Loop quantum gravity

The theory of loop quantum gravity (loop quantum gravity, loop theory, Eng. Loop quantum gravity ) is an approach to a theory of quantum gravity, that is, a theory for the unification of quantum physics with general relativity. This association is now considered one of the greatest challenges in physics.

The loop quantum gravity, the space is described as a dynamic quantum mechanical spin network, which is clearly represented by graphs of lines and nodes. One consequence of this theory would be the quantization of space and time in the range of the Planck length (about 10-35 m ) or Planck time (about 10-43 s ). On this scale, the world loses its continuity assumed in everyday life, where everything is described quantized, and the gravity and consequently the geometry.

History

The theory of loop quantum gravity is now considered the most advanced alternative to string theory. In the early 1970s suggested Roger Penrose spin networks for a theory of quantum gravity. The actual development of the theory began with work by Abhay Ashtekar, Lee Smolin and Carlo Rovelli the mid to late 1980s a. Important contributions were made by Thomas Thiemann, Jerzy Lewandowski, Jorge Pullin, Rodolfo Gambini, John C. Baez.

Martin Bojowald deals with the topics of loop quantum gravity ( SQG, Loop Quantum Gravity ) and physical cosmology. He is best known for the application of SQG to cosmological problems. He developed since 2003 as part of the SQG theory, according to which the universe. Well before the Big Bang, which is a singularity in the usual cosmological models of general relativity, where the description of the general theory of relativity has limitations, already existed

Motivation

The simultaneous application of the general theory of relativity and quantum theory to objects of the order of the Planck scale leads to contradictions. For instance, could any object that would be smaller than the Planck length, due to the uncertainty principle as much energy or mass that it would collapse into a black hole. Therefore Theoretical physicists believe that the theory of relativity and quantum theory, the rise of these orders of magnitude in a higher-level theory, which contains both theories in the sense of the correspondence principle as limiting cases.

The loop quantum gravity - as well as string theory - avoids this problem by appropriate concepts of space-time structure and includes the assumption of arbitrarily small structures.

Concept and statements

From the perspective of loop quantum gravity, space is no background for the events embedded in it, but is itself a dynamic object that obeys the laws of quantum mechanics. A quantum state of the space is described by a network of nodes that are connected with lines. The nodes are assigned to certain properties, mathematically similar to those of the spin of elementary particles. Each node can be in some sense an elementary volume assign. The distances between nodes correspond to the Planck length. For a cubic centimeter contains 1099 nodes.

For comparison it should be mentioned that the visible universe, however, contains only 1085 cubic centimeters. This would mean that the resolution of a cubic centimeter event set of the visible universe in 1014 could even fit in one cubic centimeter; So you. having a "perfect microscope ", which could zoom into the depth of a cubic centimeter unlimited, 100 trillion times might expect to see so many possible events such as with a perfect telescope, which dissolves the visible universe to centimeter length This idea generally acts very strange and would in an empirical confirmation of the loop quantum gravity far-reaching ideological consequences for the physical understanding.

Another statement of this theory is that you can not imagine the power as embedded in the room. A space as a container for the network does not exist. The network itself is space. Between the nodes and links, nothing exists. Between them is therefore located as little space as of sand is between the sand grains of a sand dune. In the nothingness between the nodes and links, however, is still much opportunity for other ( emerging ) nodes and links, each set unless violate these limits, lengths and times on the Planck scale lose their traditional everyday meaning. " Size " or " thickness" of nodes or a " length" of connecting lines are not definable or do not exist in the sense of everyday use descriptions such as the one net braid of twine. How could theory according to the quantum -loop space by adding coming from mere conjunction lot of new space " out of nothing" out arise, the space from a macroscopic point of view would be perceived as " expanding in itself ", which is why an external observer the boundaries of the whole process quite might judge to be constant.

Elementary particles correspond to network nodes or node combinations with certain properties. The motion of particles corresponds to a shift of corresponding types of nodes in the network, which move or rotate around each other.

In contrast to string theory here currently playing multi-dimensional theoretical constructions a subordinate role. It is not excluded that elude certain node or link types of the conventional observation.

In the work of reflection are calculated from the nodal lines and of the lines connecting the nodes surfaces. On the other hand, the ongoing structural changes lead in the network as the unification of nodes or to the emergence of multiple nodes from a single. The change in the spin- on time, the network is therefore called spin foam..

Just as in the room, these changes are not in the network embedded in a time, but they represent the flow of time itself Represents the means that the movements of nodes no time " lasts ", but only happens causally after the other. The sequence of cause and effect itself is time. In the image of the spin the foam indicates that the foam surface elements are not extended in any direction of the time axis, but as in a conventional foam in all directions are approximately equal, and terminate at the edges of contact with their neighbors.

