Chapter 8 Questions

In modern physics theories, forces are carried by particles. An example is the photon, a massless particle that carries the force of electromagnetism. The graviton is the name given to the particle that would carry the force of gravity. It has never been detected, but it must exist if gravity is to be understood in the same way as the other fundamental forces. This way of thinking about the nature of gravity is different from the geometrical description in Einstein's general relativity. The two points of view are not necessarily incompatible, but reconciling them (in detail) will require a more complete theory of gravity.

A space warp is a term coined in science fiction, and as such has no clear meaning. However, one could take it to mean a non-Euclidean geometry for space. Then ``warped space'' would be any nonflat space. Why have science fiction writers latched onto this? They are trying to get around the limitation of the speed of light for traveling through the universe. If the geometry of space is more complicated than just flat geometry, there might be ``shortcuts'' between different points in space (see discussion of wormholes in Chapter 9). Or maybe you could get from this point to that point by going through ``hyperspace'' which would be some higher dimensional space in which our three dimensional space is embedded. Sort of like going from New York to Sydney through the Earth instead of around on its surface; you save some distance that way. Do you suppose that in another century people will think today's science fiction is as corny as we think last century's science fiction is (e.g. traveling to the moon in a balloon, or in a projectile fired from a cannon)?

What we are looking for when we are trying to do time travel, is a timelike worldline through space-time that moves into the future of some event A and ends up in the past of event A without ever exceeding the speed of light. This is called a ``closed timelike curve.'' Remarkably, there are solutions of Einstein's equations that contain such curves. One example, discovered recently, involves two infinitely long ``cosmic strings'' which are line-like mass-energy sources. Another is the so-called Goedel solution for a rotating universe. (This is discussed in Chapter 17.) So far all such solutions have one thing in common: the closed timelike curves are built in from the start. Nobody has ever found a solution in which time travel becomes possible (after not being possible) due to the evolution of spacetime. Some think that solutions to Einstein's equations that admit closed timelike curves are forbidden, that is, while mathematically they are solutions to the equations, physically they are impossible. Nobody knows how nature would accomplish this, though.

This is the problem with taking the analogy of the sphere too far. The surface of your basic sphere is two-dimensional. Traveling through the sphere means going through a third dimension. This seems reasonable since we are 3D creatures, but it wouldn't work for 2D creatures living on the surface of the sphere. So if the universe were spherical (in 3D) "going through the sphere" would mean traveling through some higher dimension. Science fiction writers often assume the existence of so-called hyperspaces, because it provides a way to get from point A to point B rapidly. But: there is no reason why there should be any higher dimensions. Curvature is an intrinsic property of a geometry. A 3D spherical geometry doesn't require some higher dimensional flat geometry to "curve in."

I am not sure whether one twin is supposed to live on the floor of the ocean or not. The maximum would presumably be a twin on the Earth and the other removed out into space. This has a relative time dilation factor of 1.0000000008, corresponding to about 0.024 seconds per year, giving a net difference over 75 years of 1.8 seconds.

You spin it up using jets along the rim of the space station. The jets all fire tangentially to the rim in the same sense (e.g. clockwise) and the whole station begins to spin. You want to make sure that the jets fire evenly so there isn't any wobble.

Special relativity is a subset of general relativity. (Note: if there is a cosmological constant - see Chapters 10 and 11 - then, strictly, the equations of GR do not reduce precisely to SR, although locally the Lambda term will be completely negligible.) SR is useful because it is much easier to work with, and most of the time you can use Minkowski space to do your calculations of (for instance) particle physics, with negligible error (due to ignoring gravitational fields).

A metric is the "measure" of the distance between points in a geometry. The distance between two points on a geometry such as a surface is certainly going to depend on how that surface is shaped. The metric is a mathematical function that takes such effects into account when calculating distances between points.

Copyright © 2005 John F. Hawley