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Loop Quantum Gravity. and the quest for the Theory of Everything. Derek Kan Khalid Mansour Ian Nickles. What is Loop Quantum Gravity?. A theory to unite quantum mechanics and general relativity, a physicists dream.
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Loop Quantum Gravity and the quest for the Theory of Everything. Derek Kan Khalid Mansour Ian Nickles
What is Loop Quantum Gravity? • A theory to unite quantum mechanics and general relativity, a physicists dream. • The name Loop Quantum Gravity is derived from the basis of the theory: the combination of Gravitation theory and Quantum theory. The term “loop” arises from how some computations in the theory involve small loops marked out in spacetime.
What is LQG? • The idea of Loop Quantum Gravity is the theory that space and time together are made up of discrete pieces, like a cloth woven from individual fibers.
Where does LQG come from? • The term comes from the study of gravity on the quantum scale, in how it affects the shape of space-time.
The Theory • Started with no pre-assumptions of space-time, such as it is smooth and continuous. • Postulates of the theory of Loop Quantum Gravity includes the most prolific modern theories of physics • Einstein’s Theory of relativity • Quantum Theory
The Basis to 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 coordinates 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.
Quantum Spacetime • To understand the structure of space on the very smallest size scale, we must turn to a quantum theory of gravity. Gravity is involved because Einstein’s general theory of relativity reveals that gravity is caused by the warping of space and time.
Quantum Spacetime cont… • Loop quantum gravity predicts that space comes in discrete lumps, that smallest of which is about a cubic planck length, or 10-99 cubic centimeter. Time proceeds in discrete ticks of about a Planck time, or 10-43 second. The effects of this discrete structure might be seen in experiments in the near future.
Quantum Spacetime cont… • By carefully combining the fundamental principles of quantum mechanics and general relativity, physicists are led to the theory of “loop quantum gravity.” In this theory, the allowed quantum states of space turn out to be related to diagrams of lines and nodes called spin networks. Quantum spacetime corresponds to similar diagrams called spin foams.
Size Limitations for Space-Time • 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.
Spin Networks • Spin networks are used to represent states of space on an extremely small scale. Such diagrams correspond to polyhedra-shaped volumes.
Spin Networks • In a spin network, one quantum of area id represented a single line. One quantum volume is represented by a node.
Spin Foam • Spin networks represent space in loop quantum gravity, while spin foam represents the concept of spacetime. Three dimensional space is the basis for spin networks, when augmented with the time dimension, we have spin foam.
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.
Development • There were many loopholes in trying to incorporate quantum mechanics and relativity. These calculations assumed that the geometry of space is continuous and smooth, no matter how small it was examined, just as people had once assumed of matter.
Conclusion • LQG might be the solution to unifying disciplines of physics. • Much cleaner than String Theory • May alter our conception of space • Solve answer to fundamental particles
Resources • Smolin, Lee. “Atoms of Space and Time.” Scientific American. January 2004. • Loop Quantum Gravity. Wikipedia, The Fee Online Encyclopedia. 4/8/04 http://en.wikipedia.org/wiki/Loop_quantum_gravity • QGRAVITY.ORG, “Quantum Gravity, Physics and Philosophy.” 4/8/04 http://www.qgravity.org/