Physics of the Impossible

by Michio Kaku

  Yet later that year Einstein’s luck would turn. A friend arranged for him to get a job as a clerk in the Swiss Patent Office. From that lowly position Einstein would launch the greatest revolution in modern history. He would quickly analyze the patents on his desk and then spend hours contemplating problems in physics that had puzzled him since he was a child.

  What was the secret of his genius? Perhaps one clue to his genius was his ability to think in terms of physical pictures (e.g., moving trains, accelerating clocks, stretched fabrics) rather than pure mathematics. Einstein once said that unless a theory can be explained to a child, the theory was probably useless; that is, the essence of a theory has to be captured by a physical picture. So many physicists get lost in a thicket of mathematics that lead nowhere. But like Newton before him, Einstein was obsessed by the physical picture; the mathematics would come later. For Newton the physical picture was the falling apple and the moon. Were the forces that made an apple fall identical to the forces that guided the moon in its orbit? When Newton decided that the answer was yes, he created a mathematical architecture for the universe that suddenly unveiled the greatest secret of the heavens, the motion of celestial bodies themselves.

  EINSTEIN AND RELATIVITY

  Albert Einstein proposed his celebrated special theory of relativity in 1905. At the heart of his theory was a picture that even children can understand. His theory was the culmination of a dream he had had since the age of sixteen, when he asked the fateful question: what happens if you outrace a light beam? As a youth, he knew that Newtonian mechanics described the motion of objects on the Earth and in the heavens, and that Maxwell’s theory described light. These were the two pillars of physics.

  The essence of Einstein’s genius was that he recognized that these two pillars were in contradiction. One of them must fall.

  According to Newton, you could always outrace a light beam, since there was nothing special about the speed of light. This meant that the light beam must remain stationary as you raced alongside. But as a youth Einstein realized that no one had ever seen a light wave that was totally stationary, that is, like a frozen wave. Hence Newton’s theory did not make sense.

  Finally, as a college student in Zurich studying Maxwell’s theory, Einstein found the answer. He discovered something that even Maxwell did not know: that the speed of light was a constant, no matter how fast you moved. If you raced toward or away from a light beam, it still traveled at the same velocity, but this trait violates common sense. Einstein had found the answer to his childhood question: you can never race alongside a light beam, since it always moves away from you at a constant speed, no matter how fast you move.

  But Newtonian mechanics was a tightly constrained system: like pulling on a loose thread, the entire theory could unravel if you made the smallest change in its assumptions. In Newton’s theory the passage of time was uniform throughout the universe. One second on the Earth was identical to one second on Venus or Mars. Similarly, meter sticks placed on the Earth had the same length as meter sticks on Pluto. But if the speed of light was always constant no matter how fast you moved, there would need to be a major shakeup in our understanding of space and time. Profound distortions of space and time would have to occur to preserve the constancy of the speed of light.

  According to Einstein, if you were in a speeding rocket ship, the passage of time inside that rocket would have to slow down with respect to someone on Earth. Time beats at different rates, depending on how fast you move. Furthermore, the space within that rocket ship would get compressed, so that meter sticks could change in length, depending on your speed. And the mass of the rocket would increase as well. If we were to peer into the rocket with our telescopes, we would see clocks inside the rocket running slowly, people moving in slow motion, and the people would appear flattened.

  In fact, if the rocket were traveling at the speed of light, time would apparently stop inside the rocket, the rocket would be compressed to nothing, and the mass of the rocket would be infinite. Since none of these observations make any sense, Einstein stated that nothing can break the light barrier. (Because an object gets heavier the faster it moves, this means that the energy motion is being converted to mass. The precise amount of energy that turns into mass is easy to calculate, and we arrive at the celebrated equation E = mc2 in just a few lines.)

