CHAPTER NINE
The Menagerie of Possibilities
“That is the exploration that awaits you! Not mapping stars and studying nebula, but charting the unknown possibilities of existence.”
Q to Picard, in “All Good Things. ...”
In the course of more than 13 TV-years of the various Star Trek series, the writers have had the opportunity to tap into some of the most exciting ideas from all fields of physics. Sometimes they get it right; sometimes they blow it. Sometimes they just use the words that physicists use, and sometimes they incorporate the ideas associated with them. The topics they have dealt with read like a review of modern physics: special relativity, general relativity, cosmology, particle physics, time travel, space warping, and quantum fluctuations, to name just a few.
In this penultimate chapter, I thought it might be useful to make a brief presentation of some of the more interesting ideas from modern physics which the Star Trek writers have borrowedin particular, concepts I haven't concentrated on elsewhere in the book. Because of the diversity of the ideas, I give them here in glossary form, with no particular ordering or theme. In the last chapter, I will follow a similar formatthis time to sample the most blatant physics blunders in the series, as chosen by myself, selected fellow-physicists, and various trekkers. In both chapters, I have restricted my lists to the top ten examples; there are a lot more to choose from.
THE SCALE OF THE GALAXY AND THE UNIVERSE: Our galaxy is the stage on which the Star Trek drama is enacted. Throughout the series, galactic distance scales of various sorts play a crucial role in the action. Units from AUs (for Astronomical Unit: 1 AU is 93 million miles, the distance from the Earth to the Sun), which were used to describe the size of the V'ger cloud in the first Star Trek movie, to light-years are bandied about. In addition, various features of our galaxy are proposed, including a “Great Barrier” at the center (Star Trek V: The Final Frontier) and, in the original series, a “galactic barrier” at the edge (cf. “Where No Man Has Gone Before,” “By Any Other Name,” and “Is There in Truth No Beauty?”). It seems appropriate, therefore, in order to describe the playing field where Star Trek's action takes place, to offer our own present picture of the galaxy and its neighbors, and of distance scales in the universe.
Because of the large number of digits required, one rarely expresses astronomical distances in conventional units such as miles or kilometers. Instead, astronomers have created several fiducial lengths that seem more appropriate. One such unit is the AU, the distance between the Earth and the Sun. This is the characteristic distance scale of the solar system, with Pluto, the ultima Thule, being nearly 40 AU from the Sun. In Star Trek: The Motion Picture, the V'ger cloud is described as 82 AU in diameter, which is remarkably bigbigger, in fact, than the size of our solar system!
For comparison with interstellar distances, it is useful to express the Earth-Sun distance in terms of the time it takes light (or the time it would take the Enterprise at warp 1) to travel from the Sun to the Earthabout 8 minutes. (This should be the time it would take light to travel to most Class M planets from their suns.) Thus, we can say that an AU is 8 light-minutes. By comparison, the distance to the nearest star, Alpha Centauria binary star system where the inventor of warp drive, Zefrem Cochrane, apparently livedis about 4 light-years! This is a characteristic distance between stars in our region of the galaxy. It would take rockets, at their present rate of speed, more than 10,000 years to travel from here to Alpha Centauri. At warp 9, which is about 1500 times the speed of light, it would take about 6 hours to traverse 1 light-year.
The distance of the Sun from the center of the galaxy is approximately 25,000 light-years. At warp 9, it would take almost 15 years to traverse this distance, so it is unlikely that Sybok, having commandeered the Enterprise, would have been able to take her to the galactic center, as he did in Star Trek V: The Final Frontier, unless the Enterprise was essentially already there.
The Milky Way is a spiral galaxy, with a large central disk of stars. It is approximately 100,000 light-years across and a few thousand light-years deep. The Voyager, tossed 70,000 light-years away from Earth in the first episode of that series, would thus indeed be on the other side of the galaxy. At warp 9, the ship would take about 50 years to return to the neighborhood of our Sun from that distance.
At the center of our galaxy is a large galactic bulgea dense conglomeration of starsseveral thousand light- years across. It is thought to harbor a black hole of about a million solar masses. Black holes ranging from 100,000 to more than a billion solar masses are likely at the center of many other galaxies.
A roughly spherical halo of very old stars surrounds the galaxy. The
conglomerations of thousands of stars called globular clusters found here are thought to be among the oldest objects in our galaxy, perhaps as old as 18 billion years according to our current methods of datingmore ancient
even than the “black cluster” in the episode “Hero Worship,” which was said to be 9 billion years old. An even larger spherical halo, consisting of “dark matter” (about which more later), is thought to encompass the galaxy. This halo is invisible to all types of telescopes; its existence is inferred from the motion of stars and gas in the galaxy, and it may well contain 10 times as much mass as the observable galaxy.
