by Michio Kaku
Pure mathematics abounds in theorems showing that certain things are truly impossible. One simple example is that it is impossible to trisect an angle using only a compass and ruler; this was proven back in 1837.
Even in simple systems such as arithmetic there are impossibilities. As I mentioned earlier, it is impossible to prove all the true statements in arithmetic within the postulates of arithmetic. Arithmetic is incomplete. There will always be true statements in arithmetic that can be proven only if one moves to a much larger system that includes arithmetic as a subset.
Although some things in mathematics are impossible, it is always dangerous to declare that something is absolutely impossible in the physical sciences. Let me remind you of a speech given by Nobel laureate Albert A. Michelson in 1894 at the dedication of the Ryerson Physical Lab at the University of Chicago, in which he declared that it was impossible to discover any new physics: “The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote…Our future discoveries must be looked for in the sixth place of decimals.”
His remarks were uttered on the eve of some of the greatest upheavals in scientific history, the quantum revolution of 1900, and the relativity revolution of 1905. The point is that things that are impossible today violate the known laws of physics, but the laws of physics, as we know them, can change.
In 1825 the great French philosopher Auguste Comte, writing in Cours de Philosophie, declared that it was impossible for science to determine what the stars were made of. This seemed like a safe bet at the time, since nothing was known about the nature of stars. They were so distant that it was impossible to visit them. Yet just a few years after he made this claim, physicists (using spectroscopy) declared that the sun was made of hydrogen. In fact, we now know that by analyzing the spectral lines from stars emitted billions of years ago it is possible to determine the chemical nature of most of the universe.
Comte challenged the world of science by making a list of other “impossibilities”:
• He claimed that the “ultimate structure of bodies must always transcend our knowledge.” In other words, it was impossible to know the true nature of matter.
• He thought that mathematics could never be used to explain biology and chemistry. It was impossible, he claimed, to reduce these sciences to mathematics.
• He thought that it was impossible that the study of heavenly bodies would have any impact on human affairs.
In the nineteenth century it was reasonable to propose these “impossibilities” since so little was known about fundamental science. Almost nothing was known about the secrets of matter and life. But today we have the atomic theory, which has opened up a whole new realm of scientific investigation into the structure of matter. We know about DNA and the quantum theory, which have unraveled the secrets of life and chemistry. We also know about meteor impacts from space, which have not only influenced the course of life on Earth, but have helped to shape its very existence.
Astronomer John Barrow notes, “Historians still debate the suggestion that Comte’s views were partly responsible for the subsequent decline in French science.”
Mathematician David Hilbert, in rejecting Comte’s claims, wrote, “The true reason, according to my thinking, why Comte could not find an unsolvable problem lies in the fact that there is no such thing as an unsolvable problem.”
But today some scientists are raising a new set of impossibilities: we will never know what happened before the big bang (or why it “banged” in the first place), and we will never achieve a “theory of everything.”
Physicist John Wheeler commented on the first “impossible” question when he wrote: “Two hundred years ago, you could ask anybody, ‘Can we someday understand how life came into being?’ and he would have told you, ‘Preposterous! Impossible!’ I feel the same way about the question, ‘Will we ever understand how the universe came into being?’”
Astronomer John Barrow adds, “The speed at which light travels is limited and so, therefore, is our knowledge of the structure of the Universe. We cannot know whether it is finite or infinite, whether it had a beginning or will have an end, whether the structure of physics is the same everywhere, or whether the Universe is ultimately a tidy or an untidy place…All the great questions about the nature of the Universe—from its beginning to its end—turn out to be unanswerable.”
Barrow is correct in saying that we will never know, with absolute certainty, the true nature of the universe, in all its glory. But it is possible to incrementally chip away at these eternal questions and come tantalizingly close. Instead of representing the absolute boundaries of our knowledge, these “impossibilities” may perhaps better be seen as the challenges awaiting the next generation of scientists. These limits are like piecrusts, made to be broken.
DETECTING THE PRE–BIG BANG ERA
In the case of the big bang, a new generation of detectors is being built that could settle some of these eternal questions. Today our radiation detectors in outer space can only measure the microwave radiation emitted 300,000 years after the big bang, when the first atoms formed. It is impossible to use this microwave radiation to probe earlier than 300,000 years after the big bang, since radiation from the original fireball was too hot and random to yield useful information.
But if we analyze other types of radiation we may be able to get even closer to the big bang. Tracking neutrinos, for example, can take us closer to the instant of the big bang (neutrinos are so elusive that they can travel through an entire solar system made of solid lead). Neutrino radiation could take us within a few seconds after the big bang.
But perhaps the ultimate secret of the big bang will be revealed by examining “gravity waves,” waves that move along the fabric of space-time. As physicist Rocky Kolb of the University of Chicago says, “By measuring the properties of the neutrino background we can look back to one second after the Bang. But gravitational waves from [the] inflation area are relics of the universe 10-35 seconds after the bang.”
