Transcript Document

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 required
o Wikipedia, web links, and lectures only
o 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 conditions
o P-brane (black): a black hole solution generalized to 11
dimensions
o 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 action
o not all that useful
• Polyakov action
o 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 dimensions
o as small as the Planck scale (10-35 meters)
o termed "compactified"
o need small wavelength particles to fit in and "see" them
o typically "rolled up" meaning circular

o
move in this dimension and you quickly return to your
starting point
analogy: a garden hose viewed from far away appears as a twodimensional string.
String Theory: Compact Dimensions
•
Very large dimensions
o Called the "bulk"
o We live on smaller-dimensional boundaries
 termed the "brane"
•
Prediction: gravity much stronger on very small scales
o 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]