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By Root 678 0

Einstein’s before he formulated general relativity: We do have a very successful theory of gravitation that is not in conflict with any observation. And yet we know that this theory cannot be complete; we must find an extension based on general principles. Apparently, we are not as lucky as Einstein, who—an intense but short decade after perceiving the problem that Newton’s law is incompatible with the transformability of space and time—was able to propose general relativity as the solution. Special forms of singularities were found in solutions just after 1915, for instance in the solution for a nonrotating black hole determined by Karl Schwarzschild in 1916. The general existence of singularities in solutions to general relativity was demonstrated in the 1960s. In spite of numerous more recent efforts by far more theorists than in the years between 1905 and 1915, no complete theory has yet been formulated, a theory at the same time preserving the successes of general relativity and solving its singularity problem.

There is one belief guiding the majority of researchers: Next to general relativity, quantum theory is the second pillar on which twentieth-century physics is built. Quantum physics describes objects in extended, wavelike forms rather than pointlike particles, and establishes as a consequence the atomic, discrete structure of matter. Quantum theory is indispensable for a correct description of matter and implies impressive phenomena. In astrophysics, as already mentioned, the quantum nature of matter leads to new stable states such as white dwarfs and neutron stars that rely on repulsive forces caused by quantum physics. Sometimes these forces suffice to compensate the attraction of gravity, but this is not the case for large masses. What is completely left out of this picture is the quantum nature of gravity and space and time themselves, in addition to that of matter. Had we ignored the quantum theory of matter, even white dwarfs and neutron stars could not exist stably, for no repulsive classical forces would occur at their densities. This would be in conflict with observations that have confirmed the existence of such objects in the cosmos.

The quantum physics of gravity is ignored in all these investigations, since such a theory is not yet available. All the known but incomplete approaches to its formulation, moreover, are mathematically so complex that they cannot yet be applied to objects such as neutron stars or black holes as they exist in space. But there are situations in cosmology where strong evidence of new counterforces exists, forces arising in a quantum theory of gravity and possibly leading to a theory free of singularities. An understanding of far earlier times before the big bang, as well as of the interior of black holes, then comes within reach. But before we can turn to these developments of recent research, we will need the basic concepts of quantum theory.

2. QUANTUM THEORY

UNCERTAIN STABILITY

For as its belt sparkled and glittered now in one part and now in another, and what was light one instant, at another time was dark, so the figure itself fluctuated in its distinctness: being now a thing with one arm, now with one leg, now with twenty legs, now a pair of legs without a head, now a head without a body: of which dissolving parts, no outline would be visible in the dense gloom wherein they melted away. And in the very wonder of this, it would be itself again; distinct and clear as ever.

—CHARLES DICKENS, A Christmas Carol

Quantum theory is a universal framework applying to all systems, even macroscopic ones. It is indispensable for a correct description of atoms, the realm of its initial discovery. Its importance has been verified experimentally many times, and as with general relativity, no deviations between observations and its predictions have occurred to date. And yet these two dominating theories do not provide a complete picture of physics, for in their current formulations they are incompatible with each other. This is of particular importance in extreme