Comparison with loop quantum gravity
Loop Quantum Gravity (LQG) places quantization as the first natural law at the origin. Since all objects are "out of focus" in terms of quantum mechanics, the smallest unit of the universe is not postulated as a "sharp" point in space, but rather as a smallest volume, which functions quantum-mechanically:
Schematically: A point (left) is not compatible with the laws of quantum mechanics because it is not fuzzy. Elementary volumes that function according to the laws of quantum mechanics and therefore have "fuzzy" surfaces (right) are postulated as the smallest building blocks. (Figure after [1])
In the description of space-time, these elementary volumes form the nodes of a network called the spin network (since the elementary volumes have spin-like properties), which in its entirety creates space. If the temporal evolution of this network is considered, one speaks of the spin foam. An introduction gives [1].
Similarities
Although the basic arguments of LQG and the theory of the elastic universe differ significantly, there are some similarities:
- Both theories work in four dimensions, they get by without additional dimensions.
- Both theories assume a structured, non-empty space-time consisting of a network/ lattice with a shortest elementary length. This length can be limited experimentally upwards and provides arguments for falsification (see also the corresponding Chapter).
Differences
Some essential points in which LQG and the theory of the elastic universe (TeU) differ:
- The nodes of the network / grid differ: In the LQG they are modeled as quantum mechanical objects, in the TeU as classical oscillators.
- The LQG is more general in mathematical treatment than the TeU and provides a comprehensive mathematical framework.
- The LQG is a purely mathematical theory. The TeU first provides interpretations and enables new results subsequently.
- The LQG quantizes the space as a network like the TeU, in addition, the nodes are quantized again, which makes the handling of LQG much more complex than that of TeU. From the point of view of the TeU, this additional quantization is not necessary.
- TeU provides quantitative results with comparatively little effort.
References
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