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Saturday, August 27, 2011

Exploration of the Galaxy by Living Beings

Chapter 8b

Exploration of the Galaxy by Living Beings

This, of course, assumes that interstellar flight is possible. As we already saw, one problem with interstellar flight is that it takes a very long time. Even traveling close to the speed of light, it takes four years to get to the nearest star and over 30,000 years to arrive at the center of the galaxy. As we discussed in Chapter 7, these are not the times for the travelers themselves, who might be able to make a round trip to the center of the galaxy in their lifetimes. Unfortunately the energy involved may be such as to make prohibitive any more than an occasional probe. We have also seen that some extremely fanciful ideas, including ramjets driven by nuclear catalytic engines, and even superluminal starships, are consistent with current physical theory. Nevertheless, we cannot base an impossibility proof on technologies that are at best problematic, for an impossibility proof with weak links is not much of a proof (the same reasoning would apply with even greater force to the development of hyper-space travel, or some of the other fanciful inventions of science fiction writers).

Still, a velocity 1/100 that of light is within the scope of the technology described in Chapter 7. At this velocity, it would take us about eight million years to arrive at the furthest confines of the galaxy. A more centrally located species could have spread throughout the galaxy in a little over five million years, and that is only a bit more than 1/1000 the age of the Earth. Since the galaxy is at least twice as old as the Earth, if technological civilizations are as prevalent as the proponents of SETI would have it, many such civilizations should have arisen before ours. But that presumably means that they should have been here already. Even at a much lower rate of expansion, the time it takes to cover the entire galaxy is not much compared with the age of the galaxy itself. Our ancestors who migrated from Africa to the rest of the world never completed the journey themselves, but, by moving a little in each generation, eventually they covered the entire planet. And as long as the journey was, it took but a moment in the life of the homo-sapiens family.

Of course, a journey of eight million years for a species that is not yet a million years old would not be a small undertaking, but it is a journey that we may begin one step, one star, at a time. And at any rate, if we realize that complex creatures such as the dinosaurs lived for about 140 million years, and that moving into the cosmos would probably enhance the long-term survival of the species, we can see that the travel time may be relatively short for some species. Presumably this would make a complete expansion by someone or other seem almost inevitable.

There is no question that interstellar travel at that velocity would pose a variety of social difficulties for us. Chief among them is that it would take 400 years to arrive at the nearest star, perhaps 100 years with improvements in technology. Since it would be a second or third generation that would finish the trip--and if the nearest stars are not suitable, it would take an even later generation--we are not sure that we can entrust the success of the exploration to people that would not have been born when the decision to explore the galaxy is made. It may also be frightfully expensive to keep alive and healthy the many humans that would be necessary to send in a mission of that sort.

Nevertheless, we can cook up several scenarios in which the social obstacles are overcome and a species begins to migrate to the stars: an authoritarian regime forces the issue, or there is forewarning of a cosmic catastrophe, or the migration is simply a natural consequence of a long and massive colonization of the species' own planetary system. In such a case, this version looks more like the impossibility proof it is purported to be.

Moreover, a proponent of SETI cannot reply by bringing up reasons why a civilization may not choose to travel throughout the galaxy. Given that we are average, we can easily imagine why at least one of the many technological civilizations would eventually venture out with the purpose of colonization. This is easy to imagine because we can imagine why we ourselves might begin such an adventure. Accepting low odds (in the style of SETI proponents), let us say that it is one of a thousand options we have. Under certain conditions it may become the most reasonable option. Out of 1,000 advanced civilizations 100 million years ago, then chances are that one would have built starships. But where are they? As for the assumption of expansionism, again from our own case we know that we have a tendency to move onto new niches. Even if the tendency is not overwhelming, the existence of many civilizations will make it likely that at least one will act on it. And all it takes is one, as long as we assume that star travel is indeed possible and that the tendency to expand will give such a civilization the required persistence. The mediocrity principle supports this impossibility proof.

Of course, as in the previous impossibility proof, we may be able to find excuses for why we have not detected an alien presence in our solar system. Imagine for example, the enormous difficulty that we would have ourselves in trying to spot even a large starship that came within a few astronomical units from Earth, a distance that may be quite suitable for an alien species to conduct a survey of our solar system. At that sort of distance it is not easy to detect asteroids smaller than a kilometer across, even when we are searching for them. A starship may come in no closer than Saturn but send much smaller probes into orbit around the other planets. Their advanced stealth systems may be beyond our technological ability to detect. Or the ship may have been here already and gone home (or gone silent). The excuses may be limited only by our imagination.

In addition, in this discussion we have to assume that a slower conquest of the galaxy will not be hampered by lack of resources. But once again the Principle of Mediocrity comes to the rescue of the objection. In our own solar system it seems that the Kuiper Belt and the Oort Cloud would offer the resources needed for the survival of a civilization not unlike that envisioned by O’Neill’s in his proposal of space colonies. And since we are pretty much average, we should expect such resources to be spread throughout the galaxy.

As we will see below, the Principle of Mediocrity makes for an interesting philosophical target. But let us consider first whether seeking contact with advanced alien civilizations is wise.

The Wisdom of Contact

To make matters worse for SETI, if by some quirk of fortune we have not been found yet, the principle of mediocrity should lead us to question the wisdom of trying to communicate. It is clear that in our complete expansion in our own planet we have done our best to eliminate all significant competition from other species. The last thing we wish to do is advertise our presence to more advanced species who may then wish to occupy our niche, and in the process may need to get rid of the local pests, or at least bring them under control. In some circles there is the feeling that advanced creatures must somehow be wise and benevolent, although under the guidance of the principle of mediocrity it would be difficult to see why. In the first place we have a history of ruthlessness toward species that become obstacles to our aims; we have been ruthless even to other human cultures. Consider for example, as Ron Bracewell has pointed out, what the response of suburbanites might be if raccoons became much smarter. They would be such pests that suburbanites would go to great lengths to wipe them out[1]. And few of us would lose much sleep over that. Indeed when we try to poison cockroaches and rats, or hunt the coyotes that prey on our sheep, the issue of benevolence or malevolence seldom comes up.