  Since Einstein derived his famous equation, literally millions of experiments have confirmed his revolutionary ideas. For example, the GPS system, which can locate your position on the Earth to within a few feet, would fail unless one added in corrections due to relativity. (Since the military depends on the GPS system, even Pentagon generals have to be briefed by physicists concerning Einstein’s theory of relativity.) The clocks on the GPS actually change as they speed above the Earth, as Einstein predicted.

  The most graphic illustration of this concept is found in atom smashers, in which scientists accelerate particles to nearly the speed of light. At the gigantic CERN accelerator, the Large Hadron Collider, outside Geneva, Switzerland, protons are accelerated to trillions of electron volts, and they move very close to the speed of light.

  To a rocket scientist, the light barrier is not much of a problem yet, since rockets can barely travel beyond a few tens of thousands of miles per hour. But within a century or two, when rocket scientists seriously contemplate sending probes to the nearest star (located over 4 light-years from Earth), the light barrier could gradually become a problem.

  LOOPHOLES IN EINSTEIN’S THEORY

  Over the decades, physicists have tried to find loopholes in Einstein’s famous dictum. Some loopholes have been found, but most are not very useful. For example, if one sweeps a flashlight across the heavens, in principle the image of the light beam can exceed the speed of light. In a few seconds, the image of the flashlight moves from one point on the horizon to the opposite point, over a distance that can stretch over hundreds of light-years. But this is of no importance, since no information can be transmitted faster than light in this fashion. The image of the light beam has exceeded the speed of light, but the image carries no energy or information.

  Similarly, if we have a pair of scissors, the point at which the blades cross each other moves faster the farther you are from the joining point. If we imagine scissors that are a light-year long, then by closing the blades the crossing point can travel faster than light. (Again, this is not important since the crossing point carries no energy or information.)

  Likewise, as I mentioned in Chapter Four, the EPR experiment enables one to send information at speeds faster than the speed of light. (In this experiment, we recall, two electrons are vibrating in unison and then are sent speeding in opposite directions. Because these electrons are coherent, information can be sent between them at speeds faster than the speed of light, but this information is random and hence is useless. EPR machines, hence, cannot be used to send probes to the distant stars.)

  To a physicist, the most important loophole came from Einstein himself, who created the general theory of relativity in 1915, a theory that is more powerful than the special theory of relativity. The seeds of general relativity were planted when Einstein considered a children’s merry-go-round. As we saw earlier, objects shrink as they approach the speed of light. The faster you move, the more you are squeezed. But in a spinning disk, the outer circumference moves faster than the center. (The center, in fact, is almost stationary.) This means that a ruler stick placed on the rim must shrink, while a ruler placed at the center remains nearly the same, so the surface of the merry-go-round is no longer flat, but is curved. Thus acceleration has the effect of curving space and time on the merry-go-round.

  In the general theory of relativity, space-time is a fabric that can stretch and shrink. Under certain circumstances the fabric may stretch faster than the speed of light. Think of the big bang, for example, when the universe was born in a cosmic explosion 13.7 billion years ago. One can calculate that the universe originally expanded faster than the speed
of light. (This action does not violate special relativity, since it was empty space—the space between stars—that was expanding, not the stars themselves. Expanding space does not carry any information.)

  The important point is that special relativity applies only locally, that is, in your nearby vicinity. In your local neighborhood (e.g., the solar system), special relativity holds, as we confirm with our space probes. But globally (e.g., on cosmological scales involving the universe) we must use general relativity instead. In general relativity, space-time becomes a fabric, and this fabric can stretch faster than light. It can also allow for “holes in space” in which one can take shortcuts through space and time.

  Given these caveats, perhaps one way to travel faster than light is to invoke general relativity. There are two ways in which this might be done.

  1. Stretching space. If you were to stretch the space behind you and contact the space in front of you, then you would have the illusion of having moved faster than light. In fact, you would not have moved at all. But since space has been deformed, it means you can reach the distant stars in a twinkling of an eye.

