Once Before Time - Martin Bojowald [57]
But was this allowed? The calculation’s promise, including a possible resolution of the singularity problem—a major issue that had plagued gravitational research for decades—was too enticing to drop everything again. After the first excitement I remembered why I had not undertaken the simplification much earlier. There was, after all, its apparent inconsistency. With a fresh view of the old problem, I was fortunately soon able to show that the crucial simplification was not only allowed mathematically, but even necessary for implementing the symmetry completely. My initial version, without the final step, would have left space slightly squashed and distorted. With this last bit of asymmetry removed, the equations easily became amenable to standard treatments, producing explicit solutions and showing general properties.
In this way, the first results of loop quantum cosmology, developed much further in the ensuing years to lead to the universe scenarios described in the remainder of this chapter, were put on a solid footing. Now even space-times not strictly obeying the cosmological principle can be tackled, an extension of the original calculation to which many researchers have started to contribute now that its promise has been shown. Beyond the immediate implications for kick-starting loop quantum cosmology, this experience illustrates how strongly stubborn opinions can influence scientific work, or even handicap it—and what progress can come when one occasionally steps aside.
LESS IS MORE: GAINING TIME
There is nothing more precious than time, for this is the price of eternity.
—LOUIS BOURDALOUE
The universe resembles a long-distance runner, truly the hardiest ever seen. As every runner knows, one occasionally approaches physical breakdown. Muscles weaken, motion becomes uncontrolled. While a run at full strength appears to be a single smooth and sleek process, safely getting through weak periods requires every single step to be precisely measured. Too large a step costs yet more strength; too-timid ones release all muscle tension and lead to stumbles.
Right now, the universe boasts immense strength; to mock us, it even seems to have initiated a spurt a while ago—an acceleration of its expansion to be encountered in the next chapter. (It seems to have been fired up by the spectators: As can be seen from the escape velocities of distant star explosions, the acceleration began, compared to other cosmological time scales, relatively recently, “just” before mankind started its cosmological observations.)
The big bang, by contrast, resembled a period of weakness. Here, the universe was heating up and came close to a breakdown, a trouble reflected in the existing theoretical descriptions of this phase: General relativity still assumes a continuous run but quickly breaks down in a singularity. Quantum theories of gravity are more careful and pay more attention to the precise step size. Is this enough to survive the big bang without damage?
Loop quantum cosmology has brought exactly this consequence. First, by the interactive process of changing loops of space it introduces a discrete time, thus improving the old version of quantum cosmology. Time cannot change arbitrarily, but only in multiples of a smallest time step: Change happens whenever the meshed loops reconnect, but not in between these discrete stitches. Loop quantum cosmology grants the universe less time, as it were, since all moments of time falling between the grid’s smallest steps are eliminated. This happens on microscopic scales and is, due to the