The Cosmic Landscape (17 page)

Although I said that all electrons have the same mass, there is a qualification which you might have guessed. An electron’s mass depends on the value of the Higgs field at the position of the electron. If we had the technology to vary the Higgs field, the electron’s mass would depend on its location. This is true of the mass of every elementary particle, with the exception of the photon and graviton.

In our ordinary vacuum state, most of the known fields are zero. They may fluctuate due to quantum mechanics, but they fluctuate positively for a brief time and then negatively. If we ignore this rapid jittering, the fields average to zero. Changing the field away from zero costs energy. The Higgs field, however, is somewhat different. Its average value in empty space is not zero. It is as if, in addition to the fluctuating sea of virtual particles, space is filled with an additional steady fluid made of Higgs particles. Why don’t we notice the fluid? In a sense I suppose we could say we have gotten used to it. But if it were removed, we would certainly notice its absence! More precisely, we wouldn’t exist to notice anything.

“The Higgs field gives particles their mass.” What on earth does that mean? The answer is buried deep in the mathematics of the Standard Model, but I will try to give you an idea. As I mentioned earlier (on page 95), if the Higgs field (or particle) were left out of the cast of characters, the mathematical quantum field theory describing the Standard Model would be mathematically consistent only if all the other elementary particles were massless, like the photon. The actual masses of particles like electrons, quarks, W-bosons, and Z-bosons are due to their motion through the fluid of Higgs particles. I don’t want to mislead you with false analogies, but there is a sense in which the Higgs fluid creates a resistance to the motion of particles. It’s not a form of friction, which would slow moving particles and cause them to come to rest. Instead, it is a resistance to changes of velocity, in other words, inertia or mass. Once again a Feynman diagram is worth a thousand words.

If we could create a region where the Higgs field was zero, the most singular thing we would notice (assuming our own survival) is that the electron mass would be zero. The effects on atoms would be devastating. The electron would be so light that it could not be contained within the atom. Neither atoms nor molecules would exist. Life of our kind would almost certainly not exist in such a region of space.

It would be very interesting to test these predictions the same way that we can test physics in a magnetic field. But manipulating the Higgs field is vastly more difficult than manipulating the magnetic field. Creating a region of space where the Higgs field is zero would cost an enormous quantity of energy. Just a single cubic centimeter of Higgs-free space would require energy of about 10
⁴⁰
joules. That’s about the total amount of energy that the sun radiates in a million years. This experiment will have to wait a while.

Why is the Higgs field so different from the magnetic field? The answer lies in the Landscape. Let’s simplify the Landscape to one dimension by ignoring the electric and magnetic fields and include only the Higgs field. The resulting “Higgs-scape” would be more interesting than the simple parabola that represents the magnetic field Landscape. It has two deep valleys separated by an extremely high mountain.

Don’t worry if you don’t understand why the Higgs-scape looks so different. No one completely understands it. It is another empirical fact that we have to accept for now. The top of the hill is the point on the Landscape where the Higgs field is zero. Imagine that some superpowerful cosmic vacuum cleaner has sucked the vacuum clean of Higgs field. Here is the place in the Higgs-scape where all the particles of the Standard Model are massless and move with the speed of light. From the graph you can see that the top of the mountain represents an environment with a large amount of energy. It is also a deadly environment.

By contrast, our corner of the universe is safely nestled in one of the valleys where the energy is lowest. In these valleys the Higgs field is not zero, the vacuum is full of Higgs fluid, and the particles are massive. Atoms behave like atoms, and life is possible. The full Landscape of String Theory is much like these examples but infinitely richer in mostly unpleasant possibilities. Friendly, habitable valleys are very rare exceptions. But that’s a later story.

Why, in each example, do we live at the bottom of a valley? Is it a general principle? Indeed, it is.

Hermann Minkowski was a physicist with a flare for words. Here is what he had to say about space and time: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent identity.” Minkowski was talking about Einstein’s two-year-old child, the Special Theory of Relativity. It was Minkowski who announced to the world that space and time must be joined together into a single, four-dimensional space-time. It follows from the four-dimensional perspective that if the Laws of Physics can vary from one point of space to another, then it must also be possible for them to vary with time. There are things that can make all the normal rules—even the law of gravity—change, suddenly or gradually.

Imagine a very long-wavelength radio wave passing through a physics laboratory. A radio wave is an electromagnetic disturbance consisting of oscillating electric and magnetic fields. If the wavelength is long enough, a single oscillation will take a long time to pass through the lab. For argument’s sake let’s say the wavelength is two light-years. The fields in the lab will take one full year to go from zero to a maximum and back to zero.
⁷
If in our laboratory the field was zero in December, it will be maximum in June.