  2. Ripping space. In 1935 Einstein introduced the concept of a wormhole. Imagine the Looking Glass of Alice, a magical device that connects the countryside of Oxford to Wonderland. The wormhole is a device that can connect two universes. When we were in grade school, we learned that the shortest distance between two points is a straight line. But this is not necessarily true, because if we curled a sheet of paper until two points touched, then we would see that the shortest distance between two points is actually a wormhole.

  As physicist Matt Visser of Washington University says, “The relativity community has started to think about what would be necessary to take something like warp drive or wormholes out of the realm of science fiction.”

  Sir Martin Rees, Royal Astronomer of Great Britain, even says, “Wormholes, extra dimensions, and quantum computers open up speculative scenarios that could transform our entire universe eventually into a ‘living cosmos.’”

  THE ALCUBIERRE DRIVE AND NEGATIVE ENERGY

  The best example of stretching space is the Alcubierre drive, proposed by physicist Miguel Alcubierre in 1994 using Einstein’s theory of gravity. It is quite similar to the propulsion system seen in Star Trek. The pilot of such a starship would be seated inside a bubble (called a “warp bubble”) in which everything seemed to appear normal, even as the spacecraft broke the light barrier. In fact, the pilot would think that he was at rest. Yet outside the warp bubble extreme distortions of space-time would occur as the space in front of the warp bubble was compressed. There would be no time dilation, so time would pass normally inside the warp bubble.

  Alcubierre admits that Star Trek may have had a role to play in his finding this solution. “People in Star Trek kept talking about warp drive, the concept that you’re warping space,” he says. “We already had a theory about how space can or cannot be distorted, and that is the general theory of relativity. I thought there should be a way of using these concepts to see how a warp drive would work.” This is probably the first time that a TV show helped to inspire a solution to one of Einstein’s equations.

  Alcubierre speculates that a journey in his proposed starship would resemble a journey taken on the Millennium Falcon in Star Wars. “My guess is they would probably see something very similar to that. In front of the ship, the stars would become long lines, streaks. In back, they wouldn’t see anything—just black—because the light of the stars couldn’t move fast enough to catch up with them,” he says.

  The key to the Alcubierre drive is the energy necessary to propel the spacecraft forward at faster-than-light velocities. Normally physicists begin with a positive amount of energy in order to propel a starship, which always travels slower than the speed of light. To move beyond this strategy so as to be able to travel faster than the speed of light one would need to change the fuel. A straightforward calculation shows that you would need “negative mass” or “negative energy,” perhaps the most exotic entities in the universe, if they exist. Traditionally, physicists have dismissed negative energy and negative mass as science fiction. But we now see that they are indispensable for faster-than-light travel, and they might actually exist.

  Scientists have looked for negative matter in nature, but so far without success. (Antimatter and negative matter are two entirely different things. The first exists and has positive energy, but a reversed charge. Negative matter has not yet been proven to exist.) Negative matter would be quite peculiar, because it would be lighter than nothing. In fact, it would float. If negative matter existed in the early universe, it would have drifted into outer space. Unlike meteors that come crashing down onto planets, drawn by a planet’s gravity, negative matter would shun planets. It would be repelled, not attracted, by large bodies such as stars and planets. Hence, although negative matter might exist, we expect to find it only in deep space, certainly not on Earth.

  One proposal to find negative matter in outer space involves using the phenomenon called “Einstein lenses.” When light travels around a star or galaxy its path is bent by its gravity, according to general relativity. In 1912 (even before Einstein fully developed general relativity) he predicted that a galaxy might be able to act like the lens of a telescope. Light from a distant object moving around a nearby galaxy would converge as it passed around the galaxy, like a lens, forming a characteristic ring pattern when the light finally reached the Earth. These phenomena are now called “Einstein rings.” In 1979 the first of these Einstein lenses was observed in outer space. Since then, Einstein lenses have become an indispensable tool for astronomers. (For example, it was once thought that it would be impossible to locate “dark matter” in outer space. [Dark matter is a mysterious substance that is invisible but has weight. It surrounds the galaxies and is perhaps ten times as plentiful as ordinary visible matter in the universe.] But NASA scientists have been able to construct maps of dark matter since dark matter bends light as the light passes through, in the same way that glass bends light.)

