special relativity and general relativity

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```• Special theory of relativity (1905)
• general theory of relativity
Dept of Phys
M.C. Chang
Space and time
Newton
Post-Newton
Inertial frame and noninertial frame
The velocity of light
C=299792458 m/s
100+200=300
C+C=2C?
The velocity of light is the same to all
observers (in inertial frames)
Simultaneity
There is no unique “now”.
Time dilation (a moving clock ticks slower)
ct’
ct
ct’
vt
An optical clock
(ct )2  (vt )2  (ct ')2
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
The twin paradox
Length contraction
(a moving object shrinks)
Relative point of view
The barn-pole paradox
Relativistic mass
(a moving object
becomes heavier)
Nothing moves faster
than the speed of light
The most famous formula in the world
Nuclear fusion

deuterium
tritium
L. Livermore National Lab.

• Special theory of relativity
• general theory of relativity
(the theory of gravity, 1916)
Objects of different weights fall at the same speed
The principle of equivalence
=
The bending of light by gravity
Gravitational lens
Relativity in GPS (Global Positioning System)
with on-board atomic clocks
USD 350
Accuracy: 30 nanosecond → 15 meters
Gravity slows down a clock
(g/4)
Relativistic effect:
Faster by -7+45=38 microsec per day
= an error of 11 km!
Gravity balanced by pressure
Black hole
Gravitational collapse will always occur
on any star over 5 solar masses,
inevitably producing a black hole
a space-time singularity
Schwarzschild radius (1916)
Detecting gravitational wave
LIGO
Laser Interferometer Gravitational Wave Observatory,
Hanford, WA + Livingston, LA
Lisa (launch &gt; 2018 )
Laser Interferometer Space Antenna
a resolution of 20 picometers over a distance of 5 million kilometers !!
20xx?
The milky way
Our galaxy
2.6 &plusmn; 0.2 million times
the mass of the Sun
• 2.5 MLYs away
• 0.2 MLYs in diameter
• 10^12 stars
Cluster of galaxy
Large-scale structure of the universe
(each blue dot is a galaxy!)
&quot;Space is big. Really big. You just won't believe
how vastly, hugely, mind-bogglingly big it is.&quot;
The Hitchhiker's Guide to the Galaxy
Shape of the universe
http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html
Einstein’s field equation
Λ&gt;0 leads to
repulsion
Cosmological constant
(&lt;-&gt; vacuum energy)
Red shift
Hubble’s law (1929)
1 pc=3.26 ly
(The name was given
by Hoyle, 1950)
From Mather’s slide
Oldest galaxy known
Age ～ 13 billion yrs
Penzias and Wilson
1978
Background radiation
(COBE satellite)
1%
TV static
Dipole due to
earth motion 10-3
Galactic plane 10-5
The universe at age
389000 years
Mather &amp; Smoot
2006
COBE
(launched 1989)
WMAP
(launched 2001)
angular resolution～ 0.3&deg;
Space travel
Caution:
Slippery
ahead
The matricide (or grandpa) paradox
Thank you
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