Calculate, Calculate, Calculate . . .
Ah, here’s my result: the natural unit of length is about 10–33 centimeters. Holy Bernoulli! That’s far smaller than anything I’ve ever thought about. Some of those people who think about atoms say that they may be about 10–8 centimeters in diameter. That means my new natural unit is as much smaller than an atom as an atom is smaller than the galaxy!5
How about the natural unit of time? That comes out to be about 10–42 seconds! That’s unimaginably small. Even the time of oscillation of a high-frequency light wave is vastly longer than a natural time unit.
And now for mass: ah, the unit of mass is not so strange. The natural unit of mass is small but not very. It’s 10–5 grams: about the same as a dust mote. These units must have some special meaning. All the formulas of physics are so much simpler if I work in natural units. I wonder what it means?
That’s how Planck made one of the great discoveries about quantum gravity without realizing it.
Planck lived forty-seven more years, to the age of eighty-nine. But I don’t think he ever imagined the profound impact that his discovery of Planck units would have for later generations of physicists. By 1947 the General Theory of Relativity and quantum mechanics were part of the basic foundation of physics, but hardly anyone had started to think about the synthesis of the two: quantum gravity. The three Planck units of length, mass, and time were critical in the development of the discipline, but even now, we are only beginning to understand the depth of their significance. I’ll give some examples of their importance.
Earlier we discussed the fact that in Einstein’s theory, space is stretchable and deformable like the surface of a balloon. It can be stretched flat and smooth or it can be all wrinkled and bumpy. Combine this idea with quantum mechanics, and space becomes very unfamiliar. According to the principles of quantum mechanics, everything that can fluctuate does fluctuate. If space is deformable, then even it has the “quantum jitters.” If we could look through a very high-powered microscope, we would see space fluctuating, shaking and shimmering, bulging out in knots, and forming donut holes. It would be like a piece of cloth or paper. On the whole it looks flat and smooth, but if you look at it microscopically, the surface is full of pits, bumps, fibers, and holes. Space is like that but worse. It would appear not only full of texture but of texture that fluctuates incredibly rapidly.
How powerful does the microscope have to be in order to see the fluctuating texture of space? You guessed it. The microscope would have to discern features whose size is the Planck length, i.e., 10–33 centimeters. That’s the scale of the quantum-texture of space.
And how long do the features last before fluctuating to something new? Again you can guess the answer; the time scale of these fluctuations is the Planck time, 10–42 seconds! Many physicists think there is a sense in which the Planck length is the smallest distance that can ever be resolved. Likewise, the Planck time may be the shortest interval of time.
Let’s not leave out the Planck mass. To understand its importance, imagine two particles colliding so hard that they create a black hole at the collision point. Yes, it can happen; two colliding particles, if they have enough energy, will disappear and leave behind a black hole, one of those mysterious objects that will occupy chapter 11 of this book. The energy needed to form such a black hole played a role in our earlier discussion about vacuum energy. Just how large must that energy be (remembering that energy and mass are the same thing)? The answer, of course, is the Planck mass. The Planck mass is neither the smallest nor the largest possible mass, but it is the smallest possible mass of a black hole. By the way, a Planck mass black hole would be about one Planck length in size and it would last for about one Planck unit of time before exploding into photons and other debris.
As Planck discovered, his mass is about a hundred-thousandth of a gram. By ordinary standards that’s not much mass, and even if we multiply it by the speed of light squared, it’s not a huge amount of energy. It more or less corresponds to a tank full of gasoline. But to concentrate that much energy in two colliding elementary particles—that would be a feat. It would take an accelerator many light-years in size to do the job.
Recall that we estimated the vacuum energy density due to virtual particles. Not surprisingly, the answer translates to about one Planck mass per cubic Planck length. In other words, the unit of energy density that I defined as one Unit was nothing but the natural Planck unit of energy density.
