Space: The Final Frontier Wormholes in the use of time and space travel HET 605B Randall E. Hartwig

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1 Space: The Final Frontier Wormholes in the use of time and space travel HET 605B Randall E. Hartwig One of the tenets of the Special Theory of Relativity is that nothing may travel faster than light. Humans who dream of traveling between the stars face the reality that any such trip would require many years to complete. Even if a means of travel at near the speed of light could be achieved, there would be resulting time dilation effects. These difficulties have convinced some that interstellar travel is unrealistic; others are not so easily dissuaded. First postulated by Einstein, passageways known as wormholes might be used to conduct humanity on its voyages to the stars. This paper will explore the properties of wormholes and how they may, or may not, provide a means for travel in space and in time. Wormholes Predicted by Einstein s General Theory of Relativity, a wormhole is a tunnel in space and time. In theory, by entering a wormhole one could travel vast distance in a very short time. As an example, an examination of the apocryphal apple that hit Newton on the head will suffice. As the apple lay on the ground, two worms find it. They agree, as only worms can, to race to the other side. The first worm, Slinky, travels around the outside of the apple to a point on the other side. The second worm, Inchy, takes a path through the apple, a wormhole. If Inchy s wormhole is straight and true, Inchy should arrive before Slinky. Inchy takes a shortcut, in much the same way a wormhole may represent not only a shortcut through space, but also perhaps a shortcut through time. The Special and General Theories of Relativity In 1905, Albert Einstein published his Special Theory of Relativity (STR), which deals with movement at speeds close to that of light. Isaac Newton adequately explained motions of objects that are moving much slower than the speed of light, however experimental results with light and electrical fields could not be explained using Newtonian mechanics. The STR was formulated to account for these differences. In the STR, time and space interact to form what is known as four-dimensional spacetime. In STR, an object in motion will actually shorten along its direction of motion and time moves more slowly the faster the object moves 1. (1, p. 545) We do not normally see these results because everyday items move so slowly, but as speed is increased to relativistic rates these effects are observed. 2 (1, p. 542) 1 The contraction of length and time can be calculated by the use of Lorentz transformation formulas. The formula and an online calculator can be found at 2 A further general discussion of the STR can be found at 1

2 Dissatisfied with Newton s explanation of space and time being absolute, Einstein sought to describe the effect of mass on the shape of space and the resulting effect on time. In 1916, Einstein s General Theory of Relativity (GTR) was published. Einstein was able to develop mathematical equations to describe the curvature of space-time. It is this description of the curvature of space-time that led to the concept of wormholes. 3 (2) Einstein-Rosen Bridge This picture demonstrates the idea that a gravitationally massive body can cause a pucker or warp in the space-time continuum (the grid background). A smaller object enters into the gravity well and orbits around the larger object. (3) Shortly after Einstein released the GTR, mathematician Karl Schwarzschild calculated that a very massive body could warp the space-time continuum to such a degree that light could not escape. 4 These bodies have come to be known as black holes. Further examination of Schwarzschild s work revealed that this situation could also be explained as a tube connecting two regions of flat space-time. In 1935, Einstein and fellow collaborator Nathan Rosen showed that a sufficiently massive body could warp spacetime, connecting the black hole of one region to a white hole 5 of another region. 6 (2) 3 There are other concepts in the GTR that are of great significance. A general discussion of the GTR can be found at 4 An eighteenth century scientist had also calculated this using Newtonian physics. 5 A white hole is a region of space that ejects matter. It is a black hole that runs in reverse, not only in process but also in time. 6 This region can be in the same universe or in different universe. 2

