by Michio Kaku
FOUNDER OF ANTIMATTER
What is antimatter? It seems strange that nature would double the number of subatomic particles in the universe for no good reason. Nature is usually quite sparing, but now that we know about antimatter, nature seems to be supremely redundant and wasteful. And if antimatter exists, can anti-universes also exist?
To answer these questions, one has to investigate the origin of antimatter itself. The discovery of antimatter actually dates back to 1928, with the pioneering work of Paul Dirac, one of the most brilliant physicists of the twentieth century. He held the Lucasian Chair at Cambridge University, the same chair held by Newton, and the chair currently held by Stephen Hawking. Dirac, born in 1902, was a tall, wiry man who was in his early twenties when the quantum revolution broke open in 1925. Although he was studying electrical engineering at that time, he was suddenly swept up in the tidal wave of interest unleashed by the quantum theory.
The quantum theory was based on the idea that particles like electrons could be described not as pointlike particles but as a wave of some sort, described by Schrödinger’s celebrated wave equation. (The wave represents the probability of finding the particle at that point.)
But Dirac realized that there was a defect with Schrödinger’s equation. It described only electrons moving at low velocities. At higher velocities, the equation failed because it did not obey the laws of objects moving at high velocities, that is, the laws of relativity found by Albert Einstein.
To the young Dirac, the challenge was to reformulate the Schrödinger equation to accommodate the theory of relativity. In 1928 Dirac proposed a radical modification of the Schrödinger equation that fully obeyed Einstein’s relativity theory. The world of physics was stunned. Dirac found his famous relativistic equation for the electron purely by manipulating higher mathematical objects, called spinors. A mathematical curiosity was suddenly becoming a centerpiece for the entire universe. (Unlike many physicists before him, who insisted that great breakthroughs in physics be firmly grounded in experimental data, Dirac took the opposite strategy. To him pure mathematics, if it was beautiful enough, was the sure guide to great breakthroughs. He wrote, “It is more important to have beauty in one’s equations than to have them fit experiments…It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has a really sound insight, one is on a sure line of progress.”)
In developing his new equation for the electron, Dirac realized that Einstein’s celebrated equation, E = mc2, was not quite right. Although it is splattered over Madison Avenue ads, children’s T-shirts, cartoons, and even the costumes of superheroes, Einstein’s equation is only partially correct. The correct equation is actually E = ± mc2. (This minus sign arises because we have to take the square root of a certain quantity. Taking the square root of a quantity always introduces a plus or minus ambiguity.)
But physicists abhor negative energy. There is an axiom of physics that states that objects always tend to the state of lowest energy (this is the reason that water always seeks the lowest level, sea level). Since matter always drops down to its lowest energy state, the prospect of negative energy was potentially disastrous. It meant that all electrons would eventually tumble down to infinite negative energy, hence Dirac’s theory would be unstable. So Dirac invented the concept of the “Dirac sea.” He envisioned that all negative energy states were already filled up, and hence an electron could not tumble down into negative energy. Hence the universe was stable. Also a gamma ray might occasionally collide with an electron sitting in a negative energy state and kick it up into a state of positive energy. We would then see the gamma ray turn into an electron and a “hole” develop in the Dirac sea. This hole would act like a bubble in the vacuum; that is, it would have a positive charge and the same mass as the original electron. In other words, the hole would behave like an antielectron. So in this picture antimatter consists of “bubbles” in the Dirac sea.
Just a few years after Dirac made this astounding prediction, Carl Anderson actually discovered the antielectron (for which Dirac won the Nobel Prize in 1933).
In other words, antimatter exists because the Dirac equation has two types of solutions, one for matter, and one for antimatter. (And this in turn is the outcome of special relativity.)
Not only did the Dirac equation predict the existence of antimatter; it also predicted the “spin” of the electron. Subatomic particles can spin, much like a spinning top. The spin of the electron, in turn, is crucial to understanding the flow of electrons in transistors and semiconductors, which form the basis of modern electronics.
