General relativity · spacetime · clocks

Wormholes & Time

Tunnels through space, holes that only give, and clocks that disagree. One of these is proven every day; the others are honest maths with no sighting yet.

1935Einstein–Rosen bridge
1988a crossable wormhole
38 µsGPS clocks gain each day
0white holes seen

A tunnel through space

Mass curves space. Draw a slice of the space around a black hole and it dips into a funnel; Einstein's equations also allow a second funnel joined to the first at a throat. That is a wormhole: a short cut between two distant places, or two universes.

pinches

kind

0.70 r

throat

can you cross

throat

Each sheet is a slice of space; the funnel shape is how curved it is. Einstein and Rosen's bridge pinches shut faster than light could cross. Morris and Thorne's is held open, but only by matter with negative energy.

z: how far the funnel has dipped, the height in the drawing
r: distance from the centre
rₛ: the throat radius, the narrowest point

Nobody has found a wormhole. A crossable one needs matter with negative energy density. Tiny amounts of negative energy are real (the Casimir effect between metal plates), but no one knows whether enough could ever be gathered.

White holes

The equations of gravity work the same backwards in time. Reverse a black hole and you get a white hole: nothing can ever fall in, and matter and light pour out. They are a valid solution, and some think the Big Bang or the last stage of an evaporating black hole looks like one. None has been observed.

yes

can get in

never

can get out

Run a black hole's film backwards and you get a white hole: matter and light pour out of its horizon and nothing from outside can get in. General relativity allows it; no one has ever seen one.

Time travel

Travel into the future is real and measured. A fast clock ticks slower, and so does a clock deep in gravity. An astronaut moving close to light speed comes home younger than their twin. Travel into the past is a different matter: some solutions allow it (Gödel's universe, wormholes with one mouth moved fast), and most physicists expect quantum effects to forbid it.

60.0 %

traveller rate

6.00 yrs

10 yrs at home

0.800 c

speed

This is not a theory waiting for proof: GPS satellites correct for both effects every day, and in 1971 atomic clocks flown round the world came back out of step by the predicted amount.

Δt′: time that passes for the traveller
Δt: time that passes at home, far away and at rest
v: the traveller's speed
c: the speed of light, 299 792 km/s
r, rₛ: distance from a mass and its Schwarzschild radius

Timeline

1916
Karl Schwarzschild solves Einstein's equations for a point mass. Ludwig Flamm notices the solution joins two regions of space.
1935
Einstein and Nathan Rosen describe the bridge between them: the Einstein–Rosen bridge.
1949
Kurt Gödel finds a rotating universe in which you can travel into your own past.
1957
John Wheeler names them wormholes.
1962
Wheeler and Robert Fuller show the Einstein–Rosen bridge pinches off too fast for even light to cross.
1971
Hafele and Keating fly atomic clocks round the world; they come back out of step exactly as relativity predicts.
1988
Michael Morris and Kip Thorne describe a wormhole you could cross, held open by exotic matter with negative energy.
1992
Stephen Hawking proposes chronology protection: physics stops anyone building a time machine to the past.

Sources

A. Einstein, N. Rosen, “The particle problem in the general theory of relativity”, Phys. Rev. 48 (1935) 73
M. S. Morris, K. S. Thorne, “Wormholes in spacetime and their use for interstellar travel”, Am. J. Phys. 56 (1988) 395
J. C. Hafele, R. E. Keating, “Around-the-world atomic clocks”, Science 177 (1972) 166
S. W. Hawking, “Chronology protection conjecture”, Phys. Rev. D 46 (1992) 603