Equation 132 · Part 4 · The Clock That Comes Back Wrong by Exactly Its Mass
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
This is where the operational construction earns or loses its claim to be a mass gauge rather than a definition with no experimental content. Distinguish two separate clauses of Einstein’s equivalence principle. The weak equivalence principle protects the laser/center-of-mass term, forcing it to be mass-independent; that is not this paper’s target, and no version of challenges it. Local position invariance — the universality of clock rates across spacetime position — is the clause the internal-energy term actually probes, and it is a logically separate statement, untouched by the weak equivalence principle’s guarantee. The kill criterion for this whole construction is now…
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
- [9] Gravitational Redshift in Quantum-Clock Interferometry ↗
- [13] Gravitational Redshift Tests with Atomic Clocks and Atom Interferometers ↗
These citations provide research context; check each source for the exact claim it supports.