University of Delaware
PHYS146
Quarks, Gluons, and the Big Bang
Maurice Barnhill
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Last revised 1999/04/26
Class Notes X: General Relativity
This section is largely a translation out of mathematics of
Essential Relativity
by Wolfgang Rindler.
Outline
Equivalence Principle
Weak: Gravitational mass = inertial mass
F
_{C}
= k Q q / R
^{2}
= m
_{I}
a
F
_{G}
= G M m
_{G}
/ R
^{2}
= m
_{I}
a
Strong
Local inertial frames
In
free fall
Not rotating
May cover only a small region (
local
)
Implications
Space is curved
Light moving across a local inertial frame must travel in straight line, by EP
Local frame is accelerating compared to nearby bodies.
Light-path is therefore curved as seen from other bodies.
Curvature is independent of material properties.
Therefore simplest to attribute curvature to
space
.
Gravity theories that do not attribute the curvature to space eventually work their way to empirically incorrect conclusions.
Experiments agree with these results to 1% accuracy.
Gravitational red shift
Light moving against gravitation comes up through bottom of local inertial frame.
By EP this light is never Doppler shifted in inertial frame.
So for a "stationary" observer, who sees the inertial observer moving, the light must be red-shifted.
Light near large masses is therefore detectably red-shifted.
Clocks based on atomic vibrations therefore run dectably more slowly near large masses.
From E = h f , light loses energy moving against a gravitational force.
Experiments agree to 1% accuracy.
Curved Space
Rough visualizations -- spheres
Distance measures
Coordinate distance
Angular spread measure
Brightness measure
Effect of angular spread
Doppler effect: detector is moving away from photons
Red shift measure
Cosmological constant, a kind of negative pressure
Strings
Problems with point particles
Mass renormalization
Infinities
Gravity and infinities
Way strings cure problems
General makeup of strings
Strings and general relativity
Extra dimensions
Higher dimensions picked out
Compactification
Most-likely version has
"Left-moving bosons" in 26 space-time dimensions
Compactify 10 space dimensions
Right-moving "supersymmetric" objects added
Compactify 6 more space dimensions, leaving 4-dim space-time
Quarks and leptons
Supersymmetry breaking
Graviton
Cosmology
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