Once Before Time - Martin Bojowald [87]
In this regime, the repulsive forces of quantum gravity are no longer prevalent, but even the attractive contribution to the force can be subject to small changes compared to general relativity. These changes could upset the fine balance required for successful nucleosynthesis; their size and the underlying theory can be constrained, at least in principle. Such constraints, in turn, can be used to analyze the atomic structure of space-time responsible for the deviations from classical forces. Also here we have some kind of indirect microscope: Even without a direct view on space-time atoms, their properties can be probed by effects on much larger elementary particles. The required calculations, however, are quite complex and are still being developed. According to studies that I recently undertook with Rupam Das and Bob Scherrer, it seems that much more precise observations of the element abundances from nucleosynthesis than are currently available will be required in order to test quantum gravity in interesting ways.
SPACE-TIME AS A CRYSTAL: EMPTY GEMS
Given sufficiently high energies, the recent universe also allows effects that, like a microscope, could resolve the atomic structure of space-time. For light propagating in the universe, space-time itself, if it is indeed of an atomically discrete form, behaves much like a crystal. In an unstructured medium such as a vacuum, light of all wavelengths moves in the same way, in particular with the same speed—that of light, of course. In a medium of atomic nature such as a transparent crystal, by contrast, the various colors are subject to different propagation rules.
Light propagates in a medium by exciting charged particles to oscillations, allowing it to jump from atom to atom and thus propagate through the whole crystal. For light of shorter wavelengths—of higher frequencies closer to the blue than the red end of the visible spectrum—it is more difficult to excite the tardy crystal atoms to vibrations: If the wavelength comes close to the distance between crystal atoms, it gets more and more complicated for it to reach neighboring atoms. The medium appears stiffer than for waves of longer length, and the propagation speed decreases.
A well-known consequence of this so-called dispersion is the splitting of white light into bands of single colors, as in a rainbow or a prism. Changing velocities influence the refraction angles of waves at an edge where a crystal borders on, say, air. With two such nonparallel edges intersecting at a corner—as in a prism—white light, as a mixture of all colors, striking one side, leaves the crystal by the other side split into all its colors.
If space-time is atomic, resembling a crystal, light of different wavelengths no longer travels at a uniform speed even in the absence of matter. When moving through empty space, from a distant star to us, dispersion effects arise: Waves of different frequencies arrive here with different delays even if they were emitted simultaneously by the star. As before, individual corrections compared to propagation in a structureless space-time are very small. But if the star is distant enough, those tiny effects could add up during the long travels of light, and a potentially observable time delay would result.9
For a large delay after long travels, the star must be far away, making it more difficult to see. Moreover, one cannot use a uniformly glowing star; that would deprive us of any possibility of determining which parts of the radiation were emitted at the same time. No information about their time delay at arrival would result. What is needed is a faraway eruption of radiation, an explosion of short duration and yet more intense than from supernovae. The short eruption time combined with the required far distance means that we are talking about unimaginably powerful explosions. Fortunately, such events exist in the form of gamma ray bursts,10 exploding in fractions of a second and yet releasing more energy than a thousand suns