In classical and modern physics alike, symmetries are often seen as deep truths about reality. Noether’s theorem famously shows that each symmetry corresponds to a conservation law: time-translation symmetry gives energy conservation, spatial symmetry gives momentum conservation, and so on. These relationships are often taken to suggest that the universe is governed by unchanging principles — “laws of nature” that apply universally and absolutely.
A relational ontology invites a different view: that symmetries are not metaphysical absolutes, but expressions of systemic coherence — constraints that hold within specific relational configurations, not external commands imposed from above.
1. Symmetry as Invariance Under Transformation
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A symmetry is a transformation under which a system appears unchanged,
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In classical metaphysics, this suggests a fixed structure — an eternal framework in which things persist,
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But if reality is relationally constituted, then what stays the same depends on the structure of relation, not on an underlying substrate.
2. Conservation as Persistence of Coherence
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Conservation laws are often taken as evidence of intrinsic substance: energy, momentum, charge,
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In a relational framework, conservation is the persistence of a constraint pattern, not the transport of a thing,
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Energy is not a quantity stored in a particle, but a relational tension distributed across a field of interaction.
3. Context-Dependence of Symmetry
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Symmetries are not universally valid across all domains; they break under certain relational conditions,
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Symmetry breaking (e.g. in phase transitions) shows that what was once invariant becomes contingent — coherence reorganises,
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This supports the view that symmetry is emergent, not ontologically fundamental.
4. Noether’s Theorem, Reframed
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Noether’s theorem does not derive conservation laws from metaphysical principles,
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It reveals how stable relational configurations give rise to measurable regularities,
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The conservation is not in the thing, but in the invariance of affordances across transformations.
Closing
In a relational ontology, symmetry is not the fingerprint of a divine legislator or the residue of eternal truths. It is the expression of coherence within a constrained system, the rhythm of relational possibility maintaining pattern through transformation.
Conservation is not the safeguarding of substance, but the continuity of constraint — the system’s capacity to preserve its affordances under change.
In the next post, we’ll turn to the question of what physics is doing when it builds models, and what kind of reality those models presuppose or project.
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