Philosophical debates about the ontology of physics often begin with a familiar assumption: physical systems possess intrinsic properties whose values exist independently of observation.
Yet when one examines the mathematical practice of physics more closely, a curious fact emerges.
Physicists rarely calculate intrinsic properties at all.
What they actually calculate are relations between experimental arrangements and observable outcomes.
The difference is subtle but profound.
1. The Structure of Physical Prediction
Consider the basic structure of a physical prediction.
A physicist typically begins with three ingredients:
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A preparation procedure – how the system is produced or initialised.
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A theoretical model – the mathematical framework used to describe the system.
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A measurement arrangement – the experimental setup used to obtain results.
The theory is then used to compute the probability of particular outcomes given these conditions.
In other words, the calculation relates:
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preparation conditions
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measurement configurations
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statistical distributions of results.
This structure is explicit in quantum mechanics, but it also appears throughout modern physics.
The calculations describe how experimental contexts relate to one another.
They do not directly describe intrinsic properties existing independently of those contexts.
2. Quantum Mechanics Makes the Structure Explicit
Quantum theory makes this relational structure particularly clear.
Within the formalism developed by Erwin Schrödinger and Werner Heisenberg, the state of a system is represented mathematically in a space of possibilities. Observables correspond to operators that connect this state to potential measurement outcomes.
The theory then provides rules for computing probabilities of those outcomes.
The evolution of the state is governed by the Schrödinger equation, which describes how the mathematical representation changes over time.
But notice what the theory actually produces.
It does not calculate intrinsic attributes possessed by the system in isolation.
It calculates probabilities of outcomes associated with particular measurement arrangements.
3. Contextuality in the Formalism
The relational character of quantum theory is reinforced by results such as the Kochen–Specker theorem, which shows that it is impossible to assign consistent non-contextual values to all observables of a quantum system.
This result implies that measurement outcomes cannot be interpreted as revealing pre-existing intrinsic values that belong to the system independently of the measurement context.
Instead, the value obtained depends on the experimental configuration within which the measurement is performed.
In practice, physicists already account for this structure. Calculations always specify the measurement basis or experimental arrangement in which outcomes are defined.
The mathematics therefore encodes contextual relations rather than intrinsic attributes.
4. The Language of Properties
Despite this relational mathematical structure, physicists often describe their results using the language of properties.
One hears statements such as:
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“the electron has spin up,”
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“the particle has this energy,”
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“the system has this state.”
These expressions are convenient shorthand.
They compress the relational structure of preparation, measurement, and outcome into a simpler linguistic form.
But this shorthand can easily be mistaken for an ontological claim.
The statement that a system “has” a property suggests that the property exists independently of the experimental context that defines it.
The mathematics itself makes no such claim.
5. Relational Structure Across Physics
The relational character of physical calculation is not limited to quantum theory.
Across physics, theories typically describe relationships among variables rather than intrinsic properties of isolated entities.
Examples include:
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equations relating forces, masses, and accelerations in classical mechanics,
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field equations relating distributions of matter and spacetime curvature in relativity,
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statistical relations between microscopic states and macroscopic observables in thermodynamics.
In each case, the theory specifies how quantities covary within a structured system.
What the equations describe are patterns of relation.
6. The Source of the Ontological Illusion
The persistence of intrinsic-property language therefore reflects a conceptual habit rather than a mathematical necessity.
The habit originates in classical mechanics, where it seemed natural to treat quantities such as position and momentum as attributes that objects simply possess.
When later theories inherited this language, the relational structure of the mathematics was often obscured by familiar metaphors.
The illusion arises because the linguistic surface of physics remains classical even as its mathematical foundations become increasingly relational.
7. Reconsidering the Ontology of Physics
Recognising what physicists actually calculate opens a new perspective on the ontology of physics.
If the core practice of the discipline involves computing relations among experimental conditions and observable outcomes, then the metaphysical assumption that reality consists of intrinsically defined property-bearing objects becomes less compelling.
What physics consistently reveals is not a catalogue of intrinsic attributes but a network of structured relations.
The mathematical framework tracks how systems interact, transform, and produce observable phenomena within specific contexts.
8. The Quiet Lesson of Physical Practice
The remarkable success of modern physics therefore carries a quiet lesson.
The discipline works extraordinarily well when it treats the world as a system of structured relations connecting preparation procedures, interactions, and measurement outcomes.
The idea that physical systems must possess intrinsic properties independently of these relations plays little role in the calculations themselves.
It is largely an interpretive overlay inherited from earlier metaphysical traditions.
Once this is recognised, the ontology of physics begins to look different.
Reality appears less like a collection of independently defined objects and more like an organised structure of relations within which definite phenomena arise.
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