## 2018-03-15

### ２６ Loop Quantum Gravity(LQG) #Gravity #universe

２６ Loop Quantum Gravity(LQG) #Gravity #universe

[Electromagnetic force + Weak interaction＋Strong interaction ＋ Gravity]

・LQG is an attempt to merge quantum mechanics and general relativity. [1]

・Quantum gravity (QG) is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics.

２６−１ Overview [1]

○In the loop models, the basic structure of space-time turns out to be discrete. In such discrete space-times, there are smallest values for volumes and areas that are not divisible any farther.

○The granular structure of space-time gets rid of the infinities that plague quantum field theory.

○Elementary particles for each type, the rotational speed takes the value of the discrete, as the basic number of Planck constant. For example, an electron rotates at half the speed of Planck constant.

＜Decide the direction of the space from the spin direction of the particle＞

・In the 1950s, by utilizing this principles of the spin, "the Spin network" theory which defines the direction of each point in space from the direction of the electron spin published by Penrose.

・As a specific method, the theory represents a material at a point, and represents the direction at a line, and make a constant volume by planes perpendicular to the line.

・The predicted size of this structure is the Planck length, which is approximately 10−35 meters.

・Space can be viewed as an extremely fine fabric or network "woven" of finite loops. These networks of loops are called spin networks.

・This change in spin network indicates the presence of gravity and elementary particles.

・The granular structure of space-time that is implied by spin networks also gets rid of the infinities that plague quantum field theory.

※Spin networks [2]

＜Loop quantum gravity theory creates space, gravity and substance at a time＞

・The evolution of a spin network over time is called a spin foam.

・Spin form changes discretely.

• The time difference is 1 Planck seconds of the change (10-43 seconds), and the time that people feel is what this very short time is stacked.

・The main output of LQG is a physical picture of space where space is granular. It has the same nature as the granularity of the photons in the quantum theory of electromagnetism and the discrete levels of the energy of the atoms.

２６−２ Difference from super string theory

１）In string theory( a quantum theories of gravity) one generally starts with quantized excitations on top of a classically fixed background. LQG is thus described as background dependent. In contrast, LQG, like general relativity, is manifestly background independent. [1]

２）Super string theory requires that space-time have 10 dimensions; LQG is formulated in 4 dimensions. [3]

３）String theory also implies the existence of supersymmetry, in which all known particles have yet-undiscovered partners. Supersymmetry isn’t a feature of LQG. [1] [3]

４）In loop quantum gravity, there is no big bang singularity; instead, the universe´s history can be traced infinitely far into the past, step by step. [2]

※An inflationary expansion might have been driven by quantum-gravitational effects. [4]

２６−３ Tasks

○Quantum gravity effects are notoriously difficult to measure because the Planck length is so incredibly small. However recently physicists have started to consider the possibility of measuring quantum gravity effects. [5]

○The Universe can be used as a laboratory to test quantum gravity effects. First, there are accelerators in distant galaxies that produced gamma burst, 10 billion years ago, particles with energies much higher than we can produce in even the largest man-made accelerators, 10 million times higher. Secondly, due to the long times and vast distances involved, effects such as the difference in speeds of these particles (speed of light is energy dependent according to LQG) can be detected over these long distances and times. [4] [6]

○In 2015, the Advanced LIGO team announced that they had detected gravitational waves from a pair of black holes merging. [7] [8]

○We can not fully study science with something like a unified theory - Freeman Dyson explains the reason with Gödel's incompleteness theorems

【References】

1. Loop quantum gravity - Wikipedia

2. Loop quantum gravity — Einstein Online

http://www.einstein-online.info/elementary/quantum/loops

3.String Theory Meets Loop Quantum Gravity | Quanta Magazine

https://www.quantamagazine.org/20160112-string-theory-meets-loop-quantum-gravity/

4. Carol Rovelli“Loop quantum gravity”

http://igpg.gravity.psu.edu/people/Ashtekar/articles/rovelli03.pdf

5.Quantum gravity (QG) - Wikipedia

6.Duality of Spacetime and Matter - NCF.ca

http://web.ncf.ca/fm120/Physics/LQG/Duality_Spacetime_and_Matter,_draft_2004-01-07.htm

7.Gravitational wave - Wikipedia

8.Ｎｏ．３１ Gravitational Wave

【Change log】

20170421 Split into 3 items

20171030 Addition of Freeman-Dyson's words to tasks.