Theory · Intermediate · 2:25

Wormhole

A tunnel through space: how one could be held open, and what it would look like

Below are the 11 chapters of this simulation in Cosmic Scale: each one's caption, then the fuller explanation the app shows under “Read more”. Colours, arrows and lines mentioned in the text belong to the 3D scene in the app.

Open Cosmic Scale then the What if tab

1. A shortcut through space

A wormhole would be a tunnel through space joining two far-apart places. General relativity allows the shape, but no one has ever seen one. From outside it would look like a ball holding another sky.

Einstein's equations of gravity do not forbid it. In 1935 Einstein and Rosen found a “bridge” joining two regions of space, and in 1957 Misner and Wheeler named such tunnels wormholes, after the shortcut a worm bores through an apple between two points on its skin.

This is the simplest kind that could be passed through, found by Homer Ellis and Kirill Bronnikov in 1973. It has a shape but no pull: nothing inside it drags or stretches you. Its narrowest part, the throat, is a sphere, and on both sides space opens out flat.

Every ray of light in this picture is followed through the wormhole's geometry, as general relativity says. The wormhole itself is theory: nothing seen in the sky points to one existing.

2. Two mouths, one throat

Draw space as a sheet and a wormhole is a neck joining two sheets. Its narrowest part, the throat, is 2.0 km across here: the size of the wormhole in the film Interstellar.

The picture in the corner is a common trick. To show how space curves, one direction is dropped and what is left is drawn as a curved surface, every point of it standing for a circle of space. The surface of this wormhole is a catenoid, the shape a soap film takes between two rings: narrowest in the middle, flaring out to flat space on both sides.

The gold dot is you. The extra direction is only a drawing aid; nothing in the theory needs space to bend into it. One number sets the wormhole's size, the radius of its throat, and it decides how everything else looks. Kip Thorne and Christopher Nolan chose 1 km for Interstellar's.

Far from the throat, the tunnel has almost no effect: a sphere there has nearly the area a sphere has in flat space. That is why, from far off, each end looks like ordinary space with a round hole in it.

3. What holds it open

Left alone, a tunnel like this would pinch shut before anything could cross. Morris and Thorne showed in 1988 that only matter of negative energy could hold it open. It is drawn in violet.

Ordinary matter makes gravity pull things together. To keep a throat open, gravity there has to push outwards, and that takes matter whose energy is below zero, called exotic matter. It would have to fill the space round the throat, thickest at the middle and thinning out with distance.

The first tunnels found, Einstein and Rosen's bridges, are really black holes seen from both sides, and they pinch off faster than light can cross, as Fuller and Wheeler showed in 1962. Morris and Thorne turned the problem round in 1988: pick the tunnel you want, then work out what would have to fill it.

The question came from a novel. Carl Sagan, writing Contact, asked Thorne for a way his heroine could cross the galaxy without breaking physics, and Thorne and his student Mike Morris answered with wormholes. The violet glow is drawn: no one knows how such matter would be arranged.

4. Negative energy

Does negative energy exist? A very little: between two metal plates a micrometre apart the vacuum's energy is below zero, the Casimir effect. This wormhole would need 1 × 10⁴⁰ times more.

In 1948 Hendrik Casimir predicted that two uncharged metal plates, very close together in a vacuum, would be pushed towards each other by the way they change the vacuum's quantum fluctuations. Between them the energy density is below zero. Lamoreaux measured the push in 1997, and Mohideen and Roy in 1998 to within one per cent.

It is real, but tiny. At a gap of a micrometre the density is about −4 × 10⁻⁴ joules per cubic metre. A wormhole 1 km in radius would need about −5 × 10³⁶ at its throat, and about one Sun's mass of negative energy in all: roughly a Jupiter's mass for every metre of throat radius.

Quantum theory also limits how much negative energy can be gathered and for how long, as Ford and Roman showed in the 1990s. Whether nature lets matter be arranged this way at all is unknown, and it may simply forbid it.

5. Growing a throat

Wheeler guessed in 1955 that space is a froth of tiny wormholes. To catch one and blow it up to 2.0 km across would take a leap of about 6 × 10³⁷ times. The growth is drawn.

Wheeler suggested that at the smallest sizes, near the Planck length of 1.6 × 10⁻³⁵ m, space is not smooth but foams, with bubbles and handles opening and shutting all the time. Some of those handles would be wormholes, far too small to matter and gone in an instant.

Morris and Thorne, and later Matt Visser, wondered whether a civilization far beyond ours could catch one and inflate it. No known process does. A newer idea, called ER=EPR (Maldacena and Susskind, 2013), says that two particles entangled with each other are joined by a tiny wormhole; it is a conjecture, not a result.

In 2022 Google's quantum computer ran a model of a wormhole's behaviour (Jafferis and others, in Nature): a signal put in at one end came out the other, as the theory says. But it was a simulation on a few qubits of a simplified toy of quantum gravity. No space was pierced.

