Quantum Theory of Gravity

Quantum Theory of Gravity is the theory intended to possess the predictive power of General Relativity and to exhibit quantum properties. Einstein’s theory of general relativity is based on a form of mathematics called differential geometry and also on the idea that Space-time is a continuum. Continuum theories differ from Quantum Theory in several ways, the most basic being that there is some smallest size or unit in quantum theories, but not in continuum theories. Physically this means that a region of space-time can be divided into infinitely small parts and there will never be a ‘smallest’ piece.

The mathematical apparatus of each of these types of theories is totally different. Theories of the strong, weak and electromagnetic forces are all quantum theories and they are described by wave functions and probabilities. Gravitational theory, on the other and, is described by differential equations on a continuous manifold. There are no uncertainties in general relativity and no discrete quantum states. Many physicists, including Einstein himself, have endeavored to find a quantum theory of gravity that would retain the predictive power of general relativity, but also exhibit quantum properties. If one were successfully to develop such a theory, one would need to postulate th existence of an exchange particle that mediates the Gravitational Force. This Boson, called a Graviton, must be mass-less so the force is proportional to 1/r² and it must have a spin of 2. Individual gravitons have never been directly detected.

Every attempt to derive a complete quantum theory of gravity and to put it in a mathematical form similar to the other three fundamental forces has failed. Problems arise at very small distances, close to the Planck scale, where quantized theories of gravity have characteristics, described as ‘quantum foam’, that are not compatible with general relativity. This quantum foam represents fluctuations in the shape and form of the underlying space-time and would lead to physical effects that are not observed.

Superstring theory and other TOEs (Theory of Everything) are attempts to quantize gravity, and to make it compatible with the other three fundamental forces. Although these theories are progressing, they are plagued by a lack of testable predictions since the interaction energies involved are well beyond the energies achievable in nuclear accelerators. It is quite possible that cosmological observations might be the only way to test string theories of elementary particles. If we are able to conceive a working Quantum Theory of Gravity, which can accommodate both Relativistic and Quantum Mechanical Behavior, it would undoubtedly be one of the greatest achievements of mankind.

Questions to Ponder

• Is gravity quantized? What do we know about the Graviton?
• How can quantum gravity help explain the origin of the universe?