Knocking on Heaven's Door (16 page)

More complete picture of a proton

[
FIGURE 18
]
The LHC collides protons together at high energy, each of which contains three valence quarks plus many virtual quarks and gluons that can also participate in the collisions.

Now that we have descended to the scale of quarks, held together by the strong nuclear force, I would like to be able to tell you what happens at yet smaller scales. Is there structure inside a quark? Or inside an electron for that matter? As of now, we have no evidence for such a thing. No experiment to date has given any evidence of further substructure. In terms of our journey inside matter, quarks and electrons are the end of the line—so far.

However, the LHC is now exploring an energy scale more than 1,000 times higher—and hence a distance more than 1,000 times smaller—than the scales associated with the proton mass. The LHC achieves its milestones by colliding together two proton beams that have been accelerated to extremely high energy—higher energy than has ever been achieved before here on Earth. The beams of protons at the LHC consist of a few thousand bunches of 100 billion highly lined-up, or collimated, protons concentrated in tiny packets that circulate in the underground tunnel. There are 1,232 superconducting magnets located around the ring to keep the protons inside the beam pipe while electric fields accelerate them to high energies. Other magnets (392 to be exact) reorient the beams so that the two beams stop streaming by each other and collide.

Then—and here’s where all the action happens—magnets guide the two proton beams around the ring in a precise path so that they collide in a region smaller across than the width of a human hair. When this collision occurs, some of the energy of the accelerated protons will be converted to mass—as Einstein’s famous formula,
E = mc
²
,
tells us. And with these collisions and the energy they release, new elementary particles, heavier than any seen before, could be created.

When the protons meet, quarks and gluons occasionally collide with a great deal of energy in a very concentrated region—much as if you had pebbles hidden inside balloons that were smashed together. The LHC provides such high energy that in the events of interest, individual components of the colliding protons crash together. These include the two up quarks and the down quark responsible for the proton’s charge. But at LHC energies, virtual particles carry a sizable fraction of the proton’s energy as well. At the LHC, along with the three quarks contributing to the proton’s charge, the virtual “sea” of particles also collide.

And when that happens—and here is the key to all of particle physics—the numbers and types of particles can change. New results from the LHC should teach us more about smaller distances and sizes. In addition to telling us about possible substructure, it should tell us about other aspects of physical processes that could be relevant at smaller distances. LHC energies are the final short-distance experimental frontier, at least for quite some time.

BEYOND TECHNOLOGY

We’ve now finished our introductory journey to the smaller scales accessible with current or even imagined technology. However, current human limitations on our ability to explore do not constrain the nature of reality. Even if it seems that we will have a tough time developing technology to explore much smaller scales, we can still try to deduce structure and interactions at those distances through theoretical and mathematical arguments.

We’ve come a long way since the time of the Greeks. We now recognize that without experimental evidence it is impossible to be certain of what exists at these minuscule scales we would also like to understand. Nonetheless, even in the absence of measurements, theoretical clues can guide our explorations and suggest how matter and forces could behave at tinier length scales. We can investigate possibilities that could help explain and relate the phenomena that occur at measurable scales, even if the fundamental components are not accessible directly.

We don’t yet know which, if any, of our theoretical speculative ideas will turn out to be right. Yet even without direct experimental access to very small distances, the scales we have observed constrain what can consistently exist—since it is the underlying theory that has to ultimately account for what we see. That is, experimental results, even on larger distance scales, limit the possibilities and motivate us to speculate in certain specific directions.

Because we haven’t yet explored these energies, we don’t know much about them. People even speculate the existence of a
desert,
a paucity of interesting lengths or energies, between those of the LHC and those applying to much shorter distances or higher energies. Probably this is lack of imagination or data at work. But for many, the next interesting scale has to do with
unification.

One of the most intriguing speculations about shorter distances concerns the unification of forces at short distances. It is a concept that sparks both the scientific and the popular imagination. According to such a scenario, the world we see around us fails to reveal the fundamental underlying theory that incorporates all known forces (or, at least, all forces aside from gravity) together with its beauty and simplicity. Many physicists have earnestly searched for such unification from the time the existence of more than one force was first understood.

One of the most interesting such speculations was made by Howard Georgi and Sheldon Glashow in 1974. They suggested that even though we observe three distinct nongravitational forces with different strengths (the electromagnetic and the weak and strong nuclear forces) at low energies, only one force with a single strength will exist at much higher energies. (See Figure 19.)
²⁹
This one force was called a unified force because it encompasses the three known forces. The speculation was called a
Grand Unified Theory (GUT)
because Georgi and Glashow thought that was funny.

Strength of Standard Model Forces as a Function of Energy

[
FIGURE 19
]
At high energy, the three known nongravitational forces might have the same strength and, therefore, could possibly unify into a single force.