The Milky Way is an average-size spiral galaxy, containing a few hundred billion stars. There are approximately 100 billion galaxies in the observable universe, each containing more or less that many stars! Of the galaxies we see, roughly 70 percent are spiral; the rest are somewhat spherical in shape and are known as elliptical galaxies. The largest of them are giant ellipticals more than 10 times as massive as the Milky Way.
Most galaxies are clustered in groups. In our local group, the nearest galaxies to the Milky Way are small satellite galaxies orbiting our own. These objects, observable in the Southern Hemisphere, are called the Large and Small Magellanic Clouds. It is about 6 million light-years to the nearest large galaxy, the Andromeda galaxyhome to the Kelvans, who attempt to take over the Enterprise and return to their home galaxy in the original-series episode “By Any Other Name.” At warp 9, the voyage would take approximately 4000 years!
Because of the time it takes light to travel, as we observe farther and farther out, we are also observing farther and farther back in time. The farthest we can now observe with electromagnetic sensors is back to a time when the universe was about 300,000 years old. Before then, matter existed as a hot ionized gas opaque to electromagnetic radiation. When we look out in all directions, we see the radiation emitted when matter and radiation finally “decoupled.” This is known as the cosmic microwave background. Observing it, most recently with the COBE satellite launched by NASA in 1989, we get a picture of what the universe looked like when it was only about 300,000 years old.
Finally, the universe itself is expanding uniformly. As a result, distant galaxies are observed to be receding from usand the farther away they are, the faster they are receding, at a rate directly proportional to their distance from us. This rate of expansion, characterized by a quantity called the Hubble constant, is such that galaxies located 10 million light-years from us are moving away at an average rate of about 150 to 300 kilometers per second. Working backward, we find that all the observed galaxies in the universe would converge about 10 billion to 20 billion years ago, at the time of the big bang.
DARK MATTER: As I mentioned above, our galaxy is apparently immersed in a vast sea of invisible material. 1 By studying the motion of the stars, of hydrogen gas clouds, and even of the Large and Small Magellanic Clouds around the galactic center, and using Newton's laws relating the velocity of orbiting objects to the mass pulling them, it has been determined that there is a roughly spherical halo of dark material stretching out to distances perhaps 10 times as far from the center of the galaxy as we are. This material accounts for at least 90 percent of the mass of the Milky Way. Moreover, as we observe the motion of other galaxies, including the ellipticals, and also the motion of groups of galaxies, we find that there is more matter associated with these systems than we can account for on the basis of the observable material. The entire observable universe therefore seems to be dominated by dark matter. It is currently believed that between 90 and 99 percent of the mass of the universe is made of this material.
The notion of dark matter has crept into both the Next Generation and the Voyager series, and in an amusing way. For example, in the Voyager episode “Cathexis,” the ship enters a “dark matter nebula,” which, as you might imagine, is like a dark cloud, so that you cannot see into it. The Enterprise had already encountered similar objects, including the “black cluster” mentioned earlier. However, the salient fact about dark matter is not that it shields light in any way but that it does not shinethat is, emit radiationand does not even absorb significant amounts of radiation. If it did either, it would be detectable by telescopes. If you were inside a dark matter cloud, as we probably are, you would not even see it.
The question of the nature, origin, and distribution of dark matter is probably one of the most exciting unresolved issues in cosmology today. Since this unknown material dominates the mass density of the universe, its distribution must have determined how and when the observable matter gravitationally collapsed to create the galactic clusters, galaxies, stars, and planets that make the universe so interesting to us. Our very existence is directly dependent on this material. Moreover, the amount of dark matter in the universe will determine the universe's eventual fate: whether it ends in a bang (by recollapsing) or an endless whimper (by continuing to expand even as the stars eventually burn out) will depend on how much matterof whatever sortit contains,
since gravitational attraction is what slows the expansion.
Even more interesting are the strong arguments that the dark matter may be made of particles completely different from the protons and neutrons that make up normal matter. Independent limits on the amount of normal matter in the universe, based on calculations of nuclear reaction rates in the early universe and the subsequent formation of light elements, suggest that there may not be enough protons and neutrons to account for the dark matter around galaxies and clusters. Moreover, it seems that in order for the small fluctuations in the initial distribution of matter to have collapsed in the hot plasma of the early universe to form the galaxies and clusters we observe today, some new type of elementary particleof a kind that does not interact with electromagnetic radiationhad to be involved. If the dark matter is indeed made of some new type of elementary particle, then:
(a) the dark matter is not just “out there,” it is in this room as you are reading this book, passing imperceptibly through your body. These exotic elementary particles would not clump into astronomical objects; they would form a diffuse “gas” streaming throughout the galaxy. Since they interact at best only very weakly with matter, they would be able to sail through objects as big as the Earth. Indeed, examples of such particles already exist in nature notably, neutrinos (particles that should be familiar to trekkers, and which I will later discuss).