In light of these considerations, some suggest that we should lay low until we are in a better position to do battle if need be. There are others who argue that the issue is moot since we have been radiating into space our radio and television signals for a long time. That may be so, but those signals would be very weak and well scrambled by the time they leave the solar system, and in view of the difficulties we have recognized in trying to look for alien transmissions, and the low powers of most of our own transmissions, it is not unreasonable to suppose that detecting life on Earth from, say, 100 light years away would involve a rather substantial amount of luck. Of course, some transmissions, radar beams for example, are very powerful. And in any event, the great activity in the radio range alone might indicate to another civilization that a relatively advanced technology exists here. At the present time the SETI program (not longer at NASA, as I mentioned earlier) does not transmit any messages. There does not seem to be much harm in listening, anyway, and so officially the wisdom of communication is not yet a problem we must face. Nevertheless, unofficially we do have to concern ourselves with it, since some radio astronomers have already sent messages on their own.

[1] R. Bracewell. The Galactic Club. San Francisco: W. H. Freeman 1975.

Friday, August 19, 2011




Are we alone in the universe? Is it really possible that no sentient being on a faraway planet ever contemplated the stars and felt awe? That only humans ever wondered about the nature of the universe, or pondered whether similar beings might be asking similar questions? In the view of some people it is extremely parochial to suppose that we are alone – one more instance of the syndrome that once made us believe that the Earth was the center of the universe. According to those people, we have no more reason now to believe that we must be the pinnacle of creation than we had once upon a time to believe that the Earth was so special.

Thus begins the reasoning that takes them to the conclusion that extraterrestrial intelligences (ETI) are likely to exist, a presupposition without which the search for them (SETI) would make little sense. This does not mean, however, that the proponents of SETI advocate the building of starships at all. Indeed, many of its practitioners believe that star travel is not very likely, at least not for a very long time. They urge instead that we scan the skies for the radio signals of other advanced species.

Success in their mission is seen by SETI proponents as of such extraordinary importance that at some point they proposed Project Cyclops, a very elaborate, and expensive, arrays of radio telescopes to carry it out. Their proposals were not received with much sympathy by those who control the purse strings, and thus over the years they had to content themselves with ever meager levels of support (from tens of billions for the proposed Cyclops[1] to less than two million per year in actual funding, and then to nothing). But what seemed like a deplorable situation to them appeared far too exorbitant to opponents of SETI. For in the view of such opponents, the very foundation of SETI, that extraterrestrial intelligence probably exists, was not only unwarranted but preposterous. U.S. Senator William Proxmire gave the program his Golden Fleece Award, for the most inane waste of taxpayers’ money. Eventually NASA cut SETI of its budget altogether. But the program lives on, bolstered by the privately-funded SETI Institute and by the ingenuity and good will of many contributing scientists.

Ironically, the opposition to SETI is buttressed by the key assumption of the SETI proponents themselves: Carl Sagan’s so-called "Principle of Mediocrity."[2] The Principle of Mediocrity asserts that the sun is a typical star in having a planet like the Earth in which life could arise, that terrestrial life is typical in having produced intelligence, and that human intelligence is typical in giving rise to a technological civilization.

Presumably Copernicus taught us humility when he argued that the Earth was not privileged but average, and later astronomy reinforced the lesson by discovering that the sun itself was merely an average star in an average galaxy. By extending the Copernican lesson, the reasoning goes, we should learn to be humble about our own position in the scheme of life. The principle of mediocrity thus purports to recognize that humanity and the conditions that have brought it about are pretty much average. In their arguments, the opponents of SETI stretch this principle slightly to add that a technological civilization is typically expansionist. As a result they are able to produce a variety of "impossibility proofs" against the existence of extraterrestrial intelligence.

In the pages that follow I will examine the justification of SETI in light of this controversy. This examination, I trust, will lead naturally to a discussion of some of the important philosophical assumptions made by SETI in estimating our ability to communicate with ETIs if they exist, a very interesting issue in its own right. Let me begin with a brief account of the reasons for optimism with respect to SETI. I will then proceed with an explanation of how such optimism actually sets up the impossibility proofs.


First there is the incredibly large number of stars. This galaxy alone contains over 100 billion, and there may be at least 100 billion galaxies. We do not know how many of those stars have planetary systems, but most theories of star formation would encourage us to believe that planets are rather common, at least in the average stars of what is called the Main Sequence (of star evolution) such as our own Sun. As we saw in Chapter 5, this optimism has been born out by the recent discovery of over 200 Jupiter-planets and a few rocky (“terrestrial”) planets around other stars, as well as by the very credible evidence for forming planetary systems around young stars.

All this has some very convenient aspects for SETI. One is that the average stars may live longer than ten billion years. Since it has taken about four and half billion years to produce a technological civilization on this planet, it is encouraging to know that the stars that live long enough are also the ones most likely to have planets in the first place.

From here on matters generally become far more speculative. Those who are in the business of making probability estimates for SETI often use the so-called "Drake Equation" (named after Frank Drake, the contemporary astronomer who first proposed it). According to this equation, the number of intelligent civilizations in this galaxy is equal to the product of the rate of star formation, the percentage of favorable stars, the number of planets around such stars, the fraction of Earth-like planets among those, the fraction of such planets in which life begins, the fraction of planets with life in which intelligence develops, and then the number of planets with intelligence in which technological civilizations arise. This product is then multiplied by the average longevity of a technological civilization.

We believe that in this galaxy the rate of star formation is about twenty per year. And the existence of other planets is now established, although not the rate of planet formation. But as we progress through Drake's equation, the estimates are not as well grounded. This situation does not prevent SETI enthusiasts from assigning optimistic probabilities to every factor. One often hears, for example, that once life begins on a planet, intelligence is very likely to result eventually. Such optimism surely deserves examination.

Impossibility Proofs: A Summary

The most interesting impossibility proof against the existence of ETIs is the famous question by Enrico Fermi, which assumed an early version of Sagan’s Principle of Mediocrity: “Where are they?” With such good omens for the existence of ETIs, they should be everywhere, including our own solar system, watching us, making contact with us, and so on. But we don’t see them, hear them, or in any other way detect them. This of course assumes also that all the talk about UFOs, alien abductions, and the like is a delusion, or at best an illusion. So, if aliens do exist, they should be all over the place, but we have no trace of them; therefore, they do not exist.

