String Theory (Overview)

by Robert J. Nemiroff  Michigan Technological University

Physics X: About This Course

• Officially "Extraordinary Concepts in Physics"• Being taught for credit at Michigan Tech

o Light on math, heavy on concepts o Anyone anywhere is welcome

• No textbook requiredo Wikipedia, web links, and lectures onlyo Find all the lectures with Google at:

"Starship Asterisk" then "Physics X"  o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

String Theory

• attempts to explain both gravitational and quantum effects in a single theory.

• models electrons and quarks not as one dimensional points but two dimensional strings.

• Strings posses only length, not height or width. • Usually posit the existence of several extra spatial dimensions,

besides the well known 3 and time (a fourth).• Now considered as part of 11-dimensional M-theory.

RJN Note: I am not a string theorist.  My understanding of this particularly deep topic may be flawed.

String Theory: Strings of what?

What are these strings (and branes) made out of?This is rarely addressed.  Formally, only gross attributes are considered: length, spin, energy, tension, background, and boundary attributes.  One possibility is that strings are made out of a confined form of dark energy, not unlike miniature versions of cosmic strings or domain walls. Cosmic strings might then be stretched versions of particle strings from the early universe.

String Theory: Branes

• Branes (short for membranes) are more general than strings.o D-brane: string end with Dirchlet boundary conditionso P-brane (black): a black hole solution generalized to 11

dimensionso NS5-brane: a five dimensional object that can mimic a magnetic

monopole

String Theory: Open and closed strings

Strings can be open or closed.  Examples:• closed string: graviton• open string: photon

Strings have:• size• tension• vibrations• translation • the ability to split and reconnect

Designed to have many more degrees of freedom than a point particle

String theory: Different types

Type Spacetime dimensions Details

Bosonic 26 Only describes bosons;tachyons destabilizing

I 10 Supersymmetry between forces and matter

IIA 10 Supersymmetry

IIB 10 Supersymmetry

HO 10 Supersymmetry

HE 10 Supersymmetry

String Theory: Actions

Define how strings move through space.  Strings will move to minimize an "action" integral. Two types: • Nambu-Goto action

o simplest invariant actiono not all that useful

• Polyakov actiono involves string tension o better constrained by boundary conditions

String theory: Number of spatial dimensions

In classical physics, E&M, and GR, there are three space dimensions and one time dimension.  These are empirical.

In string theories, the number of dimensions is determined by things like potential energy and the need to make force-carrying particles like the photon massless.

All of these new dimensions are in space, not in time.

String Theory: Compact Dimensions

Extra space dimensions are not observed and so are hypothesized to be either very small or very large.

• Very small dimensionso as small as the Planck scale (10-35 meters)o termed "compactified"o need small wavelength particles to fit in and "see" themo typically "rolled up" meaning circular

move in this dimension and you quickly return to your starting point

o analogy: a garden hose viewed from far away appears as a two-dimensional string.

String Theory: Compact Dimensions

• Very large dimensionso Called the "bulk"o We live on smaller-dimensional boundaries

termed the "brane"

• Prediction: gravity much stronger on very small scaleso because one sees "leaking" from the bulk

String Theory: Compact Dimensions

Light and most particles are constrained to the brane.  Gravity, however, is not, and can "spread out" over all of the dimensions of the bulk.

• Acceleration due to gravity falls off as 1/r(D-1) where D is the number of spatial dimensions

• This is one reason that gravity is weaker than electricity and magnetism.

Calabi-Yau Manifold

A three dimensional projection of a multi-dimensional object having properties and symmetries inherent in a Calabi-Yau manifold.

String Theory: Falsifiable?

Does string theory make falsifiable predictions?

Historically, some famous physicists say no:• Feynman, Glashow, Smolin  

 Some string theories predict that gravity will much stronger at very short distances.  But this is not an easily falsifiable prediction.

String Theory: Falsifiable?

"I wouldn't have thought that a wrong theory should lead us to understand better the ordinary quantum field theories or to have new insights about the quantum states of black holes."  -- Edward Witten [Princeton IAS, Cite]

"For more than a generation, physicists have been chasing a will-o’-the-wisp called string theory. The beginning of this chase marked the end of what had been three-quarters of a century of progress. Dozens of string-theory conferences have been held, hundreds of new Ph.D.s have been minted, and thousands of papers have been written. Yet, for all this activity, not a single new testable prediction has been made, not a single theoretical puzzle has been solved. In fact, there is no theory so far—just a set of hunches and calculations suggesting that a theory might exist. And, even if it does, this theory will come in such a bewildering number of versions that it will be of no practical use: a Theory of Nothing." -- Jim Holt  [New Yorker, 2006]