Controls
The picture is an embedding diagram: one slice through the tunnel, drawn as a surface so you can see its shape. Up and down are not directions in space, only a way of showing how the tunnel narrows to the throat and opens out again on the far side. The dashed ring is how wide the throat has to be for a person to pass at this speed and feel no more than one g of tidal stretch.
Mouth B is carried away and brought back. Its clock runs slow on the trip, by the usual factor gamma. The tunnel is short, so it joins the two mouths at equal readings of their own clocks. The diagram is a spacetime diagram: space across, home time up, with the gap between the mouths not to scale. Press play and the trip runs in about eight seconds, both dials turning as it goes.
Things to notice
The throat bound grows with speed
In the throat view set the speed to 0.01c. The dashed one-g ring sits at 1,000 km for the Ellis tunnel and at 500 km if you switch to Morris and Thorne's own shape, the register's number. Slide the speed to 0.1c and both grow tenfold. The ring scales as γv.
Register HAZ-3Bigger is safer and dearer
Slide the throat radius up. The tension at the throat falls, but the mass of negative-energy matter needed to hold it open grows in step with the radius: about 170 suns' worth at 500 km, about 3,400 at 10,000 km.
Register STA-2One trip makes a time machine
Switch to the time machine, set 0.9c and one year. Mouth B comes home 0.56 years younger than mouth A, and the tunnel now leads 0.56 years into the past. Nothing on the diagram ever moves faster than light.
Register CAU-3Watch the clocks drift apart
In the time machine view press play. Mouth B climbs its V on the diagram while A's dial turns at the home rate and B's at 1/γ of it, so the gap between the two readings opens on the way out and keeps opening on the way home. When B lands the crossing arrow appears, and its height is the lag the two dials now show.
Why no FTL is neededThe twin paradox does all the work
Push the trip speed toward 0.95c: the offset climbs toward 69 percent of the trip time. The whole effect is ordinary time dilation plus a tunnel that keeps the two clocks in step. That is why every wormhole owes this bill.
Why no FTL is neededThe conjectured stop
Hawking's chronology protection: as the loop is about to close, the energy of quantum fields piles up on the edge of the time-travel region and the back reaction shuts it. Set any offset you like on the diagram; this is the claim that the last step never happens. A conjecture, not a theorem.
Register CAU-2It cannot be a shortcut at all
Topological censorship: if the averaged null energy condition holds, no wormhole beats the outside route. The tunnel drawn here is a shortcut, so it needs a violation no known field supplies. The modern traversable wormholes obey the theorem by being long, and the time-machine step fails on them.
Register ENE-7What is going on
Morris and Thorne, in 1988, wrote down the tunnel a traveller would want, a throat with no horizon and gentle tides, and asked Einstein's equations what would have to be inside it. The answer is matter with negative energy density along the light rays that thread the throat, which they called exotic matter. Nothing known supplies it, and the amount grows with the size of the throat. That is STA-2 in the register. The size of the throat is set by comfort: one Earth g of tidal stretch across a two-metre body, which bounds the tidal terms at the throat by about (108 m)-2 and gives a throat radius that scales with the speed of the crossing, about 500 km at one percent of light speed for their design shape. That is HAZ-3.
Within the year, with Yurtsever, they showed that any such wormhole is a time machine with an assembly step: carry one mouth away at high speed and bring it back, and its clock lags the other by T(1 − 1/γ), while the tunnel still joins the mouths at equal clock readings. Walk in at the mouth that travelled and you step out of the other one in the past. That is CAU-3. Hawking's reply in 1992, chronology protection, CAU-2, conjectures that quantum back reaction stops the loop from ever closing. And a theorem of Friedman, Schleich and Witt from 1993, with the averaged null energy condition proved for the geodesics it needs between 2007 and 2017, says a wormhole in ordinary flat surroundings cannot be a shortcut at all: that is topological censorship, ENE-7. The traversable wormholes built since 2017 by Gao, Jafferis and Wall and by Maldacena, Milekhin and Popov obey it by being longer inside than the way round, which is also why they cannot be turned into time machines.