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String Theory: Basics

For Galileo Programme 2010 PIS
by

Gabriel Tan

on 10 August 2010

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Transcript of String Theory: Basics

string theory:
the basics Unified Field Theory Unifying all four forces Quantum mechanics Gravity Strong nuclear
interaction Weak nuclear
interaction Electromagnetism A master equation Difficulties? quantum + gravity = not renormalizable loses predictive power equations run into infinity Does not make sense! High energy scale Very hard to test such theories Well beyond reach of current accelorometers + A whole list of other difficulties Broken electroweak symmetry Higher energies? String Theory Loop Quantum Gravity Other minor field theories Posits that all particles are 1-dimensional strings Properties of strings Move Vibrate gives properties of particles flavour charge mass spin Open or closed The result? Five different theories resulted from the equations of string theory Open type 1A Closed type 2A Closed type 2B Heterotic string theory SO(32) Heterotic string theory E8*E8 Then something remarkable happened... At a conference, Professor Edward Witten (see picture), decided that these 5 theories were actually the same theory by looking at different mathematical perspectives. M-theory Was similar to string theory Was given 11 dimensions instead of the usual 10 Why one more? Allowed strings to transform into a membrane, or a brane for short A string could then be interpreted as a 1-brane, or a one dimensional brane Branes in M-theory can extend its size, and could be as large as a universe. The Multiverse Idea Branes would be a universe by itself Strings with endpoints would stick to the brane, like matter in a certain universe. The branes cluster, and form a 'bulk'. Don't understand what is going on? Consider a loaf of bread. That would be the 'bulk'. Each slice is a universe by itself. All matter in a universe is then stuck to each slice of a bread, like jam on toast. Parallel universes Originally, each 'theory' had 10 dimensions, which is summed as follows. 3 spatial dimensions One time dimension 6 dimensions coming out of equations 10 dimensions But how do you imagine extra dimensions?
That: in a moment. Very early string theories require 26 dimensions Strings were then bosons. The 26 dimensions come from the Polyakov equation, which is unfortunately just too complicated to put here. :) Now we have 10 dimensions. Wait, no, 11 dimensions coming from M-theory. So just how do we cope with extra dimensions? Compactify them! Maybe it is just that these extra dimensions are too small to see. It is now considered that each point in the universe now has the extra dimensions compacted into a Calabi-Yau manifold. Still don't get the idea of compacting dimensions? Consider a garden hose. From far away, it will look as if the hose was just some raffia string. But near enough... From a point of view of an ant crawling on the hose, we see that there is an additional dimension. And from a fly's point of view, it would have 3 dimensions. Brane World scenario Probably we are stuck on a 3+1 dimensional world. There could be areas in our brane that probably have a higher dimension as well! These areas would be different from the surrounding areas, like creases on a paper. Coping with extra dimensions Effects of these extra dimensions Gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions ...but their shape has a profound effect on how the forces between the strings appear in our four-dimensional universe It is possible to deduce the nature of those extra dimensions... ...BUT it is just not practical
(remember HIGH energies!) Problems? Is string theory predictive? Background independence?
Mathematical Inconsistencies
and incorrect predictions So is string theory your... ? Any questions? So now let's go back to dimensions. Here's a little history. That's the idea! So could string theory just be a theory of nothing? Many string theorists believe that it's just got to be right. But well, you still don't have a clue which one of these theories is going to be right anyway. :) That's why theoretical physics is so interesting. It keeps you on your ______. And who knows, string theory may be right after all! ;) Jan Zaanen
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