The world at the Planck scale is a very unfamiliar place, where geometry is constantly changing, space and time are barely recognizable, and high-energy virtual particles are perpetually colliding and forming tiny black holes that last no longer than a single Planck time. But it’s the world in which string theorists spend their working days.
Let me take a bit of space and time to summarize the two difficult chapters that you’ve worked your way through and the dilemma they lead to. The microscopic laws of elementary particles in the form of the Standard Model are a spectacularly successful basis for calculating the properties not only of the particles themselves, but of nuclei, atoms, and simple molecules. Presumably, with a big enough computer and enough time, we could calculate all molecules and move on to even more complex objects. But the Standard Model is enormously complicated and arbitrary. In no way does it explain itself. There are many other imaginable lists of particles and lists of coupling constants that are every bit as mathematically consistent as those found in nature.
But things get worse. When we combine the theory of elementary particles with the theory of gravity, we discover the horror of a cosmological constant big enough to not only destroy galaxies, stars, and planets but also atoms, and even protons and neutrons—unless. Unless what? Unless the various bosons, fermions, masses, and coupling constants that go into calculating the vacuum energy conspire to cancel the first 119 decimal places. But what natural mechanism could ever account for such an unlikely state of affairs? Are the Laws of Physics balanced on an incredibly sharp knife-edge, and if so, why? Those are the big questions.
In the next chapter we will discuss what determines the Laws of Physics and just how unique they are. What we will find is that these laws are not at all unique! They can even vary from place to place in the megaverse. Could it be that there are special rare places in the megaverse where the constants conspire in just the right way to cancel the vacuum energy with sufficient precision for life to exist? The basic idea of a Landscape of possibilities that allows such variation is the subject of chapter 3.
CHAPTER THREE
The Lay of the Land
Navigator, is it gaining on us?” The captain’s face was grim as sweat beads rolled down his bald dome and dropped from his chin. The veins in his forearm bulged as his hand clenched the control stick.
“Yes Captain, I’m afraid there is no way to outrun it. The bubble is growing and unless my calculation is way off, it’s going to engulf us.”
The captain winced and punched the desktop in front of him. “So this is how it ends. Swallowed by a bubble of alternate vacuum. Can you tell what the laws of physics are like inside it? Any chance we can survive?”
“Not likely. I compute that our chances are about one in ten to the one-hundredth power—one in a googol. My guess is the vacuum inside the bubble can support electrons and quarks, but the fine structure constant is probably way too large. That’ll blow the hell out of our nuclei.” The navigator looked up from his equations and smiled ruefully. “Even if the fine structure constant is okay, the chances are overwhelming that there is a big CC.”
“CC?”
“Yeah, you know—cosmological constant. It’s probably negative and big enough to squash our molecules like that.” The navigator snapped his fingers. “Here it comes now! Oh god, no, it’s supersymmetric.1 No chance. . . .” Silence.
. . .
That was the beginning of a very bad science-fiction story that I started to write. After a few more paragraphs, I concluded that
I am a sadly untalented sci-fi author and abandoned the project. But the science may be a good deal better than the fiction.
It is gradually becoming accepted, by many theoretical physicists, that the Laws of Physics may not only be variable but are almost always deadly. In a sense the laws of nature are like East Coast weather: tremendously variable, almost always awful, but on rare occasions, perfectly lovely. Like deadly storms, bubbles of extremely hostile environments may propagate through the universe causing destruction in their wake. But in rare and special places, we find Laws of Physics perfectly suited to our existence. In order to understand how it came to pass that we find ourselves in such an exceptional place, we have to understand the reasons for the variability of the Laws of Physics, just how large the range of possibilities is, and how a region of space can suddenly change its character from lethal to benign. This brings us to the central concern of this book, the Landscape.
As I have said, the Landscape is a space of possibilities. It has geography and topography with hills, valleys, flat plains, deep trenches, mountains, and mountain passes. But unlike an ordinary landscape, it isn’t three-dimensional. The Landscape has hundreds, maybe thousands, of dimensions. Almost all of the Landscape describes environments that are lethal to life, but a few of the low-lying valleys are habitable. The Landscape is not a real place. It doesn’t exist as a real location on the earth or anywhere else. It doesn’t exist in space and time at all. It’s a mathematical construct, each of whose points represents a possible environment or, as a physicist would say, a possible vacuum.
