I heard that cosmological strings were a possible route to time travel. Please explain.
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.
Why is the recurring universe (closed model that bounces) unlikely? How do we know it hasn't happened already? Couldn't this model be possible?
Certainly the cyclic universe is possible, but it 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.
The classical analogue of the Schroedinger equation would be an equation like F=ma, which we can use to locate the position of a particle as a function of time in the presence of a force. The Schroedinger equation differs from the classical equation, however, in that it solves not for an exact position, but for a probability distribution: for example, it might give the likelihood of a particle being in a specific location.
It is impossible to know with infinite precision both a particle's position and its momentum (or a particle's energy at some infinitely precise time). This has many consequences, including the existence of virtual particles in the vacuum.
What does GR teach about time-travel?
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. (See pp. 456-7.) 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 (pp. 455). 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.
Do you personally think that time travel is possible?
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.)
Why is time travel considered in this course? It doesn't seem relevant to anything other than the general concept of time.
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.
How does the 2nd law of thermodynamics apply to the cases of time-symmetry and time-asymmetry?
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.
How does the strong tidal force of a black hole relate to the arrow of time?
Tidal forces can be associated with the entropy of a black hole. A black hole is maximally contracted and has very high entropy, so its formation increases the entropy of the universe, and increasing entropy is related to the arrow of time.
Shouldn't entropy decrease with an expanding universe?
You are probably thinking that an expanding universe should dilute everything, much in the way that it decreases the matter density. However, this is not necessarily the case. The number of matter particles is a quantity that doesn't decrease; the particles just spread out. If we define entropy as the number of photons in the universe, then the number of photons will stay the same or increase, even though those photons are spread out over larger volumes. Nuclear reactions in stars will increase the number of photons, and hence the entropy. The formation of black holes will also increase entropy.
How exactly can observing at the slits of the interferometer cause the light to behave as particles? Does this mean that you get particle or wave behavior depending on whether you close one eye or not?
We need to clarify what is meant by "observing" here. We cannot see individual electrons or photons; furthermore, if we are talking about literally using a human eye as a detector, then closing one eye doesn't change anything; you would still see two slits. (Closing one eye merely shifts the near field of vision somewhat.) What we mean in this two-slit experiment is that we might set up some apparatus at each slit that could detect an individual electron as it arrived at the slit from its source. In the history of physics, this kind of device was called a "Maxwell's demon," i.e. something that could examine individual atoms, molecules, or particles. (Maxwell, the same Maxwell as in electromagnetics, originally proposed it with regard to some work he did in statistical mechanics; he died before quantum theory was developed. But the name applies to any such device.) Now Maxwell's demon has at least a partial reality, because there exist photocells and semiconductor devices that are sufficiently sensitive to detect a few or even a single photon or electron. So let us suppose that we set up our screen and install at each slit a Maxwell demon that will inform us when an electron arrives. When we do this, we will no longer see a wave-interference pattern at our phosphorescent detector at the other side of the screen, but will see two discrete smears, one for each slit. In order to observe the electron, we must necessarily disturb it, and the wave interference is destroyed. The Maxwell demon has selected for the particle nature of the electron.
Because it has zero rest mass. All particles with rest mass must travel less than the speed of light. Particles with zero rest mass must travel at the speed of light.
What sort of ideas are there that might apply to the Planck epoch?
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.
I am not sure I understand the idea of multiple, infinite universes (many worlds interpretation). Do all people exist in all those universe? What would happen if you went from one universe to another?
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.
Is there any theory for parallel universes or is it all science fiction?
Excluding "many-worlds" universes, which are not really "parallel universes" in this sense (see Question above), one possible physical theory for parallel universes is chaotic inflation, described on page 457. Briefly, in this theory some patches of the universe undergo inflation and pinch off via wormholes from the "mother" universe. There is no particular reason to expect that any of these "daughter" universes would resemble each other in any way. They could even potentially have different laws of physics. There is especially no reason to think that there might be a parallel universe that is identical to ours except in some crucial way, e.g., that everyone good in "our" universe is evil in "theirs" and vice versa. However, if there is an infinite number of "daughter" universes and all possibilities occur, then such a parallel could exist. But since the universes cannot communicate we would never have the opportunity to meet our evil selves.
What is the difference between parallel worlds and the "many worlds hypothesis."
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.
Yes. Certain applications of theory suggest the possibility of multiple universes, although generally these universes are separated in such a way that communication between them cannot occur. If another universe exists but can have no causal relationship with ours, then what significance does it have?
Are there any quantum gravity hypotheses that are gaining support amongst physicists?
String theory is probably the currently most favored hypothesis, but it is probably fair to say that it is regarded as a promising start and not as a full Theory of Everything (including quantum gravity).
Is there any practical application to the knowledge of the ultimate fate of the universe aside from the intrinsic interest in the answer?
Why is it necessary to have a quantum gravity model, and why is it so hard to figure out?
Without a theory of quantum gravity, we cannot say that we are anywhere near understanding some of the fundamentals of the universe. It means that we do not completely understand force unification. It prevents us from understanding the meaning and behavior of singularities. It might also be inhibiting our comprehension of the arrow of time.
