Introductory Notes on Quantum Gravity

Introductory Notes on Quantum Gravity The following paragraphs are intended to briefly summarize the basic principles of both String Theory and Loop Quantum Gravity in a way that is palatable for students with little mathematical background. It is apparent that most other non-mathematical introductions make contradictory assertions that only provide more confusion to the reader. This piece was originally written as a concomitant to the article The Failed Discussion of Quantum Gravity in Popular-Science, which was also published on this blog. The modern treatment of gravity in Physics is based on the General Theory of Relativity as produced by Albert Einstein in 1915. Any candidate theory of quantum gravity must be able to reproduce Einstein's theory of General Relativity as a classical limit of a quantum theory. While there have been a multitude of dedicated research programs and theories (such as asymptotically safe gravity, twistor theory, and non-commutative geometry), two theories – Loop Quantum Gravity and String Theory – dominate popular-science. String Theory employs a hypothetical particle known as the graviton in order to bridge the gap between Quantum Mechanics and General Relativity. In String Theory, all particles are represented as vibrational states of a ‘string’, a simple one-dimensional object that replaces the point-like particles of traditional particle physics. The graviton is therefore one of the many possible vibrational states of an individual string. These strings make up a so-called background. Loop Quantum Gravity does not require the implementation of gravitons, and therefore does not include a background. LQG is described as background-independent (as is General Relativity), meaning that the formulation of the theory doesn’t endorse a particular geometry of space-time. Since LQG never introduces a background or excitations (string vibrational states) living on this background, it doesn’t require the implementation of gravitons. Instead, these theorists expect that something similar to gravitons may become apparent in a semiclassical limit or weak field limit. In LQG, the geometry of space is described by spin-networks. Spin-networks are graphs with edges labeled by the familiar ‘spin’ quantum number of Quantum Mechanics. In this model, any surface gets its area from the spin-network edges that puncture it. While LQG inherits the standard set of dimensions of General Relativity (3 spatial and 1 time), String Theory breaks from this by adding an additional 6 dimensions to traditional 4 dimensional space-time. This would create a problem in describing real physical phenomena as these extra dimensions haven’t been observed. In order to reconcile the discrepancy with physical data, clever theorists have invented tactics to explain the apparent absence of a 10 dimensional universe. The standard approach to explaining the number of dimensions is called compactification. This is a scenario where the extra dimensions have closed upon themselves. In the limit where these ‘curled up’ dimensions become very small, a theorist may obtain a description of space-time with an effectively lower number of dimensions. An oversimplified, though common analogy describing compactification, is that of a pipe being viewed by an observer at a distance. When viewed at a far, the pipe appears to have only a single dimension (length), but upon approaching, the circumference of the pipe becomes apparent. In this analogy, we are supposed to be the distant observer, unable to perceive the true geometry of the universe. All String Theory variants require additional dimensions, supersymmetry, and the unification of the four fundamental forces into a single force. LQG differs from String Theory in that it is formulated in 3 and 4 dimensions and without supersymmetry or extra dimensions. There are many variations of String Theory. M-Theory, the most celebrated, is actually an amalgamation of 5 different String Theory variants. While the spacetime of a traditional String Theory is 10 dimensional, M-Theory is composed in 11 dimensions. Due to the inclusion of extra dimensions, string/M-Theory has reinvigorated the speculative imagination of science fiction writers by adding credibility to the concepts of hyperspace and parallel universes. Many string-theorists authoring popular science books also heavily indulge these ideas in their writing. For readers looking for an introduction with more breadth, Lee Smolin – one of the founders of LQG – wrote an excellent book on the subject appropriately titled The Trouble with Physics. Being published in 2005, some of the general knowledge presented has fallen out of date, though it remains one of the most insightful analyses of the field in publication. Many of the themes in Smolin’s book are echoed in this post but the book provides a depth of history and detail that can’t be compressed into a single blog. There is also a decent Wikipedia article on M-Theory that provides an easy-to-digest introduction. “... String Theory needs to be developed in an open atmosphere, in which it is considered as one idea among several, without any presuppositions as to its ultimate success or failure. What the new spirit of physics cannot tolerate is a presumption that one idea has to succeed, whatever the evidence.” – Lee Smolin (The Trouble with Physics, 2005) Have suggestions about future content or need help solving a physics/math problem? Tweet @ThePhysicsBlog