SETI proponents like Bernard Oliver, however, argued that the reason we don’t see them is because star trekking takes too long, since the distances between solar systems are so vast. So no one can really be expected to undertake such a trip. That is why we need to resort to electromagnetic signals as a means to search for ETIs, as well as a means for communicating with them if we ever find them.

We have seen in the previous two postings why Oliver’s case is not as good as he might have thought. We cannot rule out the possibility of travel between the stars, either by traveling space colonies, or by ships that approach the speed of light. It is also physically possible, as we have seen, that warp engines might actually allow us to go faster than light (cf. Alcubierre[3]). Nevertheless we cannot affirm it either. This result weakens the impossibility proof some, but not completely: It still manages to cast serious doubt upon the existence of very advanced civilizations.

Some opponents of SETI have brushed Oliver’s response aside for a different reason. Even if star trekking takes too long for living things, an advanced civilization could still send self-reproducing machines to report about every interesting solar system, including ours. All they need do is send one. Once it gets to the backyard of another star, it will make copies of itself, which will then move on to other stars and do likewise. This self-reproducing probes will reproduce and cover any galaxy, give or take a few million years, the way a bacteria culture ends up taking over a petri dish. Thus Fermi’s question arises all over again: “Where are they?”

I do not believe that this impossibility proof succeeds. It is based on John von Neumann’s “proof” for the possibility of self-reproducing automata. I make two main points against such proof as the basis for exploring the galaxy in the fashion considered here. The first is that the conditions that make von Neumann’s proof plausible are not likely to be met under the exigencies of exploration. The second is that von Neumann assumes that a genome is like a computer program, and I think that such an assumption is unwarranted. I then criticize some clever proposals to apply von Neumann’s ideas to interstellar exploration (e.g. with space probes based on collections of nanorobots). Unfortunately I will have to ask my readers’ forgiveness for not providing the details of my arguments. As it turns out, such details will appear in my contribution to a book on imaging outer space that will be published in December. I promised the editor, Prof. Alexander Geppert, that I would not post the article, since the publisher would be naturally upset were my chapter to appear in this blog right before the publication of the book.

I will, however, provide a little plug for the book, since it is likely to interest most of you (I do not share in the profits). The title of my chapter is “Self-Reproducing Automata and the Impossibility of SETI.” The title of the book is Imagining Outer Space, and the editor is Alexander C. T. Geppert, as I said. The publisher will be Palgrave MacMillan

You can find out more information about the volume by clicking on this link:

[1] For a descripton of Cyclops see Bernard Oliver’s description in Carl Sagan, ed., Communication with Extraterrestrial Intelligence, MIT Press, 1973, pp. 279-301. The report on the project was published by NASA: CR 11445.

[2] Carl Sagan, Pale Blue Dot, Random House, 1994, pp. 39, 372-73.

[3] It seems that I left out the reference to Alcubierre’s seminal paper in my previous posting. It is as follows: Miguel Alcubierre (1994): "The Warp Drive: Hyper-Fast Travel within General Relativity". Classical and Quantum Gravity, 11: L73-L77.

Monday, August 15, 2011

Faster-Than-Light Starships

Chapter 7F

Faster-Than-Light Starships

The second fantastic proposal is even more interesting from the theoretical point of view. I am referring now to the prohibition that the special theory of relativity places on attempts to reach and surpass the speed of light. A way around this prohibition may be to move beyond the special theory. The basic intuition behind this idea is as follows: The speed barrier applies within the special theory of relativity, which requires the formula for addition of velocities we have seen above, and which presupposes non-accelerated frames. But does it have to hold within the accelerated frames of the general theory of relativity, or within a theory of quantum gravity?

Indeed the suggestions that have aroused the greatest interest in the last twenty years or so concerning travel faster than light both make use of the General Theory. I will discuss briefly two of them, the most interesting two. Please keep in mind, however, that at this stage the goal of the discussion is not to determine which of these suggestions is more likely to take us to the stars in faster-than-light starships, but whether physical theory permits traveling faster than light.

The first suggestion is Kip S. Thorne’s idea to use a Wheeler quantum wormhole to travel in a very short time to places that in normal spacetime could be thousands or even millions of light years away[1]. Imagine that space time is folded (for example in a fifth dimension in addition to the three of space and the one of time). That fold may bring close together, in that fifth dimension (or in so called “hyperspace”), regions of space that are extremely far from one another in the normal three space dimensions. It is as if we took a long cloth and brought close together the two ends. If the cloth were laid flat the two ends might be separated by a distance of one meter, but now that we have folded the cloth, the two ends might be only, say, a millimeter apart. If we could only make a little tube that connected them across that millimeter, the trip from end to end would be far shorter. John Archibald Wheeler’s proposed that, in extremely small regions (around a Planck length, 1x10-33 cm), strong gravitational quantum fluctuations create a sort of “quantum foam,”[2] in which we might find such a little tube, a “wormhole.” The trick is to find one wormhole in the foam, to enlarge it so a ship can go through it, and then to keep it open so it will not crush the ship.

Let us consider all three aspects of Thorne’s idea, which he developed upon a request from his friend Carl Sagan. The first problem is to find the wormhole. No one has ever detected one, and we do not even know if they exist. If none exist, or we cannot find them, an alternative would be to create one, as long as wormholes could exist. But can they? Wheeler’s results came from his attempts to construct a theory of quantum gravity. Unfortunately, half a century later we do not yet have an adequate theory on the subject. It is difficult to say then, even if we take Wheeler’s imaginative idea seriously, that physical theory does not forbid faster-than-light travel. The special theory of relativity certainly seems to forbid it. Does Wheeler’s joining of the General Theory and quantum theory somehow bring to light enough evidence to show some limitations to the special theory? It might if it were true, but that is precisely what we do not know.

