Light should be

deflected

(= accelerated)

by gravity

Principle of

Equivalence

)

Vacuum

Least tightly

bound

Einstein, again:

Light can only emit or

absorb energy in quantized

units:

Ephoton=h

h = Planck’s constant!

= work func.

Electrons

in metal Energy

Distance

Kmax

Meta

l

Su

rface

h

Light behaves in some

ways like a particle of zero

rest mass and:

Ephoton = h,

and if “E = mc2 “(more later)

mphoton= h/c2,

with (relativistic) momentum

Pphoton = E/c = h/c = h/

A

V

1. Deflection of

light by the

sun’s

gravitational

field FIRST

OBSERVED

IN 1919

General relativity:

Experimental verifications:

”Gravitational

lensing” by

stars/galaxies

2. ”Gravitational lensing” by

stars/galaxies Star

Four images of star:

“The Einstein Cross”

Galaxy

More discussion and great

images at:

http://csep10.phys.utk.edu/astr1

62/lect/galaxies/lensing.html

“The Einstein Cross”—Possible Explanation

Spiral Galaxy

Quasar

Earth

”Gravitational lensing” by stars/galaxies--theory

T. Tyson, UCD--More details at: http://www.lsst.org/Science/darkmatter2.shtml

Four images of the same uniquely shaped galaxy

”Gravitational lensing” by stars/galaxies + dark matter

Star

More discussion and great

images at:

http://csep10.phys.utk.edu/astr1

62/lect/galaxies/lensing.html

Dark matter: 20% of

mass of universe

Visible matter

Dark matter

J.A. Tyson, UCD Physics

”Gravitational lensing” by stars/galaxies + dark matter

Star

Also see effects of “dark energy”: 70-75% of mass/energy in universeaccelerating

expansion of universe: altogether dark matter and dark energy = 90-95%

More discussion and great

images at:

http://csep10.phys.utk.edu/astr1

62/lect/galaxies/lensing.html

? ?

Dark matter: 20% of

mass of universe

And “dark energy”

2008

5,000

light-

years

21,000

light-

years

8

Consequences:

Light (photons) attracted by gravity→black holes

and gravitational lensing”seeing” dark matter

Time contraction or dilation between clocks at

different points in gravitational potential (planes, GPS)

Motion of Mercury orbit (perihelion)

Gravity waves? Probably observed, but LIGO looking

more directly

Frame dragging? Now observed

Quiz #1--Last 20 min. of Thursday class

2. Wavelength

shifts in

gravitational

fields

Also implies that observer

on ground sees time

passing faster above—

reverse of time dilation in

Special Relativity! →time contraction

and dilation

t’

t < t’

In 22.6 meters, the fractional

gravitational red shift is just

4.92 x 10-15, but the Mossbauer effect

with the 14.4 keV gamma ray from

iron-57 has a high enough resolution

to detect that difference. In the early

60's physicists Pound, Rebka,and

Snyder at the Jefferson Physical

Laboratory at Harvard measured the

shift to within 1% of the predicted shift.

– Average lifetime of 14.4 keV level

144.8 138.3 ns + 0.2 ns

– natural width of this level, from Et =(h) h/2 = , gives 2.389

neV or doppler width of 0.097 mm/s

The Harvard Tower Experiment

Vibrating source on speaker:

Doppler shift of frequency to

cancel effect of gravity

3. Escape from

stars→Black

Holes

General relativity--Experimental verifications: If ’ → 0,

Black Hole: Black

inside!

2

22

/

/Schwartzchild

h GMh c R

R GM c

2

2 2

1 2

( / )( )

1 1' 1 1

( ) ( )

photonGMm GM h cV r

r r

GM GMh h h

r R rc c R

Had J. Robert Oppenheimer not led the US effort to build the

atomic

bomb, he might still have been remembered for conceiving of

black

holes. His 1939 Physical Review paper, written with graduate

student Hartland Snyder, described how a star might collapse

into

an object so dense that not even light could escape its

gravitational clutches. The paper was hardly noticed until the

1960s, when astrophysicists began to seriously consider that

such

extreme objects might exist. John Wheeler of Princeton

University

then came up with the name "black holes" for these now

standard

elements of astrophysics.

