LQG Outline: Draft
Slide 1: What is Loop Quantum Gravity (LQG)?
- LQG is the theory that unites quantum mechanics to general relativity.
- LQG predict that time and space are composed of discrete time pieces.
- Is an alternative to the string theory
- Postulates the size and structure of space.
Slide 2: Where does the title LQG come from?
- The term quantum refers to the study of quantum mechanics.
- Gravity arises as a consequence of space and time being curved by the presence of
matter, like a rubber sheet and bowling ball analogy (Bowling ball is matter, rubber sheet
is space-time, indentation, as a result of matter, is force of gravity.
- Looping is a result of computations that shows that there are small loops marked out in
space-time.
- In summary, the “Quantum” refers to the finite size of space and time, which is
referenced by “Gravity.”
Slide 3: LQG = Quantum Theory of Space-Time
- The main problem in physics today is the incompatibility of the areas of quantum
mechanics and general relativity. General relativity is non-quantized, or continuous,
whereas quantum physics designated certain allowable conditions before changes occur.
LQG attempts to solve this problem by assuming that space and time, in accordance to
the principles of quantum mechanics, are also quantized. Could be though of as
“quantum theory of space-time.”
- Many approaches have tried to unify the two fields of physics, most notably string
theory, but all failed due to the assumption that the theories of general relativity were not
quantized, yet smooth no matter how minutely examined.
Slide 4: The Two Pre-Requisites of Calculating LQG.
- Background Independence: The geometry of space-time is not fixed; rather, is an
evolving and dynamic quantity. This requires that the effects if matter and energy is
relevant in the dynamics of this system.
- Diffeomorphism Invariance: One is free to choose any set of coordiates to map
space-time and express the equations. Points in space-time are defined by what happens
to them, not by what location it is located according to a special set of coordinates.
- By combining these two theories along with the approach of quantum theory, a
mathematical language was assimilated to show that space-time is really quantized.
- The size of space-time:
Minimum Volume: 10^-99 cubic centimeters = one cubic planck length
Minimum Area: 10^-66 cm^2 = one square planck length
Minimum Length: 10^-33 cm = one cubic planck length
Slide 5: Size Limitations for Space-Time
(Pg. 69 illustr.)
- Like the quantized excitation energy levels of Hydrogen (c), The quantum area (a) of
space-time has an absolute minimum level, and all higher areas are restricted to discrete
series of numbers. Same analogy for (b) with volumes.
Slide 6: Spin Networks
(Pg. 70, a-h: a-d just quickly referenced to better explain nodes and lengths)
- A quantum area is represented by a single line, whereas an area is represented by many
lines. Volume, like polyhedral example, represented by a node and lines to represent
dimensions. Large volume is network of nodes.
- Why use Spin networks over polyhedrons? Anything drawn by polyhedron can be
drawn by spin networks, but spin networks can also represent distortions of the spacetime field.
- The lines and nodes are not the actual shape of space-time, rather exist in a relational
organization where their connections define the geometry of space. Matter exists at the
nodes of spin networks.
- If all universe was to be represented by spin network, with all curvature caused by
black holes and gravities of galaxies, there would be app. 10^184 nodes!
Slide 7 :How do you Test this Theory?
- Since undetectably small, can we consider the spin networks as “threads in a cloth” and
measure the average affect on the cloth as a representation of the individual threads?
Progress has been made for certain configurations, but the jury is still out.
-
By analyzing similar phenomena shared with black holes. Black holes must have
entropy relative to their surface area, as well as emit radiation. By analyzing
these tiny boundaries to be the event horizons of the black holes, they should emit
radiation and undergo entropy, yet the radiation calculated to be released is too
small to be viewed.
- (The GLAST satellite will help).
Slide 8: What Could LQG do for Us?
- Could open up windows to better explain cosmological questions such as the origin of
the universe and the beginning of time.
- Could unite all forces, including gravity, as an aspect of a single, fundamental force, as
a result of spin-network interactions?
- Most importantly, unite quantum mechanics with general relativity.
- Unfortunately, how classical reality arises from quantized space-time is still being
worked on.