Stephen Hawking regrets that Dirac did not patent his equation. He writes, “Dirac would have made a fortune if he had patented the Dirac equation. He would have had a royalty on every television, Walkman, video game and computer.”
Today Dirac’s celebrated equation is etched in the stone of Westminster Abbey, not far from the tomb of Isaac Newton. In the entire world, it is perhaps the only equation given this distinctive honor.
DIRAC AND NEWTON
Historians of science seeking to understand the origins of how Dirac came up with his revolutionary equation and the concept of antimatter have often compared him to Newton. Strangely, Newton and Dirac share a number of similarities. Both were in their twenties when they did their seminal work at Cambridge University, both were masters of mathematics, and both shared another stark characteristic: a total lack of social skills, to the point of pathology. Both were notorious for their inability to engage in small talk and simple social graces. Painfully shy, Dirac would never say anything unless asked directly, and then he would reply “yes,” or “no,” or “I don’t know.”
Dirac was also extremely modest and detested publicity. When he was awarded the Nobel Prize in Physics, he seriously considered turning it down because of the notoriety and trouble that it would generate. But when it was pointed out to him that rejecting the Nobel Prize would generate even more publicity he decided to accept it.
Volumes have been written about Newton’s peculiar personality, with hypotheses ranging from mercury poisoning to mental illness. But recently a new theory has been proposed by Cambridge psychologist Simon Baron-Cohen that might explain both Newton’s and Dirac’s strange personalities. Baron-Cohen claims that they both probably suffered from Asperger’s syndrome, which is akin to autism, like the idiot savant in the movie Rain Man. Individuals suffering from Asperger’s are notoriously reticent, socially awkward, and sometimes blessed with enormous calculational ability, but unlike autistic individuals they are functional in society and can hold productive jobs. If this theory is true, then perhaps the miraculous calculational power of Newton and Dirac came at a price, being socially apart from the rest of humanity.
ANTIGRAVITY AND ANTI-UNIVERSES
Using Dirac’s theory, we can now answer a host of questions: What is the antimatter counterpart of gravity? Do anti-universes exist?
As we discussed, antiparticles have the opposite charge of ordinary matter. But particles that have no charge at all (such as the photon, a particle of light, or the graviton, which is a particle of gravity) can be their own antiparticle. We see that gravitation is its own antimatter; in other words, gravity and antigravity are the same thing. Hence antimatter should fall down under gravity, not up. (This is universally believed by physicists, but it has actually never been demonstrated in the laboratory.)
Dirac’s theory also answers the deep questions: Why does nature allow for antimatter? Does that mean anti-universes exist?
In some science fiction tales, the protagonist discovers a new Earth-like planet in outer space. In fact, the new planet seems identical to Earth in every way, except everything is made of antimatter. We have antimatter twins on this planet, with anti-children, who live in anti-cities. Since the laws of anti-chemistry are the same as the laws of chemistry, except charges are reversed, people living in such a world would never know they were made of antimatter. (Physicists call this the
charge-reversed or C-reversed universe, since all charges are reversed in this anti-universe, but everything else remains the same.)
In other science fiction stories scientists discover a twin of the Earth in outer space, except that it is a Looking Glass universe, where everything is left-right reversed. Everyone’s heart is on the right side and most people are left-handed. They live out their lives never knowing that they live in a left-right reversed Looking Glass universe. (Physicists call such a Looking Glass universe a parity-reversed or P-reversed universe.)
Can such antimatter and parity-reversed universes really exist? Physicists take questions about twin universes very seriously, since Newton’s and Einstein’s equations remain the same when we simply flip the charges on all our subatomic particles or reverse the left-right orientation. Hence, C-reversed and P-reversed universes are in principle possible.
Nobel laureate Richard Feynman posed an interesting question about these universes. Suppose one day we make radio contact with aliens on a distant planet but cannot see them. Can we explain to them the difference between “left” and “right” by radio? he asked. If the laws of physics allow for a P-reversed universe, then it should be impossible to convey these concepts.
