Quantum gravity

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The quantum gravity is a theory currently being under development which the quantum physics and general relativity should, so the two great physical theories of the 20th century unite. While the general theory of relativity describes only one of the four elementary forces of the universe, namely gravity , quantum theory deals with the other three elementary forces ( electromagnetic interaction , weak interaction and strong interaction ). The unification of these two theories is worth striving for, among other things because of their overlap, but also because of their different scientific- philosophical consequences.

backgrounds

In general, the general theory of relativity describes the structure of the universe on a large scale and is practicable for large masses and accelerations . Quantum theory, on the other hand, describes the interaction between the smallest particles in small areas of space.

Although gravitation is the weakest of the elementary forces, it not only determines the worldview of physics , but also dominates the phenomena on a large scale despite its "smallness" compared to the other interactions : It is the only one of the four elementary forces that, according to today's knowledge, acts exclusively attractive, since there is only one gravitational charge (the mass), and therefore there are no opposing charges that can cancel each other out. The other elementary forces, on the other hand, are only of importance for microscopic processes, although they are generally much larger than gravity in terms of magnitude - with the exception of the electromagnetic interaction, which is quite macroscopic and, in the case of interstellar plasma or the magnetic fields of, for example, the sun and earth, also cosmic scales . Overlapping of the two theories occurs in some extreme cases.

Some physicists associate the unification of gravitation with the other elementary forces, which has yet to be formulated, with the hope that formally infinite terms no longer occur in such a theory and that extreme cases in which all elementary forces must be taken into account equally can then be calculated.

In addition, quantum gravity is considered a possible candidate for a TOE ( T heory O f E verything).

Problems

So far, however, gravity has persistently resisted attempts by physicists to insert it into a quantum model . This is based on the fact that all forces are divided into elementary portions , the quanta , whereby the statements about the measured quantities of the theory are only statements of probability (see e.g. quantum mechanical states ). These statements about the forces broken down into individual quanta can be precisely calculated and justified in quantum theory (and only there, see e.g. the EPR paradox ).

Gravitation, however, cannot be broken down into quanta that easily. Even with classical treatment in general relativity, the superposition of space-time curvatures already produces new space-time curvatures (non-linearity of Einstein's field equations ). Today, therefore, various theories are put forward to make this possible.

The main problem when formulating a theory of quantum gravity is that established methods that are known from other quantum field theories cannot be directly transferred to general relativity. In particular, the perturbation-theoretical quantization and renormalization of gravitation fails . If one tries to construct the theory using gravitons and their interactions (using Feynman diagrams ), one finds the infinities known from other quantum field theories; however, the elimination of these infinities is not possible with the established methods. Qualitatively, the remaining infinities can be explained by the non-linearity of the gravitational interaction described above, since when adding up high-energy processes for gravitons, new coupling processes and resulting divergences from loop processes can arise, which can no longer be explained by the parameters of the original Lagrangian. For a theory of quantum gravity, new methods for quantization or renormalization must be constructed, which should have a non-perturbative character due to the previously discussed aspect . However, if one restricts oneself to gravitation effects at a low energy scale, the quantization of gravitation as an effective field theory or as a semiclassical theory of gravity (e.g. in the context of the description of long-wave gravitational waves) can already be successfully implemented today.

Candidates for a theory of quantum gravity

A contender for quantum gravity is string theory , in which all elementary particles are represented by one-dimensional strings. However, according to the current state of knowledge, this theory can only be formulated in a 10-, 11- or 26-dimensional universe. Furthermore, it is unclear whether and in what way it reproduces the well-known standard model of elementary particles.

An alternative is loop quantum gravity (also loop quantum gravity LQG ), in which space and time are also quantized. In the course of loop quantum gravity, the general theory of relativity is initially reformulated as a gauge theory and a modified quantization rule is applied. Today (2018) it has not yet been finally clarified whether the theory so defined is inherently consistent and whether it reproduces the results of the general theory of relativity in the classic limit case.

Another alternative is the approach of so-called asymptotic security, a generalization of asymptotic freedom , which aims at a non-perturbation-theoretical quantization and renormalization of general relativity. The above-mentioned problems of perturbative quantization are avoided; the coupling constants and physical quantities such as scatter amplitudes remain finite.

The causal dynamic triangulation represents an approach that gravity in a discretized version comparable lattice gauge theory using path integral quantization and Monte Carlo simulation to solve. This formulation allows the calculation of different “phases” of quantum gravity; In the long-range Limes, a de-sitter universe automatically results , that is, the causal dynamic triangulation possibly reproduces a universe with non-vanishing cosmological constant and accelerated expansion without additional assumptions .

The Super gravity refers to a class of field theory, the theory of general relativity to extensions of super symmetric fields, in particular to the hypothetical gravitino as a spin-3/2-partner of the (likewise hypothetical) Spin-2- graviton result. Different classes of supergravity arise as borderline cases of superstring theories in the limit of vanishing string length. The idea behind supergravity is that it should both encompass the standard model of elementary particles and solve the renormalization problem. The latter could not be clearly proven until today (2018).

These are only a few theories, there are a number of other explanatory models.

Classification of quantum gravity

Fundamental interactions and their descriptions
Strong interaction Electromagnetic interaction Weak interaction Gravity
classic Electrostatics & magnetostatics ,
electrodynamics 		Newton's law of gravitation ,
general relativity
quantum
theory 		Quantum
( standard model ) 		Quantum electrodynamics Fermi theory Quantum gravity  ?
Electroweak Interaction
( Standard Model )
Big Unified Theory  ?
World formula ("theory of everything")?
Theories at an early stage of development are grayed out.

The Planck scales

If one forms the characteristic physical quantities of the theory using the associated natural constants of gravitation theory and quantum theory and compares them with one another, one can obtain the characteristic lengths, times and energies of the Planck era :

This works roughly as follows: The characteristic gravitational energy of two “Planck masses” at a distance of one Planck length is: with the gravitational constant . On the other hand, the (reduced) Planck constant and the Planck time (= Planck length / c , with the speed of light c ) result in the same characteristic energy from the identity . By equating one obtains if one also substitutes for the associated Compton wavelength .

Overall, this results in a very high value for the Planck energy (≈ 10 19  GeV) and very small values ​​for the Planck length (≈ 10 −35  m) and the Planck time (≈ 10 −43  s). This shows that quantum gravity is an extreme process that does not play a role in everyday life. However, these processes are important for policy issues.

See also

literature

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