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By Root 688 0

attraction, a world shrinking through the disappearance and fading away of its atoms of space, approaches the State of Hell, the reign of absolute shallowness of space. The history of the universe becomes one of utter turmoil, chaos, and confusion. Space is fluctuating and disintegrating, much worse than any shaking ground. All forces struggle for dominance, raining punishing blows not just on matter but even on space and time. In this climactic battle, an ancient power is rising to absolute prominence. Gravity, belittled by its fundamental competitors when tempers were still low, now holds the key. It sets itself against the wide converging tide it had released, then calms the seas and lets the universe expand to vent its anger.

How can quantum gravity concretely provide forces counteracting its own classical attraction? Mathematically as well as intuitively, this is a direct consequence of discrete time: Taking all points in time together, there is not a continuous line but a lattice, or grid. Such a time lattice has only a finite amount of storage space for energy: Like a sponge, which can absorb a limited amount of water but when fully soaked repels surplus water, the time lattice acts repulsively once too much energy threatens to be present at one time.

Here, the quantum nature of all matter is important, requiring wave functions to be used for its description. Energy is encoded in the frequency of the wave function, that is, the number of oscillations per unit time interval. As with light, the higher the frequency, the more energetic the wave. Ultraviolet light of high frequency is much more energetic and damaging than the lower-frequency infrared light. High frequency, on the other hand, means that the oscillation length of such a wave is small: Only a brief amount of time passes between two successive intensity maxima of the wave. A continuous time line could support very short oscillations, and thus any amount of energy. A time grid, by contrast, can allow only oscillation lengths larger than its grid size. Such a wave would become discrete and distorted when drawn on a lattice, but it would still be a recognizable wave. Shorter waves, however, would simply disappear, since their oscillations would fall between the gridpoints. In this way, a discrete time cuts off too-rapid oscillations, and too-large energies (figure 14).

Owing to the smallness of time steps, the lattice can absorb a great deal of energy, but not an infinite amount. While not essential in most regimes, the resulting energy bound is important at the big bang, the most highly energetic event in the universe. According to general relativity, energy densities in a contracting universe should grow unboundedly, an expectation incompatible with a lattice of finite storage space. A consistent theory with a time lattice, as it arises in loop quantum cosmology, must cause repulsion of surplus energy. But there is nothing outside the universe into which energy could be pushed. Too large an energy can be prevented only by stopping the collapse itself, the cause of the energy growth, and turning it into expansion. In this way, a less of local times in the lattice provides a physical counterforce to the collapse, and thus a more of time beyond the big bang.

14. If we sample waves by taking their elevations only at the nodes of a grid with fixed spacing, for instance as the result of the atomic nature of space, short wavelengths are suppressed. The top wave with a wavelength larger than the spacing is not distorted much by the sampling; its smooth behavior is still recognizable by the discrete set of values it takes at the grid points. When the wavelength comes close to or is smaller than the spacing, however, the discrete samples give a picture very different from the original smooth wave (bottom two waves). In particular, oscillations of the sample points show a wavelength always larger than the grid spacing, even if the original wave had a smaller wavelength.

For a large universe of low energy density the discreteness is unimportant, but it is essential