Warped Passages (38 page)

Although unification to this day remains a conjecture, the unification of forces, if true, would be a major leap towards a simpler description of nature. Because unifying principles are so intriguing, physicists studied the strength of the three forces at high energies to see whether or not they converge. Back in 1974, nobody had measured the interaction strengths of the three nongravitational forces with very great accuracy. Howard Georgi, Steven Weinberg, and Helen Quinn (who was then an unpaid Harvard postdoctoral fellow, now a physicist at the Stanford Linear Accelerator Center and president of the American Physical Society) used the imperfect measurements that were then available and did a renormalization group calculation to extrapolate the strength of the forces to high energies. They discovered that the three lines representing the strength of nongravitational forces did indeed appear to converge to a single point.

The famous 1974 Georgi-Glashow paper on their Grand Unified
Theory begins with these words: “We present a series of hypotheses and speculations leading inescapably to the conclusion…that all elementary particle forces (strong, weak, and electromagnetic) are different manifestations of the same fundamental interaction involving a single coupling strength. Our hypotheses may be wrong and our speculations idle, but the uniqueness and simplicity of our scheme are reasons enough that it be taken seriously.”
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Perhaps those were not the most modest of words. However, Georgi and Glashow did not really think that that uniqueness and simplicity were sufficient evidence that their theory was the correct description of nature. They also wanted experimental confirmation.

Although an enormous leap of faith was required to extrapolate the Standard Model to ten trillion times the energy anyone had directly explored, they realized that their extrapolation had a testable consequence. In their paper, Georgi and Glashow explained that their GUT “predicts that the proton decays,” and that experimenters should try to test this prediction.

Georgi and Glashow’s unified theory predicted that protons wouldn’t last for ever. After a very long time, they would decay. Such a thing would never happen in the Standard Model. Quarks and leptons are ordinarily distinguished by the forces they experience. But in a Grand Unified Theory, the forces are all essentially the same. So, just as an up quark can change into a down quark via the weak force, a quark should be able to change into a lepton via the unified force. That means that if the GUT idea is correct, the net number of quarks in the universe would not remain the same, and a quark could change into a lepton, making the proton—a composite of three quarks—decay.

Because the proton can decay in a Grand Unified Theory that links quarks and leptons, all familiar matter would ultimately be unstable. However, the decay rate of the proton is very slow—the lifetime would far exceed the age of the universe. That means that even as dramatic a signal as a proton decaying would not stand much chance of being detected: it would happen much too rarely.

To find evidence of proton decay, physicists had to build extremely large and long-lasting experiments that studied a huge number of protons. That way, even if any single proton is unlikely to decay, a large number of protons would greatly increase the odds that the experiment could detect the decay of one of them. Even though your likelihood of winning the lottery is small, it would be much greater if you bought millions of tickets.

Physicists did build such large, multi-proton experiments, including the Irvine/Michigan/Brookhaven (IMB) experiment located in the Homestake Mine in South Dakota, and the Kamiokande experiment, a vat of water and detectors buried a kilometer deep underground in Kamioka, Japan. Although proton decay is an extremely rare process, these experiments would already have found evidence of it if the Georgi-Glashow GUT were correct. Unfortunately for grand ambitions, no one has yet discovered such decay.

This doesn’t necessarily rule out unification. In fact, thanks to more precise measurement of the forces, we now know that the original model proposed by Georgi and Glashow is almost certainly incorrect, and only an extended version of the Standard Model can unify forces. As it turns out, in such models the predictions for the proton lifetime are longer, and proton decay shouldn’t have been detected yet.

Today, we don’t actually know whether unification of forces is a true feature of nature or, if it is, what it signifies. Calculations show that unification could happen in several models I’ll discuss later, including supersymmetric models, the Hořava-Witten extra-dimensional models, and the warped extra-dimensional models that Raman Sundrum and I developed. The extra-dimensional models are particularly intriguing because they could bring gravity into the unification fold and truly unify all four known forces. These models are also important because in the original unification models it was assumed there were no new particles to be found above the weak scale other than those with GUT scale masses.
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These other models demonstrate that unification might happen even if there are many new particles that could be produced only at energies above the weak scale.

However, fascinating as unification of forces can be, physicists are
currently divided about its theoretical merits according to whether they favor a top-down or a bottom-up approach to physics. The idea of a Grand Unified Theory embodies a top-down approach. Georgi and Glashow made a bold assumption about the absence of particles with mass between one thousand and one thousand trillion GeV and hypothesized a theory based on this assumption. Grand Unification was the first step in the particle physics debate that continues today with string theory. Both theories extrapolate physical laws from measured energies to energies at least ten trillion times higher. Georgi and Glashow later became skeptical about the top-down approach that string theory and the search for Grand Unification represent. They have since reversed their tracks and now concentrate on lower-energy physics.

Although unified theories have some appealing features, I’m not really sure whether studying them will lead to correct insights into nature. The gap in energy between what we know and what we extrapolate to is huge, and one can imagine many possibilities for what can happen in between. In any case, until proton decay (or some other prediction) is discovered—if it ever is—it will be impossible to establish with certainty whether forces truly unify at high energy. Until then, this theory remains in the realm of grand, but theoretical, speculation.

What to Remember

• Virtual particles
  are particles that have the same charges as true physical particles, but have energies that seem to be wrong.
  
• Virtual particles exist for only a very short time; they temporarily borrow energy from the
  vacuum
  —the state of the universe without any particles.
  
• Quantum contributions
  to physical processes arise from virtual particles that interact with real particles. These contributions from virtual particles influence the interactions of real particles by appearing and disappearing, and acting as intermediaries between the real particles.
  
• The
  anarchic principle
  tells us that quantum contributions always have to be taken into account when considering a particle’s properties.
  