  Therefore it should be possible to use Einstein lenses to search for negative matter and wormholes in outer space. They should bend light in a peculiar way, which should be visible with the Hubble Space Telescope. So far, Einstein lenses have not detected the image of negative matter or wormholes in outer space, but the search is continuing. If one day the Hubble Space Telescope detects the presence of negative matter or a wormhole via Einstein lenses, it could set off a shock wave in physics.

  Negative energy is different from negative matter in that it actually exists, but only in minute quantities. In 1933 Hendrik Casimir made a bizarre prediction using the laws of the quantum theory. He claimed that two uncharged parallel metal plates will attract each other, as if by magic. Normally parallel plates are stationary, since they lack any net charge. But the vacuum between the two parallel plates is not empty, but full of “virtual particles,” which dart in and out of existence.

  For brief periods of time, electron-antielectron pairs burst out of nothing, only to be annihilated and disappear back into the vacuum. Ironically, empty space, which was once thought to be devoid of anything, now turns out to be churning with quantum activity. Normally tiny bursts of matter and antimatter would seem to violate the conservation of energy. But because of the uncertainty principle, these tiny violations are incredibly short-lived, and on average energy is still conserved.

  Casimir found that the cloud of virtual particles will create a net pressure in the vacuum. The space between the two parallel plates is confined, and hence the pressure is low. But the pressure outside the plates is unconfined and larger, and hence there will be a net pressure pushing the plates together.

  Normally the state of zero energy occurs when these two plates are at rest and sitting far apart from each other. But as the plates come closer together, you can extract energy out of them. Thus, because kinetic energy has been taken out of the plates, the energy of the plates is less than zero.


  This negative energy was actually measured in the laboratory in 1948, and the results confirmed Casimir’s prediction. Thus, negative energy and the Casimir effect are no longer science fiction but established fact. The problem, however, is that the Casimir effect is quite small; it takes delicate, state-of-the-art measuring equipment to detect this energy in the laboratory. (In general, the Casimir energy is proportional to the inverse fourth power of the distance of separation between the plates. This means that the smaller the distance of separation, the larger the energy.) The Casimir effect was measured precisely in 1996 by Steven Lamoreaux at the Los Alamos National Laboratory, and the attractive force is 1/30,000 the weight of an ant.

  Since Alcubierre first proposed his theory, physicists have discovered a number of strange properties. The people inside the starship are causally disconnected from the outside world. This means that you cannot simply press a button at will and travel faster than light. You cannot communicate through the bubble. There has to be a preexisting “highway” through space and time, like a series of trains passing by on a regular timetable. In this sense, the starship would not be an ordinary ship that can change directions and speeds at will. The starship would actually be like a passenger car riding on a preexisting “wave” of compressed space, coasting along a preexisting corridor of warped space-time. Alcubierre speculates, “We would need a series of generators of exotic matter along the way, like a highway, that manipulate space for you in a synchronized way.”

  Actually, even more bizarre types of solutions to Einstein’s equations can be found. Einstein’s equations state that if you are given a certain amount of mass or energy, you can compute the warping of space-time that the mass or energy will generate (in the same way that if you throw a rock into a pond, you can calculate the ripples that it will create). But you can also run the equations backward. You can start with a bizarre space-time, the kind found in episodes of The Twilight Zone. (In these universes, for example, you can open up a door and find yourself on the moon. You can run around a tree and find yourself backward in time, with your heart on the right side of your body.) Then you calculate the distribution of matter and energy associated with that particular space-time. (This means that if you are given a bizarre collection of waves on the surface of a pond, you can work backward and calculate the distribution of rocks necessary to produce these waves). This was, in fact, the way in which Alcubierre derived his equations. He began with a space-time consistent with going faster than light, and then he worked backward and calculated the energy necessary to produce it.