33
Image courtesy of Wikipedia. Welcome back to 8.033!
Image courtesy of Wikipedia.
Welcome back
to 8.033!
E2-B2 is Lorentz-invariant
E•B is Lorentz-invariant
Summary of electromagnetism:
Summary of electromagnetism:
Maxwell details and Greek index stuff won’t be on tests
The Standard Model Lagrangian
(From T.D. Gutierrez)
L=
Summary of last lecture:
Note to self: do we need to permission the image of this equation?
MIT Course 8.033, Fall 2006, Lecture 16Max Tegmark
Today’s topic: General Relativity basics• Principle of equivalence
• Light bending, gravitational redshift
• Metrics
Practical stuff:
• Taylor & Wheeler notation alerts: c=G=1, m0=m, fluffy
Journalist: Professor Eddington, is it really true that only three people in the world understand Einstein's theory of general relativity?
Eddington: Who is the third?
Q: What medium is a gravitational wave a vibration of?
Onion
Tegm
ark
2002
, Sci
ence
, 296
, 142
7-14
33A: Space!
Space can vibrate, stretch, curve – perhaps even “melt”!
Note to self: we need to get IP permission from Science for this image?
Courtesy of Science. Used with permission.
The laws of physics are the
same in all inertial frames
The laws of physics are the
same in all inertial frames
Who’s gone bungee
jumping?
ELEVATOR MOVIES, BUZZ MOVIE
Figure by MIT OCW.
Figure by MIT OCW.
10-8
10-7
10-9
10-10
10-11
10-12
10-13
10-14
1900
1920
1940
1960
1970
1980
1990
2000
Eolvos
Renner
Princeton
Boulder
Eol-Wash
Fifth-forcesearches
Free-fall
Eol-Wash II
η =
η
a1 - a2
(a1 - a2)/2
Year of Experiment
Tests Of The Weak Equivalence Principle
LureMoscow
Figure by MIT OCW.
EP implication 1:Gravity bends light
Lensing
Gravitational lensing
Image courtesy of NASA.
EP implication 2:Gravitational
redshift
Over 22.6 meters, the gravitational redshift is only 5x10-15, but the Mössbauer effectwith the 14.4 keVgγ−ray from iron-57has a high enough resolution to detect that difference.
Harvard Tower Experiment(Pound & Rebka 1960)
Gamma photons launched upward
Gamma photons dropped
57Fe Source
57Fe Source
57Fe Detector
57Fe Detector
22.6 m 22.6 m
Figure by MIT OCW.
EP implication 3:It’s all geometry
(learn how to work with metrics!)
METRICS
• Derive Newtonian metric from gravitational redshift
• Test that Newtonian metric reproduces Newton
Next lecture:
cosmology
