Loop quantum gravity

from Wikipedia, the free encyclopedia

The theory of loop quantum gravity ( loop quantum gravity , loop theory , engl. Loop quantum gravity ) is an approach to a theory of quantum gravity , d. H. a theory to unite quantum physics with general relativity . Combining them is one of the greatest challenges in physics today.

The loop quantum gravity describes the space as a dynamic quantum mechanical spin network , which can be clearly represented by diagrams of lines and nodes. A consequence of this theory would be the quantization of space and time in the area of Planck length (approx. 10 −35  m) or Planck time (approx. 10 −43  s). On scales of this magnitude, all phenomena of physics, including gravitation and geometry , are no longer described as a continuum , but in a quantized manner.

history

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

Martin Bojowald deals with the topics of loop quantum gravity (SQG, Loop Quantum Gravity) and physical cosmology . He became known for the application of the SQG to cosmological problems. From 2008 onwards, as part of the SQG, he developed a theory according to which the universe already existed before the Big Bang (which in the usual cosmological models of general relativity theory represents a singularity at which the description of general relativity theory reaches its limits).

motivation

The simultaneous application of general relativity and quantum theory to objects of the order of magnitude of the Planck scale leads to contradictions. For example, any object that is smaller than Planck's length would have so much energy or mass , due to the uncertainty relation , that it would collapse into a black hole . Although this is resolved in string theory through the interpretation of the strings as black holes, theoretical physicists assume that relativity and quantum theory would have to merge into a superordinate theory at these magnitudes, which contains both theories as borderline cases in the sense of the correspondence principle .

Loop quantum gravity - just like string theory - circumvents this problem through appropriate concepts of space-time structure and excludes the assumption of structures of any size .

Concept and statements

Structural changes in the spin network

From the point of view of loop quantum gravity, space is not a background for the events embedded in it, but rather a dynamic object that obeys the laws of quantum mechanics . A quantum state of space is described by a network of nodes that are connected with lines. The nodes are assigned certain properties that are mathematically similar to the spin of elementary particles . In a certain sense, an elementary volume can be assigned to each node. The node distances correspond to the Planck length . So one cubic centimeter contains 10 99 knots.

For comparison, it should be mentioned that the visible universe, on the other hand, only contains 10 85 cubic centimeters. This would mean that the set of events in the visible universe resolved to one cubic centimeter fits 10 14 times into one cubic centimeter. With a “perfect microscope ” that could zoom indefinitely to a depth of one cubic centimeter, one could see 100 trillion times as many possible events as with a perfect telescope that resolves the visible universe down to a centimeter. This idea seems very strange in general and would have far-reaching ideological consequences for the physical understanding of an empirical confirmation of loop quantum gravity. Another proposition of this theory is that the network cannot be imagined as being embedded in space. A space as a container for the network does not exist. The network itself is space. Nothing exists between the nodes and connections. So there is just as little space between them as there is sand between the grains of sand in a sand dune. In the nothing between the nodes and connections, however, there is still plenty of opportunity for further (emerging) nodes and connections, as long as they do not violate the respective set limits, whereby length and time information on the Planck scale lose their conventional everyday meaning. The “size” or “thickness” of knots or the “length” of connecting lines cannot be defined or do not exist in the sense of everyday descriptions, such as that of a network of twine . Theoretically, new space could arise in the quantum loop space by adding a mere amount of connection “out of nowhere”, whereby the space would be perceived as “expanding in itself” from a macroscopic point of view, which is why an external observer definitely limits the entire process could judge as constant.

Elementary particles correspond to network nodes or node combinations with certain properties. The movement of particles corresponds to a shift in corresponding node types in the network, which can move or rotate around one another.

In contrast to string theory, multi-dimensional theoretical constructions currently play a subordinate role here. It cannot be ruled out that certain types of nodes or connections may elude conventional observation.

Spin foam as a description of the structural change in space as a function of time.
The characteristic length of the structures shown is of the order of magnitude of the Planck length (~ 10 −33  cm) or less .

As we proceed, the nodes become lines and the line networks become areas. This process is similar to the world lines of point particles, which in string theory become world surfaces. On the other hand, the continuous structural changes in the network also lead to the union of nodes or to the emergence of several nodes from a single one. That is why the net is allegorically compared to a foam (the spin foam ), which can grow figuratively or even collapse.

As in the case of space, these changes in the network are not embedded in a time, but represent the flow of time themselves. This means that only the movements of the nodes, as causal events, create graduality and thus countability for the interpretation of an elapsed time. In the image of the spin foam, this means that the pieces of foam are not extended arbitrarily in the direction of the time axis, but are roughly the same size in all directions, as is usual with foam, and end at the edges of contact with their neighbors.

The spin nets, also called graphs, are subject to certain structural rules and correspond to a kind of shorthand within the framework of the associated mathematical formalism. Although they have a certain superficial similarity to the Feynman diagrams , which are used to describe the interactions between particles, they are fundamentally structurally completely different. In principle, space-time is considered with combinatorial concepts.