It is difficult to arrive at such a theory because we are still trying to understand matter at very high energies. (We still do not have a successful theory of unification of strong, weak, and electromagnetic forces yet.) Furthermore, unlike the other three forces, it is not immediately obvious how to cast the theory. The others are independent of space and time and so we may set up coordinates in the usual way, up to certain known transformations. But gravity seems to be involved in the existence of space and time themselves, and quantum gravity must apply at scales at which space and time as we know them break down. One stumbling block to quantum gravity has been just trying to understand which coordinates might be appropriate. The apparent geometrical nature of gravity is also a factor, since that does not fit into our current understanding of particle physics. It seems likely that the correct theory will recover this geometrical appearance for large scales, but it is unclear how to go from the geometrical theory to a more complete theory; it is quite unlike going from (for example) classical electromagnetics to quantum electromagnetics.
One thing that seems likely is that the eventual theory of quantum gravity may turn out to be very complicated in its details, but will be quite simple conceptually.
String theory is a theory of force unification and in principle would tell us about the earliest moments of the universe, as well as about the nature of matter. For more, try this page on String Theory.
Superstring theories and other attempts at grand unification involve higher dimensions than just the usual 3 space dimensions. These other dimensions are "compact" so we don't see them in our present universe.
There are no tests today, although any version of string theory must be compatible with all currently known physics and experimental results, and that is itself a stringent constraint. It is difficult to know whether superstring theory will prove correct ultimately. Are the difficulties physicists encounter with it because they will ultimately find it to be on the wrong track, or simply because it is fundamentally complicated, or because the true, final, beautiful, simplifying principle is not yet uncovered?
What kind of mathematics describe string theory?
The mathematics is pretty much the same as in other areas of advanced physics, including general relativity. It includes tensor analysis (a tensor is a quantity with many components that transform in a certain way under changes of coordinates), partial differential equations, the theory of "generalized functions," and so forth.
Quantum mechanics prohibits infinite subdivisions. We believe that time and space themselves are "quantized," i.e. exist in finite, fixed quantities, at the level of the Planck scale of approximately 10-31 cm or 10-43 seconds. Below this scale it is probably not possible to describe the universe in terms that we would find familiar.
Alan Guth once speculated (in a jocular vein) that our universe may have begun in somebody's garage as an experiment. There has been a recent suggestion that the singularities in black holes are the spawning ground of new universes that share properties of the universe that created them. If that were the case the new universe is cut off from our universe by a horizon, and presumably our universe is inside some horizon from its parent universe. These are interesting, although completely untestable, speculations.
I suppose the evidence in favor of quantum mechanics in general indicates that the many worlds theory is possible, but there is currently no evidence to support the proposition that it is correct.
Some people argue just that. On the other hand, it may yet turn out to be testable, or we may find that it is impossible to construct a consistent quantum cosmology without something like it.
There are several different attempts to create a quantum mechanics without the "observer." Start at this page for further information: Foundations of Quantum Mechanics.
Is the end of the universe a worry? Should you be worried about this experiment? Probably not, for the first, and No for the second.
Seriously folks, there are cosmic rays (ultra high energy particles) colliding with the Earth all the time which have more energy than being contemplated in the lab. There is no evidence that mini-black holes exist in the cosmos. Apparently nature doesn't create them. And the experiment won't do anything that nature doesn't already do.
Note that the cause of concern (given in the article unreferenced here) is that "it has been theorized by Steven Hawkings (sic) that from this quark-gluon plasma other forms of matter are also formed." Hawking hypothesized that the only place in the universe where miniblack holes might form would be in the very beginning of the big bang itself, at fabulously higher energies that mankind can even contemplate creating. The hypothesis has been examined since it was proposed and seems unlikely. In any case its irrelevant to this experiment. (Citing a famous scientist always lends an air of credibility.)
Let's consider an experiment that really was dangerous. 50 years ago people were worried that atomic testing would blow a hole in the ocean floor and drain the water out, knock the Earth off of its axis, set fire to the atmosphere over the whole Earth, shatter the Earth into pieces.... All concerns that are easy to show are absurd with simple physics calculations. Of course what they should have been worrying about was that these bombs obliterate cities and kill millions of humans, release fallout that increases the likelihood of cancer in humans, but that wasn't enough for some people. Our meddling had to have cosmic consequences.
You want some things to keep you up at night? Try overpopulation, starvation, plague, warfare, pollution.... These are things that are real threats, and things we could do something about if we get our collective act together, species-wise.
However, I sense an opportunity here. Anyone for black hole insurance?
NB: the question was about an article in 1999. As of today, we are still here. I checked.
We could infer their existence if the existence of our universe seemed to require them or the laws of physics when completely understood predicted their existence.
Current theories can be expanded to include the possibility of other universes. This would mean that what we call the t=0 point isn't really the beginning of everything, just the beginning of what we refer to as our universe.
Copyright © 2002 John F. Hawley