Visualisation
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A wormhole — a throat connecting two distant regions of spacetime — and the one question that decides everything: can anything actually get through?
Send a traveller. Press Send traveller, or drag left and right anywhere on the scene to push a glowing traveller down one funnel, through the throat, and — if the geometry allows — out the far side. The Traveller / time slider does the same by hand.
Switch the model. Einstein–Rosen is the original 1935 bridge: watch the throat pinch shut and trap the traveller. Morris–Thorne is the traversable tunnel: the throat is held open and the traveller comes out the other side. Schwarzschild shows a lone black-hole throat — one-way, ending at a horizon. Shortcut folds a single universe so the two mouths sit side by side.
Throat radius. The slider sets how wide the throat is. It drives the tidal stretch (a narrow throat would rip you apart; a wide one is gentle) and the amount of negative energy required. The scroll wheel does the same.
Toggles. Show or hide the rippling spacetime grid, the far side (second sheet), the exotic-matter ring that props the throat open, the view through the throat inset, and the slow auto-rotation.
An embedding diagram — and why the famous funnel is a picture of curvature, not a hole in space.
The funnel is a trick of drawing. Take the flat sheet of space around the throat and let its curvature push it out of the page into a third direction. That extra height isn't a real dimension you could fall into — it's a way to see how stretched the geometry is. Real space has no funnel poking out of it; what's real is the throat, a region where the distance around a circle stops shrinking as you head inward and starts growing again.
Two sheets, one throat. The upper funnel (near) and the lower funnel (far) are two regions — two different places, or even two universes — that meet only at the throat. Travel down one, through the narrow waist, and you emerge somewhere the long way round might be billions of light-years away.
The throat is the whole story. For the geometry to be a passage rather than a dead end, the circumference has to reach a minimum and flare back out — the flaring-out condition. The Schwarzschild throat technically flares, but it does so behind a horizon and as a dynamic pinch; the Morris–Thorne throat is engineered to flare gently and stay open.
The view through. Look down a real traversable throat and the far region appears as a round, lensed window — light from the other side gathered into a disk. Down a black-hole throat you'd instead see a black circle: the horizon, the edge past which no light returns. The inset shows the difference.
Both are real solutions of Einstein's equations. Only one lets you through — and at a price.
ds² = −e2Φ(ℓ)c²dt² + dℓ² + r(ℓ)²dΩ² · r(ℓ) = √(r₀² + ℓ²)
Two functions set everything. The shape function b(r) bends space into the throat; the redshift function Φ(r) governs time and gravity. A throat exists where r reaches a minimum r₀; it is traversable only if Φ stays finite (so there is no horizon) and the throat obeys the flaring-out condition b′(r₀) < 1 — the funnel must widen as you leave the waist. The example above, r(ℓ)=√(r₀²+ℓ²) with Φ=0, is the simplest such tunnel: the zero-tidal-force Ellis wormhole.
A prehistory. Ludwig Flamm drew the paraboloid embedding of Schwarzschild as early as 1916, months after the solution itself. The name “wormhole” was coined by Misner and Wheeler in 1957, part of Wheeler's geometrodynamics — his dream of building particles, charge and mass out of pure twisted spacetime (“charge without charge”: electric field lines threading a tiny handle, so the mouths look like a + and − charge). That dream faded, but the geometry stayed.
The Einstein–Rosen bridge (1935). Einstein and Rosen noticed the Schwarzschild solution — the geometry of a black hole — can be extended into two exterior sheets joined at the throat. It is exact, textbook general relativity. But it is a fraud as a doorway: in the fully extended (Kruskal) picture the bridge is dynamic. It grows from zero, reaches its widest, and pinches back to zero — and Fuller and Wheeler (1962) showed the pinch-off is so quick that not even a light ray can cross before the throat closes and crushes it at the singularity. The bridge is non-traversable. The deep lesson: a black hole is, in a sense, half a wormhole.
The Morris–Thorne tunnel (1988). Kip Thorne's student Mike Morris took a phone call from Carl Sagan, who wanted a scientifically respectable way to move his heroine across the galaxy in Contact. They ran Einstein's equations backwards: instead of choosing matter and solving for the geometry, they chose a geometry — a throat with no horizon, finite tidal forces, a traveller-friendly tunnel — and asked what matter it would take to hold it open. The answer was unavoidable. To make the throat flare out, the stress–energy at the throat must violate the null energy condition: it needs negative energy density as seen by a light ray — exotic matter.
Does exotic matter exist? A little. The Casimir effect — two mirrors in vacuum — produces a region of genuinely negative energy density, and squeezed quantum states do the same. But quantum inequalities sharply limit how much negative energy you can gather and for how long. No one knows a way to assemble enough, at the scale and stability a macroscopic wormhole needs. And there is a further twist: if you could build one and move one mouth at near-light speed, the wormhole would become a time machine — which is why Hawking floated a chronology protection conjecture that nature quietly forbids it. Unproven, either way.
The time-machine twist. In the same year, 1988, Morris, Thorne and Yurtsever showed how to turn a wormhole into a time machine: take one mouth on a near-light-speed round trip so its clock lags the other's, and the throat now links two different times — a loop into the past. That a shortcut through space is almost automatically a shortcut through time is why physicists take the exotic-matter barrier so seriously: it may be the universe's way of keeping cause before effect. Whether quantum gravity actually slams the door — Hawking's 1992 conjecture — is one of the open questions this whole subject hangs on.
