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Equation 67 · No Particle Without a Cosigner

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pinertial(Ω)p_{\rm inertial}(\Omega)

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pinertialp_{\rm inertial}

Symbol p_rm inertial

0/0 : undefined.

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Ω\Omega

Symbol Omega

Omega is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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An inertial worldline’s Wightman function is the flat-space, two-point function of the free vacuum, whose Fourier transform against e−iΩΔτe^{-i\Omega\Delta\tau} has support only for Ω\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 F˙inertial(Ω)\dot{\mathcal F}_{\rm inertial}(\Omega) = 0 identically for every Ω\Omega>0 , not approximately, not in some limit — exactly zero. The normalization integral ∫0∞\int_0^\infty F˙inertial(Ω′)\dot{\mathcal F}_{\rm inertial}(\Omega')\,dΩ\Omega' is therefore also exactly zero, and pinertial(Ω)p_{\rm inertial}(\Omega) is…
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An inertial worldline’s Wightman function is the flat-space, two-point function of the free vacuum, whose Fourier transform against e−iΩΔτe^{-i\Omega\Delta\tau} has support only for Ω\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 F˙inertial(Ω)\dot{\mathcal F}_{\rm inertial}(\Omega) = 0 identically for every Ω\Omega>0 , not approximately, not in some limit — exactly zero. The normalization integral ∫0∞\int_0^\infty F˙inertial(Ω′)\dot{\mathcal F}_{\rm inertial}(\Omega')\,dΩ\Omega' is therefore also exactly zero, and pinertial(Ω)p_{\rm inertial}(\Omega) is 0/0 : undefined.

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