$$\int_0^\infty \dot{\mathcal F}_{\rm inertial}(\Omega')\,d\Omega'$$

Equation 66 · Evolutionary Physics

No Particle Without a Cosigner

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

An inertial worldline’s Wightman function is the flat-space, two-point function of the free vacuum, whose Fourier transform against $e^{-i\Omega\Delta\tau}$ has support only for $\Omega$<0 — this is nothing more exotic than vacuum stability, the same textbook fact that says an unaccelerated atom in its ground state, coupled to the electromagnetic vacuum, never spontaneously jumps up in energy [ 6 ] . Consequently $\dot{\mathcal F}_{\rm inertial}(\Omega)$ = 0 identically for every $\Omega$>0 , not approximately, not in some limit — exactly zero. The normalization integral $\int_0^\infty$ $\dot{\mathcal F}_{\rm inertial}(\Omega')$\,d$\Omega$' is therefore also exactly zero, and $p_{\rm inertial}(\Omega)$ is…

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