welcome back to 8.033! - mit...
TRANSCRIPT
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Image courtesy of Wikipedia.
Welcome back
to 8.033!
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E2-B2 is Lorentz-invariant
E•B is Lorentz-invariant
Summary of electromagnetism:
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Summary of electromagnetism:
Maxwell details and Greek index stuff won’t be on tests
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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?
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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
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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?
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Q: What medium is a gravitational wave a vibration of?
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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.
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The laws of physics are the
same in all inertial frames
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The laws of physics are the
same in all inertial frames
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Who’s gone bungee
jumping?
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ELEVATOR MOVIES, BUZZ MOVIE
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Figure by MIT OCW.
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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.
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EP implication 1:Gravity bends light
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Lensing
Gravitational lensing
Image courtesy of NASA.
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EP implication 2:Gravitational
redshift
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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.
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EP implication 3:It’s all geometry
(learn how to work with metrics!)
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METRICS
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• Derive Newtonian metric from gravitational redshift
• Test that Newtonian metric reproduces Newton
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Next lecture:
cosmology