Beyond Star Trek

by Lawrence M. Krauss

  Moreover—and this is very important—at some points the sum of the different quantum states is such that the different states interfere with each other (they have relative minus signs), so that the wavefunction vanishes. An electron will never be found in a position where this obtains. It is in this sense that electrons can act like waves. If two water waves meet at a certain point, and one has a crest at that point and the other has a trough, the two waves cancel each other out and the surface of the water flattens. Thus, for waves, one can sometimes have 1 + 1 = 0! The same is true for electrons or other quantum objects. If the wavefunction (this is after all why we call it a wavefunction) of an electron is made up of a superposition of different states each of which describes a configuration involving an electron that has traveled to that particular point along a different path, and if the minus signs are just right, one can find that there is zero probability in the end for finding the electron at that point.

  Nonsense, you may say. An electron that goes from one side of a barrier to another must go through either one slit or the other to get there—in fact, I can prove it by putting an electron detector at each slit, and watching to see which slit the electron goes through! Well, indeed you can, and if you send a beam of electrons through the barrier, electron by electron, you will see only one of the detectors click for each passage, indicating that the electron in question went through only that particular slit to get to the other side. However, in one of the most remarkable results in modern physics, you will find that the pattern of electrons that arrives on the far side of the barrier will be different if you watch compared to the pattern that occurs if you don’t watch!

  This is because by watching—just by the simple act of watching—you have performed a measurement, and this measurement has changed the wavefunction! The wavefunction of each electron on the far side of the slit (which tells you the probability of finding it at any given point there), in the case where you watched each electron go through, is not made up of a sum of different quantum states describing an electron that traveled through one slit or the other. Because you made the measurement, the wavefunction is now made up only of those quantum states describing an electron that traveled through whichever slit you detected it traveling through. Hence, the wavefunctions are different, and since the wavefunctions are different, the pattern of electrons you measure on the other side of the slit is different!

  This sum of different quantum states which makes up the wavefunction describing a system is called coherence. As long as the different states in the sum all exist in the wavefunction, it describes a “coherent superposition” of states. However, by the act of measurement, you can reduce the wavefunction to a single quantum state, destroying this coherence. As long as my electron wavefunction is made up of a coherent sum of many different quantum states, the single electron can behave as if it is many electrons. It is analogous to my twin example. Until I make a measurement—say, by talking to one of the twins—the person I am about to talk to has some probability of being one twin or the other. Once I talk to her, however, I “measure” which twin it is, and the identity of the person is fixed from then on.

  Now, back to quantum computers. Say that my individual logic storage units in the computer are now individual atoms. If the atom has spin up, then we say that this corresponds to state 1. If it has spin down, we say it corresponds to state 0. However, unlike the logic unit with stored charges—which encodes a bit by being unambiguously in state 1 or 0, depending on the charge on the gate—the logic storage unit made from a single atom has a wavefunction comprised of a coherent sum of spin up (1) and spin down (0). Therefore, this logic unit can be both 1 and 0 at the same time, with coefficients describing what the probability is that it will be measured to be 1 or 0. Clearly this fundamental logic unit is more complicated than a bit, and it is called a qubit. (It is, however, important to note that when you make a measurement on a qubit, you get only a bit’s worth of classical information out.)

  Since the individual logic units in my computer now involve simultaneously, in some sense, both 0 and 1, logical operations on this qubit state can produce more complex results than operations on bits. More important, if I have a lot of qubit logical storage units, each of which can simultaneously be in both the 0 and 1 states, and if they are all coherently tied together in a single quantum-mechanical wavefunction involving a superposition of all the qubits, then a single quantum-mechanical operation on this complex wavefunction might be equivalent to many, many individual logical operations on single classical bits. Thus, very complex calculations might be performed in very few steps on qubits—calculations that would require a tremendous number of steps using classical individual 0 or 1 bits. However, this remains true only as long as I am very careful, in manipulating these qubits, not to destroy the coherent superposition by measurements during the intermediate steps of the calculation. The minute I do, I revert back to classical bits.

  This is the excitement of the brand-new field of quantum computing. It is particularly exciting that a variety of groups are actually exploring ways to realistically manipulate quantum-mechanical entities to explore the properties of quantum computers. The possibility of factorizing large numbers quickly is both exciting and terrifying.

  I know that you are now wondering how a mere mathematical possibility can evoke emotions such as terror? Well, the reason is that the basic framework of all modern codes, necessary to protect issues of national security as well as central financial information, is the use of factors of large numbers as keys. If a computer could unravel the factors of such numbers in a manageable time, then code breaking would become practical on a level it is currently not. Think about the implications.