Since we do not have an acceptable theory of quantum gravity, we are simply in a state of ignorance. From that ignorant perspective, travel faster than light may or may not be permitted by the laws of the universe (which we do not really know). The situation would be similar to asking in, say, 1855, whether it is possible in principle for a ship to travel at 300.000 Km/s. Nothing would seem to forbid such a feat, but only because Einstein’s formula for the relativistic addition of velocities was still 50 years away from appearing in print. Some may believe that the situation is actually worse, since we have no trustworthy theory to give us even seemingly reliable guidance – in 1855 we had Newton’s.

Some reason for optimism comes from the Casimir effect, which demonstrates that the vacuum is indeed teeming with virtual particles coming in and out of existence, as we would expect in Wheeler’s account. Cassimir suggested in 1948 that if two metal plates were placed micrometers away from each other in a vacuum, and in the absence of an electromagnetic field, some virtual photons would not appear between them because of their long wavelengths. In that case, there would be a greater density of virtual photons outside the plates than between them. This difference in density would result in pressure being applied to the plates from the outside, and thus they would move towards each other. The confirmation of the Casimir effect in 1958 is strong evidence for the hypothesis that virtual particles are prevalent in the vacuum, and many now see it as confirmation also that there is some sort of spacetime foam a la Wheeler. Notice, however, that the Casimir effect seems accounted for within quantum theory and is, at the very least, neutral about possible interactions between gravity and quantum effects.

Suppose, however, that we do find or create a Wheeler wormhole. Unlike the wormholes that might exist as a result of black hole singularities (in which the matter that disappears into the singularity “tunnels out” to another universe or another part of the universe, and in which the tunnel would close too quickly and the extraordinary gravity would crush any would-be traveler), Wheeler wormholes would be extremely small, of Planck dimensions. It would be necessary to make them longer, so as to connect one of the entrances with some desirable destination, and wider and stable, so we could send our astronauts through them. How could this be accomplished? The favorite answer: exotic matter. Now exotic matter is truly exotic. Presumably it would have negative mass, or at least exert negative energy (it would push the walls of the wormhole outward). And of course we have no idea whether it could exist. But Thorne and his coworkers think that something like the Casimir effect might produce negative energy inside the wormhole to keep it open.[3]

Think back, however, to the description of the Casimir effect given above. If we think of the vacuum as having zero energy, then we could think of the volume between the metal plates as having negative energy. It is a relative assignment of sign given the description we choose. But it does not seem sensible to say, for example, that the virtual particles within that volume have negative mass, or anything of the sort. Those photons have no peculiar properties compared to the virtual photons outside of the plates. So it is not as if we could go looking for some exotic matter to spoon into the wormholes. But perhaps what Thorne is after is what he calls “exotic fluctuations,” which would create negative energies, and which Hawking presumably showed existed at the event horizon of a black hole. Such exotic fluctuations would account for Hawking’s radiation. Nevertheless, a less exotic description is that the black hole pulls a member of a virtual particle pair inside the horizon while letting the other member escape into the universe, thus creating a glow of energy around the event horizon. We may then say that this positive energy is compensated by negative energy being sucked into the black hole (again a relative assignment of sign).

In any event, to expand a wormhole’s diameter along these lines, it would seem that a great deal of energy would have to be concentrated into the small region of the mouth of the wormhole so as to create a pronounced spacetime curvature in that region. Whether this would really lead to the desired opportunity for faster-than-light travel would have to be determined by a good theory of the interaction of gravity and quantum phenomena. If we only had one.

Of course, some of these theoretical ideas may turn out to be correct. Perhaps new experimental work that concentrates large energies into small regions could confirm the existence of spacetime foam, wormholes, and exotic matter (or at least some way of bringing about something akin to the Casimir effect inside a wormhole). But until such a time we will not really be in a position to say that travel faster than light is possible.

Imagine, nevertheless, that we do find or create a Wheeler wormhole, expand it and ensure its stability. We are still faced with a major conceptual difficulty: an outcome of travel through the wormhole is that an astronaut would also travel back in time. You may return before you take off! This gives rise to all sorts of puzzles about landing on your infant grandfather and killing him, which would make it then impossible for you to be born and thus to go on the trip in the first place. This absurd consequence would be a possibility in an established wormhole, if we do find one, that is, since it is a possibility in general for travel faster than light, as has been known for a long time. An example I recall from my student days was that if you had a gun that shot tachyon bullets, one such bullet could ricochet off the wall and kill you before you pulled the trigger (tachyons are particles that always travel faster than light, and thus do not violate special relativity since they never accelerate to the velocity of light).

Thorne offers an interesting illustration of time travel in a manufactured wormhole. He imagines making a short wormhole with one mouth in his living room and the other in a starship sitting just outside on his lawn. His wife takes off in the starship traveling at close to the speed of light. Obviously, the two mouths of the wormhole have different times, once her trip begins, as measured in a framework outside of the wormhole, although inside the wormhole the times remain the same. Thorne’s wife returns some hours later (her ship time), although years have gone by on Earth. She has two choices. She can meet Thorne on the lawn upon the landing of the ship and notice how much he has aged. Or she can crawl back using the wormhole to a time before she left on her space journey. Of course, she would then meet her own old self getting ready to go on her space journey. And of course, accidents could happen that would prevent her old self from starting that journey.

These paradoxes make travel back in time conceptually absurd, which makes this type of faster-than-light travel also conceptually absurd. But could the paradoxes be resolved? One suggestion is that unknown laws of quantum physics (or quantum gravity, or who knows what) prevent anyone, or anything, to travel to the past and create impossibilities (it is impossible to go back and kill your grandfather if you were never born because you killed him when he was an infant). This possibility is not only ad hoc but mere wishful thinking[4].

Another is that the astronauts traveling through a wormhole would not create any inconsistent “time loops” because they would actually end up in an Everett alternative universe (according to Everett, each of two possible alternative quantum states is real, although each is real in a different historical line (or world, or parallel universe).[5] So you would not really land on your grandfather, you would land on your grandfather’s equivalent in a different historical line. It is difficult to distinguish this physics from science fiction, but even a less cynical appraisal of this possibility should let us see that we are no longer talking about going to the past but rather to a different dimension or universe that is almost like your past and landing (and killing) someone who is exactly like your infant grandfather. It is also obvious that you never arrive at your destination, but at a planet around a star that is exactly like the one you were trying to reach, except for being located in another dimension or universe. And it seems that one should expect similar dislocation on the return trip; that is, you can never come home. Wormholes appear to be problematic enough without combining them with Everett’s interpretation of quantum mechanics.

