to assume something quite strong: that a successful model ought, in principle, to apply everywhere.
This assumption is rarely stated. It operates silently, as part of the metaphysical background against which scientific explanation is judged.
But locality unsettles this assumption.
A model can be:
perfectly lawful within its frame,
maximally predictive across a wide domain,
internally consistent in every respect,
and still fail to integrate into a single global description.
When this happens, the failure is not in the model. It is in the expectation of universality.
Singularities as Boundary Signals
Understood through locality, a singularity functions as a boundary marker rather than a metaphysical abyss.
It signals:
the edge of a model’s domain,
the point at which extrapolation becomes illegitimate,
the moment where global closure is silently imposed.
The drama arises only because this signal is misread.
Instead of recognising a limit of applicability, we interpret the divergence as a feature of reality itself — something that must be repaired, resolved, or explained away.
This is a familiar pattern.
We have already seen it in:
systems that are locally impeccable but globally non-integrable,
constructions that remain lawful but uninhabitable,
anomalies that appear only when closure is demanded.
Singularities belong to this family.
From Breakdown to Cartography
If singularities are artefacts of globalisation, then the task of theory changes subtly but decisively.
The aim is no longer to eliminate singularities by force, or to posit deeper ontologies that restore universality.
It is to map precisely where a model holds — and to stop where it does not.
This is not a retreat from explanation. It is a refinement of explanatory discipline.
Science becomes less a search for a single, all-encompassing world-description, and more a careful cartography of lawful domains.
A First Reorientation
Seen in this light, singularities are not failures to be feared. They are instructions.
This post is the first step in a short series exploring what physics looks like when we take that reminder seriously — when we stop demanding global integration, and attend instead to the conditions under which our models genuinely hold.
The next step brings this lesson into sharper focus, by examining event horizons — and what happens to events themselves when global coordination fails.
No comments:
Post a Comment