In common usage the word vacuum means empty space, space from which all air, water vapor, and other material has been sucked out. That’s also what it means to an experimental physicist who deals in vacuum tubes, vacuum chambers, and vacuum pumps. But to a theoretical physicist, the term vacuum connotes much more. It means a kind of background in which the rest of physics takes place. The vacuum represents potential for all the things that can happen in that background. It means a list of all the elementary particles as well as the constants of nature that would be revealed by experiments in that vacuum. In short, it means an environment in which the Laws of Physics take a particular form. We say of our vacuum that it can contain electrons, positrons, photons, and the rest of the usual elementary particles. In our vacuum the electron has a mass of .51 Mev,2 the photon’s mass is zero, and the fine structure constant is 0.007297351. Some other vacuum might have electrons with no mass, a photon with mass 10 Mev, and no quarks but forty different kinds of neutrinos and a fine structure constant equal to 15.003571. A different vacuum means different Laws of Physics; each point on the Landscape represents a set of laws that are, most likely, very different from our own but which are, nonetheless, entirely consistent possibilities. The Standard Model is merely one point in the Landscape of possibilities.
And if the Laws of Physics can be different in other vacuums, so can all of science. A world with much lighter electrons but heavier photons would have no atoms. No atoms means no chemistry, no periodic table, no molecules, no acids, no bases, no organic substances, and of course, no biology.
The idea of universes with alternative laws of nature seems like the stuff of science fiction. But the truth is more mundane than it sounds. Modern medical technology routinely produces alternative universes inside MRI machines. The abbreviation MRI was not the original name for this technology: it replaced NMR, which stands for Nuclear Magnetic Resonance. But patients got scared by the word nuclear and wouldn’t go near the thing. So the name was changed to Magnetic Resonance Imaging to emphasize the magnetic aspects of the technology instead of the nuclear. In fact the nuclei that are involved in NMR are not uranium or plutonium nuclei as in nuclear warheads, they are the patient’s own nuclei that are ever so gently tickled by the magnetic field of the machine.
An MRI machine is basically a cylinder of empty space with a coil of wire surrounding it. An electric current through the coil creates a powerful magnetic field in the cylinder. It’s essentially a very strong electromagnet. The patient in the interior of the MRI machine is in a small private universe, where as we will see, the properties of the vacuum are slightly different from those on the outside. Imagine waking up one morning inside the machine, not knowing where you were. Something would seem amiss about the Laws of Physics. The most obvious thing you would notice is that iron objects would move in very odd ways, even presenting serious danger. If you happened to have a compass, it would rigidly lock into place along some particular direction.
It probably wouldn’t be a good idea to have a TV in the MRI machine, but let’s suppose you did. The picture would be distorted in bizarre ways. If you know how a television operates, you would trace the strange distortion to the motion of electrons. The strong magnetic field inside the cylinder exerts forces on the electrons that curve their trajectories from straight lines to corkscrew spirals. A theoretical physicist who knew about Feynman diagrams would say that something was different about the electron propagator. The propagator is not just a picture of an electron moving from one point to another, it’s also a mathematical expression that describes the motion.
The constants of nature would also be slightly unusual. The strong magnetic field interacts with an electron’s spin and even modifies the electron’s mass. Funny things happen to atoms in strong magnetic fields. The magnetic forces on the atomic electrons cause the atom to be slightly squashed in directions perpendicular to the field. The effects in a real MRI machine would be tiny, but if the magnetic field could be made much stronger, atoms would get squeezed into strands resembling spaghetti along the magnetic field lines.
The effects of the magnetic field can also be detected from small changes in the energy levels of atoms and, consequently, the spectrum of light they emit. There are changes in the precise manner in which electrons, positrons, and photons interact with one another. If the field were made strong enough, even the vertex diagrams would be affected. The fine structure constant would be a little different and depend on which way the electron moves.