(b) the dark matter might be detected directly here on Earth, using sophisticated elementary-particle-detection techniques. Various detectors designed with a sensitivity to various dark matter candidates are currently being constructed.
(c) the detections of such particles might revolutionize elementary particle physics. It is quite likely that these objects are remnants of production processes in the very early universe, well before it was 1 second old, and would thus be related to physics at energy scales comparable to or even beyond those we can directly probe using modern accelerators.
Of course, as exciting as this possibility is, we are not yet certain that the dark matter may not be made of less exotic stuff. There are many ways of putting protons and neutrons together so that they do not shine. For example, if we populated the galaxy with snowballs, or boulders, these would be difficult to detect. Perhaps the most plausible possibility for this scenario is that there are many objects in the galaxy which are almost large enough to be stars but are too small for nuclear reactions to start occurring in their cores. Such objects are known as brown dwarfs, and Data and his colleagues aboard the Enterprise have discussed them (for instance, in “Manhunt”). In fact, there are interesting experiments going on right now to find out whether or not brown dwarfsknown in this context as MACHOs (for Massive Astrophysical Compact Halo Objects)make up a significant component of the dark matter halo around the Milky Way galaxy. While these objects are not directly observable, if one of them were to pass in front of a star the star's light would be affected by the MACHO's gravity in such a way as to make the star appear brighter. This “gravitational lensing” phenomenon was first predicted by Einstein back in the 1930s, and we now have the technology to detect it. Several experiments are observing literally millions of stars in our galaxy each night, to see if this lensing phenomenon takes place. The sensitivity is sufficient to detect a dark matter halo of MACHOS, if they do indeed make up most of the dark matter surrounding our galaxy. Preliminary data have set upper limits that tend to suggest that the dark matter halo is not composed of MACHOs, but the question is still open.
NEUTRON STARS: These objects are, as you will recall, all that is left of the collapsed cores of massive stars that have undergone a supernova. Although they typically contain a mass somewhat in excess of the mass of our Sun, they are so compressed that they are about the size of Manhattan! Once again, the Star Trek writers have outdone themselves in the nomenclature department. The Enterprise has several times encountered material expelled from a neutron stara material that the writers have dubbed “neutronium.” Since neutron stars are composed almost entirely of neutrons held so tightly together that the star is basically one huge atomic nucleus, the name is a good one. The Doomsday machine in the episode of the same name was apparently made of pure neutronium, which is why it was impervious to Federation weapons. However, in order for this material to be stable it has to be under the incredibly high pressure created by the gravitational attraction of a stellar mass of material only 15 kilometers in radius. In the real world, such material exists only as part of a neutron star.
The Enterprise has had several close calls near neutron stars. In the episode “Evolution,” when the Nanites began eating the ship's computers, the crew was in the act of studying a neutron star that was apparently about to erupt as it accreted material. In the episode “The Masterpiece Society,” the Enterprise must deflect a stellar core
fragment hurtling toward Moab IV.
There are no doubt millions of neutron stars in the galaxy. Most of these are born with incredibly large magnetic fields inside them. If they are spinning rapidly, they make wonderful radio beacons. Radiation is emitted from each of their poles, and if the magnetic field is tilted with respect to the spin axis, a rotating beacon is created. On Earth, we detect these periodic bursts of radio waves, and call their sources pulsars. Rotating out in space, they make the best clocks in the universe. The pulsar signals can keep time to better than one microsecond per year. Moreover, some pulsars produce more than 1000 pulses per second. This means that an object that is essentially a huge atomic nucleus with the mass of the Sun and 10 to 20 kilometers across is rotating over 1000 times each second. Think about that. The rotation speed at the neutron star surface is therefore almost half the speed of light! Pulsars are one illustration of the fact that nature produces objects more remarkable than any the Star Trek writers are likely to invent.
OTHER DIMENSIONS: As James T. Kirk slowly drifts in and out of this universe in “The Tholian Web,” we find that the cause is a “spatial interphase” briefly connecting different dimensional planes, which make up otherwise “parallel universes.” Twice before in the series, Kirk encountered parallel universesone made of antimatter, in “The Alternative Factor,” and the other accessed via the transporter, in “Mirror, Mirror.” In The Next Generation, we have the Q-continuum, Dr. Paul Manheim's nonlinear time “window into other dimensions,” and of course subspace itself, containing an infinite number of dimensions, which aliens, like the ones who kidnapped Lieutenant Riker in “Schisms,” can hide in.
The notion that somehow the four dimensions of space and time we live in are not all there is has had great tenacity in the popular consciousness. Recently a Harvard psychiatrist wrote a successful book (and apparently got in trouble with the Medical School) in which he reported on his analysis of a variety of patients, all of whom claimed they had been abducted by aliens. In an interview, when asked where the aliens came from and how they got here, he is reported to have suggested, “From another dimension.”
