Symbol U
U is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
For a static observer at position in a stationary spacetime, define U() := d/dt , the local rate of proper time relative to coordinate time. Two clocks compared through any phase-coherent link that depends only on their respective proper frequencies report the ratio / = U()/U() — a fact about stationary spacetimes that follows from the timelike Killing vector generating t -translations, and one on which the standard treatments of relativity in a geodetic or navigational setting already rely [ 10 , 14 ] . The dependence on endpoints only, never on the path connecting them, is not an approximation: because / t generates a…
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Symbol x
x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol d
d is an input to the expression that computes the quantity on the left.
Read this term in its guide →Symbol τ
τ is an input to the expression that computes the quantity on the left.
Read this term in its guide →Symbol t
t is an input to the expression that computes the quantity on the left.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 6 · Evolutionary Physics
The Bend an Elevator Cannot Fake
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
For a static observer at position in a stationary spacetime, define U() := d/dt , the local rate of proper time relative to coordinate time. Two clocks compared through any phase-coherent link that depends only on their respective proper frequencies report the ratio / = U()/U() — a fact about stationary spacetimes that follows from the timelike Killing vector generating t -translations, and one on which the standard treatments of relativity in a geodetic or navigational setting already rely [ 10 , 14 ] . The dependence on endpoints only, never on the path connecting them, is not an approximation: because / t generates a…
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