Symmetry is central to modern physics. From Noether’s theorems to gauge theories and conservation laws, symmetries are said to underpin the very structure of physical reality. A symmetry is typically defined as an invariance under transformation: a property of a system remains unchanged when rotated, translated, reflected, or otherwise transformed.
But what, ontologically, does this mean?
In mainstream physics, symmetry assumes something that persists through transformation — a form, a field, or a dynamic law that remains constant as coordinates shift.
This presupposes an object or substrate that possesses properties, and a set of external transformations applied to it.
In a relational ontology, this picture collapses.
1. No Substrate, No Transformation
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Invariance presumes a thing that can be transformed without being altered — a persistent identity,
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But if there are no things, only relations, then symmetry can no longer be about properties of objects,
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Instead:
Symmetry is indistinction within a relational field — the inability to differentiate configurations under certain re-construals.
It is not invariance under transformation, but invariance of constraint across potential reconfiguration.
2. Symmetry as Modal Equivalence
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From a relational perspective, the field is a space of potential,
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A symmetry is not a geometric transformation of a background space, but:
An equivalence class of configurations that produce indistinguishable affordances under the system’s constraints.
That is, different relational configurations make no difference to the field’s structure of possible actualisation.
3. Noether’s Theorem Revisited
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Noether’s theorem states: every continuous symmetry of a system’s action corresponds to a conserved quantity (e.g. time-translation symmetry → energy conservation),
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But this presumes both a Lagrangian formalism and an objective time parameter,
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In relational terms, conservation laws are not derived from symmetries of an external action, but:
They reflect deep constraints in how relational configurations transform — stabilities in the topology of potential.
What is “conserved” is the systemic coherence of a particular mode of actualisation.
4. Gauge Symmetry Without Gauges
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Gauge theories hinge on redundancy — certain field variables can be altered without changing physical predictions,
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This is framed as local symmetry: freedom to redefine internal frames without affecting observables,
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In relational terms, this is not a feature of field equations but:
An expression of the field’s internal perspectival flexibility — multiple relational construals that yield the same systemic coherence.
The "gauge" is not hidden structure; it is indeterminacy in construal within the relational web.
5. Spontaneous Symmetry Breaking
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In physics, symmetry breaking occurs when a system governed by symmetric laws adopts an asymmetric configuration (e.g. a magnet picking a direction),
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This often leads to particle masses or emergent forces,
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In relational terms:
Symmetry breaking is not the loss of a formal symmetry, but the actualisation of one relational configuration over others in a degenerate potential landscape.
The system doesn’t choose a direction; it resolves tension by stabilising a coherence.
Relational Definition
We might say:
Symmetry is the indistinction of relational configurations under systemic constraint — a condition in which multiple construals yield equivalent patterns of potential.
It is not about operations on objects, but about the field’s own internal indistinguishability.
Closing
In a world without objects, symmetry cannot be about sameness of form across transformations of substance. It must be understood as a meta-constraint — a limit on what kinds of difference can matter within a coherent field.
The elegance of physics has long been associated with symmetry. In a relational ontology, that elegance arises not from formal invariance, but from the coherence of relational possibility — the harmony of constraints, not the geometry of things.
In the next post, we’ll examine measurement — not as the uncovering of properties, but as the punctualisation of potential within an experimental cut.
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