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

Gravitational waves 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. 2

Gravitational waves 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 detected (2015) the signal from two black holes (both about 30M) colliding. This event radiated about 3M  of energy-equivalent in about 10 millisec. Its peak power output was about 9.5x1022L, or 100 x the luminosity of the entire visible Universe! Three (probably four) mergers have been observed. The rapid detection of these events suggest black holes are more common than thought, and could possibly account for dark matter (despite the large amount of theoretical models and data suggesting that MACHOs are relatively rare). LISA (Laser Interferometer Space Antenna) is a similar concept, using a constellation of satellites. Launch in the 2030s? 3

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 4

Einstein-Rosen (ER) 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 5

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 6

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. Mass Energy Pressure Exotic matter negative negative negative Matter positive positive positive Antimatter positive positive positive Dark matter positive positive? positive? Dark energy zero? positive negative 7 7

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 8

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 9

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 10

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 11

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. The warp bubble and its enclosed object, therefore, move at arbitrarily high speeds. 12 12

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 13

Quantum Mechanics—Review… Remember how Schrödinger and quantum argued that unmeasured aspects of objects do not have values? That objects really exist as probability distributions (wavefunctions)? And that they exist in a simultaneous superposition of all possible states? (Hence Schrödinger’s cat…) They argued that the moment of observation collapsed the wavefunction into a fixed value…and their ideas work!

“spooky action at a distance” Quantum Entanglement Einstein, Podolsky, and Rosen (EPR) opposed quantum and its probability distributions, feeling that there were hidden variables that quantum just didn’t handle properly. EPR noted that if you believed in quantum, you could get systems that were “entangled.” Also, you could affect things at a distance, hence: “spooky action at a distance” The key to understanding entanglement is the notion that, somehow, something’s wavefunction can be forced to collapse to a specific value. Entanglement has been repeatedly demonstrated in labs. It is real. The transmission of information like this is called quantum teleportation, but it is completely different from what you might think of as a “teleporter.”

Physics and locality There is NO resolution to this. No one understands how this works. Most physicists prefer Niels Bohr’s approach to this problem—fuggedaboudit! It seems that somehow, physics suggests that in some cases, laws can act in violation of “locality”—that things can affect each other instantly, across arbitrarily large amounts distances in space. People love talking about quantum entanglement, but hardly anyone understands what they’re talking about…

It gets worse…. Suppose two particles are entangled. Then you observe the state of second particle, but you don’t tell anyone your observation. Then really, you aren’t collapsing the wavefunction of anything—you’re just entangled with the second particle, too. And anything interacting with you becomes entangled. The Universe consists of an infinite number of entanglements. It’s like the infinite number of entangled elements of the Universe are connected by entanglement-connectors, whatever THOSE are…

ER=EPR? Here is a possible resolution to the EPR problem. It appears that general relatively would allow a solution to the locality issue…if an Einstein-Rosen (ER) wormhole connected entangled objects. This would explain why locality seems violated, but really isn’t—the ER bridge connects the two entangled objects. Indeed, the Universe would be a seething mass of wormholes, connecting the infinite number of entanglements. Does this mean exotic matter exists to stabilize these wormholes? I have not read anyone addressing that issue.

Or does space not exist? What if space doesn’t really exist. Instead, the Universe consists of all the particles of matter—space does not exist—but the particles all interact with each other with varying amounts of force. In order to make sense of this, we interpret the differing force-strengths as corresponding to different “spatial distances.” We say that weakly interacting particles are separated by “large distances”, while strongly interacting particles are “close to each other.” “Space” would simply be a useful fiction, that is a misinterpretation of other processes. If true, space is similar to “temperature” or “pressure”—a derived quantity that depends upon some underlying reality…a fiction, however useful, but a fiction nonetheless.

Concepts of spacetime Newton Space is an empty stage. Einstein’s Special Relativity Space and time are linked into spacetime. Einstein’s General Relativity Spacetime can be warped. Quantum Space is flat, and is filled with particles mediating forces String Theory There might be seven additional, curled up dimensions of spacetime. If gravity is quantized, then space might be quantized on a Planck scale. Nonlocality/Quantum entanglement Space might simply be a misinterpretation of something else. 20 20