This love affair with higher dimensions no doubt has at its origin the special theory of relativity. Once three- dimensional space was tied with time to make four-dimensional spacetime by Hermann Minkowski, it was natural to suppose that the process might continue. Moreover, once general relativity demonstrated that what we perceive as the force of gravity can be associated with the curvature of spacetime, it was not outrageous to speculate that perhaps other forces might be associated with curvature in yet other dimensions.
Among the first to speculate on this idea were the Polish physicist Theodor Kaluza in 1919 and, independently, the Swedish physicist Oskar Klein in 1926. They proposed that electromagnetism could be unified with gravity in a five-dimensional universe. Perhaps the electromagnetic force is related to some “curvature” in a fifth dimension, just as the gravitational force is due to curvature in four-dimensional spacetime.
This is a very pretty idea, but it has problems. In fact, in any scenario in which one envisages extra dimensions in the universe, one has to explain why we don't experience these dimensions as we do space and time. The proposed answer to this question is very important, because it crops up again and again when physicists consider the possibility of higher dimensions in the universe.
Consider a cylinder and an intelligent bug. As long as the circumference of the cylinder is large compared to the size of the bug, then the bug can move along both dimensions and will sense that it is crawling on a two- dimensional surface.
However, if the circumference of the cylinder becomes very small, then as far as the bug is concerned it is crawling on a one-dimensional objectnamely, a line or a stringand can move only up or down:
Now think how such a bug might actually find out that there is another dimension, corresponding to the circumference of the cylinder. With a microscope, it might be able to make out the “string's” width. However, the wavelength of radiation needed to resolve sizes this small would have to be on order of the diameter of the cylinder or smaller, because, as I noted in chapter 5, waves scatter off only those objects that are at least comparable to their wavelength. Since the energy of radiation increases as its wavelength decreases, it would require a certain minimum energy of radiation to resolve this “extra dimension.”
If somehow a fifth dimension were “curled up” in a tight circle, then unless we focused a lot of energy at a small point, we would not be able to send waves traveling through it to probe its existence, and the world would continue to look to us to be effectively four-dimensional. After all, we know that space is three-dimensional because we can probe it with waves traveling in all three dimensions.
If the only waves that can be sent into the fifth dimension have much more energy than we can produce even in high-energy accelerators, then we cannot experience this extra dimension.
In spite of its intrinsic interest, the Kaluza-Klein theory cannot be a complete theory. First, it does not explain why the fifth dimension would be curled up into a tiny circle. Second, we now know of the existence of two other
fundamental forces in nature beyond electro-magnetism and gravitythe strong nuclear force and the weak nuclear force. Why stop at a fifth dimension? Why not include enough extra dimensions to accommodate all the fundamental forces?
In fact, modern particle physics has raised just such a possibility. The modern effort, centered around what is called superstring theory, focused initially on extending the general theory of relativity so that a consistent theory of quantum gravity could be constructed. In the end, however, the goal of a unified theory of all interactions has resurfaced.
I have already noted the challenges faced in developing a theory wherein general relativity is made consistent with quantum mechanics. The key difficulty in this effort is trying to understand how quantum fluctuations in spacetime can be handled. In elementary particle theory, quantum excitations in fieldsthe electric field, for exampleare manifested as elementary particles, or quanta. If one tries to understand quantum excitations in the gravitational fieldwhich, in general relativity, correspond to quantum excitations of spacetime the mathematics leads to nonsensical predictions.
The advance of string theory was to suppose that at microscopic levels, typical of the very small scales (that is, 10 -33 cm) where quantum gravitational effects might be important, what we think of as pointlike elementary particles actually could be resolved as vibrating strings. The mass of each particle would correspond in some sense to the energy of vibration of these strings.
The reason for making this otherwise rather outlandish proposal is that it was discovered as early as the 1970s that such a theory requires the existence of particles having the properties that quantum excitations in spacetimeknown as gravitonsshould have. General relativity is thus in some sense imbedded in the theory in a way that may be consistent with quantum mechanics.
However, a quantum theory of strings cannot be made mathematically consistent in 4 dimensions, or 5, or even 6. It turns out that such theories can exist consistently only in 10 dimensions, or perhaps only 26! Indeed, Lieutenant Reginald Barclay, while he momentarily possessed an IQ of 1200 after having been zapped by a Cytherian probe, had quite a debate with Albert Einstein on the holodeck about which of these two possibilities was more palatable in order to incorporate quantum mechanics in general relativity.
This plethora of dimensions may seem an embarrassment, but it was quickly recognized that like many embarrassments it also presented an opportunity. Perhaps all the fundamental forces in nature could be incorporated in a theory of 10 or more dimensions, in which all the dimensions but the four we know curl up with diameters on the order of the Planck scale (10 -33 cm)as Lieutenant Barclay surmised they mustand are thus
unmeasurable today.