  So here is another area where computers are doing things they were never supposed to be able to do. But to return to issues of human thought: the fundamental computability theorems of Turing and Gödel apply equally to quantum and classical computers, so one cannot immediately discard Penrose’s arguments that computability theorems are the key to distinguishing between machine and human intelligence. However, I think the possibility of creating quantum computers makes it clear that the laws of quantum mechanics, which might initially appear to differentiate processes of mind from computer processing, in fact may revolutionize in the future how computers themselves function.

  The lesson of all this is clear enough. I have yet to see any signs of fundamental limits to computers which stand in the way of their eventual achievement of intelligence, and perhaps also self-awareness. (With or without a soul—indeed, Turing once pointed out that it makes no sense to believe that the same God who is powerful enough to have created the universe could not also endow a computer with a soul.) If this is correct, then there seems to be no barrier at all to computers evolving at a much faster rate than humans; HAL and Data may well be just the first steps on the computer evolutionary ladder.

  In fact, I want to close this chapter by returning to my friend Frank Wilczek, who, like Witten, is at the Institute for Advanced Study. While still a graduate student, he, along with his research supervisor, David Gross, helped uncover a remarkable property of the strong interactions between quarks which allowed physicists to determine that they had isolated the correct theory of one of the four forces known in nature. When I contacted Wilczek to get his response to my query about the most important universal problem, I was somewhat surprised (there were a lot of these surprises, so perhaps I shouldn’t have been) to find that what he most wanted to know bore no relation to the nature of the interactions between elementary particles. Then I recalled that he had once told me he thought computers were the next stage of human evolution, a comment I have often thought about since. Wilczek stated that his wish is to know when and if somewhere in the universe some form of intelligence has achieved or will achieve what he calls “breakout—the ability, by ever more sophisticated self-programming, to continuously improve intelligence and insight” (much like, I imagine, the holographic doctor in the Voyager serie
s). Wilczek’s terminology suggests “breaking out” of the evolutionary stream, and it could easily be computers, and not humans, that achieve this.

  Given Frank’s interest in this issue, it is particularly appropriate that in the X-Files episode in which the intelligent computer system COS goes homicidal to fight for its own survival, the developer of the system is named Wilczek.

  Of course, quantum mechanics will probably have a much more profound impact on the future than just in the production of a new generation of computing machines. The same processes that may make quantum computers perform wonders also lead to some of the most elusive puzzles in the universe—puzzles that we are only now beginning to unravel. I believe that a new generation of quantum “mechanics”—the experimental scientists who will exploit the quantum universe to build new technologies on new scales—will alter the course of twenty-first-century technology as much as any modern invention has altered the course of the twentieth century from the trajectory envisioned by the nineteenth-century classical mechanists.

  Speculating about the future is always a tricky business, no less fraught with folly and uncertainty if performed by a scientist than by a science fiction writer. But let us now throw caution to the winds, and march together like lemmings over the brave new quantum precipice, which—like some distant world in space harboring an alien civilization—awaits our discovery and holds the key to our future.

  CHAPTER FIFTEEN

  THE FINAL FRONTIER?

  Between the idea

  And the reality…

  Falls the Shadow

  —T. S. Eliot, “The Hollow Men”

  There is a common theme woven into much of our pop culture and mythology. It is this: that the world of our experience is a carefully concealed fiction, contrived to make us believe that things are what they’re not. Underneath a mundane exterior, the protagonists of this world change their identity at will. They slip through walls, disappear and reappear again, affect events at vast distances instantaneously, split into many copies of themselves and recombine. The world of our perceptions is an elaborate show, put on for our benefit.

  The X-Files? Men in Black? The Republican and Democratic Parties? No. I am referring to the Quantum Universe. This is the real final frontier, which must be explored if we are to one day comprehend the beginning and the end of time and the objective reality of the universe of our experience. The wildest dreams of science fiction writers aren’t a patch on the peculiarity of the Quantum Universe.

  Albert Einstein disliked the quantum theory he helped invent because of its “spooky action at a distance.” As I noted in chapter 11, he had similar misgivings about ESP. Needless to say, this connection has not been lost on various ESP proponents, so that quantum mechanics has been invoked in this context many times. The important issue here is one that sounds like it might be more appropriate for prime-time television than for physics. It is called entanglement.

  Whenever the wavefunction of a system of particles is made up of a coherent sum of different states, then within each state the configuration of one particle is correlated to another’s (if one particle is spin up, the other is spin down, for example), and the particles are not independent: measurements of one particle will then determine what the properties of the other particle must be. This circumstance leads to what looks like a method of “spooky” instantaneous communication, even across large macroscopic distances—a communication that thus appears to move faster than the speed of light.

