Knocking on Heaven's Door - Lisa Randall [48]
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