Symbol f
f is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
The two calculations agree exactly. This is the covariance check the construction has to pass: [] does not care which energy convention is used, provided the convention is applied consistently — local energy paired with proper time, or Killing energy paired with coordinate time, never a local energy stapled to a coordinate-time integral or the reverse. That last error is precisely the one the naive “free thoughts” argument makes. It takes the huge blueshift factor 1/ multiplying local energy and pairs it with the huge 1/ multiplying elapsed coordinate time, double-counting the same factor as though it were two independent windfalls rather than one factor and its…
Read the representative guide
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
Published contexts (2)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 54 · Evolutionary Physics
A Horizon Is a Toll Booth, Not a Loophole
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The two calculations agree exactly. This is the covariance check the construction has to pass: [] does not care which energy convention is used, provided the convention is applied consistently — local energy paired with proper time, or Killing energy paired with coordinate time, never a local energy stapled to a coordinate-time integral or the reverse. That last error is precisely the one the naive “free thoughts” argument makes. It takes the huge blueshift factor 1/ multiplying local energy and pairs it with the huge 1/ multiplying elapsed coordinate time, double-counting the same factor as though it were two independent windfalls rather than one factor and its…
Equation guide → · Article →Equation 55 · Evolutionary Physics
A Horizon Is a Toll Booth, Not a Loophole
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
multiplying local energy and pairs it with the huge 1/ multiplying elapsed coordinate time, double-counting the same factor as though it were two independent windfalls rather than one factor and its own reciprocal. Priced honestly, in whichever single currency the experimenter actually holds, the redshift and the blueshift are not two effects. They are one identity, and an identity cannot fund a subsidy.
Equation guide → · Article →