Of course the field in the MRI machine is very weak, and the effects on the laws regulating charged particles are minute. If the field were very much stronger, the patient would feel funny. A field strong enough to seriously affect those laws would be absolutely fatal. The effects on atoms would have terrible consequences for chemical and biological processes.
There are two ways to view this, both of which are right. One is conventional: the Laws of Physics are exactly what they always were, but the environment is modified by the presence of the magnetic field. The other way to think about it is that the rules for Feynman diagrams have been changed and that something has happened to the Laws of Physics. Perhaps the most precise thing to say is:
The Laws of Physics are determined by the environment.
Fields
Fields, as we’ve seen, are invisible properties of space that influence objects moving through them. The magnetic field is a familiar example. Everyone who has played with magnets has discovered the mysterious action-at-a-distance forces they exert on paper clips, pins, and steel nails. Most people who have had a science course in school have seen the effect of a magnetic field on iron filings—tiny bits of iron—sprinkled on a surface in the vicinity of a magnet. The field assembles the filings into long filaments that look like hairy threads, lined up along the direction of the field. The filaments follow mathematical lines called magnet lines of force or magnetic field lines. The magnetic field has a direction at every point, but it also has a strength that determines how forceful the field is in pushing pieces of iron. In the MRI machine the field is more than ten thousand times stronger than the earth’s magnetic field.
The electric field is a slightly less familiar close relative of the magnetic field. It has no observable effects on iron filings, but it causes small bits of paper to move when there is some static electricity on them. Electric fields aren’t caused by electric current but by accumulations of static electric charge
. For example, rubbing one material on another—your rubber shoe soles on the carpet, say—causes the transfer of electrons. One material becomes charged negatively, and the other positively. The charged objects create an electric field around them that, like magnetic fields, have both direction and strength.
Ultimately the Laws of Physics are variable because they are determined by fields, and fields can vary. Switching on magnetic and electric fields is one way to change the laws, but it is by no means the only way to modify the vacuum, or even the most interesting way. The second half of the twentieth century was a time of discovery of new elementary particles, new forces, and above all, new fields. Einstein’s gravitational field was one, but there were many others. Space can be filled with a wide variety of invisible influences that have all sorts of effects on ordinary matter. Of all the new fields that were discovered, the one that has the most to teach us about the Landscape is the Higgs field.
The discovery of the Higgs field wasn’t an experimental discovery in the usual sense.3 Theoretical physicists discovered that the Standard Model, without the Higgs field, is mathematically inconsistent. Without it the Feynman rules would lead to nonsensical results like infinite and even negative probabilities. But theorists in the late 1960s and early 1970s figured out a way to fix all the problems by adding one additional elementary particle: the Higgs particle.
Higgs particle, Higgs field—what’s the connection between particles and fields that leads us to call them by the same name? The field idea first appeared in the mid-nineteenth century in the form of the electromagnetic field. Michael Faraday imagined a field to be a smooth disturbance in space that affects the motions of electrically charged particles, but the field itself was not supposed to be made of particles. For Faraday, and Maxwell who followed him, the world was composed of particles and fields, and there was no doubt whatsoever about which was which. But in 1905 Albert Einstein, in order to explain Planck’s formula for heat radiation, proposed an outlandish theory. Einstein claimed that the electromagnetic field was really composed of a very large number of indivisible particles that he called photons. In small numbers, photons, or what are the same thing, light quanta behave like particles, but when many of them move in a coordinated way, the whole collection behaves like a field—a quantum field. This relation between particles and fields is very general. For each type of particle in nature, there is a field, and for each type of field there is a particle. Thus, fields and particles often go by the same name. The electromagnetic field (the collective name for electric and magnetic fields) could be called the photon field. The electron has a field. So, too, does the quark, the gluon, and each member of the cast of characters of the Standard Model, including the Higgs particle.