I'm wondering, has anyone read
Black Holes & Time Warps by theoretical physicist, Kip Thorne?
In the glossary at the end, Kip Thorne defines "spacetime curvature" as:
The property of spacetime that causes freely falling particles that are initially moving along parallel world lines to subsequently move together or apart. Spacetime curvature and tidal gravity are different names for the same thing.
Black Holes & Time Warps defines "spacetime" as:
The four-dimensional "fabric" that results when space and time are unified.
...while "tidal gravity" is defined as:
Gravitational accelerations that squeeze objects along some directions and stretch them along others. Tidal gravity produced by the Moon and Sun is responsible for the tides of the Earth's oceans.
The Elegant Universe defines "spacetime" as:
A union of space and time originally emerging from special relativity. Can be viewed as the "fabric" out of which the universe is fashioned; it constitutes the dynamical arena within which the events of the universe take place.
When you think of space and time and their respective definitions, you can understand that these two concepts are extraneous, where neither really mean anything "real" or "tangible." They are concepts used by scientists for measurements in experiments and conceptual thought. It's more convenient to think of the "spacetime continuum" as proposed by Einstein's general relativity than to ponder for long hours over the definition of what this really might mean. With this in mind, people can move forward and derive various theorems using mathematical formulae and experiments, to gain a better idea as to how nature and "reality" really work. This is why the most common analogy of the geometric curvature of space is of a type of mass that bends and curves a type of sheet (example, a suspended rubber membrane warped by the weight of a bowling ball in its center).
Black holes are thought to be an extreme point of general relativity in which mass/energy densities warp spacetime in such a way that the escape velocity (the velocity needed to escape from the object mass) becomes greater than that of the speed of light. They are thought to be created by massive stars greater than 1.4 solar masses that have expended all possibilities of further nuclear reactions and that have a greater gravitational attraction than can be sufficiently countered through electron or neutron degeneracy. The star then collapses upon itself. An "apparent/event horizon" is created at the point where escape is no longer possible from the surface of the star. The mass of the star continues to implode to a high-density point due to excessive amounts of mass and gravity. Some physicists then think that it then creates what is known as the "singularity."
Kip Thorne describes a singularity as:
A region of spacetime where spacetime curvature becomes so strong that the general relativistic laws break down and the laws of quantum gravity take over. If one tries to describe a singularity using general relativity alone, one finds (incorrectly) that tidal gravity and spacetime curvature are infinitely strong there. Quantum gravity probably replaces these infinities by quantum foam.
In
The Elegant Universe, by string theorist, Brian Greene, Greene continues the notion of a black hole by giving a postulate that two ends of a black hole could "glue" together through "topology-changing transitions." In the proposed senario, the very "end" of a black hole (i.e., the point at which spacetime is most warped in a black hole; singularity) would "tear" the fabric of spacetime. (This is an unusual thought to ponder. What I usually do is consider all of spacetime to be some sort of floating membrane of dimensions in a realm of unreality, that is, hyperspace. If anyone has ever read
Flatterland by Ian Stewart, it may be more understandable. Afterall,
Force is an illusion--a by-product of warped space-time ~ Michio Kaku) Ordinarily, this "tear" would suck everything into it because it is essentially a hole through spacetime in "hyperspace" that needs to be filled. Greene continues on by stating that this universal doom is bypassed by a three-brane superstring forming a barrier around the tear that protects the universe from this hazard. In some cases, the two ends of a black hole may tear the fabric of spacetime, then re-glue with each other through "topology-changing transitions" to form a new wormhole. This may be how they are created in the first place, that the end of a black hole (where a singularity is located) may puncture spacetime and re-glue. Kip Thorne calls this the "classical strategy" for creating a wormhole (referring to classical mechanics and relativity). *(For more information about this, please check out
The Elegant Universe by Brian Greene, Chapters 11 and 13.)
In the book
Black Holes & Time Warps, by theorist, Kip Thorne, Thorne also gives an explanation of the "classical strategy" for creating a wormhole: the "tear-and-sew" method.
In a classical strategy, our infinitely advanced civilization would try to warp and twist space on macroscopic scales (normal, human scales) so as to make a wormhole where previously none existed. It seems fairly obvious that, in order for such a strategy to succeed, one must tear two holes in space and sew them together.
In Chapter 14, Kip Thorne goes on to explain how he was introduced into the area of wormholes and the invistigation spurred by his friend, Carl Sagan. He describes his search for a "traversable wormhole," one that would be suitable for interstellar space travel (for use in
Contact, by Carl Sagan), since the tunnels known before him were either highly unstable or unreasonable. He eventually came up with the solution to what he was looking for: exotic matter.
First, the only way to hold the wormhole open is to thread the wormhole with some sort of material that pushes the wormhole's walls apart, gravitationally. I shall call such material exotic because, as we shall see, it is quite different from any material that any human has ever yet met.
Second, I discovered that, just as the required exotic material must push the wormhole's walls outward, so also, whenever a beam of light passes through the material, the material will gravitationally push outward on the beam's light rays, prying them apart from each other. In other words, the exotic material will behave like a "defocusing lense"; it will gravitationally defocus the light beam. See Box 14.1.
Third, I learned from the Einstein field equation that, in order to gravitationally defocus light beams and gravitationally push the wormhole's walls apart, the exotic material threading the wormhole must have a negative average energy density, as see by a light beam traveling through it. This requires a bit of explination. Recall that gravity (spacetime curvature) is produced by mass (Box 2.6) and that mass and energy are equivalent (Box 5.2, where the equivalence is embodied in Einstein's fameous equation E = Mc^2). This means that gravity can be thought of as produced by energy. Now, take the energy density of the material inside the wormhole (its energy per cubic centimeter), as measured by a light beam--that is, as measured by someone who travels through the wormhole at (nearly) the speed of light--and average that density along the light beam's trajectory. The resulting averaged energy density must be negative in order for the material to be able to defocus the light beam and hold the wormhole open--that is, in order for the wormhole's material to be "exotic."
...Then, in 1974, came a great surprise: Hawking inferred as a by-product of his discovery of black-hole evaporation (Chapter 12) that vacuum fluctuations near a hole's horizon are exotic: They have negative average energy density as seen by outgoing light beams near the hole's horizon.
...We also know that, if an infinitely advanced civilization somehow acquires a wormhole, then the only way to hold the wormhole open (so it can be used for interstellar travel) is by threading it with exotic material. We know that cacuum fluctuations of the electromagnetic field are a promising form of exotic material: They can be exotic (have a negative average energy density as measured by a light beam) in curved spacetime undera wide variety of circumstances. However, we do not yet know whether they can be exotic inside a wormhole and thereby hold the wormhole open.
I hope this helps you in some way to understanding what "spacetime" really is and how wormholes are created. There are other theories of the matter (such as the one given by Mentat concerning a hypothetical "white hole"), so this issue may not be resolved any time soon, making most of this simply pieces of a hypothesis and philosophy (much like string theory itself, for now).
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References
Thorne, Kip.
Black Holes & Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton & Company, Ltd., 1994.
Greene, Brian.
The Elegant Universe. New York: W. W. Norton & Company, Ltd., 1999.
