1. Wormholes and space warps Topics Ripples in space Wormholes Time warps Space warps Motivation A few spacetime oddities. 1

2. The structure of spacetime is determined by the distribution of matter. Changes in the distribution of matter results in changes to spacetime. Non-spherically symmetric objects, such as dumbbells or binary stars, if accelerated, will create disturbances in spacetime called gravitational waves. A consequence of a passing gravitational wave would be to start a ring of particles into motion. Gravitational waves 2

3. Detectors Joseph Weber built 1 m diameter aluminum bars 2 m long, and looked for gravitational waves in the 1960s (ultimately unsuccessfully). LIGO (Laser Interferometer Gravitational-Wave Observatory) is a pair of giant interferometers in Washington and Louisiana. It ran 2002-2010 but did not produce any detections. It is being upgraded for 2015. LISA (Laser Interferometer Space Antenna) is a similar concept, using six satellites. This was cancelled, but a smaller version with three satellites is under consideration. Gravitational waves 3

4. Spacetime wormhole The name “wormhole” was coined by John Wheeler in 1957 to describe an alternate pathway through spacetime. General relativity does not forbid the formation of wormholes, nor does it insist or even prove they exist. However, general relativity does allow mathematical solutions of the Einstein field equations that involve wormholes. 4

5. Einstein-Rosen bridge The first mathematical description of wormhole spacetime geometry was discovered by Albert Einstein and Nathan Rosen (1935), hence the “Einstein-Rosen bridge.” Wheeler (1962) found that the Einstein-Rosen bridge was unstable. While energy or matter could enter the wormhole at one end, the wormhole connection would pinch off so quickly that not even light could make the journey from one end to the other. 5

6. Stable wormholes In 1988, in part because of free-wheeling theorizing encouraged by Carl Sagan, Kip Thorne and Mike Morris proposed a new solution for a wormhole; in this new formulation, matter was used to fill spacetime in the narrow wormhole throat. The result of this trick was to stabilize the wormhole so it became traversable. The catch is that the stuff you use to line the wormhole is exotic matter. 6

7. What is exotic matter? This kind of exotic matter (there are others) has negative mass, and as a result, a negative energy and a negative pressure. MassEnergyPressure Exotic matter negativenegativenegative Matterpositivepositivepositive Antimatterpositivepositivepositive Dark matterpositivepositive?positive? Dark energyzero?positivenegative 7

8. What is exotic matter? Gravity would be repulsive to negative mass. A force acting upon the negative mass would make it accelerate in the opposite direction than expected from Newton’s Laws. Exotic matter is purely a mathematical oddity, but there is nothing in physics that says it cannot exist…except for the complete lack of experimental evidence. 8

9. Creating a wormhole There is no known way to create a wormhole—even the most outrageously speculative studies of the concept consider only stabilizing an already-existing wormhole. One possibility is that you might somehow find a micro-wormhole in the Planck-size spacetime foam, if the foam exists (with micro-wormholes) and is not overly quieted by string theory effects. Such a micro-wormhole could be enlarged (via magic) to macro scales, and stabilized. 9

10. Wormholes and time travel When a wormhole is created, both ends link to time normally. Suppose you hold one end of the wormhole stationary in your frame, but manipulate the other end so it experiences time more slowly because of relativistic effects. 1) You move the other end at near-light speeds, so special relativistic time dilation occurs. 2) You could lower one end of the wormhole to near the surface of a black hole, or whip it around in an accelerating circle. The far end will experience time at a slow rate because of general relativity. 10

11. Wormholes and time travel While your end of the wormhole is attached to the present, the far end of the wormhole is now attached to the past. A wormhole, properly arranged, could be a time machine to the past—to a time as far back as when the wormhole was initially formed. 11

12. Alcubierre metric Alcubierre solved the field equations in a novel way. He developed a specific space warp and asked how it could be formed. (Instead of asking how matter warps space.) He developed a warp bubble in which space is curved symmetrically around it. Space is contracted in front of the object, and shrunk behind it. 12 The warp bubble and its enclosed object, therefore, move at arbitrarily high speeds.

13. Alcubierre metric In addition to the usual comments that this is strictly hypothetical, exotic matter is, again, needed to stabilize this structure. Similar to wormholes, it appears that one cannot create the warp bubble; rather one might have to be harvested from the spacetime foam. The nature of this metric is highly controversial. Many potentially critical flaws in the metric have been noted, which may or may not be valid. 13