A third suggestion is that there are indeed many worlds, more or less a la Everett, but that some are destroyed by inconsistent “time loops.” Our world exists because no one has killed his grandfather, etc., in any travel to the past. Time-travel consistency would function as a selection factor for possible worlds. The problem is, however, that when time travel alters the past it destroys a history that could be tens, hundreds, thousands, millions, or billions of years long. We do not know from when the fatal time traveler is going to come. Moreover, he may arrive tomorrow at noon, or a million years ago. And we would no longer be. In fact, in the second scenario, we would no longer have been. This suggestion does not seem to work well as a solution to the paradox.

Thorne proposes an apparently more sensible approach. He discovered that some round-trip trajectories through a wormhole may be perfectly consistent: a billiard ball may return and hit itself a glancing blow that will still permit its earlier version to go on the trip.[6] Presumably, since this loop is causally consistent, we no longer face a paradox. Paul Davies seems to agree and provides an interesting variant: A rich man travels back in time, meets his (young) grandmother and unwittingly gives her information about stock prices in her future. She invests her money using that information, which leads to immense wealth for her and for her grandson. Davies claims that “[N]o paradox ensues here.”[7] Surprisingly he finds paradox in a case essentially alike. A professor travels to the future, finds a mathematical formula in a book, returns to his time and gives the formula to a student, who then publishes it. That is the publication that the professor reads many years later. But neither the professor nor the student created the formula. Thus information has come from nowhere, or rather just from the time travel. In the earlier case the grandmother could not have created her fortune (or the student written the paper) without the foreknowledge made possible by the relevant time traveler (grandson, professor). Because the association between information and entropy, Davies thinks that this “free” information is “equivalent to heat flowing backward from cold to hot.”[8]

It seems to me that the situation is even more dire than that. In Thorne’s example a sequence of events, a history, leads to a future event that in turn causes a destruction of that very history and its replacement by another. Something had happened, and now it has not. But if it has not, how could the inconsistent causal loop arise in the first place? Those who have no trouble accepting something like Everett’s many-worlds view, or the even fancier notions of string theory, perhaps are not bothered by this new paradox all that much. But it must be pointed out, as it is generally accepted, that the empirical evidence for the first is scant and for the second non-existent. In Davies’ examples, there is not even an original history to create the conditions for the consistent causal loop: the man is already rich (without his grandmother having made the right investments), the professor already finds the mathematical formula (that no one has really invented). The loop just is. Causality is violated. Jorge Luis Borges would be pleased. But on the basis of such physics we do not have enough to say that faster-than-light travel is possible.

One point of logic needs to be considered. Even if causally consistent time loops did not fall prey to these objections, it is difficult to see how such loops fix the conceptual absurdity of going to the past. The paradox is not that every time we go to the past we kill our infant grandfather, etc. The paradox is that we could, accidentally or otherwise.[9] Thorne’s proposed solution is that there may be consistent loops. But, the danger still exists that, for example, the rich man’s son, years after his father’s time trip, indeed, years after his father’s death, finds the time machine, pushes the wrong button and ends up landing on his infant great grandmother, crushing her to death. That would make his family’s history, including the presumed consistent causal loop, become non-existent! The paradox has not been resolved.

One might think that if it is possible for someone from further in the future to annihilate that consistent loop, then that consistent loop was part of a longer but inconsistent loop; but in that case the longer loop itself would have been eliminated, and thus we have nothing to fear from time travel. Therefore we have no paradox. This response might make some sense if we hold to a metaphor of a frozen four-dimensional spacetime (like a vine made up of time slices of the other three dimensions). In that metaphor time is already all laid out and some Cosmic Pruner has cut out all the inconsistent loops from the cosmic vine. This would be as ad hoc as it is convenient. But the universe we experience unfolds in time, and we need a rather long causal sequence of events to create the conditions under which someone can go back to his past to wipe it out. That sequence of events, however, would have no particular marks to distinguish it from the one humans find themselves in already. Since the building of an actual time machine is presumably way in the future, if ever, we would not know whether we are in a real world (because either we will not invent time machines, or if we do the time loops they bring about will all be consistent) or in a world that one unexpected day will no longer have existed.

No wonder, then, that to save physics from absurdity, Hawking conjectured that the unknown laws of quantum gravity provide chronology protection, that is, that the universe does not allow time machines. This protection, he said, will “keep the world safe for historians.”[10]

To say that faster-than-light travel is possible, then, we need to show that we have accepted some relevant theories that permit it, or else we need to point to empirical evidence that, even in the absence of theory, suggest that possibility (e.g. people knew that flight was possible because they saw birds and insects fly, long before they had any theories that explained the flight of birds and insects). One problem with the theories of quantum gravity I have mentioned is that they have not been accepted because the empirical support is not there. I suspect the reason their proponents openly pursue such wild imaginings is that relativity and quantum theory presumably granted physicists the license to make unintuitive claims. Hypotheses about Wheeler wormholes, branes, the multiverse, and the like, it seems, do not sound any stranger today than, say, the wave-particle duality of light and matter did almost a hundred years ago. But I think there is a difference. When Einstein accounted for the photoelectric effect by suggesting quanta of light, his explanation was generally rejected, even by those who used his calculations. Bohr, for example, pointed out that Einstein’s account was contradicted by many experiments that showed clearly the wave nature of light.[11] Eventually Compton’s X-ray scattering experiments made Bohr accept the dual nature of light and this led to his famous principle of complementarity. The moral of the story is that physicists were forced by the phenomena to propose and accept otherwise extremely unintuitive views. Their experiments were their warrant. Perhaps other, more sensible views would have done the job, but no one proposed a persuasive one. Moreover, as I have argued elsewhere, the unintuitive character of their views, at least in the case of the principle of complementarity, was due to the general acceptance of a mistaken epistemology.[12] Einstein’s theory of relativity, although not similarly prompted by experimental results, was nevertheless soon an important tool in contrasting our ideas with the world.[13] None of this is the case with the highly speculative ideas so much in vogue today, and as we have seen, those ideas do not permit us to say whether we will ever be able to go faster than light.