The slowly changing fields will mean that the behavior of electrons will slowly change with time. For the winter months, when the fields are smallest, the electrons, atoms, and molecules will behave normally. In the summer, when the fields are at their maximum, the electrons will move in strange orbits, and atoms will be squashed in directions perpendicular to the magnetic field. The electric field will also distort the shapes of atoms by pulling the electrons and nuclei in opposite directions. The Laws of Physics will appear to change with the seasons!

What about the Higgs field? Can it change with time? Remember that normal empty space is full of Higgs field. Imagine that an evil physicist invented a machine—a “vacuum cleaner”—that could sweep away the Higgs field. The machine would be so powerful that it could push the universe, or part of it, up the hill to the top of the mountain in the middle of the Higgs-scape. Bad things would happen; atoms would disintegrate, and all life would terminate. What happens next is surprisingly simple. Pretend the Higgs-scape really is a Landscape with a high hill separating two valleys. The universe would act like a small, round BB ball, balancing precariously on the knife-edge between falling to the left and falling to the right. Obviously the situation is unstable. Just a tiny tap one way or the other would send the ball plummeting toward a valley.

If the surface of the Landscape were perfectly smooth, without any friction, the ball would overshoot the valley, climb up the other side, and then roll back past the valley, up the hill, over and over. But if there is the smallest amount of friction, the ball will eventually come to rest at the lowest point of one of the valleys.
⁸

That is how the Higgs field behaves. The universe “rolls” around on the Landscape and eventually comes to rest in a valley representing the usual vacuum.

The bottoms of valleys are the only places where an imaginary ball can stand still. Placed on a slope, it will roll down. Placed at the top of a hill, it will be unstable. In the same way, the only possible vacuum with stable, unchanging Laws of Physics is at the bottom of a valley in the Landscape.

A valley does not necessarily have to be the absolute lowest point on the Landscape. In a mountain range with many valleys, each surrounded by peaks, some of the valleys may be quite high, higher in fact than some of the summits. But as long as the rolling universe arrives at the bottom of a valley, it will remain there. The mathematical term for the lowest point of a valley is a
local minimum.
At a local minimum, any direction will be uphill. Thus, we arrive at a fundamental fact: the possible stable vacuums—or equivalently, the possible stable Laws of Physics—correspond to the local minima of the Landscape.

No mad scientist is ever going to sweep the Higgs field away. As I mentioned earlier, just to sweep out one cubic centimeter of space would require all of the energy radiated by the sun in a million years. But there was a time roughly fourteen billion years ago when the temperature of the world was so high that there was more than enough energy to sweep away the Higgs field from the entire known universe. I am referring to the very early universe, just after the Big Bang, when the temperature and pressure were tremendously large. Physicists believe that the universe began with the Higgs field equal to zero, i.e., up at the top of the hill. As the universe cooled, it rolled down the slope to the valley that we now “inhabit.” Rolling on the Landscape plays a central role in all modern theories of cosmology.

The Higgs-scape has a small number of local minima. That one of the minima should have vacuum energy as small as 10-
¹²⁰
is incredibly improbable. But as we will see in chapter 10, the real Landscape of String Theory is far more complex, diverse, and interesting. Try to imagine a space of five hundred dimensions with a topography that includes 10
⁵⁰⁰
local minima, each with its own Laws of Physics and constants of nature. Never mind. Unless your brain is very different from mine, 10
⁵⁰⁰
is far beyond imagining. But one thing seems certain. With that many possibilities to choose from, it is overwhelmingly likely that the energy of many vacuums will cancel to the accuracy required by Weinberg’s anthropic argument, namely 119 decimal places.

In the next chapter I want to take a break from technical aspects of physics and discuss an issue having to do with the hopes and aspirations of physicists. We will come back to “hard science” in chapter 5, but paradigm shifts involve more than facts and figures. They involve esthetic and emotional issues and fixations on paradigms that may have to be abandoned. That the Laws of Physics may be contingent on the local environment, somewhat like the weather, represents a devastating disappointment to many physicists, who have an almost spiritual feeling that nature must be “beautiful” in a certain special mathematical sense.

“God used beautiful mathematics in creating the world.”

— PAUL DIRAC

“If you are out to describe the truth, leave elegance to the tailor.”

— ALBERT EINSTEIN

“Beauty is worse than wine, it intoxicates both the holder and beholder.”

— ALDOUS HUXLEY