Once Before Time - Martin Bojowald [34]
Planck’s formula shows that the energy distribution of matter at high frequencies—corresponding to small wavelengths of radiation—behaves differently from what is expected with classical understanding. Like the stabilization of atoms, this may have consequences for a complete description of quantum gravity, for it is energy that, according to relativity, is equivalent to mass and thus gravitationally active. If energy behaves differently at small wavelengths or small distances than expected in the (non-quantum) general theory of relativity, a modified form of space-time as it is determined by matter should result. Space-time curvature and the gravitational force it implies would differ from its form in classical solutions. Such extreme scales would be significant especially at the big bang, when the universe is very small, or in the collapsed centers of black holes. If the quantum theoretical gravitational force were no longer purely attractive in these regimes, an infinite increase of energy could perhaps be prevented, and stable situations thanks to repulsive gravitational forces would result. Whether this is the case can be answered only with a concrete quantum theory of gravity. But it is encouraging to see that two independent consequences of quantum theory—the stability of atoms and the finiteness of black body radiation—both suggest this possibility.
PLANCK SCALES:
ON THE ENORMITY OF BEING QUANTUM
Before turning to possible quantum theories of gravity after the next chapter, we should take a more direct look at the scales to be expected. So far, as already mentioned, general relativity agrees very well with observations. Nobody would expect quantum gravity to be needed anytime soon to explain directly observed phenomena. In contrast to the numerous practical problems before quantum mechanics was developed, the need to develop a theory of quantum gravity is of an entirely conceptual nature, motivated by, for instance, the desire to avoid the singularity problem. While similar types of problems did occur in the classical physics of matter before the development of quantum mechanics, they were marginalized by the wealth of concrete observations.
The role played by quantum gravity for observations can be understood by looking at the relevant length scales, in particular the Planck length (not to be confused with Planck’s constant). Although Planck was no quantum gravity researcher, he had already introduced this important quantity.3 He had noticed that the speed of light, Newton’s constant for the gravitational force, and the later named Planck constant taken together allow, by suitable multiplications and taking roots, the definition of a length: the Planck length. By different combinations one can also obtain a time, the Planck time, and a mass, the Planck mass. This looked fascinating because no actual length measurement is required to determine the speed of light, the gravitational constant, and Planck’s constant—and yet one obtains a unique length by simple mathematical combinations. Possibly, this connection could be exploited for sensitive measurement methods or a new reliable convention for the unit of length.
So far, these thoughts have not played a technological role, due in part to the extreme smallness of the Planck length. Compared to the radius of an atom of about 0.000000001 meter (a billionth of a meter) or even that of a nucleus of 0.000000000000001 meter (a quadrillionth of a meter), the Planck length is infinitesimal.