Order-of-magnitude figures — the kind that turn “you'd need exotic matter” into something you can feel.
The exotic-energy bill. Roughly, holding a throat of radius b₀ open takes negative energy with a mass-equivalent of order |E|/c² ≈ (c²/G)·b₀. That scales straight up with size: a 1-metre throat needs about Jupiter's mass in negative energy; 1 km needs about the Sun's; 1 AU needs roughly a billion Suns; and a 1-light-year throat needs about a whole galaxy's worth. There is no small wormhole and no cheap one.
But you can't use the small ones. Tidal forces at the throat go as ≈ c²/b₀². Across a 2-metre body that is about 1016 g for a 1-metre throat — instant spaghetti — and stays lethal until the throat is roughly an astronomical unit wide, where it finally drops below 1 g. So a survivable wormhole must be planet-to-AU scale, which pushes the energy bill toward the mass of a galaxy. The two requirements fight each other.
And the cupboard is nearly bare. The one place we make real negative energy — the Casimir gap between two plates a micron apart — yields about −10−4 joules per cubic metre. A metre-scale throat needs an energy density near 1044 J/m³ of the opposite sign. That is a shortfall of some forty-odd orders of magnitude, and quantum inequalities (Ford–Roman) say you can't simply pile the negative energy up: borrow a lot and you must pay it back fast. Use the Real scale chips in the panel to watch these numbers move.
Estimates use |E|≈(c²/G)·b₀ and tidal ≈ c²/b₀²; exact prefactors depend on the wormhole's shape and redshift functions, but the scales — and the gap to anything we can build — are robust.
The same honest line as the rest of the site, drawn in plain sight.
The geometry here is real general relativity: both wormholes are genuine solutions of Einstein's equations, and the throat, the two sheets and the flaring waist are drawn from their actual metrics. The liberties are all about display — the funnel is an embedding aid, the throat radius is dialled to human scale, and the playback is slowed. The one thing this visualisation never softens is the verdict: the bridge pinches shut, and the tunnel needs matter no one has ever made.
| Feature | Tier | What that means |
|---|---|---|
| Embedding profiles — Ellis throat r(ℓ)=√(r₀²+ℓ²); Flamm paraboloid z=2√(r₀(r−r₀)) | T1 Established | Exact embeddings of the spatial geometry of the Morris–Thorne and Schwarzschild solutions. Sets the shape of every funnel on screen. |
| The Einstein–Rosen bridge is a solution of GR | T1 Established | The maximally extended Schwarzschild geometry (Kruskal), two exterior sheets joined at a throat — exact, since 1935. |
| The bridge pinches off before light can cross → non-traversable | T1 Established | The dynamic throat of Kruskal spacetime (Fuller & Wheeler, 1962). A real, rigorous result, not an artistic choice. |
| A traversable throat requires exotic matter (null energy condition violated) | T1 Established | A theorem: the flaring-out condition at the throat forces ρc² + pr < 0 there. Morris & Thorne, 1988. |
| Tidal force ∝ 1/r₀²; no horizon ⇒ redshift stays finite (Morris–Thorne) | T1 Established | Direct from the metric. A wide throat is gentle; a horizon-free throat has no infinite-redshift surface to trap you. |
| Real-scale figures: negative energy ≈ planet→galaxy mass; tidal across 2 m; Casimir ≈ 10⁻⁴ J/m³, ~40+ orders short | T3 Stylised | Order-of-magnitude estimates (|E|≈(c²/G)·b₀, tidal≈c²/b₀²). Exact prefactors depend on the shape & redshift functions; the scales and the Casimir gap are robust. |
| On-canvas labels and the live metric/formula box | T1 Established | They name the real parts of the geometry and print the actual metric for the chosen model; only the funnel they annotate is an embedding aid (below). |
| Whether exotic matter exists in the amount/stability a macroscopic wormhole needs | T2 Open | Casimir & squeezed states give tiny, real negative energy; quantum inequalities limit it. No known route to enough, at scale. Genuinely unsettled. |
| Wormhole as a time machine; chronology protection | T2 Open | Moving one mouth relativistically would create closed timelike curves. Hawking conjectured quantum effects forbid it — unproven. |
| View-through-the-throat lensing window | T3 Stylised | The far region really would appear as a round, lensed disk (and a black hole as a dark one); the inset sketches that, it is not a ray-traced image. |
| The funnel as a 3-D surface; rotation; flowing grid; the "fold/shortcut" picture | T4 Illustrative | Space is not literally a surface in a higher dimension. The funnel faithfully shows the intrinsic curvature; the extra height, the spin and the folded sheet are drawing aids. |
| Throat radius set to human scale; slowed playback / "travel time" | T4 Illustrative | Dialled so the throat and the crossing are visible. The real sizes and timescales depend entirely on the (unknown) source. |
In one line: the geometry, the pinch-off and the exotic-matter requirement are exact, established physics; only the funnel picture, the throat size and the playback speed are dialled up so you can see what the equations are saying.