Gravity waves were first predicted by Einstein in 1916; they may eventually become the most important probe for astronomy. Historically each time a new form of radiation was harnessed, a new era in astronomy was opened up. The first form of radiation was visible light, used by Galileo to investigate the solar system. The second form of radiation was radio waves, which eventually enabled us to probe the centers of galaxies to find black holes. Gravity wave detectors may unveil the very secrets of creation.
In some sense gravity waves have to exist. To see this, consider the age-old question: what happens if the sun suddenly disappears? According to Newton, we would feel the effects immediately. The Earth would be instantly thrown out of its orbit and plunged into darkness. This is because Newton’s law of gravity does not take into account velocity, and hence forces act instantly throughout the universe. But according to Einstein, nothing can travel faster than light, so it would take eight minutes for the information about the sun’s disappearance to reach the Earth. In other words, a spherical “shock wave” of gravity would emerge from the sun and eventually hit the Earth. Outside this sphere of gravity waves, it would appear as if the sun were still shining normally, because information about the disappearance of the sun would not have reached Earth. Inside this sphere of gravity waves, however, the sun would have already disappeared, as the expanding shock wave of gravity waves travels at the speed of light.
Another way to see why gravity waves must exist is to visualize a large bed sheet. According to Einstein, space-time is a fabric that can be warped or stretched, like a curved bed sheet. If we grab a bed sheet and shake it rapidly we see that waves ripple along the surface of the bed sheet and travel at a definite velocity. In the same way, gravity waves can be viewed as waves traveling along the fabric of space-time.
Gravity waves are among the fastest-moving
topics in physics today. In 2003 the first large-scale gravity wave detectors became operational—called LIGO (Laser Interferometer Gravitational Wave Observatory), measuring 2.5 miles in length, one is based in Hanford, Washington, and another in Livingston Parish, Louisiana. It is hoped that LIGO, at a cost of $365 million, will be able to detect radiation from colliding neutron stars and black holes.
The next big leap will take place in 2015, when an entirely new generation of satellites will be launched that will analyze gravitational radiation in outer space from the instant of creation. The three satellites that make up LISA (Laser Interferometer Space Antenna), a joint project of NASA and the European Space Agency, will be sent into orbit around the sun. These satellites will be capable of detecting gravitational waves emitted less than a trillionth of a second after the big bang. If a gravity wave from the big bang still circulating around the universe hits one of the satellites, it will disturb the laser beams, and this disturbance can then be measured in a precise way, giving us “baby pictures” of the instant of creation itself.
LISA consists of three satellites circling the sun arranged in a triangle, each connected by laser beams 3 million miles long, making it the largest instrument of science ever created. This system of three satellites will orbit the sun about 30 million miles from the Earth.
Each satellite will emit a laser beam with only half a watt of power. By comparing the laser beams coming from the other two satellites, each satellite will be able to construct an interference pattern of light. If a gravity wave disturbs the laser beams, it will change the interference pattern, and the satellite will be able to detect this disturbance. (The gravity wave does not make the satellites vibrate. It actually creates a distortion in the space between the three satellites.)
Although the laser beams are very weak, their accuracy will be astounding. They will be able to detect vibrations to within one part in a billion trillion, corresponding to a shift 1/100 the size of an atom. Each laser beam will be able to detect a gravity wave from a distance of 9 billion light-years, which covers most of the visible universe.
LISA has the sensitivity to potentially differentiate between several “pre–big bang” scenarios. One of the hottest topics in theoretical physics today is calculating the characteristics of the pre–big bang universe. At present, inflation can describe quite well how the universe evolved once the big bang took place. But inflation cannot explain why the big bang took place in the first place. The goal is to use these speculative models of the pre–big bang era to calculate the gravity radiation emitted by the big bang. Each of the various pre–big bang theories makes different predictions. The big bang radiation predicted by the Big Splat theory, for example, differs from the radiation predicted by some of the inflation theories, so LISA might be able to rule out several of these theories. Obviously, these pre–big bang models cannot be tested directly, since they involve understanding the universe before the creation of time itself, but we can test them indirectly since each of these theories predicts a different radiation spectrum emerging afterward from the big bang.
Physicist Kip Thorne writes, “Sometime between 2008 and 2030, gravitational waves from the Big Bang singularity will be discovered. There will ensue an era, lasting at least until 2050…These efforts will reveal intimate details of the Big Bang singularity, and will thereby verify that some version of string theory is the correct quantum theory of gravity.”
If LISA is unable to differentiate between different pre–big bang theories, its successor, the Big Bang Observer (BBO) might. It is tentatively scheduled for launch in 2025. The BBO will be able to scan the entire universe for all binary systems involving neutron stars and black holes with mass less than one thousand times the mass of the sun. But its main goal is to analyze gravity waves emitted during the inflationary phase of the big bang. In this sense, the BBO is specifically designed to probe the predictions of the inflationary big bang theory.
