The Cosmic Landscape (14 page)

But Weinberg took the practical route a little further. He said that whatever the meaning of the Anthropic Principle and the mechanism that enforces it, one thing was clear. The principle may tell us that λ is small enough to not kill us, but there is no reason why it should be exactly zero. In fact there is no reason for it to be very much smaller than what is needed to ensure life. Without worrying about the deeper meaning of the principle, Weinberg was, in effect, making a prediction. If the Anthropic Principle is correct, then astronomers would discover that the vacuum energy was nonzero and probably not much smaller than 10
^–120
Units.

The process of discovery has always fascinated me. I’m referring to the mental process; what was the line of reasoning—the insight—that led to the “eureka” moment? One of my favorite daydreams is to put myself in the mind of a great scientist and imagine how I might have made a crucial discovery.

Let me share with you how I would have made the first great contribution to the quantum theory of gravity. It was a full sixteen years before young Einstein would invent the modern theory of gravity and twenty-six years before those upstarts Werner Heisenberg and Schrödinger invented modern quantum mechanics. As a matter of fact I, Max Planck, did it without even realizing it.

Recently I made the most wonderful discovery of a completely new fundamental constant of nature. People are calling it my constant,
Planck’s constant.
I was sitting in my office thinking to myself: why is it that the fundamental constants like the speed of light, Newton’s gravitational constant, and my new constant have such awkward values? The speed of light is 2.99 × 10
⁸
meters per second. Newton’s constant is 6.7 × 10
¹¹
square meters per second-kilogram. And my constant is even worse, 6.626 × 10
^–34
kilogram-square meters per second. Why are they always so big or so small? Life for a physicist would be so much easier if they were ordinary-size numbers.

Then it hit me! There are three basic units describing length, mass, and time: the meter, kilogram, and second. There are also three fundamental constants. If I change the units, say, to centimeters, grams, and hours, the numerical value of all three constants will change. For example, the speed of light will get worse. It will become 1.08 × 10
¹⁴
centimeters per hour. But if I use years for time and light-years for distance, then the speed of light will be exactly one since light travels one light-year per year. Doesn’t that mean that I can invent some new units and make the three fundamental constants anything I want? I can even find units in which all three fundamental constants of physics are equal to one! That will simplify so many formulas. I’ll call the new units natural units since they’re based on the constants of nature. Maybe if I’m lucky, people will start calling them Planck units.

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.

N
avigator, 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.