To rule on that possibility, we need, in addition to the requirements of theory or empirical evidence mentioned above, a way of travel that does not imply going back to the past. A way out of this difficulty is to realize that the speed of light operates as a limit only within the special theory of relativity. But within the general theory we may find ways to travel faster than light without going back in time.

Miguel Alcoubierre argued in a paper published in The Journal of Classical and Quantum Gravity in 1994 that, if we built an engine that contracts spacetime in front of the starship, and expands it behind it, we could accelerate the starship to a velocity arbitrarily higher than that of light. Since the local spacetime for the ship would be flat, the astronauts would not violate the relativistic speed limit at any one point in their journey, although, from the perspective of the Earth-bound observers, the ship might be traveling much faster than light. By thus warping spacetime, the ship may make a return trip to Vega, which is 25 light years away, in, say, three or four Earth years, from the point of view of Earth-bound observers, instead of more than fifty, as would be the case under special-relativity considerations. Alcoubierre’s arrangement also has the ship move only into the future, as airplanes and slugs do, and so we do not have to worry about time paradoxes.

Of course, from this theoretical possibility to building a starship with a “warp” engine there is a long gap. What kind of technology could possibly contract spacetime? Some have suggested strange matter, but we have discussed that enough in this work not to pin our hope on it. We actually do not know what would work. But we do know that spacetime can expand, for that is precisely what dark energy accomplishes. We do not know how dark energy does it, just as we do not know what dark energy is. A hypothesis, however, is that the expansion of spacetime results from some kind of scalar field. To understand how a scalar field works, let us think about a spring that is pulled open until suddenly returns to its original state, or how a rubber ball pressed on all sides suddenly expands. If one takes seriously the suggestion by string theorists that there exist “space atoms,” then one can also imagine that only a limited amount of energy can be held in one of those atoms. Once it reaches the maximum, the energy “bounces” like the rubber of the compressed ball, carrying spacetime with it as it expands[14]. But these are all metaphors. What matters is that it happens, that spacetime does seem to expand, even if we cannot explain why. Birds did fly at a time when people could not explain how they could fly. Besides, such expansions, and contractions, of spacetime could be seen as variants of the lambda term that Einstein added to his equations to keep the universe from expanding.

Perhaps to construct the right kind of machine we may still need an acceptable theory of quantum gravity. For example, to produce the required local expansions and contractions we may use some form of interaction between electromagnetic and gravitational forces in very small volumes. But further speculations along these lines go beyond the intent of this work. What matters is that the desired processes are possible, given Einstein’s theory of general relativity and the existence of dark energy. Theory and experience thus permit travel faster than light, as long as such travel does not include the possibility of traveling to the past. Alcubierre’s proposal accords with the conceptual requirements, although of course there are no guarantees that such a spaceship will ever travel through interstellar space, just as there are no guarantees that we will ever achieve relativistic velocities either.

Whether these technologies will ever come to fruition I do not know. But what seems rather clear to me is that the physical expansion of humankind into the cosmos will vastly enhance our ability to preserve the dynamic character of science, while at the same time making it far more likely that a sun, some sun, will rise on the world of our descendants in a future so distant that most species on the surface of the Earth will have long disappeared. It is the process toward that long expansion that will make it possible to determine whether the relativistic velocities are technologically possible. I can only hope that we will set in motion the events that will ultimately allow our descendants to make that determination if they so choose.

This possibility of continuous expansion offers, then, a double bounty for our species. It increases our chances of survival, as we have seen. And it also preserves for a long time the opportunity to challenge our views of the universe. As Robert Goddard wrote in a letter to H.G. Wells, in 1932, "there can be no thought of finishing, for `aiming at the stars,' both literally and figuratively is a problem to occupy generations, so that no matter how much progress one makes, there is always t

[1] K.S. Thorne, Black holes and time warps: Einstein’s outrageous legacy. W.W. Norton and Company. 1994.

[2] J.A. Wheeler. (1962): Geometrodynamics. Academic Press.

[3] ^Morris, M., Thorne, K. and Yurtsever, U. (1988): Wormholes, time machines, and the weak energy condition”, Physical Review, 61, 13, pp. 1446 – 1449.

[4] Another approach is to nip all these speculations in the bud, by pointing out, as Jeffrey Barrett does, that “One might argue that there can be no threat of temporal paradoxes in GTR (General Theory of Relativity) since a particular mass-energy distribution and spacetime either is or isnot a solution to the field equations--if it is, then the solution provides a model for all spacetime events” (personal communication).

[5] Deutsch, David (1991): "Quantum mechanics near closed timelike curves". Physical Review D 44: pp. 3197–3217.

[6] Thorne, K. (1994): pp. 508-516.

[7] Davies, P. (2003): How to build a time machine. Penguin Books, p. 96.

[8] Ibid., pp. 102-105.

[9] For some strange reason many physicists, including Thorne and Davies, thought at one time that the paradoxes of time travel arose out of the exercise of free will. Obviously that is not so.

[10] As quoted in Thorne (2003), p. 521. Vacuum fluctuations would destroy the wormhole before it can become a time machine.

[11] For a fascinating account see Brush, S.G.

[12] See, for example, “Bohr and evolutionary relativism,” Ch. 3 of my Evolution and the Naked Truth, Ashgate (1998).

[13] Few ideas in the history of science have been corroborated as much as, say, Einstein’s formula for relativistic mass (discussed above). Practically every time we use a particle accelerator we confirm it with millions, perhaps billions of instances.

[14] Another possibility – and this is admittedly speculation – would be a machine capable of producing the gravito-magnito effect described in Ch. 5. Ning Li predicted that a rapidly rotating disk (this experiment uses superconductors) would produce the kind of distortion of spacetime that the Gravity B Probe may measure for the planet Earth. Objects placed in front of such objects would show a decrease in mass! Experiments carried out by Podkletnov in 1992 apparently confirmed Li’s astonishing prediction. Unfortunately no one has been able to reproduce Podkletnov’s results.

