Time, space, and matter cannot really be pulled apart: you cannot have any one of them without the other two. The argument makes that point abstractly earlier; here it appears under the ordinary names physics already uses: spacetime, fields, conservation, and symmetry. There is even a loose echo in physics's own habits: real laws can always be rewritten so that the choice of units (meters or miles, seconds or years) cancels out. What shifts with our choices is just the bookkeeping; the way the three lock together does not.

Each axis composes with itself: tensed and tenseless time in [§7.2](<7.2 Time.md>), absolute and relational space in [§7.3](<7.3 Space.md>), matter and energy in [§7.4](<7.4 Substance.md>). The axes also compose with each other. The cross-axis composition was stated formally as the Triconditional Cross-Entailment ([§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>)), the law-level statement that the three structural conditions of Nature obtain together if and only if each obtains: T ↔ (S ∧ Φ), S ↔ (T ∧ Φ), Φ ↔ (T ∧ S), with the pairwise corollaries T ↔ S, S ↔ Φ, T ↔ Φ. Each role holds in a world if and only if the other two do; no role floats free of the other two. What follows is the same structure at the Ontological Identity ([§2.6.8](<2.6.8 Ontological Identity.md>)), the being-level statement of the same three-way binding, read off the actual physical structure rather than the law-level formulation, under the standard names physics had already settled on independently. The match runs at the level of *what must hold* (that there are these binding-registers), not at the level of which specific physical theory realizes them: the modal claim is structural; the specific physics that fills in each register is contingent. Physics' own methodology offers a partial illustration (though not, on its own, a confirmation) of how a description-side choice can be separated from the content it describes. Physical laws are always expressible as relations among dimensionless ratios: combinations in which the particular unit system cancels out. The Buckingham π theorem formalizes the point: any physically meaningful equation can be rewritten in terms of dimensionless groups, independent of whether lengths are measured in meters or miles, times in seconds or years, or masses in kilograms or pounds (Edgar Buckingham, 1914); (Percy Williams Bridgman, 1922). The unit system is a description-side choice; the relations among the quantities it names are not. But the analogy has to be handled with care, because the line the theorem draws is not the line this chapter draws. Unit-invariance separates measurement convention from physical content; the structural/contingent distinction runs *inside* physical content: the binding relations among the conditions are structural, yet much of the rest is equally unit-invariant and still contingent (which fields exist, which symmetries hold, the values of the dimensionless constants). The theorem therefore shows that some features of a description are pure bookkeeping while others are not; it does not by itself certify that the *binding* relations fall on the structural side. That they do is established on modal grounds ([§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>)), not read off from dimensional analysis. One constraint at three registers ([§2.6.9](<2.6.9 Triunity of Nature.md>)); [§7.5](<7.5 Binding of the Conditions.md>) is its physical face.


- [7.5.1 Spacetime](<7.5.1 Spacetime.md>)
- [7.5.2 Field](<7.5.2 Field.md>)
- [7.5.3 Conservation](<7.5.3 Conservation.md>)
- [7.5.4 Symmetry](<7.5.4 Symmetry.md>)
- [7.5.5 What is Concluded](<7.5.5 What is Concluded.md>)


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← [7.4.5 What is Concluded](<7.4.5 What is Concluded.md>) | [7.5.1 Spacetime](<7.5.1 Spacetime.md>) →
