The Alcubierre bubble

The ship sits still in a patch of flat space. Space squeezes in front of that patch and stretches behind it, and the patch is carried along faster than light. Here is the bubble from above, the shape of its wall and the bill for building it.

the ship the bubble, where space is carried contraction expansion negative energy

Controls

The picture is a slice through the bubble, seen from above, with the ship heading right. The wall is drawn thick enough to see; the readout says how thick it really is. Speed only changes the strength of the fields and the bill, not the shape of the wall. The strip at the bottom is the field along the dashed line.

Things to notice

Watch the grid get carried

Leave the grid on "carried" and slide the carry distance up. Every vertex inside the bubble moves as one block and nothing outside moves at all, so the wall squeezes the lines together ahead and pulls them apart behind. That squeeze and stretch is the expansion view, drawn with particles instead of colour.

What the grid is

The ship never breaks the speed limit

Pick the shape view and push the speed to 10c. The flat patch around the ship, where the shape function is 1, does not change at all. Only the wall does any work. Inside, clocks tick at the home rate and nobody feels any push.

Why nothing happens inside

Above c the crew cannot steer

Slide the speed past 1c and a dashed ring appears in the wall. That ring is a horizon: light sent forward from the ship gets no further. The front of the wall is out of the crew's reach, so the pilot's chair is decorative.

Register CON-1

The route has to be laid in advance

Keep the speed above 1c and look at the front wall. The stuff that shapes it is ahead of anything the ship can send, so it cannot be put there from the ship. Someone has to build the track first, at sublight speed.

Register CON-2

A thicker wall is cheaper, and forbidden

Drag the wall thickness up and watch the bill fall: it goes as 1 over Δ. Then look at the bar under the slider. Past the tick the wall is thicker than the quantum inequalities allow at this speed, and the bar turns red.

Register ENE-3

Shrink the bubble, keep the room: the pocket trick

Drag the radius down and the bill falls as R squared. Van Den Broeck's idea is to make the bubble a few femtometres across while the room inside stays 200 m. The readout runs the same formula for that case: about a third of a solar mass for the wall.

Register ENE-4

Do not slow down near anything you like

Set the speed above 1c. Everything the front wall meets on the way gets stuck in it and stays stuck. Slide the speed back below 1c and it all comes out at once, forwards, as a beam of very fast particles aimed at wherever you were going.

Register HAZ-1

What is going on

In 1994 Miguel Alcubierre wrote down a spacetime, not a machine. He chose a shape for the geometry first, a bubble of radius R with a wall of thickness Δ moving at speed vs, and then asked Einstein's equations what matter would be needed to produce it. The answer is the picture above. Space contracts ahead of the bubble and expands behind it, and the ship inside rides along without ever moving faster than light through its own patch of space. The wall has to be filled with negative energy. That last part is the whole problem. The dossier is Alcubierre 1994, and the class it founded is WRP-1.

How much negative energy depends on how thin the wall is, and quantum field theory has a say in that. The quantum inequalities of Ford and Roman bound how much negative energy can sit in one place for how long. Pfenning and Ford applied them to this bubble in 1997 and found the wall can be no thicker than about 10² vs Planck lengths, which makes the total for a 100 m bubble about ten orders of magnitude more than the mass of everything we can see. That is ENE-3. Van Den Broeck's pocket, ENE-4, cuts the bill to a few solar masses by making the bubble tiny and the room inside big. The horizon that stops the crew steering is CON-1 and the need to lay the route first is CON-2. The burst on arrival is HAZ-1.