Sunday, August 7, 2011

To the Stars!

Chapter 7E

To the Stars!

Note: Although a little technical in a couple of places, I hope the reader will bear with me, for this is one of those cases where I need to bring up the technicalities for discussion. As I hope you will see, it is easier to see the point by doing a little bit of elementary algebra or chemistry.

Human Expansion throughout the Galaxy

With present technology a trip to the nearest stars would take tens of thousands of years. Perhaps with an extension of our present capabilities we may be able to cut the journey to only a few centuries. Unless a truly fantastic technology for suspended animation is discovered, the trip would have to be completed by the descendants of the astronauts that begin it. Under those conditions the best way to travel to the stars might be to turn one of O'Neill's colonies into a vehicle and set it to depart from our solar system. But surely, some critics might say, people in their right minds would not wish to take their space colony into interstellar space for journeys that would last thousands of years -- although how preposterous the idea is will have to be determined by a level of technology and an abundance of resources in interstellar space that we are in no position to predict now. At any rate, even people in their right minds may consider precisely such a journey if they knew of some unavoidable catastrophe that was to befall the solar system, or for other reasons that we may not fathom at this time.

Nevertheless, in journeys so long that only the descendants of the original travelers can complete them, a successful outcome may seem remote at best. Accordingly, some feel that the next great barrier to space exploration is the development of technology that would permit interstellar travel during a human lifetime. Since the closest stars are at least four light years away, and our galaxy is about one hundred thousand light years across, we would need starships that achieve velocities close to that of light.

Many scientists, however, believe that Einstein's special theory of relativity does not permit to accelerate spaceships close to that of light. And accelerating spaceships beyond the speed of light is simply forbidden by that theory. Nevertheless as we will see below, Einstein's physics does not in principle preclude either of these options.

Let us consider the first option. Although Alpha Centauri is only four light years away, the majority of stars of interest in the galaxy are tens, hundreds, or thousands of light years away. It may seem then that even if we could achieve relativistic velocities, traveling to the stars may take as long as the astronauts’ life spans, or longer. Fortunately, distance and time are relative to the inertial frame of reference in which they are measured (in an inertial frame of reference the velocity is uniform). In a ship that travels at great velocity with respect to us, time slows down and distances shorten, even though the astronauts themselves detect no abnormality. At velocities close to that of light, 300,000 Km/s, distances are so short (or alternatively, the dilation of time is so large that apparently unbelievably long journey became feasible. According to calculations by Carl Sagan, we could go to many interesting stars and come back in a decade or two, ship time[1]. Six years of ship time would go by in a round trip to Alpha Centaury (eight years Earth time), 22 to the Pleiades (800 years Earth time), and to the Galaxy of Andromeda, which is over a million light years away, the round trip would only take about five decades!

In the meantime nearly three million years would have gone by on the Earth, and so the return may offer more of a shock than what we might find in Andromeda. Most of us would not want to go on such a journey, but I imagine that the project would suffer no dearth of volunteers. The main problem, however, would be the energy required. At a constant acceleration of 1 g our spaceship would reach 99% of the speed of light in one year. But in reaching a velocity that high we would need to spend, according to some calculations, energy equal to the entire consumption in United States during a period of a million years! Enthusiasts like to point out that the first spaceship that went to the Moon spent an amount of energy tens of thousands of times larger than what many societies used only a century earlier. Bernard Oliver, who frowned on the idea of interstellar travel, thought that the requirements would be of this order of magnitude[2]. Even if such calculations are off by an order of magnitude or two, we are talking about staggering amounts of energy.

Some skeptical theorists have thought that the project is impossible, anyway, because as the velocity increases, so does the mass (also according to the special theory of relativity). But a larger mass requires larger energies to increase the velocity, which then increases the mass, and so on. This continuous increase in the mass of the spaceship eventually defeats the attempt to increase its velocity: we never reach a velocity close to that of light.

I do not believe that this objection works, however, for it does not take into account that from the point of view of the ship itself the mass has not increased. On the contrary, as most ships are conceived, it necessarily decreases as the engine burns fuel.

The skeptics’ suggestion is, again, that as the traveler approaches the speed of light, the mass increases so that it takes more and more energy to keep accelerating at the same rate. Many physicists, using this line of reasoning, conclude that it is impossible to travel at the speed of light, let alone faster. At least it seems that such is the reasoning that leads physicists like Smolin to conclude that, “…her mass increases as she approaches the speed of light. Were her speed to match that of light, her mass would become infinite. But one cannot accelerate an object that has infinite mass, hence one cannot accelerate an object to the speed of light and beyond.”[3] Similar remarks are made by Brian Greene[4] and even by Stephen Hawking[5].

I think this line of reasoning is misleading in two ways. First, once again, as far as the special theory of relativity is concerned, the mass and the corresponding energy requirements increase only from the point of view of the observers left behind on Earth. But from the point of view of the star travelers, who are at rest with respect to the ship, the mass of the ship does not increase at all, and therefore accelerating the ship is not particularly more daunting than it was at lower velocities. If anything, it is easier because the longer the ship accelerates the more fuel it uses, and therefore the more mass it loses, as I pointed out above. At speeds close to that of light, its rest mass should be considerably less than at the beginning of its journey, as long as you have the standard means of propulsion, i.e., shooting something out the back. In practice, or course, the faster a starship travels, the greater the resistance from the interstellar medium, which could become significant depending on the ship’s design and other factors. But this is a different type of concern altogether.

Second, the reason why the ship cannot match the speed of light has nothing to do with the mass becoming infinite. What physicists like Smolin, Greene, and Hawking have in mind is Einstein’s equation:

m= m0/(1- v2/c2 )1/2

where m is the mass of the ship from the point of view of the observer, m0 is the rest mass, v is the velocity of the ship with respect to the observer, and c is the speed of light.

As v gets closer to c, the term v2/c2 approaches 1. This means that the denominator approaches 0, which makes m approach infinity.

But m can never reach infinity for the simple reason that, if the velocity of the ship reached that of light, the denominator would become 0 and the function would be undefined. The problem is not that an infinite mass is physically inconceivable, but that the mathematical expression makes no sense.

