Quantime — The Tail That Never Touches Zero

Same wavefunction · two axes · two stories

your amplitude |ψ|² your twin's location the value the linear view hides

What you're seeing

Top — linear axis: the familiar picture. The hump is sharp, the rest of the universe looks empty. At your twin's position the curve appears pinned to the floor — apparent detachment.
Bottom — logarithmic axis: the same numbers, plotted by their order of magnitude. Now the tail is a clean descending line (a Gaussian becomes a downward parabola in log-space) that crosses the whole universe and keeps going. It never reaches the floor because there is no floor.
Follow the tail: the zoom marker rides out along the curve. Watch the readout: the exponent keeps growing more negative, the probability keeps shrinking — and stays resolutely above zero, at every distance you can name.

Why the linear view lies by omission

A screen pixel can show maybe 3–4 orders of magnitude of height before the rest is rounding error. A Gaussian tail at 20 standard deviations is already down by ~10⁻⁸⁷; at your twin it's far beyond any notation. No linear plot on any screen — or any sheet of paper the size of the observable universe — could render a mark that short. So the figure shows zero. The mathematics never did.

The Quantime reading — the book's conjecture

If the fundamental object is a single amplitude in configuration space, then "you" and "your twin" are not two wavefunctions that happen to overlap by a vanishing amount — they are one amplitude, thin in the middle. The tail is not a remote possibility bolted onto a separate object; it is the connective tissue that was there all along, buried under emergent distance. Separation is what the amplitude looks like once space has cooled around it. The curve never touching zero is the mathematical signature of a connection that never truly breaks.

Honest caveats

Two, so the chapter can't be ambushed. First, a freely spreading position-space packet does fall off as a Gaussian and is genuinely nonzero everywhere — but a sharp-walled box would force exact zeros at its walls; "never zero" is the rule for smooth, physically realistic potentials, which is the relevant case. Second, "nonzero probability of being 600 light-years away" is a statement about the amplitude, not a claim that you can be detected there without the enormous energy that localisation costs — that cost is the subject of the Convergence page. Here the single, clean point stands: the amplitude is small, never zero, and the linear axis has been hiding it from every reader for a century.

Model notes: ψ(x) is a normalised Gaussian of adjustable width; |ψ|² is plotted linearly (top) and as log₁₀ (bottom). The readout reports the exact tail value at the marker using log-space arithmetic, so it stays accurate far below what floating point could represent directly.