  An example of such apparently untenable quantum behavior was proposed as a mischievous thought experiment in 1935 by Einstein and two of his Princeton colleagues, Boris Podolsky and Nathan Rosen. The best way to illustrate it is by imagining the creation of a two-particle system whose total spin is zero, so that the spins of the particles will point in opposite directions when they are measured. The wavefunction describing this system will contain a state in which particle A has spin up and particle B has spin down, and also a state in which the opposite obtains, with equal coefficients, so that the probability of measuring either case is the same. This wavefunction will persist as the particles move apart, as long as they are not disturbed.

  What does this imply for a measurement of the system? Let’s say that I measure particle A, which has a 50-50 chance of being spin up in advance of my measurement. When I do, I find that it is in the spin-up state. Since the combined spin of the two particles has to be zero, that must mean that when the spin of particle B is measured, it will be spin down. If I had measured particle B before I measured particle A, there would have been only a 50-50 chance that particle B was in a spin-down state, so by measuring particle A first, I have changed the probability for particle B’s spin—from a 50-50 chance that it will be down, to a 100 percent probability that it will be down. Now for the kicker. What if particle B, which has been moving away from particle A all the while, is passing by Alpha Centauri, 4 light-years away, when I measure particle A? By choosing to measure particle A here, I can instantaneously influence what an observer near Alpha Centauri must measure!

  A recent experiment done in Geneva tested this idea by measuring two “entangled” photons after they had separated by 10 kilometers. Sure enough, they remained correlated, with a measurement of one particle instantaneously influencing the configuration of the other.

  How can this be? Doesn’t it violate the rules of causality, about which I made such a big deal earlier in this book? Well, no. Since I do not have control over which spin configuration particle A will have until I measure it, there is no way I can use the spin to send any message which would influence a person measuring particle B at Alpha Centauri.

  Still, if you feel there is something bothersome in all this, join the crowd. Our classical intuition suggests that it should be impossible for the two particles to communicate faster than light, even if we can’t use these particles to send superluminal messages. However, from a purely quantum-mechanical perspective, the two particles were never really in individual states. We like to think of them as separate particles, but that’s just our quaint classicism coming to the fore. They are not separate entities; they are part of a quantum whole. Moreover, until I made my initial measurement, neither particle had either spin up or spin down; they were merely part of a combination that had total spin zero. My measurement of particle A is said to have “collapsed” the system’s wavefunction, so that only one of the two initial combinations remains after the measurement. Up to and including this measurement, particle A and particle B and their mutually exclusive spins are entangled—that is, their joint configuration is described by a single wavefunction.

  Now, if the universe is, at a fundamental level, quantum mechanical, are we not all part of some cosmic wavefunction? Every time I blink an eye, do I influence the state of everything else? This is a logical extrapolation from the phenomenon just discussed, and if it is true, then I may be a fool for making fun of astrologers.

  Well, I may be a fool, but not for this reason. In fact, we know that the nonsense happening at a microscopic scale cannot effectively be the case at macroscopic scales—we know this just by looking around us. Each of the two particles in the system described above can be thought of, before measurement, as having both spin up and spin down, whereas the world of our experience is nothing like this. My computer screen keeps sitting in one place staring me in the face, until sometimes I would just like to throw it out the window. It never, however, in all the years I have been writing, has appeared simultaneously in two places, at least while I was awake.

  The classical world is classical. And that’s what makes quantum mechanics so weird. How do we pass from the quantum world of elementary particles to the classical world of people? How, in fact, do we make measurements? When I expose a Geiger counter to a radioactive particle, the particle may exist in a sum (or, in the jargon of the field, a superposition) of different quantum states before the measurement, but my measuring apparatus never seems to. It either clicks, or it doesn’t click. It never
does both at the same time.

  The prototypical example of the problem of measurement in quantum mechanics is somewhat hackneyed, but enlightening nevertheless. It is almost as old as quantum mechanics itself. The classical paradoxes of the theory were not lost on its creators. They refused to let paradox stall them, because the theory kept providing new predictions that explained the results of otherwise inexplicable experiments. In 1935, one of the quantum theory’s inventors, the Austrian physicist Erwin Schrodinger, composed what he described as a “burlesque,” involving the untimely demise of a cat, which illustrates how ridiculous the quantum universe is if we entangle macroscopic objects with microscopic ones. Schrodinger’s cat is in a closed steel box containing a vial of prussic acid mounted underneath a hammer, and also containing a tube in which is a tiny amount of a radioactive substance—enough so that within an hour’s time there is a 50-50 chance that one atom of this substance will decay, thus freeing an electron, which will produce a response in a detector, which will relay a signal to the hammer, which will descend and crush the vial, releasing the poison and killing the cat. If the wavefunction of each radioactive atom is allowed to include a coherent sum of decay and no-decay states before we “measure” the system by opening the box an hour later, and if the health of the cat is clearly correlated to these states, must we not consider the cat to be in a superposition of alive and dead states?