The main insight is flawed, in any event. Infinite mass has nothing to do with the relativistic speed limit. The reason why a ship cannot accelerate to the speed of light is that Einstein’s formula for addition of velocities (based in part on the postulate that the speed of light is a constant) will always yield final velocities less than c.

If I am traveling in a ship at .5 c, the speed of a ray of light with respect to me, whether it goes towards me or away from me, still is 300,000 km/sec. If I fire a probe that travels at .5 c with respect to me, the speed of that ray of light would still be 300,000 km/sec with respect to the probe.

The result is that, according to Einstein[6], in the special theory of relativity I cannot just add the velocities of my ship with respect to the ground (vs) and of the probe with respect to me (vp).

That addition must be divided by the term 1+ vs.vp/c2. When I add the velocities (my ship’s plus the probe’s) I do not get c, therefore, but only .8 c.

This corrected interpretation of the situation (from the point of view of the astronaut, and the appropriate equations from the special theory of relativity) still seems to forbid travel at or faster than the speed of light. It leaves open the question of building a spaceship that comes very close to the speed of light, though.

There have been other attempts to prove that near-light speed travel is impossible, and there have been many refutations of such attempts as well. Of the presently available starship technologies (available in theory, that is) some form of controlled fusion may offer the best hope to achieve relativistic speeds (though just barely about 1/10 of the velocity of light). The ideal apparently would be a matter- antimatter engine, for it would convert all of the fuel's mass into energy as the particles and antiparticles annihilate each other. A serious problem is how to produce the necessary amounts of antimatter without spending more energy than that required to propel the starship. And if you do produce it, you then have to worry about how to channel it so it goes out the nozzle only, otherwise it will radiate in all directions. And there is also the already familiar difficulty that if you include all the fuel you need to keep accelerating the starship, then you need to build a much larger starship, which then needs even more fuel, and thereby an even larger starship.

To get around these problems we might employ starships that do not carry their fuel on board but take it from their environment. The first such "design" was for an interstellar fusion ram-jet that would scoop hydrogen ions from space, the Bussard Ramjet[7]. Bussard’s interesting idea was marred by several difficulties, especially that it would require a scoop 160 Km in diameter and that it would use a proton-proton fusion reaction that may work only in temperatures as hot as the interior of stars[8]. A modified version, the Whitmire catalytic nuclear ramjet,[9] apparently solves some of the main theoretical problems (it works by scooping up the hydrogen ions and running them through a catalytic nuclear reaction cycle, i.e., a nuclear reaction that repeats itself again and again, and that returns to the starting point of the reaction extremely fast so a new batch of protons can be used to propel the starship).

One possible sequence or reactions would be, for example, that of the catalytic cycle of carbon-nitrogen-oxygen (CNO), which occurs in the thermonuclear reactions of very hot starts:

12C + 1Hà13N + γ

13N + 1Hà14O + γ

14Oà14N + e+ + ν

14N + 1Hà15O + γ

15Oà15N + e+ + ν

15N + 1Hà12C + 4He

As we can see, the hydrogen ions (protons) react with the carbon isotope (12C) to begin the cycle, which, after utilizing a total of four protons, ends again in 12C plus a helium nucleus that is expelled out the nozzle, thus propelling the ship forward. The positrons (e­+) react with the electrons that remain from the ionization process and liberate additional energy in the form of gamma rays[10].

Whitmire and others[11] have worked on the possibility of either electromagnetic or electrostatic scoops of dimensions in the hundreds of meters, rather than kilometers, to reduce the immense proton and electron drag expected to affect a ship moving at relativistic speed (and that would be more efficient in the collection of protons). There are several practical problems with Whitmire’s design, the most nagging of which is that the temperatures in his reactor might reach temperatures of one billion degrees Kelvin!

There are also problems raised by the gravitational impact of a ship that moves through a medium with respect to which its mass increases extraordinarily (even if it does not change for the astronauts). It is possible that the ship may affect the structure of spacetime in its path. There would be additional problems to describe mathematically the interactions between the ship and the environment, using the general theory of relativity, for the ship will exchange energy with the particles closest to it as it accelerates, which would then cause all sorts of difficulties for the calculation of the relevant masses.

Whether these problems can be solved eventually, I do not know. Nevertheless the interesting result is that, in principle, interstellar hydrogen can be used to accelerate a starship at 1g to achieve speeds arbitrarily close to that of light.

[1] C. Sagan, “Direct Contact Among Galactic Civilizations by Relativistic Spaceflight,” Planetary and Space Science 11 (1963): 485-498.

[2] B.M. Oliver, “Efficient Interstellar Rocketry,” Paper IAA-87-606, presented at 38th I. A. F. Congress, Brighton, UK., 10-17 October 1987.

[3] Smolin…

[4] Brian Greene, The Elegant Universe, Vintage Books (2003): 52.

[5] Stephen Hawking, The Universe in a Nutshell, Bantam Books (2001):12.

[6] Albert Einstein, “On the Electrodynamics of Moving Bodies,” reprinted in The Principle of Relativity, with H.A. Lorenz, H. Minkowski and H. Weyl, Dover Publications, 1952 (republication of translation published by Methuen and Company, 1923). His equation as it appears in Section 5 of the article (“Composition of Velocities”), when the direction of motion of v and w is along the X axis, is:

V= v + w/1+ vw/c2

[7] R.W. Bussard, “Galactic Matter and Interstellar Spaceflight,” Astronautica Acta 6 (1960): 179-194.

[8] For an interesting discussion of this and other possible starships, please see E. Mallowe and G. Matloff, The Starflight Handbook: A Pioneer’s Guide to Interstellar Travel, John Wiley and Sons, Inc (1989): 89-149.

[9] D. P. Whitmire, “Relativistic Spaceflight and the Catalytic Nuclear Ramjet,” Acta Astronautica 2 (1975): 497-509.

[10] Otros ciclos catalíticos como el del 20Ne también serían posibles. El tope de la energía generada por el reactor de Whitmire sería unos 1011 megawatts, cerca de 10.000 veces lo producido por el mundo entero hoy en día (Mallowe y Matloff, p. 114).

[11] See again Mallove and Matloff, op. cit., 124-133.