Wormhole Throat Geometry (2D)

Live readout

Throat length

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Long way

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Shortcut factor

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State

idle

Adjust the throat, then launch a light ray to compare the wormhole shortcut with the long way around.

Throat geometry

Throat radius b₀ 1.00

Flare length Z 5.0

Comparison & motion

External separation D 120

Ray speed 1.0×

Presets

How it works

The curve is a Morris–Thorne embedding: a static, spherically symmetric traversable-wormhole slice embedded in flat 3D so its shape becomes visible. With throat radius b₀ the simplest such profile is:

r(z) = √( z² + b₀² ),  −Z ≤ z ≤ Z
r'(z) = z / √( z² + b₀² )

At z=0 the radius is minimal (r=b₀, the throat); away from the throat r(z) grows and flattens toward each mouth's asymptotically flat region — exactly the two-funnel-joined-by-a-neck shape drawn here. A light ray moving along a meridian (fixed angle, varying z) is a geodesic of this surface of revolution, so its physical path length through the wormhole is the true arc length:

s = ∫[-Z,Z] √( 1 + r'(z)² ) dz   (computed numerically, Simpson's rule)

That is compared against an external separation D — the ordinary-space distance you would have to travel to get from one mouth to the other without using the wormhole. When D ≫ s (its usual regime here), the wormhole is a genuine shortcut: both rays launch at the same instant and travel at the same speed, but the through-wormhole ray arrives after time s/v while the long-way ray needs D/v.

⌨️ Space — pause/resume · R — reset · L — launch ray.