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Relativity + Quantum + Gravity
• These three concepts are the basis of physics.
• They contain the three fundamental constants
c,ħ,G , which form a complete system of units.
• Are these concepts compatible with each other?
- Relativity and gravity (= general relativity) are
designed to be compatible.
- Relativity and quantum physics are made compatible by quantum field theory.
- Quantum physics and gravity are incompatible
when trying it with quantum field theory.
The weakness of gravity
String theory
A quantum theory of gravity:
Various attempts to combine gravity and
quantum physics failed . Gravity is very
different from the other three forces. It
is much weaker, and its boson has spin 2.
Ed Witten,
string guru
Infinities pose a mathematical problem:
Point-like particles create mathematical
problems when two particles meet. The
forces become infinite. This problem is
avoided in string theory by stretching a
point out into a tiny loop, a string.
Feynman diagrams in string theory
Time (c t)
Space (x)
• World lines become tubes in string theory.
• They connect smoothly.
• That avoids dealing with infinitely small points.
What happens at the
smallest conceivable
length ?
Quantum physics meets gravity
at the Planck length.
The uncertainty relation makes
space itself uncertain.
String theorists view space as a
collection of vibrating strings.
Brian Greene: “The elegant Universe”
Strings on Nova
Strings can vibrate in many ways
A single string can explain
a whole zoo of particles :
Different vibration frequencies f
Different energy quanta (Planck’s E = hf )
Different particle masses (Einstein’s E = m c2)
Results of string theory
• A string can produce a boson with spin 2. That’s what
one needs for the graviton, the boson that mediates
gravity (analogous to the photon in electromagnetism).
• So string theory produces a quantum theory of gravity.
• This is our best attempt to make gravity compatible
with quantum physics without getting into trouble with
Extra dimensions
• String theory requires 10-dimensional space-time for
mathematical reasons.
• How do we get from 10 dimensions down to our fourdimensional space-time ?
• Two proposals:
A) Make the extra dimensions tiny by folding them
tightly down to the Planck length.
B) Make the extra dimensions large and restrict our
space-time to a 4-dimensonal surface (membrane)
of a higher-dimensional bulk region.
Small extra dimensions
A huge number of different folding options. Which one ?
Large extra dimensions
Gravity is so weak, because it
lives on a different membrane
(= brane) and gets diluted by
connecting with us across the
5-dimensional bulk.
(Physics Today, July 2007, p. 80)