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