Alas, this great hope has remained no more than that. We have, at the present time, absolutely no idea whether the tentative proposals of string theory can produce a unified Theory of Everything. Also, just as with the Kaluza- Klein theory, no one has any clear notion of why the other dimensions, if they exist, would curl up, leaving four- dimensional spacetime on large scales.
So, the moral of this saga is that Yes, Virginia, there may be extra dimensions in the universe. In fact, there is now some reason to expect them. However, these extra dimensions are not the sort that might house aliens who could then abduct psychiatric patients (or Commander Riker, for that matter). They are not “parallel universes.”
They also cannot be mixed up with the four dimensions of spacetime in a way that would allow objects to drift from one place to another in space by passing through another dimension, as “subspace” seems to allow in the Star Trek universe.
Nevertheless, we cannot rule out the possibility that there might exist microscopic or even macroscopic “bridges” to otherwise disconnected (or parallel) universes. Indeed, in general relativity, regions of very high curvature inside a black hole, or in a wormholecan be thought of as connecting otherwise disconnected and potentially very large regions of spacetime. I know of no reason to expect such phenomena outside black holes and wormholes, based on our present picture of the universe, but since we cannot rule them out, I suppose that
Federation starships are free to keep finding them.
ANYONS: In the Next Generation episode “The Next Phase,” a transporter mix-up with a new Romulan cloaking device that puts matter “out of phase” with other matter causes Geordi LaForge and Ro Laren to vanish. They are presumed dead, and remain invisible and incommunicado until Data modifies an “anyon emitter” for another purpose and miraculously “dŽphasŽs” them.
If the Star Trek writers had never heard of anyons, and I am willing to bet that they hadn't, their penchant for pulling apt names out of the air is truly eerie. Anyons are theoretical constructs proposed and named by my friend Frank Wilczek, a physicist at the Institute for Advanced Study in Princeton, and his collaborators. Incidentally, he also invented another particlea dark matter candidate he called the axion, after a laundry detergent. “Axionic chips” also crop up in Star Trek, as part of an advanced machine's neural network. But I digress.
In the three-dimensional space in which we live, elementary particles are designated as fermions and bosons, depending on their spin. We associate with each variety of elementary particle a quantum number, which gives the value of its spin. This number can be an integer (0,1, 2,... ) or a half integer (1/2, 3/2, 5/2,...). Particles with integer spin are called bosons, and particles with half integer spin are called fermions. The quantum mechanical behavior of fermions and bosons is different: When two identical fermions are interchanged, the quantum mechanical wavefunction describing their properties is multiplied by minus 1, whereas in an interchange of bosons nothing happens to the wavefunction. Therefore, two fermions can never be in the same place, because if they were, interchanging them would leave the configuration identical but the wavefunction would have to be multiplied by minus 1, and the only thing that can be multiplied by minus 1 and remain the same is 0. Thus, the wavefunction must vanish. This is the origin of the famous Pauli exclusion principleoriginally applied to electronswhich states that two identical fermions cannot occupy the same quantum mechanical state.
In any case, it turns out that if one allows panicles to move in only two dimensionsas the two-dimensional beings encountered by the Enterprise (see next item) are forced to do; or, more relevantly, as happens in the real world when atomic configurations in a crystal are arranged so that electrons, say, travel only on a two- dimensional plane the standard quantum mechanical rules that apply in three-dimensional space are changed. Spin is no longer quantized, and particles can carry any value for this quantity. Hence, instead of fermi-ons or bos-ons, one can have any-ons. This was the origin of the name, and the idea that Wilczek and others have explored.
Back to the Star Trek writers: What I find amusing is that the number by which the wavefunction of particles is multiplied when the particles are interchanged is called a “phase.” Fermion wavefunctions are multiplied by a phase of minus 1, while bosons are multiplied by a phase of 1 and hence remain the same. Anyons are multiplied by a combination of 1 and an imaginary number (imaginary numbers are the square roots of negative numbers), and hence in a real sense are “out of phase” with normal particles. So it seems fitting that an “anyon emitter” would change the phase of something, doesn't it?
COSMIC STRINGS: In the Next Generation episode “The Loss,” the crew of the Enterprise encounters two- dimensional beings who have lost their way. These beings live on a “cosmic-strings fragment.” In the episode, this is described as an infinitesimally thin filament in space, with a very strong gravitational pull and vibrating with a characteristic set of “subspace” frequencies.
In fact, cosmic strings are objects proposed to have been created during a phase transition in the early universe. One of the world's experts on these theoretical objects recently joined the faculty at Case Western Reserve, so I hear a lot about cosmic strings these days. Their properties would be similar in some respects to the object encountered by the Enterprise.
