Chapter 17 Questions

Cosmological strings correspond to a string-like line of mass-energy density. Such a string produces a gravitational field, and hence curves space. J Richard Gott of Princeton found that if you had two infinitely long, moving cosmic strings in the universe it was possible to travel around them in a certain way that would lead to a "closed time-like curve". Admittedly, this is a pretty contrived situation. Like the Godel universe, this is an example of a spacetime where time travel could occur, but only if the closed time-like curves are built into the universe from the start. In this example, you need infinite cosmic strings, and you can't get these strings from evolving a more "normal" space-time. This suggests that there is a "no time travel" condition that applies to physically possible solutions of Einstein's equations.

The cyclic universe doesn't seem to fit well with the known laws of physics or with current observations. In a cyclic model, each manifestation of the universe has spherical geometry and recollapses; of the standard models, this geometry has the least observational support. Moreover, there are physical difficulties with the model. At each collapse to a singularity, only two behaviors can occur: either the universe retains its entropy, or it does not. (The possibility that it might retain only a part of the old entropy seems highly unlikely, but remembering any part of the entropy would have the same ultimate consequence as retaining all the entropy; the inevitable would be merely delayed.) If the universe did remember the old entropy, then each successive universe would begin in a state of ever-higher entropy. After only a few cycles, the initial entropy would be so high that no useful energy could be extracted, and life could never form. Since our universe appears to have begun in a state of low entropy, this would suggest that if we do live in a cyclic universe, our current universe is very near or possibly even at the beginning of the cycles, which brings us back to a special initial condition.

The only way a cyclic model could repeat endlessly would be for the entropy of each manifestation to be wiped out in the singularity. This seems strange, since the recollapse of a standard spherical model is like the collapse of a black hole and results in a state of very high entropy. Until we have an understanding of quantum gravity, we cannot be certain of the behavior of singularities. However, if quantum gravity is connected to the arrow of time, as some physicists have suggested, then entropy and gravity are intimately related.

General relativity has little to say beyond what special relativity says, despite the wishes of science-fiction aficionados. The most important effect due to general relativity is that spacetime curvature provides a physical mechanism for closed timelike curves to occur. This does not mean that closed timelike curves are possible in any particular general-relativistic spacetime; in fact, most known solutions do not permit them, or else allow them only under highly special circumstances that would be useless to material objects larger than an elementary particle. However, a few solutions, most notably the Godel solution, do admit closed timelike curves. The physical consequences of such an acausal universe are not particularly well understood. It may be that the rest of the laws of physics, as we understand them, could not operate in such a universe. Certainly the structure of a cosmology such as the Godel model would be quite different from a causal universe; and evidence is strong that our universe is causal.

Even if our universe is causal overall, however, the possibility still exists for closed timelike curves under restricted circumstances. If any such curve could be traversed by macroscopic objects, then we encounter all the paradoxes inherent in time travel. General relativity per se is time symmetric; the principle of causality is an additional axiom by which we select appropriate solutions.

A better comprehension of gravity may tell us about the relationship between gravity and causality. It may seem that we hide behind "quantum gravity" to explain all ignorances, but the fact remains that gravity is not fully understood.

What anyone thinks personally is not particularly significant, since future observations could always prove one wrong (or right, but that could be just luck). However, based on our present understanding of physics most scientists do not believe that time travel for macroscopic objects is possible. (Note the difference between an opinion, and an expert opinion. When Kip Thorne suggests that time travel for macroscopic objects is unlikely, take it seriously.)

Aside from the intrinsic interest in the idea of time travel, whether it is or is not possible tells us some fundamental truths about the nature of time and the structure of the universe. It affects the validity of the principle of causality, it may be related to the type of universe permitted by the eventual theory of gravity, and it indicates whether time has a preferred or even inviolable direction.

This is actually a topic of current research. However, we can state that the second law of thermodynamics suggests a time asymmetry. (It does not require it; logically there need not be any connection between entropy and time, although physically there certainly seems to be such a relationship.)

The known microscopic laws of physics are time-symmetric. There is no preferred direction to time; processes could run backward as easily as forward. Symmetries are related to conservation laws (see p. 361). In particular, symmetry in time implies conservation of energy. The second law is a statement about a quantity, entropy, which is not, in general, conserved. Thus the second law must be connected to some asymmetry, and the relationship between entropy and time indicates that the second law makes a statement about time asymmetry.

Symmetry is the property of remaining invariant under certain changes. A cube is invariant under rotations of 90 degrees, for example. Supersymmetry is a form of grand unified theory which invokes certain abstract symmetries. The main implication is that every fermion (the particles that make up matter) has a corresponding boson (the particles that carry forces) and vice versa; hence the expression "supersymmetry." Supersymmetry is of interest because theories based upon them can potentially unify gravity with the other forces.

Shouldn't entropy decrease with an expanding universe?

There are plenty of ideas, but not too many with a well-developed physical theory. The most fundamental and best-supported is the belief that during the Planck epoch, all four forces were unified and of comparable scale. Beyond that, ideas are mostly that--ideas, not yet full theories. String theory is under active research and may yield some solid results. According to string theory, at the Planck scales reality consists of quantum loops and strings. (This means that the "things" that make up the most fundamental aspects of the universe are described by equations that are similar to the equations used to describe the behavior of strings and loops. This would be in contrast to "things" that behave like point particles.) Several spatial dimensions exist (10 in most theories of this nature), as well as time. The vibrations and oscillations of the quantum loops manifest themselves in our four-dimensional spacetime as the truly elementary particles (quarks and leptons).

Some other ideas are that the Planck scales (length and time) represent the smallest quanta of their respective dimensions. Thus space and time themselves are not continuous, but are quantized at the Planck scales. Note that the Planck scales exist today--however, during the Planck epoch the entire universe was of this scale.

You are certainly not alone in having difficulty comprehending the many-worlds interpretation! However, one must not think of these "parallel universes" in the same way as one might imagine a parallel universe in science fiction. These universes are not independent entities, but represent the set of all possible outcomes of all processes. It is impossible to travel from one such universe to another. Indeed, in the many-worlds view the "universe" could be regarded as an infinite meta-universe which continually branches into non-communicating subuniverses.

In this interpretation, humans and everything else exist in the appropriate number of universes. (E.g. if you participate in a trial of Russian roulette with a six-shooter and the trial is fair, i.e. equal probabilities, then afterwards you exist in five universes and not in the sixth.) All processes are quantum in nature, ultimately, and there is no distinction between an "observer" and a "system." This is difficult to imagine, but remember that when special relativity was first introduced in 1905, it was widely regarded as too bizarre to be possible. Assuming that consciousness is a quantum process, like any other although very complicated, then it too is subject to the laws of quantum mechanics. From that point of view, the existence of one apparent person (or cat, for that matter) in different universes is not qualitatively different from whether a particular uranium atom exists or has decayed in a given (sub) universe.

The many-worlds interpretation is not as well studied as the Copenhagen interpretation. The Copenhagen interpretation works extremely well for virtually all circumstances in which quantum mechanics is applied, so most physicists ignore its philosophical difficulties. Further work on the measurement problem and the various interpretations of quantum mechanics may yield a clearer understanding of the many-worlds viewpoint.

The parallel universes of chaotic inflation (or, for that matter, science fiction) are independent entities that may have a common "mother" universe, but continue along their own paths with their own existences. The multiple universes of the many-worlds interpretation represent the set of all possible outcomes of all processes. At each "decision point," a given universe branches. These branches are preordained by the possible outcomes and their probabilities. Thus they are not independent, and they cannot communicate, since only one outcome can occur in a given manifestation.