Equation 143 · Part 4 · The Entry a Relabeling Cannot Write
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
Cosmology removes the Killing vector altogether rather than merely complicating it. The Friedmann-Lemaître-Robertson-Walker spacetime describing the large-scale universe has no timelike Killing vector in comoving coordinates: its metric depends explicitly on time through the scale factor, and no coordinate change removes that dependence globally. There is consequently no analog of the ADM or Bondi construction supplying a global conserved energy for, say, the universe’s total photon population. A single photon’s cosmological redshift is the precise observational face of that absence: its frequency, and with it its energy, decreases as the universe expands, and this is exactly what an absent…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.