Special theory of relativity (1905) general theory of relativity M.C. Chang Dept of Phys.

• Special theory of relativity (1905)• general theory of relativity

M.C. Chang

Dept of Phys

Space and time

Newton Post-Newton

Inertial frame and noninertial frame

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)

Simultaneity

There is no unique “now”.

Time dilation (a moving clock ticks slower)

ct

vtct’

2 2 2( ) ( ) ( ')ct vt ct

An optical clock

ct’

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

Relative point of view

Length contraction

(a moving object shrinks)

The barn-pole paradox

Relativistic mass

(a moving object becomes heavier)

Nothing m

oves faster than the speed of light

The most famous formula in the world

由氘及氚組成的靶

Nuclear fusion

deuterium

tritium

L. Livermore National Lab.

核融合設施 (NIF)

• 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

Accuracy: 30 nanosecond → 15 meters

USD 350

Relativistic effect:

Faster by -7+45=38 microsec per day = an error of 11 km!

(g/4)

Gravity slows down a clock

Gravity balanced by pressure

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

LIGO

Laser Interferometer Gravitational Wave Observatory, Hanford, WA + Livingston, LA

Detecting gravitational wave

Lisa (launch > 2018 )

20xx?

Laser Interferometer Space Antenna

a resolution of 20 picometers over a distance of 5 million kilometers !!

The milky way

Our galaxy

2.6 ± 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!)

"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

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

Hubble’s law (1929)

Red shift

1 pc=3.26 ly

(The name was given by Hoyle, 1950)

From Mather’s slide

Age ～ 13 billion yrsOldest galaxy known

Penzias and Wilson 1978

Background radiation (COBE satellite)

Dipole due to earth motion 10-3

Galactic plane 10-5

1% TV static

2006

The universe at age 389000 years

Mather & Smoot

COBE (launched 1989)

WMAP (launched 2001)

angular resolution ～ 0.3°

Space travel

Caution:Slippery ahead

The matricide (or grandpa) paradox

Thank you