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Equation 17 · Part 3 · A Neutron Star Is a Redshift Standard

superscript

η=(−1.5±2.3±1.5)×10−15\eta=(-1.5\pm2.3\pm1.5)\times10^{-15}
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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.

The passage around this formula

That test would not be a marginal addition to existing equivalence-principle work. The emitting atoms on a neutron-star surface sit in a gravitational potential Φs\Phi_s/c2c^2 of order 0.2 to 0.4 — a QCD-dominated binding environment seven to eight orders of magnitude deeper than anything a terrestrial free-fall experiment reaches. MICROSCOPE’s satellite test of the weak equivalence principle, the most precise ever flown, bounds a titanium-platinum pair’s differential free fall at η\eta=(-1.5±\pm2.3±\pm1.5)×\times10^{-15} [ 13 ] , but at a potential difference near 10^{-10} — many orders shallower than a neutron star’s surface. In the dilaton-coupling framework Thibault Damour and John Donoghue laid…

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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.

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Sources cited in the surrounding passage

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