Naming

The loop quantum gravity owes its name to a formulation of the general theory of relativity proposed by the Indian physicist Abhay Ashtekar in 1986 and which in many respects resembles Maxwell's theory of electromagnetism . From this it takes over the concept of field lines . Both in Maxwell's theory and in related theories such as the quantum theory of strong interaction , i.e. H. of quantum chromodynamics , closed field lines can occur.

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

Starting points

The starting point of loop quantum gravity are two basic principles of general relativity:

  • The so-called background independence : This means that the geometry of space-time is already dynamic in the context of the general theory of relativity and that it would generally be wrong to mark a very specific space-time and only consider small perturbations of it.
  • The so-called diffeomorphism invariance: This denotes the fact that in general relativity any coordinate systems are equally well suited for describing spacetime, provided that certain prerequisites with regard to differentiability are met.

Background independence is the more important of the two principles. It is through them that loop quantum gravity differs from string theory, whose equations are formulated in a classical and a priori fixed space-time.

Previous successes

First of all, loop quantum gravity is a promising candidate for a background-independent and renormalizable quantization of gravity. This alone is a significant step forward after decades of unsuccessful attempts to transfer quantization rules from conventional quantum field theories to gravity.

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

Verifiable predictions

  • From a special variant of the loop quantum gravity with cosmological constant it follows that the speed of light depends on the wavelength of the light. The deviations from the usual value are particularly significant when the wavelength is comparable to the node distances and thus the Planck length, so that the photons can feel the quantum structure of space-time, so to speak. Even for the highest energy cosmic rays, however , the relative difference is only about one billionth. Such an effect would result in time differences between the various spectral radiation components in cosmic gamma ray bursts . Various measurements of gamma-ray bursts of the 500 million light-years away Blasar Markarjan 501 with the MAGIC telescope , carried out since 2005, have shown such time differences, but do not yet provide a sufficiently reliable statement about their cause. Launched on 11 June 2008 gamma rays - Satellite Fermi Gamma-ray Space Telescope was able to delay differences during outbreaks at a distance of billions of light years to prove.
  • According to the current theory, the range of protons with kinetic energies above 10 19 electron volts in space should be so short that they cannot reach the earth ( GZK cutoff ) due to the scattering of photons of the cosmic background radiation . In contradiction to this, however, the Japanese Agasa experiment has already detected several such protons. In the context of loop quantum gravity, however, the threshold for this scattering at higher proton energies is in agreement with the experimental data.
  • A certain spectral structure of the mentioned Hawking radiation of black holes follows from the loop quantum gravity. An experimental investigation of this radiation is, however, a long way off.

Open questions

The current state of loop quantum gravity leaves a number of fundamental questions open:

  • It has not yet been possible to derive the general theory of relativity as a limit case in the sense of the correspondence principle from loop quantum gravity.
  • It is assumed that the loop quantum gravity leads to certain corrections of the special theory of relativity for speeds close to the speed of light, the nature of which, however, is still unknown.

criticism

Loop quantum gravity is controversial. It also questions the conclusiveness of many of their claimed successes and predictions. Criticism of loop quantum gravity is mainly formulated by representatives of string theory , in particular with the following arguments:

  • It is not clear how the behavior of space-time, which is continuous and constant above the Planck length, results as the limit value of the discrete network of nodes.
  • The theory uses a different quantization rule; it is not clear whether the theory so defined is completely consistent or whether it contains so-called anomalies.
  • Closely related to this is the problem of the Hamilton operator; this underlies the theory of the canonical quantization of the theory. However, to date there is no generally accepted or mathematically consistent formulation for this object.
  • In order to calculate the probability of a (quantum mechanical) process in classical space-time from theory, an infinite number of constants must be determined using additional plausible assumptions. The situation is therefore no better than in the attempt to canonical quantization of the (non-renormalizable) general relativity theory.
  • A work published in 2014 suggests that discrete spacetime models, as used in loop quantum gravity, are unable to reproduce the Unruh effect predicted by quantum field theory .

literature

criticism

Web links

Wiktionary: Loop quantum gravity  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. ↑ Rovelli Loop Quantum Gravity , Living Reviews in Relativity, Section History of LQG ( Memento of the original from April 13, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / relativity.livingreviews.org
  2. ↑ Martin Bojowald : Back to the Big Bang. The whole history of the universe. S. Fischer, Frankfurt am Main 2009, ISBN 978-3-10-003910-1 .
  3. ^ G. 't Hooft, The Black Hole Interpretation of String Theory
  4. ^ C. Rovelli, Zakopane lectures on loop gravity
  5. ↑ MUXIN Han, Cosmo Logical Constant amplitude in LQG Vertex
  6. ↑ G. Amelino-Camelia, Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
  7. ↑ G. Amelino-Camelia, Quantum Spacetime Phenomenology
  8. ↑ MAGIC Collaboration, Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope (PDF; 101 kB), 2007
  9. ^ Hermann Nicolai, Kasper Peeters, Marija Zamaklar: Loop quantum gravity, an outside view. in: Classical and quantum gravity. London 22.2005, R193. ISSN  0264-9381
  10. ↑ Absence of Unruh effect in polymer quantization, Golam Mortuza Hossain, Gopal Sardar .