The BBO is somewhat similar to LISA in design. It will consist of three satellites moving together in an orbit around the sun, separated from each other by 50,000 kilometers (these satellites will be much closer to one another than LISA’s satellites). Each satellite will be able to fire a 300-watt laser beam. BBO will be able to probe gravity wave frequencies between LIGO and LISA, filling an important gap. (LISA can detect gravity waves from 10 to 3,000 hertz, while LIGO can detect gravity waves of frequency 10 microhertz to 10 millihertz. BBO will be able to detect frequencies that include both ranges.)
“By 2040 we will have used those laws [of quantum gravity] to produce high-confidence answers to many deep and puzzling questions,” Thorne writes, “including…What came before the Big Bang singularity, or was there even such a thing as a ‘before’? Are there other universes? And if so, how are they related to or connected to our own universe?…Do the laws of physics permit highly advanced civilizations to create and maintain wormholes for interstellar travel, and to create time machines for backward time travel?”
The point is that in the next few decades there should be enough data pouring in from gravity wave detectors in space to differentiate between the various pre–big bang theories.
THE END OF THE UNIVERSE
The poet T. S. Eliot asked the question, Will the universe die with a bang or a whimper? Robert Frost asked, Will we all perish in fire or ice? The latest evidence points to the universe dying in a Big Freeze, in which temperatures will reach near absolute zero and all intelligent life will be extinguished. But can we be sure?
Some have raised another “impossible” question. How will we ever know the ultimate fate of the universe, they ask, since this event is trillions upon trillions of years in the future? Scientists believe that “dark energy” or the energy of the vacuum seems to be pushing the galaxies apart at an ever increasing rate, indicating that the universe seems to be in a runaway mode. Such an expansion would cool the temperature of the universe and ultimately lead to the Big Freeze. But is this expansion temporary? Could it reverse itself in the future?
For example, in the Big Splat scenario, in which two membranes collide and create the universe, it appears as if the membranes can collide periodically. If so, then the expansion that appears to lead to a Big Freeze is only a temporary state that will reverse itself.
What is driving the current acceleration of the universes is dark energy, which in turn is probably caused by the “cosmological constant.” The key, therefore, is to understand this mysterious constant, or the energy of the vacuum. Does the constant vary with time, or is it really a constant? At present, no one knows for sure. We know from the WMAP satellite currently orbiting the Earth that this cosmological constant seems to be driving the current acceleration of the universe, but we don’t know if it is permanent or not.
This problem is actually an old one, dating back to 1916 when Einstein first introduced the cosmological constant. Soon after proposing general relativity the previous year, he worked out the cosmological implications of his own theory. Much to his surprise, he found that the universe was dynamic, that it either expanded or contracted. But this idea seemed to contradict the data.
Einstein was encountering the Bentley paradox, which had bedeviled even Newton. Back in 1692 the Reverend Richard Bentley wrote Newton an innocent letter with a devastating question. If Newton’s gravity was always attractive, Bentley asked, then why doesn’t the universe collapse? If the universe consists of a finite collection of stars that mutually attract each other, then the stars should come together and the universe should collapse into a fireball! Newton was deeply troubled by this letter, since it pointed out a key flaw in his theory of gravity: any theory of gravity that is attractive is inherently unstable. Any finite collection of stars will inevitably collapse under gravity.
Newton wrote back that the only way to create a stable universe was to have an infinite and uniform collection of stars, with each star being pulled in all directions, so that all the forces cancel out. It was a clever solution, but Newton was
smart enough to realize that such stability was deceptive. Like a house of cards, the tiniest of vibrations would cause the whole thing to collapse. It was “metastable” that is, it was temporarily stable until the slightest perturbations caused it to crash. Newton concluded that God was necessary to periodically nudge the stars a bit so the universe did not collapse.
In other words, Newton saw the universe as a gigantic clock, wound up by God at the beginning of time and obeying Newton’s laws. It has been ticking automatically ever since, without divine intervention. However, according to Newton, God was necessary to tweak the stars once in a while so the universe did not collapse into a fireball.
When Einstein stumbled on the Bentley paradox in 1916, his equations correctly told him that the universe was dynamic—either expanding or contracting—and that a static universe was unstable and would collapse due to gravity. But the astronomers insisted at that time that the universe was static and unchanging. So Einstein, bowing to the observations of the astronomers, added the cosmological constant, an antigravity force that pushed the stars apart to balance the gravitational pull causing the universe to collapse. (This antigravity force corresponded to the energy contained within the vacuum. In this picture even the vast emptiness of space contains large quantities of invisible energy.) This constant would have to be chosen very precisely in order to cancel out the attractive force of gravity.
Later, when Edwin Hubble showed in 1929 that the universe was, in fact, expanding, Einstein would say that the cosmological constant was his “greatest blunder.” Yet now, seventy years later, it appears as if Einstein’s “blunder,” the cosmological constant, could in fact be the largest source of energy in the universe, making up 73 percent of the matter-energy content of the universe. (By contrast, the higher elements that make up our bodies constitute only .03 percent of the universe.) Einstein’s blunder will likely determine the ultimate fate of the universe.
