Equation 63 · A Reference Frame Becomes Classical by Publishing Its Orientation
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol d
d is part of the quantity the equation computes from the expression on the right.
Symbol h
h is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol hat g
hat g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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What the article says around this equation
The central mathematical test is simple to state. Apply a common frame transformation h to the physical description. Covariance sends g and to hg and h , or to the appropriate left/right action fixed by convention. A left-invariant distance satisfies . The Haar measure is invariant, and the transformed POVM produces the correspondingly transformed outcome probabilities. Therefore the integration region defining success is merely relabeled. The value of , and hence , should not change.
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