Eddington argued that material rods and clocks, being composed of matter governed by field equations, are self-authenticating probes of the metric in a way that wave propagation, requiring medium-independent assumptions, is not.

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Eddington(the main person making the argument in this statement): Arthur Eddington was a famous British physicist in the early 1900s who thought deeply about how we measure and understand the physical world, especially through relativity and quantum mechanics.
Metric(in mathematical analysis): A specific way of measuring distance or defining what 'closeness' means in a mathematical space.
field equations(the laws that control matter according to this argument): Mathematical equations that describe how physical forces (like gravity or electromagnetism) behave throughout space—think of them as the rules that govern how the physical world works.
medium-independent(a characteristic of waves that Eddington saw as a weakness for measurement): Not depending on a specific substance or material for something to work—for example, light can travel through empty space without needing anything to carry it.

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