3 Types of Wormholes On the left is a diagram of an Einstein-Rosen Bridge or wormhole connecting two parallel universes. On the right a diagram showing a connection between two points in the same universe. (4) A Schwarzschild wormhole is one based upon a non-rotating black hole. At the center of the black hole is the singularity, all the matter that has been collapsed down to a single point that has zero volume. (1, p. 553) The structure of the wormhole consists of a tube, a white hole and a black hole. While a Schwarzschild wormhole exists in mathematical equations, there is no evidence that they can exist in nature. (2) A Lorentzian wormhole, like the previous one, is gravitationally based. However, Lorentzian wormholes have a spinning black hole that changes the structure of the spacetime continuum. This rotation arises from the fact the most stars are rotating, and as the star collapses the conservation of angular momentum would dictate an increase of speed. A rotating black hole is known as a Kerr black hole and theoretically should exhibit some remarkable characteristics 7. Instead of a singularity that is a point, the singularity is an infinitely thin ring. (1, p. 555) According to one prominent physicist 8, after ten years of hard work, we cannot prove that they (Lorentzian wormholes) do not exist. (5) This is a diagram that demonstrates how space coordinates are affected by the rotation of the black hole. (6) 7 The edge of no return, the point where gravity is so strong that light cannot escape is called the event horizon. A rotating black hole drags space-time with it resulting in an area surrounding the black hole where it is impossible to be at rest. (1, p. 555) 8 Matt Visser, Assistant Professor of Physics at Washington University, St. Louis. 3

4 Near a rotating black hole, frame dragging is so severe that there is a non-spherical region outside the event horizon called the ergosphere where any particle must move in the same direction that the black hole rotates. The outer boundary of the ergosphere is called the static limit, so named because once inside this boundary a particle cannot possibly remain at rest there (i.e., be static) relative to the distant stars. (7) The collision and destruction of particles on a very small scale may create Euclidean wormholes. These collisions result in complicated folds and tears in the space-time continuum and possible wormholes. The result may be very small, so small that no particle may pass through, and very short-lived wormholes. (2) Alternatively, the very small opening in space-time known as quantum foam may provide a source of Euclidean wormholes. (8) Wormholes and Time Travel One of the remarkable possibilities associated with wormholes is that they could be used as a time machine. This leads to the possibility of paradoxes. However, some scientists feel that time travel cannot be achieved in this manner. Locating Wormholes In order to be able to use a wormhole for travel, one must first find a wormhole. Wormholes are not in our space as they are in hyperspace. Referring back to the apple, the peel of the apple represents space-time and the inside of the apple represents hyperspace. We may find wormholes associated with black holes. The presence of black holes at the center of galactic nuclei has been fairly well established. (1, p. 545) The problem with using a black hole is that it may be very far away and the inherent characteristics of intense radiation and gravitational tides would have to be dealt with. Theoretically Euclidean wormholes could be found or made, but we do not yet have full understanding of the physics. (8) In addition, theoretical computations have demonstrated that any wormhole would be very unstable. (2) Negative Energy 4

5 Theoretically, applying negative energy to the wormhole should hold it open. (8) Negative energy is a product of the Heisenberg Uncertainty Principle that states the energy density of an electric or magnetic field fluctuates. By manipulating the field, it is possible to catch the fluctuation when there is less than zero energy, or negative energy. An example of this is the Casimir Effect. (9) There are a number of methods that can produce negative energy in small amounts. By applying the negative energy to a wormhole, the pressure may stabilize the wormhole, although vast amounts of negative energy may be required. Time Travel and Wormholes This figure shows (left) an actual apparatus used to conduct an experiment that will result in the formation of negative energy. The diagram (right) shows the basic idea: 2 charged plates are placed inside a vacuum. (10) It is possible that a wormhole could have mouths in different times in the same universe. It is also hypothetically possible that a wormhole could be made into a time machine. If a wormhole starts with both mouths at Earth in the same time, moving one of the mouths a distance at near the speed of light would result in that mouth suffering a time dilation, slowing time down for it. When the traveling mouth returns to Earth, that mouth would be at an earlier time then the stationary mouth. Hypothetically, a traveler could enter the stationary mouth and exit the traveling mouth before departure. (11, p. 135) One major limitation of this type of time machine is that the traveler cannot go back in time before the time machine was built. In addition, many scientists have serious reservations about the possibility of time travel. Paradoxes and the Chronology Protection Conjecture If time travel could be achieved, it would be possible then for the creation of paradoxes. A paradox is scenario that arises as a result of time travel but is clearly impossible. For instance, if you entered a wormhole and arrived at your starting point you could stop yourself before you left. (11, p. 136) Kip Thorne of Cal Tech and Stephen Hawking of Cambridge University have been actively contemplating the concept of time travel for at least the last 15 years. Hawking 5