During a phase transition in materialsas when water boils, say, or freezesthe configuration of the material's constituent particles changes. When water freezes, it forms a crystalline structure. As crystals aligned in various directions grow, they can meet to form random lines, which create the patterns that look so pretty on a window in the winter. During a phase transition in the early universe, the configuration of matter, radiation, and empty space (which, I remind you, can carry energy) changes, too. Sometimes during these transitions, various regions of the universe relax into different configurations. As these configurations grow, they too can eventually meet sometimes at a point, and sometimes along a line, marking a boundary between the regions. Energy becomes
trapped in this boundary line, and it forms what we call a cosmic string.
We have no idea whether cosmic strings actually were created in the early universe, but if they were and lasted up to the present time they could produce some fascinating effects. They would be infinitesimally thinthinner than a protonyet the mass density they carry would be enormous, up to a million million tons per centimeter. They might form the seeds around which matter collapses to form galaxies, for example. They would also “vibrate,” producing not subspace harmonics but gravitational waves. Indeed, we may well detect the gravitational wave signature of a cosmic string before we ever directly observe the string itself.
So much for the similarities with the Star Trek string. Now for the differences. Because of the way they are formed, cosmic strings cannot exist in fragments. They have to exist either in closed loops or as a single long string that winds its way through the universe. Moreover, in spite of their large mass density, cosmic strings exert no gravitational force on faraway objects. Only if a cosmic string moves past an object will the object experience a sudden gravitational force. These are subtle points, however; on the whole, the Star Trek writers have done pretty well by cosmic strings.
QUANTUM MEASUREMENTS: There was a wonderful episode in the final season of The Next Generation, called “Parallels,” in which Worf begins to jump between different “quantum realities.” The episode touches, albeit incorrectly, on one of the most fascinating aspects of quantum mechanicsquantum measurement theory.
Since we live on a scale at which quantum mechanical phenomena are not directly observed, our entire intuitive physical picture of the universe is classical in character. When we discuss quantum mechanics, we generally use a classical language, so as to try and explain the quantum mechanical world in terms we understand. This approach, which is usually referred to as “the interpretation of quantum mechanics” and so fascinates some philosophers of science, is benighted; what we really should be discussing is “the interpretation of classical mechanics”that is, how can the classical word we seewhich is only an approximation of the underlying reality, which in turn is quantum mechanical in naturebe understood in terms of the proper quantum mechanical variables?
If we insist on interpreting quantum mechanical phenomena in terms of classical concepts, we will inevitably encounter phenomena that seem paradoxical, or impossible. This is as it should be. Classical mechanics cannot account properly for quantum mechanical phenomena, and so there is no reason that classical descriptions should make sense.
Having issued this caveat, I will describe the relevant issues in classical mechanics terms, because these are the only tools of language I have. While I have the proper mathematical terms to describe quantum mechanics, like all other physicists I have recourse only to a classical mental picture, because all my direct experience is classical.
As I alluded to in chapter 5, one of the most remarkable features of quantum mechanics is that objects observed to have some property cannot be said to have had that property the instant before the observation. The observation process can change the character of the physical system under consideration. The quantum mechanical wavefunc-tion of a system describes completely the configuration of this system at any one time, and this wavefunction evolves according to deterministic laws of physics. However, what makes things seem so screwy is that this wavefunction can encompass two or more mutually exclusive configurations at the same time.
For example, if a particle is spinning clockwise, we say that its spin is “up.” If it is spinning counterclockwise, we say that its spin is “down.” Now, the quantum mechanical wavefunction of this particle can incorporate a sum with equal probabilities: spin up and spin down. If you measure the direction of the spin, you will measure either spin up or spin down. Once you have made the measurement, the wavefunction of the particle will from then on include only the component you measured the particle to have; if you measured spin up, you will go on measuring this same value for this panicle.
This picture presents problems. How, you may ask, can the particle have had both spin up and spin down before the measurement? The correct answer is that it had neither. The configuration of its spin was indeterminate before the measurement.
The fact that the quantum mechanical wavefunction that describes objects does not correspond to unique values for observables is especially disturbing when one begins to think of living objects. There is a famous paradox called “Schršdinger's cat.” (Erwin Schršdinger was one of the young Turks in their twenties who, early in this century, helped uncover the laws of quantum mechanics. The equation describing the time evolution of the quantum mechanical wavefunction is known as Schršdinger's equation.) Imagine a box, inside of which is a cat. Inside the box, aimed at the cat, is a gun, which is hooked up to a radioactive source. The radioactive source has a certain quantum mechanical probability of decaying at any given time. When the source decays, the gun will fire and kill the cat. Is the wavefunction describing the cat, before I open the box, a linear superposition of a live cat and a dead cat? This seems absurd.
Similarly, our consciousness is always unique, never indeterminate. Is the act of consciousness a measurement? If so, then it could be said that at any instant there is a nonzero quantum mechanical probability for a number of different outcomes to occur, and our act of consciousness determines which outcome we experience. Reality then has an infinite number of branches. At every instant our consciousness determines which branch we inhabit, but an infinite number of other possibilities exist a priori.