Certain things, he reasoned, are easy to communicate, such as the shape of our bodies and the number of our fingers, arms, and legs. We can even explain to the aliens the laws of chemistry and biology. But if we try to explain to them the concept of “left” and “right” (or “clockwise” and “counterclockwise”), we would fail each time. We would never be able to explain to them that our heart is on the left side of our body, in which direction the Earth rotates, or the way a DNA molecule spirals.
So it came as a shock when C. N. Yang and T. D. Lee, both at Columbia University at the time, disproved this cherished theorem. By examining the nature of subatomic particles they showed that the Looking Glass, P-reversed universe cannot exist. One physicist, learning of this revolutionary result, said, “God must have made a mistake.” For this earthshaking result, called the “overthrow of parity,” Yang and Lee won the Nobel Prize in Physics in 1957.
To Feynman, this conclusion meant that if you are talking to aliens on a radio, it is possible to set up an experiment that could enable you to tell the difference between left- and right-handed universes by radio alone. (For example, electrons emitted from radioactive cobalt-60 do not spin in equal numbers in a clockwise or counterclockwise fashion, but actually spin in a preferred direction, thereby breaking parity.)
Feynman then envisioned that a historic meeting finally takes place between the aliens and humanity. We tell the aliens to stick out their right hand when we first meet, and we will shake hands. If the aliens actually stick out their right hand, then we know that we have successfully communicated to them the concept of “left-right” and “clockwise-counterclockwise.”
But Feynman then raised an unsettling thought. What happens if the aliens stick out their left hand instead? This means that we have made a fatal mistake, that we have failed to communicate the concept of “left” and “right.” Worse, it means that the alien is actually made of antimatter, and that he performed all the experiments backward, and hence got “left” and “right” mixed up. It means when we shake hands, we will explode!
That was our understanding until the 1960s. It was impossible to tell the difference between our universe and a universe in which everything was made of antimatter and was parity-reversed. If you flipped both the parity and the charge, the resulting universe would obey the laws of physics. Parity by itself was overthrown, but charge and parity was still a good symmetry of the universe. So a CP-reversed universe was still possible.
This meant that if we were talking to aliens on the phone, we could not tell the difference between an ordinary universe and one that was both parity- and charge-reversed (i.e., left and right are interchanged, and all matter is turned into antimatter).
Then in 1964 physicists received a second shock: the CP-reversed universe cannot exist. By analyzing the properties of subatomic particles, it is still possible to tell the difference between left-right, clockwise-counterclockwise if you are talking by radio to another CP-reversed universe. For this result, James Cronin and Val Fitch won the Nobel Prize in 1980.
(Although many physicists were upset when the CP-reversed universe was shown to be inconsistent with the laws of physics, in hindsight the discovery was a good thing, as we discussed earlier. If the CP-reversed universe were possible, then the original big bang would have involved precisely the same amount of matter and antimatter, and hence 100 percent annihilation would have taken place, and our atoms would not have been possible! The fact that we exist as a leftover from the annihilation of unequal amounts of matter and antimatter is proof of CP violation.)
Are any reversed anti-universes possible? The answer is yes. Even if parity-reversed and charge-reversed universes are not possible, an anti-universe is still possible, but it would be a strange one. If we reversed the charges, the parity, and the march of time, then the resulting universe would obey all the laws of physics. The CPT-reversed universe is allowed.
Time reversal is a bizarre symmetry. In a T-reversed universe, fried eggs jump off the dinner plate, reform on the frying pan, and then jump back into the egg, sealing the cracks. Corpses rise from the dead, get younger, turn into babies, and then jump into their mother’s womb.
Common sense tells us that the T-reversed universe is not possible. But the mathematical equations of subatomic particles tell us otherwise. Newton’s laws run perfectly well backward or forward. Imagine videotaping a billiard game. Each collision of the balls obeys Newton’s laws of motion; running such a videotape would make for a bizarre game, but it is allowed by the laws of Newton.
