If distinct tetrad fields related by local Lorentz transformations can ground physically distinct geometric structures, the metric does not merely underdetermine tetrads up to Lorentz equivalence but fails to determine the relevant physical geometry at all.
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Mathematical operations that change how you measure space and time at a specific location, based on Einstein's theory of relativity; they're 'local' because they can be different at different places.
physically distinct(as used in philosophy of physics)
Different in a way that actually matters for how the universe behaves; not just mathematically different on paper, but actually producing different physical outcomes.
tetrad fields(as used in physics and geometry)
Mathematical objects used in physics to describe how space and time are structured at each point in the universe; think of them as tiny reference frames that tell you which directions are 'up,' 'forward,' etc. at every location.