• In a
  unified theory
  , a single high-energy force turns into the three known nongravitational forces at low energies. For the three forces to unify, they must have the same strength at high energies.
  

12

The Hierarchy Problem: The Only Effective Trickle-Down Theory

The highway is for gamblers, better use your sense.

Take what you have gathered from coincidence.

Bob Dylan

Ike Rushmore III came to an ignominious end when he drove his resplendent new Porsche into a lamppost. He was nonetheless happy in Heaven, where he could play games all the time. He was a gambling man at heart.

One day, God Himself invited Ike to a rather strange game. God told him to write down a sixteen-digit number. God would roll the heavenly icosahedral die. Unlike a normal, cubic die with six sides, this die had twenty sides, with the digits 0 through 9 written twice. God explained that He would throw this die sixteen times and construct a sixteen-digit number by listing the results, one after the other. If God and Ike came up with the same enormous numbers—that is, if all the digits matched in the correct order—God would win. If the numbers weren’t exactly the same—that is, if any of the digits failed to match—Ike would defeat God.

God began to roll. The first side that came up was the number 4. This agreed with the first digit of Ike’s number, which was 4,715,031,495,526,312. Ike was surprised that God rolled correctly, since the odds were only one in ten. Nonetheless, he was pretty sure the second or third number would be wrong; the odds of God’s rolling both numbers correctly in succession was only one in a hundred.

God threw the die for a second and then a third time. He rolled a 7 and then a 1, which were also correct. He kept rolling until, to Ike’s astonishment, He had rolled all sixteen digits correctly. The chances of this happening randomly were only 1 in 10,000,000,000,000,000. How could God have won?

Ike was a bit angry (one can’t get very angry in Heaven) and asked how something so ridiculously unlikely could have happened. God sagely replied, “I am the only one who could expect to win, since I am both omniscient and omnipotent. However, you must have heard, I do not like to play dice.”

And with that, gambling forbidden was posted on a cloud. Ike was furious (of course, only a little). Not only had he lost the game, he’d also lost the right to gamble.

By this point, you have hopefully learned quite a lot about particle physics and some of the beautiful theoretical elements with which physicists built the Standard Model. The Standard Model works exceptionally well in explaining many diverse experimental results. However, it rests uneasily on an unstable foundation that poses a deep and significant mystery, one whose solution is almost bound to lead to new insights into the underlying structure of matter. In this chapter we’ll explore this mystery, known to particle physicists as the
hierarchy problem
.

The problem is not that the Standard Model’s predictions disagree with experimental results. The masses and charges associated with the electromagnetic, weak, and strong forces have been tested to incredibly high accuracy. Experiments at the colliders at CERN, SLAC, and Fermilab have all confirmed with exquisite precision the Standard Model predictions for interactions and decay rates of the known particles. And the strengths of the forces in the Standard Model pose no significant mysteries either. Their relationship to one another is in fact highly suggestive, and underlies the idea of a Grand Unified Theory. Furthermore, the Higgs mechanism perfectly explains how the vacuum breaks electroweak symmetry and gives masses to the W and Z gauge bosons, as well as the quarks and the leptons.

However, even the most idyllic-seeming families can reveal undercurrents of tension when investigated more closely. Despite
well-coordinated behavior and a happy, harmonious appearance, a devastating hidden family secret can be lurking underneath. The Standard Model has just such a skeleton in the closet. Everything agrees with predictions if you uncritically assume that the strength of the electromagnetic force, the strength of the weak force, and the gauge boson masses take the values that have been measured in experiments. But we’ll soon see that the mass parameter (the weak scale mass that determines the elementary particle masses), though very well measured, is ten million billion times, or sixteen orders of magnitude, lower than the mass that physicists would expect from general theoretical considerations. Any physicist who would have guessed the value of the weak scale mass based on a high-energy theory would have gotten it (and therefore all particle masses) completely wrong. The mass seems to come out of thin air. This puzzle—the hierarchy problem—is a gaping hole in our understanding of particle physics.

In the Introduction I explained the hierarchy problem as the question of why gravity is so weak, but we will now see that this problem can be restated as the question of why the Higgs particle’s mass, and hence the weak gauge boson masses, are so small. For those masses to take their measured values, the Standard Model has to incorporate a fudge that is as unlikely as someone winning the guessing game against Ike and randomly choosing a sixteen-digit number correctly. Despite its many successes, the Standard Model relies on this unconscionable fudge to accommodate the known elementary particle masses.

This chapter explains this problem, and why I, and most other particle theorists, think it’s so important. The hierarchy problem tells us that whatever is responsible for electroweak symmetry breaking is bound to be more interesting than the two-field Higgs example presented in Chapter 10. Possible solutions all involve new physical principles, and the solution will very likely guide physicists to more fundamental particles and laws. Identifying what plays the role of the Higgs field and breaks electroweak symmetry will reveal some of the richest new physics we are likely to nail down in my lifetime. New physical phenomena will almost certainly appear at an energy of about a TeV. Experimental tests of competing hypotheses are near at hand, and within a decade there should be a dramatic revision in our
understanding of fundamental physical laws that will incorporate whatever is discovered there.

The hierarchy problem tells us that before extrapolating physics to extremely high energies, we have at least one urgent low-energy problem to attend to. For the last thirty years or so, particle theorists have been searching for the structure that predicts and protects the weak scale energy, the relatively low energy at which electroweak symmetry breaks. I and others think that there must be a solution of the hierarchy problem, and that it will provide one of the best clues about what lies beyond the Standard Model. To understand the motivation for some of the theories I’ll soon present, it is useful to know a little about this somewhat technical but very important problem. The search for its solution has already led us to investigate new physical concepts, such as the ones later chapters will explore, and the solution will almost certainly revise our current views.