Equation 13 · Part 1 · No Particle Without a Cosigner
Symbol Omega
What this part means
conjugate to that same proper time.
Its job in the formula
Omega is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol Omega→Article meaning
Where the article explains it
Second, is conjugate to that same proper time; it is an energy gap measured in the detector’s own instantaneous rest frame, not a coordinate-frame frequency.
The passage around this formula
…is proper time — the detector’s own clock, the only time variable with unambiguous physical meaning for a single worldline — never the coordinate time of whatever chart the trajectory happens to be written in. Second, is conjugate to that same proper time; it is an energy gap measured in the detector’s own instantaneous rest frame, not a coordinate-frame frequency. Third, the field state enters only through W , and changing the field state — the ordinary vacuum, a thermal state, the Boulware,…
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Sources cited in the surrounding passage
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