6. The recipe, in order

Put together, a wormhole would be made in four steps: catch a tiny one from the quantum foam, blow it up to 2.0 km across, thread it with negative energy, and keep it steady. The recipe is imagined from physics: every step is beyond us, and the last two may be forbidden.

1. Catch a tiny wormhole. At the Planck length, 1.6 × 10⁻³⁵ metres, space may foam with tiny handles, as Wheeler guessed in 1955, or entangled particles may be joined by wormholes (ER=EPR, 2013). Nothing shows that either is a thing one could take hold of.

2. Inflate it. A throat 1 km in radius is 6 × 10³⁷ times wider than the Planck length. No known process grows a wormhole; Morris and Thorne imagined a civilization far beyond ours doing it.

3. Fill it with exotic matter. The throat needs about one Sun's mass of negative energy, most of it round the throat: some 10⁴⁰ times the Casimir effect's density, in an arrangement no known matter takes.

4. Keep it steady. Shinkai and Hayward showed in 2002 that a disturbed throat either collapses into a black hole or blows up, so it would need active control. Each step is a requirement of the mathematics, not a machine.

7. What it would look like

From outside it would be a ball of sky from another place. It has no mass to pull, but its shape bends light: stars behind it are pushed apart, and at its edge the far sky is squeezed into thin bright rings.

Light takes the shortest paths through curved space. A ray aimed at the middle of the throat goes straight through; one that just misses the edge is bent round it, and some go round and round before leaving. This picture follows every ray as general relativity says. The team behind Interstellar did the same (James and others, 2015).

The wormhole's negative energy would act as a lens that pushes light apart. In 1995 Cramer and colleagues suggested that one passing in front of a distant star would make it brighten in a pattern no ordinary mass produces. Searches for it have found nothing.

The other sky is drawn: that end could open anywhere. Here it is another galaxy, so that the two skies can be told apart.

8. Flying through

Aim at the middle and you pass straight through. Ahead, the ball of the other sky opens out until it is everywhere. At the throat, half the sky around you is each place. Nothing pulls on you.

In this wormhole nothing drags on you: it has no gravity to speak of, and none of the tides that would stretch you near a black hole. All you notice is the sky changing. The throat is where the view splits: half of it is the place you left, half the place you are going to.

Watch the rim of the ball as you close in. Light that grazes the throat circles it several times before it reaches you, so rings of the same stars are repeated, thinner and thinner, one inside the next. The flight here is speeded up.

At a jet airliner's speed, about 250 metres a second, you would cover the last kilometre before the throat in four seconds. The passage feels more like a change of scene than a fall.

9. The other side

Out of the far end, turn round: the place you came from is now a ball of sky behind you. A wormhole has two mouths, and each looks the same from its own side.

The far mouth is just as round and just as small. Seen from it, the mouth you left is a ball holding a piece of our sky, bent the same way. Nothing tells you which end is which.

Where the far mouth sits is the wormhole's own business. It could be next door, on the far side of the galaxy or, as some have imagined, in another universe: the equations do not say. That is the point of the idea. The distance along the tunnel has nothing to do with the distance outside, so a short tunnel could join places light-years apart.

10. A time machine?

Take one mouth on a fast round trip and its clock falls behind the other's; step through and you come out earlier. Morris, Thorne and Yurtsever showed this in 1988. Hawking argued in 1992 that nature prevents it.

Time runs slower for something moving near the speed of light. Take one mouth on a fast round trip and bring it back beside the other, and their clocks now disagree by whatever time the trip saved. The mouths are at different times but in the same place.

Go in at the later mouth and you come out of the earlier one: a path back in time, and a loop in which you could meet yourself. That is a closed timelike curve, the thing time-travel stories need. Morris, Thorne and Yurtsever pointed out in 1988 that a wormhole, once made, could be turned into one.

Stephen Hawking proposed in 1992 his chronology protection conjecture: quantum fluctuations of the vacuum would pile up just as the machine became possible, growing without limit and destroying the wormhole first. Calculations so far agree, but no one has a full proof.

11. Has anyone seen one?

No. Wormholes have been sought in starlight, in gravitational waves and near our galaxy's black hole, and every search has come back empty. It stays an idea that general relativity allows, not a thing we know exists.

Lensing searches have found no star brightening the way a wormhole should. When two black holes merge, a wormhole in their place would send gravitational-wave echoes; searches in the LIGO, Virgo and KAGRA data have found no convincing sign of them.

The images of the black holes in M87 and in our own galaxy, made by the Event Horizon Telescope, agree with black holes. They cannot yet rule out every alternative, but nothing in them needs a wormhole.

So a wormhole stays where it began, in the equations. What it has taught us is real all the same: how space can be shaped, and how much of the possible is held back by the need for negative energy.

Objects in this story

• Sagittarius A* — Supermassive black hole
• M87* — Supermassive black hole