This “many worlds” interpretation of quantum mechanicswhich says that in some other branch of the quantum mechanical wavefunction Stephen Hawking is writing this book and I am writing the forewordis apparently the basis for poor Worf's misery. Indeed, Data says as much during the episode. When Worf's ship traverses a “quantum fissure in spacetime,” while simultaneously emitting a “subspace pulse,” the barriers between quantum realities “break down,” and Worf begins to jump from one branch of the wavefunction to another at random times, experiencing numerous alternative quantum realities. This can never happen, of course, because once a measurement has been made, the system, including the measuring apparatus (Worf, in this case), has changed. Once Worf has an experience, there is no going back ... or perhaps I should say sideways. The experience itself is enough to fix reality. The very nature of quantum mechanics demands this.
There is one other feature of quantum mechanics touched upon in the same episode. The Enterprise crew are able to verify that Worf is from another “quantum reality” at one point by arguing that his “quantum signature at the atomic level” differs from anything in their world. According to Data, this signature is unique and cannot change due to any physical process. This is technobabble, of course; however, it does relate to something interesting about quantum mechanics. The entire set of all possible states of a system is called a Hubert space, after David Hubert, the famous German mathematician who, among other things, came very close to developing general relativity before Einstein. It sometimes happens that the Hubert space breaks up into separate sectors, called “superselection sectors.” In this case, no local physical process can move a system from one sector to another. Each sector is labeled by some quantityfor instance, the total electric charge of the system. If one wished to be poetic, one could say that this quantity provided a unique “quantum signature” for this sector, since all local quantum operations preserve the same sector, and the behavior of the operations and the observables they are associated with is determined by this quantity.
However, the different branches of the quantum mechanical wave-function of a system must be in a single superselection sector, because any one of them is physically accessible in principle. So, unfortunately for Worf, even if he did violate the basic tenets of quantum mechanics by jumping from one branch to another, no external observable would be likely to exist to validate his story.
The whole point of the many-worlds interpretation of quantum mechanics (or any other interpretation of quantum mechanics, for that matter) is that you can never experience more than one world at a time. And thankfully there are other laws of physics that would prevent the appearance of millions of Enterprises from different realities, as happens at the end of the episode. Simple conservation of energy a purely classical conceptis enough to forbid it.
SOLITONS: In the Next Generation episode “New Ground,” the Enterprise assists in an experiment developed by Dr. Ja'Dor, of the planet Bilana III. Here a “soliton wave,” a nondispersing wavefront of subspace distortion, is used to propel a test ship into warp speed without the need for warp drive. The system requires a planet at the far end of the voyage, which will deliver a scattering field to dissipate the wave. The experiment nearly results in a disaster, which is of course averted at the last instant.
Solitons are not an invention of the Star Trek writers. The term is short for “solitary waves” and in fact refers to a
phenomenon originally observed in water waves by a Scottish engineer, John Scott Russell, in 1834. While conducting an unpaid study of the design of canal barges for the Union Canal Society of Edinburgh, he noticed something peculiar. In his own words:
I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stoppedNot so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded smooth and well defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed, I followed it on horseback and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished and after a chase of one or two miles I lost it in the windings of the channel. Such in the months of August 1834 was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation. 2
Scott Russell later coined the words “solitary wave” to describe this marvel, and the term has persisted, even as solitons have cropped up in many different subfields of physics. More generally, solitons are nondissipative, classically extended, but finite-size objects that can propagate from point to point. In fact, for this reason the disasters that drive the plot in “New Ground” could not happen. First of all, the soliton would not “emit a great deal of radio interference.” If it did, it would be dissipating its energy. For the same reason, it would not continue to gain energy or change frequency.
Normal waves are extended objects that tend to dissipate their energy as they travel. However, classical forces resulting from some interaction throughout space, called a “field”generally keep soli-tons intact, so that they can propagate without losing energy to the environment. Because they are self-contained energetic solutions of the equations describing motion, they behave, in principle, just like fundamental objectslike elementary particles. In fact, in certain mathematical models of the strong interaction holding quarks together, the proton could be viewed as a soliton, in which case we are all made of solitons! New fields have been proposed in elementary-particle physics which may coalesce into “soliton stars”objects that are the size of stars but involve a single coherent field. Such objects have yet to be observed, but they may well exist.
