Fear of Physics (31 page)

 

 

Considerations of scale open up a whole new world of physics in just the same way as they did when we first encountered them in the context of our spherical cow at the beginning of this book. Indeed, returning to that example, we can see explicitly how this happens. First, if I determine by experiment the density and the strength of a normal cow’s skin, I can tell you what will be the density of a supercow, which is twice as big. Moreover, I
can predict the results of any measurement performed on such a supercow.

Is then the Spherical Cow Theory an Ultimate Theory of Cows? A priori we could never prove that it is, but there are three different ways of finding out if it isn’t or is unlikely to be: (1) at a certain scale the theory itself predicts nonsense, (2) the theory strongly suggests that something even more simple than a sphere can do the same job, or (3) we can perform an experiment at some scale that distinguishes features not predicted in the theory. Here is such an experiment. Say I throw a chunk of salt at a spherical cow. The prediction is that it will bounce off:

In reality, if I throw a chunk of salt in one direction at a cow, it will not bounce off. I will discover a feature not accounted for in the original theory—a hole, where the mouth is.

By the same token, exploring the scale dependence of the laws of nature provides crucial mechanisms to hunt for new fundamental physics. My brief history of the weak interaction was one classic example. I’ll now describe some other, more current ones.

The scaling laws of fundamental physics can follow either a trickle-down or a bottom-up approach. Unlike economics, both techniques work in physics! We can explore those theories we
understand at accessible length scales and see how they evolve as we decrease the scale in an effort to gain new insights. Alternatively, we can invent theories that may be relevant at length scales much smaller than we can now probe in the lab and scale them up, systematically averaging over small scale processes, to see what they might predict about physical processes at the scales we can now measure.

These two approaches encompass the span of research at the frontier today. I described in chapter 2 how the theory of the strong interaction, which binds quarks inside protons and neutrons, was discovered. The idea of asymptotic freedom played an essential role. Quantum chromodynamics (QCD), the theory of the strong interaction, differs from QED in one fundamental respect: the effect of virtual particles at small scales on the evolution of the parameters of the theory is different. In QED, the effect of the virtual-particle cloud that surrounds the electron is to “shield” to some extent its electric charge from the distant observer. Thus, if we probe very close to an electron, we will find the charge we measure effectively increases compared to the value we would measure if we probed it from the other side of the room. On the other hand, and this was the surprise that Gross, Wilczek, and Politzer discovered, QCD (and
only
a theory like QCD) can behave in just the opposite way. As you examine the interactions of quarks that get closer and closer together, the effective strong charge they feel gets weaker. Each of their clouds of virtual particles effectively increases their interaction with distant observers. As you probe further inside this cloud, the strength of the strong interaction among quarks gets weaker!

Furthermore, armed with a theory that correctly describes the small distance interactions of quarks, we can try to see how things change with scale as we increase the scale. By the time
you get to the size of the proton and neutron, one might hope to be able to average over all the individual quarks and arrive at an effective theory of just protons and neutrons. Because by this scale the interactions of quarks is so strong, however, no one has yet been able to carry it out directly, although large computers are being devoted to the task and have thus far yielded results that are in accord with observation.

The great success of scaling arguments applied to the strong interaction in the early 1970s emboldened physicists to turn them around, to look to scales smaller than those which can be probed using the energy available in current laboratories. In this sense, they were following the lead of Lev Landau, the Soviet Feynman. By the 1950s this brilliant physicist had already demonstrated the fact that electric charge on electrons effectively increases as you reduce the distance scale at which you probe the electron. In fact, he showed that, at an unimaginably small scale, if the processes continued as QED predicted, the effective electric charge on the electron would become extremely large. This was probably the first signal, although it was not seen as such at the time, that QED as an isolated theory needed alteration before such small scales were reached.

QED gets stronger as the scale of energy is increased, and QCD gets weaker. The weak interaction strength is right in the middle. Round about 1975, Howard Georgi, Helen Quinn, and Steven Weinberg performed a calculation that altered our perception of the high-energy frontier. They explored the scaling behavior of the strong, weak, and electromagnetic interactions, under various assumptions about what kinds of new physics might enter as the scale of energy increased, and found a remarkable result. It was quite plausible that, at a scale roughly fifteen orders of magnitude smaller in distance than had ever been probed in the laboratory,
the strength of all three fundamental interactions could become identical. This is exactly what one would expect if some new symmetry might become manifest at this scale which would relate all these interactions, an idea that had been independently suggested by Sheldon Glashow, along with Georgi. The notion that the universe should appear more symmetrical as we probe smaller and smaller scales fit in perfectly with this discovery. The era of Grand Unified Theories, in which all the interactions of nature, aside from gravity, arise from a single interaction at sufficiently small scales, had begun.

It is almost twenty years later and still we have no further direct evidence that this incredible extrapolation in scale is correct. Recent precision measurements of the strength of all the forces at existing laboratory facilities have, however, given further support for the possibility that they could all become identical at a single scale. But, interestingly they do not do so unless we supplement the existing Standard Model with new physics, which could naturally result if we posit a new symmetry of nature, called Supersymmetry.