This possibility of the strength of forces converging seems to be more than idle speculation. Calculations using quantum mechanics and special relativity indicate it might well be the case.
³⁰
But the energy scale at which it would occur is far above the energies we can study with collider experiments. The distances where the unified force would operate is about 10-30 cm. Even though such a size is far removed from anything we can directly observe, we can look for indirect consequences of unification.

One such possibility is proton decay. According to Georgi and Glashow’s theory—which introduces new interactions between quarks and leptons—protons should decay. Given the rather specific nature of their proposal, physicists could calculate the rate at which this should occur. So far, no experimental evidence for unification has been found, ruling out their specific suggestion. That doesn’t mean that unification is necessarily incorrect. The theory may be more subtle than the one they proposed.

The study of unification demonstrates how we can extend our knowledge beyond scales we directly observe. Using theory, we can try to extrapolate what we have experimentally verified to as yet inaccessible energies. Sometimes we’re lucky and clever experiments suggest themselves that allow us to test whether the extrapolation agrees with data or was somehow too naive. In the case of Grand Unified Theories, proton-decay experiments permitted scientists to indirectly study interactions at distances far too tiny for direct observation. These experiments allowed them to test the proposal. One lesson from this example is that we occasionally gain interesting insights into matter and forces and even come up with ways to extend the implications of our experiments to much higher energies and more general phenomena by speculating about distance scales that at first seem to be too remote to be relevant.

The next (and last) stop on our theoretical journey is a distance known as the
Planck length,
namely, 10-33 cm. To give a sense of just how minuscule this length is, its size is about as small relative to a proton as a proton is relative to the width of Rhode Island. At this scale, even something as fundamental as our basic notions of space and time will probably fail. We don’t even know how to imagine a hypothetical experiment to probe distances smaller than the Planck length. It is the smallest possible scale we can imagine.

This lack of experimental probes of the Planck length could be more than a symptom of our limited imagination, technology, or even funding. The inaccessibility of shorter distances could be a true restriction imposed by the laws of physics. As we will see in the following chapter, quantum mechanics tells us that small probes require high energies. But once the energy trapped in a small region is too big, matter collapses into a black hole. At this point, gravity takes over. More energy then makes the black holes bigger—not smaller—much as we are accustomed to from more familiar macroscopic situations where quantum mechanics plays only a limited role. We just don’t know how to explore any distance tinier than the Planck length. More energy doesn’t help. Very likely, traditional ideas about space no longer apply at this tiny size.

I recently gave a lecture where, after explaining the current state of particle physics and our suggestions for the possible nature of extra dimensions, someone quoted back to me a statement I had forgotten I’d made about the possible limitations of our notion of spacetime. I was asked how I could reconcile speculations about extra dimensions with the idea of spacetime breaking down.

The speculations for the breakdown of space and possibly time apply only at the unobservably small Planck length. Since no one has observed scales smaller than 10-17 cm, the requirement of a nice smooth geometry at measurable distances is not violated. Even if the notion of space itself breaks down at the Planck scale, this is still much smaller than the lengths we explore. There is no inconsistency so long as a smooth recognizable structure emerges when we average over larger, observable scales. After all, different scales often exhibit very different behaviors. Einstein can talk about smooth geometries of space on large scales. But his ideas might break down at smaller scales—so long as they’re so tiny and yield such negligible effects on measurable scales that the new more fundamental ingredients have no discernible impact we can observe.

Independently of whether or not spacetime breaks down, a critical feature of the Planck length that our equations certainly tell us would be true is that at this distance, gravity, whose strength is minuscule when acting on fundamental particles at the distances we can measure, would become a strong force—comparable in strength to the other forces we know. At the Planck length, our standard formulation of gravity according to Einstein’s theory of relativity would cease to apply. Unlike larger distances where we know how to make predictions that agree well with measurements, quantum mechanics and relativity are inconsistent when we apply the theories we generally use in this tiny regime. We don’t even know how to try to make predictions. General relativity is based on smooth classical spatial geometry. At the Planck length, quantum fluctuations can make a spacetime foam with too much structure for our conventional formulation of gravity to apply.

To address physical predictions at the Planck scale, we need a new conceptual framework that combines quantum mechanics and gravity into a single more comprehensive theory known as
quantum gravity.
The physical laws that work most effectively at the Planck scale must be very different from the ones that have proven successful on observable scales. The understanding of this scale could conceivably involve a paradigm shift as fundamental as the transition from classical to quantum mechanics. Even if we can’t make measurements at the tiniest distances, we have a chance of learning about the fundamental theory of gravity, space, and time through increasingly advanced theoretical speculations.