QUASARS: In the episode “The Pegasus”wherein we learn about the Treaty of Algon, which forbade the Federation to use cloaking deviceswe find Picard's Enterprise exploring the Mecoria Quasar. Earlier, in the original-series episode “The Galileo Seven,” we learned that the original Enterprise had standing orders to investigate these objects whenever they might be encountered. But neither ship would in fact likely ever encounter a quasar while touring the outskirts of our galaxy. This is because quasars, the most energetic objects yet known in the universe (they radiate energies comparable to those of entire galaxies, yet they are so small that they are unresolvable by telescopes), are thought to be enormous black holes at the center of some galaxies, and to be literally swallowing up the central mass of their hosts. This is the only mechanism yet proposed that can explain the observed energies and size scales of quasars. As matter falls into a black hole, it radiates a great deal of energy (as it loses its potential gravitational energy). If million- or billion-solar-mass black holes exist at the centers of some galaxies, they can swallow whole star systems, which in turn will radiate the necessary energy to make up the quasar signal. For this reason, quasars are often part of what we call “active galactic nuclei.” Also for this reason, you would not want to encounter one of these objects up close. The encounter would be fatal.
NEUTRINOS: Neutrinos are my favorite particles in nature, which is why I saved them for last. I have spent a fair fraction of my own research on these critters, because we know so little about them yet they promise to teach us much about the fundamental structure of matter and the nature of the universe.
Many times, in various Star Trek episodes, neutrinos are used or measured on starships. For example, elevated
neutrino readings are usually read as objects traverse the Bajoran wormhole. We also learn in the episode “The Enemy” that Geordi LaForge's visor can detect neutrinos, when a neutrino beacon is sent to locate him so that he can be rescued from an inhospitable planet. A “neutrino field” is encountered in the episode “Power Play,” and momentarily interferes with the attempt to transport some noncorporeal criminal life-forms aboard the Enterprise.
Neutrinos were first predicted to exist as the result of a puzzle related to the decay of neutrons. While neutrons are stable inside atomic nuclei, free neutrons are observed to decay, in an average time of about 10 minutes, into protons and electrons. The electric charge works out fine, because a neutron is electrically neutral, while a proton
has a positive charge and an electron an equal and opposite negative charge. The mass of a proton plus an electron is almost as much as the mass of a neutron, so there is not much free energy left to produce other massive particles in the decay, in any case.
However, sometimes the proton and electron are observed to travel off in the same direction during the decay. This is impossible, because each emitted particle carries momentum. If the original neutron was at rest, it had zero momentum, so something else would have to be emitted in the decay to carry off momentum in the opposite direction.
Such a hypothetical particle was proposed by Wolfgang Pauli in the 1930s, and was named a “neutrino” (for “little neutron”) by Enrico Fermi. He chose this name because Pauli's particle had to be electrically neutral, in order not to spoil the charge conservation in the decay, and had to have, at most, a very small mass, in order to be produced with the energy available after the proton and electron were emitted.
Because neutrinos are electrically neutral, and because they do not feel the strong force (which binds quarks and helps hold the nucleus together), they interact only very weakly with normal matter. Yet because neutrinos are produced in nuclear reactions, like those that power the Sun, they are everywhere. Six hundred billion neutrinos per second pierce every square centimeter of your body every second of every day, coming from the Sunan inexorable onslaught that has even inspired a poem by John Updike. You don't notice this neutrino siege, because the neutrinos pass right through your body without a trace. On average, these solar neutrinos could go through 10,000 light-years of material before interacting with any of it.
If this is the case, then how can we be sure that neutrinos exist other than in theory, you may ask? Well, the wonderful thing about quantum mechanics is that it yields probabilities. That is why I wrote “on average” in the above paragraph. While most neutrinos will travel 10,000 light-years through matter without interacting with anything, if one has enough neutrinos and a big enough target, one can get lucky.
This principle was first put to use in 1956 by Frederick Reines and Clyde Cowan, who put a several-ton target near a nuclear reactor and indeed observed a few events. This empirical discovery of the neutrino (actually, the antineutrino) occurred more than 20 years after it was posited, and well after most physicists had accepted its existence.
Nowadays we use much larger detectors. The first observation of solar neutrinos was made in the 1960s, by Ray Davis and collaborators, using 100,000 gallons of cleaning fluid in a tank underground at the Homestake Gold Mine in South Dakota. Each day, on average, one neutrino from the Sun would interact with an atom of chlorine and turn it into an atom of argon. It is a tribute to these experimenters that they could detect nuclear alchemy at such a small rate. It turns out that the rate that their detector and all subsequent solar-neutrino detectors measured is different from the predicted rate. This “solar neutrino puzzle,” as it is called, could signal the need for new fundamental physics associated with neutrinos.
The biggest neutrino detector in the world is being built in the Kamiokande mine in Japan. Containing over 30,000 tons of water, it will be the successor to a 5000-ton detector, which was one of two neutrino detectors to see a handful of neutrinos from a 1987 supernova in the Large Magellanic Cloud, more than 150,000 light-years away!
Which brings me back to where I began. Neutrinos are one of the new tools physicists are using to open windows on the universe. By exploiting every possible kind of elementary-particle detection along with our conventional electromagnetic detectors, we may well uncover the secrets of the galaxy long before we are able to venture out and explore it. Of course, if it were possible to invent a neutrino detector the size of Geordi's visor, that would be a great help!