6 has postulated the chronology protection conjecture that states the laws of physics conspire to prevent time travel by macroscopic objects. (11, p.153) However, Hawking steadfastly refuses to wager with anyone about the validity of this postulate as that person may be a time traveler. (11, p. 153) Wormholes and Space Travel The structure of a wormhole implies that it would also be hypothetically possible to enter a wormhole and exit somewhere else in the universe, or possibly in some other universe. Thus one could step through a wormhole on Earth and step out in another galaxy. This proposal has excited numerous science fiction writers as it allows the circumvention of the restriction on faster than light travel. In addition, some scientists are beginning to contemplate the requirements of travel through a wormhole. Space travelers approaching a wormhole may seem something like this (with the aid of their advanced technology) (12) Using Wormholes to Travel through Space Since STR prohibits travel faster then the speed of light, a wormhole could be used to significantly reduce travel time. A wormhole could connect a departure point with a destination point creating a shortcut through hyperspace. The hard part would be getting the wormhole mouths to right place. Either an existing wormhole would have to be mastered, or engineering on a vast scale completed to construct it. Hypothetical spacecraft designed to generate a wormhole are beginning to be explored. Fantastically advanced technology may generate a static, cylindrically symmetric ultramagnetic field. (12) Then as the spacecraft enters, the field would change shape, and the craft would head off on its way. Details of the exact procedures are left to future generations; this is simply a concept meant to stimulate debate and experimentation. 6

7 Concept WHIP (Wormhole Induction Propulsion) ship. (12) Conclusion Obviously there are some significant problems with the use of wormholes, not the least of which is the lack of evidence that they actually exist. To move a wormhole would require technology far beyond us. Manipulation of black holes involves dealing with masses many time that of our sun, intense radiation and crushing gravity. Negative energy can be produced in the laboratory, but the amount needed to keep a wormhole open is enormous. Clearly any civilization that could achieve such results or build spacecraft capable of generating transversable wormholes would be fantastically advanced. While science fiction writers can simply skip the details and use wormholes to journey all over the universe, scientists must attempt to master numerous disciplines simultaneously to glimpse the true nature of these hypothetical interstellar subways. At this time, the best scientific use of wormholes is to stimulate the imagination of and the debate between theoretical physicists. By examining wormholes and related concepts, scientists begin to achieve a greater understanding of the nature of the universe. References: 1. Kaufmann, William J. and Freedman, Roger A. Universe. 6 th Edition. New York: W.H. Freeman and Company, George, Samuel Joseph. The Einstein-Rosen Bridge. Samuel George s Homepage. m. April 2, Scientific American Follow-up. Scientific American Home Page. April 3, Lightman, Alan. Einstein Revealed: Relativity and the Cosmos. Nova Webpage. April 2, Dark Mystery s of the Universe: Wormholes and Time Machines. Think Quest Home Page. April 2, Kerr s Rotating Black Holes. Niels Bohr Institute for Astronomy, Physics, and Geophysics Home Page. April 3,

8 7. Kerr Holes. Stockholm Observatorium Home Page. April 3, Time Travel: Transcripts. Nova Web Page. April 3, Ford, Lawrence H. and Roman, Thomas A. Negative Energy, Wormholes and Warp Drive. Scientific American. January University of Hong Kong Physics Home Page. April 3, Short, Nicholas M. Oddball Universes. Goddard Space Flight Center Home Page. April 3, Hawking, Stephen. The Universe in a Nutshell. New York: Bantam Books Davis, Eric. Wormhole Induction Propulsion (WHIP). National Institute for Discovery Science Home Page. April 3,