Supersymmetry relates different elementary particles in nature in new ways. It turns out that elementary particles can be classified in two different types, either as “fermions,” or “bosons.” The former classification, named after Enrico Fermi, describes particles whose quantum mechanical angular momentum is quantized in half-integer multiples of some fundamental unit, and we call them spin [fr 1/2] particles etc. The latter, named after the Indian physicist Satyendra Nath Bose, describes particles whose quantum mechanical angular momentum is quantized in integer multiples, and we call them spin 1 particles.

It turns out that bosons and fermions behave in profoundly different ways. The fact that electrons, for example, are fermions, is
responsible for all of chemistry, because, as Wolfgang Pauli first showed, two fermions cannot exist in precisely the same quantum state at the same place. Thus, as one adds electrons to atoms, for example, the electrons must occupy progressively higher and higher energy levels.

Bosons, on the other hand, can exist in the same quantum state in the same place, and in fact, if conditions allow, this is their preferred configuration, called “Bose condensation.” The background fields that have been posited to spontaneously break fundamental symmetries in the universe, for example, are imagined to be Bose condensates. Recently, under very special conditions, experimentalists have created Bose condensates in the laboratory, made from configurations of hundreds or thousands of atoms. The hope is that these very special configurations may result in new technologies, so that the first experimenters to produce these configurations were awarded the Nobel Prize several years ago.

While bosons and fermions thus appear to be totally different, supersymmetry is a new possible symmetry of nature that relates bosons and fermions, and predicts, for example, that for every fermionic particle in nature there should be a bosonic particle of the same mass, charge, etc. Now at this point you might remark that this is manifestly not the observed case in nature. However, by now you may also anticipate my response. If supersymmetry is a broken symmetry, then it turns out the fermionic and bosonic “superpartners” of the ordinary particles we observe in nature may be so heavy as to have not yet been discovered by producing them in accelerators.

What could be the possible motivation for introducing a new mathematical symmetry in nature that is not manifest in what we observe? Just as with the case of the standard model, introducing
such a symmetry can resolve certain paradoxes in preexisting theories. In fact, the complete motivation for assuming broken supersymmetry in particle theory is too convoluted to do justice to here, and again I have tried to do so at length in a recent book. One of the chief rationales, however, was that this symmetry might help explain why the electroweak scale is so much lower than the scale of gravity.

Be that as it may, it is fascinating that if one assumes that supersymmetry exists as a new symmetry of nature that is broken at a distance scale just a bit smaller than the electroweak scale, then incorporating the host of new heavy particles that must then exist into our calculations of the strength of the known forces in nature causes them to become identical in strength at a single scale approximately sixteen orders of magnitude smaller than the size of a proton.

Whether or not this idea is correct, this result, more than any other in the postwar era, turned theoretical and experimental physicists’ minds toward exploring the possibility of new physics on scales vastly different than those we could yet measure directly in the laboratory. In my opinion, the results have been mixed. The previous close connection between theory and experiment, which has always previously governed the progress of particle physics (and indeed all the rest of physics) has diminished somewhat, even as the stakes have increased as physicists turned their attention to possibly unifying all of the forces in nature, including gravity.

 

 

There is, in physics, on astronomically high-energy scale that has been staring us in the face for the better part of this century. Fermi’s weak interaction theory is not the only fundamental theory
that is clearly sick at high energies and small distances. General relativity is another. When one tries to incorporate quantum mechanics and gravity, numerous problems arise. Foremost among them is the fact that at a scale roughly nineteen orders of magnitude smaller than the size of a proton, the effects of virtual particles in gravitational interactions become unmanageable. Like Fermi’s theory, gravity does not appear to be a theory that can be a fundamental quantum theory as it stands. Some new physics presumably plays a role to alter the behavior of the theory at these small scales.

String theory is currently the most popular candidate for this new physics. At the scale where virtual particles would otherwise cause gravity to break down as a quantum theory, the string-like nature of particles in this theory changes the way the mathematics works, taming what would otherwise become unmanageable infinities. Moreover, gravity itself arises naturally in a fundamental theory of strings. The only catch is that strings themselves don’t make sense as quantum objects in four dimensions. To get a consistent theory one needs at least ten or eleven dimensions, six or seven of which are thus far invisible.

When string theory first arose, it was touted as a Theory of Everything, or, to put it in terms that are more relevant to the present discussion, the End of Physics. It was a theory that was supposed to be truly fundamental and that could apply at all scales. New symmetries would cause the scale dependence of the theory to stop, and the theory would be truly complete, never to be replaced by a more fundamental theory at smaller scales and reducing to the known laws of physics at larger scales.

At the time these claims were made, many of us were skeptical, and our skepticism has thus far been vindicated. It is now clear that in fact even strings themselves might, within the context of mathematical models currently under investigation, be effective
objects, to be replaced by yet other more fundamental objects that might operate in yet higher dimensions. Moreover, even after twenty years of hard effort by some of the brightest theorists around, very little progress has been made. String theory remains more a hope of a theory than an actual theory, and there is no evidence whatsoever, beyond the theoretical motivations I described above, that string theory has anything to do with nature.

Any Theory of Everything should address the fundamental question that most interested Einstein, and most interests me: Is there any choice in the creation of the Universe? Namely, is there just one set of consistent physical laws that hang together consistently, so that if one changed even one number the whole edifice would fall apart? Certainly this was the hope that had driven physics for several hundred years and that had been so touted by string theorists in the early days: The grand hope to explain exactly why the universe was the way it was, and why it had to be that way.