The spin- networks, also called graphs are, subject to certain structural rules and correspond to a kind of shorthand in the context of the associated mathematical formalism. You have now indeed a certain superficial resemblance to the Feynman diagrams with which the interactions between particles are described, but they are structurally completely different principle. In principle, this spacetime is viewed with combinatorial concepts.

Naming

Owes its name to the loop quantum gravity a formulation of general relativity, the Indian physicist Abhay Ashtekar 1986 proposed and is similar in many respects to Maxwell's theory of electromagnetism. From this it takes the concept of the field lines. Both in the Maxwell theory as well as in the related theories such as quantum theory of strong interactions, namely quantum chromodynamics, closed field lines can occur.

In the same year, 1986, Ted Jacobson and Lee Smolin formulated the so-called Wheeler - DeWitt equation of quantum cosmology according to the concept of Ashtekar. They found a class of exact solutions of these equations, the Wilson loops, or briefly, Loops ' of loop quantum gravity.

Starting points

Start of the loop quantum gravity are two basic principles of general relativity:

• The so- called background independence: This refers to the assumption that the geometry of spacetime is dynamic at the microscopic level.
• The so-called diffeomorphism invariance: This refers to the fact that in general relativity, any coordinate system for the description of space-time are well suited equal, provided that certain conditions are met regarding the differentiability.

The background independence is the more important of the two principles. Through them, the loop quantum gravity by string theory, whose equations are formulated in a classical space-time differs.

Achievements so far

The loop quantum gravity is able to describe some already known or suspected phenomena correctly:

• The formula of Jacob Bekenstein, according to which the entropy of a black hole is proportional to its surface.
• The Hawking radiation that black holes emit.
• A positive cosmological constant, for the existence of astronomical observations have provided compelling evidence follows relatively naturally from the loop quantum gravity.
• Martin Bojowald developed in 2008 as part of the SQG theory, according to which the universe already existed before the Big Bang. The usual cosmological models of general relativity there are limits due to the singularity shown.

Testable predictions

• From the loop quantum gravity follows that the speed of light depends on the wavelength of light. The deviations from the normal value fall particularly important when the wavelength is comparable to the node distances and hence the Planck length, so that the photons in a sense to feel the quantum structure of spacetime. The relative difference even for the highest energy cosmic rays is, however, only about one- billionth. Such an effect would delay differences of the various spectral radiation components in cosmic gamma-ray bursts result. Studies carried out since 2005 measurements of gamma-ray bursts of 500 million light-years distant blazar Markarian 501 with the MAGIC telescope showed such maturity differences, however, do not have any reasonable statement about their cause. The 11 June 2008 launched gamma-ray satellite Fermi Gamma - ray Space Telescope would be able to detect run-time differences in outbreaks in a distance of several billion light years.
• According to current theory, the range of protons should be as low kinetic energies about 1019 electron volts in space due to scattering of photons of the cosmic background radiation that they can not reach the earth ( GZK cutoff ). In contradiction, however, the Japanese Agasa experiment has already demonstrated several such protons. Within the loop quantum gravity but the threshold for this dispersion is higher proton energies, in accordance with the experimental data location.
• From the loop quantum gravity follows a specific spectral structure of the mentioned Hawking radiation of black holes. An experimental study of this radiation lies in the distant future.

Open Questions

The current state of loop quantum gravity can be a number of basic questions unanswered:

• Still, it has not been able to derive the general theory of relativity as a limiting case in the sense of the correspondence principle out of the loop quantum gravity.
• It is assumed that the loop quantum gravity has certain corrections of the special theory of relativity for velocities close to the speed of light result, the nature of which, however, is still unknown.
• An important component of a successful theory of quantum gravity is the union or even derivation of all the fundamental forces of physics. This problem could not yet be solved.

Criticism

The loop quantum gravity is discussed controversially. In this case, the consistency of many of their claimed successes and predictions is questioned. Criticism of loop quantum gravity is formulated mainly by representatives of the string theory and in particular with the following arguments:

• It was not clear how the above the Planck length continuous and steady behavior of space-time would result as the limit of the discrete network of nodes.
• This theory do not recognize the constant velocity of light in vacuum and say a minimally greater velocity for photons with extremely short wavelengths advance.
• To be calculated from the theory, the likelihood of ( quantum mechanical ) process in the conventional space-time, to be an infinite number of fixed constants. So the situation is not better than in attempting canonical quantization of ( nichtrenormierbaren ) general relativity.