In the quantum theory things are more complicated. T-reversal by itself violates the laws of quantum mechanics, but the full CPT-reversed universe is allowed. This means that a universe in which left and right are reversed, matter turns into antimatter, and time runs backward is a fully acceptable universe obeying the laws of physics!
(Ironically, we cannot communicate with such a CPT-reversed world. If time runs backward on their planet, it means that everything we tell them by radio will be part of their future, so they would forget everything we told them as soon as we spoke to them. So even though the CPT-reversed universe is allowed under the laws of physics, we cannot talk to any CPT-reversed alien by radio.)
In summary, antimatter engines may give us a realistic possibility for fueling a starship in the distant future, if enough antimatter could be made on Earth, or found in outer space. There is a slight imbalance between matter and antimatter because of CP violation, and this in turn may mean that pockets of antimatter still exist and can be harvested.
But because of the technical difficulties involved in antimatter engines, it may take a century or more to develop this technology, making it a Class I impossibility.
But let’s tackle another question: Will faster-than-light starships be possible thousands of years in the future? Are there loopholes to Einstein’s famous dictum that “nothing can go faster than light”? The answer, surprisingly, is yes.
11: FASTER THAN LIGHT
It’s quite conceivable that [life] will eventually spread through the galaxy and beyond. So life may not forever be an unimportant trace contaminant of the universe, even though it now is. In fact, I find it a rather appealing view.
—ASTRONOMER ROYAL SIR MARTIN REES
It is impossible to travel faster than the speed of light, and certainly not desirable, as one’s hat keeps blowing off.
—WOODY ALLEN
In Star Wars, as the Millennium Falcon blasts off the desert planet Tatooine, carrying our heroes Luke Skywalker and Han Solo, the ship encounters a squadron of menacing Imperial battleships orbiting the planet. The Empire’s battleships fire a punishing barrage of laser blasts at our heroes’ ship that steadily break through its force fields. The Millennium Falcon is outgunned. Buckling
under this withering laser fire, Han Solo yells that their only hope is to make the jump into “hyperspace.” In the nick of time the hyperdrive engines spring to life. All the stars around them suddenly implode toward the center of their view screen in converging, blinding streaks of light. A hole opens up, which the Millennium Falcon blasts through, reaching hyperspace and freedom.
Science fiction? Undoubtedly. But could it be based on scientific fact? Perhaps. Faster-than-light travel has always been a staple of science fiction, but recently physicists have given serious thought to this possibility.
According to Einstein, the speed of light is the ultimate speed limit in the universe. Even our most powerful atom smashers, which can create energies found only at the center of exploding stars or the big bang itself, cannot hurl subatomic particles at a rate faster than the speed of light. Apparently the speed of light is the ultimate traffic cop in the universe. If so, any hope of our reaching the distant galaxies seems to be dashed.
Or maybe not…
EINSTEIN THE FAILURE
In 1902 it was far from obvious that the young physicist Albert Einstein would be hailed as the greatest physicist since Isaac Newton. In fact, that year represented the lowest point in his life. A newly minted Ph.D. student, he was rejected for a teaching job by every university he applied to. (He later found out that his professor Heinrich Weber had written horrible letters of recommendation for him, perhaps in revenge for Einstein’s having cut so many of his classes.) Furthermore, Einstein’s mother was violently opposed to his girlfriend, Mileva Maric, who was carrying his child. Their first daughter, Lieserl, would be born illegitimate. Young Albert was also a failure at the odd jobs he took. Even his lowly tutoring job abruptly ended when he was fired. In his depressing letters he contemplated becoming a salesman to earn a living. He even wrote to his family that perhaps it would have been better had he never been born, since he was such a burden to his family and lacked any prospects for success in life. When his father died, he felt ashamed that his father had died thinking that his son was a total failure.
