← All parts of this equation

Equation 70 · Part 2 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol c^2

mop=ℏc2 ∂Δϕ∂Δτ,mop[LG]=ℏ ∂Φ∂(b⋅v).m_{\rm op}=\frac{\hbar}{c^2}\,\frac{\partial\Delta\phi}{\partial\Delta\tau},\qquad m_{\rm op}[\mathcal L_{\rm G}]=\hbar\,\frac{\partial\Phi}{\partial(\mathbf b\cdot\mathbf v)}.
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Before pointing this construction at an interferometer, one methodological trap needs naming. A single measured phase Φ\Phi at one fixed loop area cannot, by itself, distinguish m from an unknown additive offset baked into the apparatus — any constant phase shift from an uncalibrated pulse timing, an unaccounted path-length difference, or a stray field looks identical to a rescaling of b\mathbf b⋅\cdotv\mathbf v . The estimator that survives this is a derivative, not a snapshot: mop=ℏc2 ∂Δϕ∂Δτ,mop[LG]=ℏ ∂Φ∂(b⋅v)m_{\rm op}=\frac{\hbar}{c^2}\,\frac{\partial\Delta\phi}{\partial\Delta\tau},\qquad m_{\rm op}[\mathcal L_{\rm G}]=\hbar\,\frac{\partial\Phi}{\partial(\mathbf b\cdot\mathbf v)}. The sign convention on the proper-time form follows the phase of a free relativistic particle, Δ\Deltaϕ\phi=-mc2c^2Δ\Deltaτ\tau/ℏ\hbar , so that m_{\rm…

Read this part in the article →

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 →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.