special theory of relativity (1905) general theory of relativity m.c. chang dept of phys
TRANSCRIPT
![Page 1: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/1.jpg)
![Page 2: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/2.jpg)
• Special theory of relativity (1905)• general theory of relativity
M.C. Chang
Dept of Phys
![Page 3: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/3.jpg)
Space and time
Newton Post-Newton
![Page 4: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/4.jpg)
Inertial frame and noninertial frame
![Page 5: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/5.jpg)
The velocity of light
100+200=300
C+C=2C?
C=299792458 m/s
The velocity of light is the same to all observers (in inertial frames)
![Page 6: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/6.jpg)
Simultaneity
There is no unique “now”.
![Page 7: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/7.jpg)
Time dilation (a moving clock ticks slower)
ct
vtct’
2 2 2( ) ( ) ( ')ct vt ct
An optical clock
ct’
![Page 8: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/8.jpg)
In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation .
Eastward Journey Westward Journey
Predicted -40 +/- 23 ns + 275 +/- 21 ns
Measured -59 +/- 10 ns + 273 +/- 7 ns
![Page 9: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/9.jpg)
The twin paradox
![Page 10: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/10.jpg)
Relative point of view
Length contraction
(a moving object shrinks)
![Page 11: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/11.jpg)
The barn-pole paradox
![Page 12: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/12.jpg)
Relativistic mass
(a moving object becomes heavier)
Nothing m
oves faster than the speed of light
![Page 13: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/13.jpg)
The most famous formula in the world
![Page 14: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/14.jpg)
由氘及氚組成的靶
Nuclear fusion
deuterium
tritium
![Page 15: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/15.jpg)
L. Livermore National Lab.
核融合設施 (NIF)
![Page 16: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/16.jpg)
![Page 17: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/17.jpg)
• Special theory of relativity• general theory of relativity (the theory of gravity, 1916)
![Page 18: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/18.jpg)
Objects of different weights fall at the same speed
![Page 19: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/19.jpg)
The principle of equivalence
=
![Page 20: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/20.jpg)
The bending of light by gravity
![Page 21: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/21.jpg)
Gravitational lens
![Page 22: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/22.jpg)
Relativity in GPS (Global Positioning System) with on-board atomic clocks
Accuracy: 30 nanosecond → 15 meters
USD 350
![Page 23: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/23.jpg)
Relativistic effect:
Faster by -7+45=38 microsec per day = an error of 11 km!
(g/4)
Gravity slows down a clock
![Page 24: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/24.jpg)
Gravity balanced by pressure
![Page 25: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/25.jpg)
a space-time singularity
Gravitational collapse will always occur on any star over 5 solar masses, inevitably producing a black hole
Schwarzschild radius (1916)
Black hole
![Page 26: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/26.jpg)
LIGO
Laser Interferometer Gravitational Wave Observatory, Hanford, WA + Livingston, LA
Detecting gravitational wave
![Page 27: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/27.jpg)
Lisa (launch > 2018 )
20xx?
Laser Interferometer Space Antenna
a resolution of 20 picometers over a distance of 5 million kilometers !!
![Page 28: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/28.jpg)
![Page 29: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/29.jpg)
The milky way
![Page 30: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/30.jpg)
Our galaxy
![Page 31: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/31.jpg)
2.6 ± 0.2 million times the mass of the Sun
![Page 32: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/32.jpg)
![Page 33: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/33.jpg)
• 2.5 MLYs away
• 0.2 MLYs in diameter
• 10^12 stars
![Page 34: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/34.jpg)
Cluster of galaxy
![Page 35: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/35.jpg)
Large-scale structure of the universe (each blue dot is a galaxy!)
"Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is." The Hitchhiker's Guide to the Galaxy
![Page 36: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/36.jpg)
Shape of the universe
Einstein’s field equation
Cosmological constant (<-> vacuum energy)
http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html
Λ>0 leads to repulsion
![Page 37: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/37.jpg)
Hubble’s law (1929)
Red shift
1 pc=3.26 ly
![Page 38: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/38.jpg)
(The name was given by Hoyle, 1950)
![Page 39: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/39.jpg)
From Mather’s slide
![Page 40: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/40.jpg)
Age ~ 13 billion yrsOldest galaxy known
![Page 41: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/41.jpg)
Penzias and Wilson 1978
![Page 42: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/42.jpg)
Background radiation (COBE satellite)
Dipole due to earth motion 10-3
Galactic plane 10-5
1% TV static
![Page 43: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/43.jpg)
2006
The universe at age 389000 years
Mather & Smoot
COBE (launched 1989)
WMAP (launched 2001)
angular resolution ~ 0.3°
![Page 44: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/44.jpg)
![Page 45: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/45.jpg)
![Page 46: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/46.jpg)
Space travel
Caution:Slippery ahead
![Page 47: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/47.jpg)
![Page 48: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/48.jpg)
![Page 49: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/49.jpg)
The matricide (or grandpa) paradox
![Page 50: Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys](https://reader036.vdocuments.site/reader036/viewer/2022081508/56649f005503460f94c15b5a/html5/thumbnails/50.jpg)
Thank you