(J. R. Oppenheimer and H. Snyder, Phys. Rev. 56, 455 (1939))

Link to the paper: http://link.aps.org/abstract/PR/v56/p455

COMPLETE Focus story at http://focus.aps.org/story/v13/st23

J. Robert Oppenheimer

UC Berkeley Physics Professor

1929-1967

The first good candidate for a black hole—Cygnus X-1

…And the center of

the Milky Way Galaxy

(and probably all

other galaxies?) has a

black hole:

MMilky Way 3 x 106 MSun

100,000 light-years

Disk Nuclear bulge Sun

Halo

Globular cluster

Black hole?

MILKY WAY

GALAXY

Anti-matter in our universe—not much but:

http://svs.gsfc.nasa.gov/v

is/a000000/a000100/a0001

81/

New York Times, 4/29/97

Black

hole

of ~3 x 106

MSun

http://www.nytimes.com/2011/12/06/scienc

e/space/astronomers-find-biggest-black-

holes-yet.html?_r=1&hp

Astronomers Find Biggest Black Holes Yet

Such monster black holes seem to inhabit the centers of all galaxies — the

bigger the galaxy, the bigger the black hole

21 billion suns

2. Wavelength shifts in

gravitational fields—more

accurate view

2

2 2

1 2

( / )( )

1 1' 1 1

( ) ( )

photonGMm GM h cV r

r r

GM GMh h h

r R rc c R

_

+ r1

r2

(See disc. of Fig. 2.20-Special &

Example 15.1-Due to General,

clocks in airplanes are both

too fast as measured on the

ground at the end of the flight)

Faster Slower | | |

96 ns 184 ns Special: Time dil.

tO tW tE

140 ns*

4023 ns- Theory

5910 ns- Expt.

179 ns*

27521 ns

2737 ns

General: Gravity@104 m

41.2 flight hours

48.6 flight hours

*Slightly different

paths around the earth

inlatitude/longitude

Special and General

Relativity—essential to GPS

systems

http://en.wikipedia.org/wi

ki/File:ConstellationGPS.

gif

Actually ca. 30, with backups

Time accuracy among all satellite+earth

clocks must be 20 x 10-9 s

→ time for light to travel

(3.0x108)(20x10-9) = 6 m

→overall GPS accuracy of 5-10 m

Special Relativity:

v = 14,000 km/hr; seconds

per day = 86,400 s; β =

(1.4x107 m-hour-1)/(3.6x103 s-

hour-1) (3.0x108 ms-1) =

0.130x10-4; 1+0.5β2 =

1.0000000000845; therefore

per day, clock in satellite is

slower by (8.45x10-

11)(8.64x104) = 73x10-7 s =

7.3x10-6s per day as

measured on the ground

General Relativity: assume g

constant

H = 20,000 km;

hsat(1+gH/c2) = hground

tsat/tground = (1+gH/c2) =

1+(9.8ms-2)(2.0x107ms-1)/(3.0x108)2

1+2.17x10-9;

therefore per day, clock in

satellite is faster by

(2.17x10-9)(8.64x104) = 18.7x10-5s

= 187 x 10-6 s per day* as

measured on the ground

H = 20,000 km

v = 14,000 km/hr

M =

5.98 x 1024 kg

Relativity and GPS systems (cont’d.)

General Relativity: more accurate

H = 20,000 km >>R = 6,380 km

Seconds per day = 86,400

hsat/hground=

tsat/tground = 1+GM/c2[1/r1-1/r2 ] =

1+(6.67x10-11)(6.0x1024kg)/(3.0x108)2x

[1/6,380,000-1/26,380,000]

=1+4.44x10-3[1.56x10-7 - 0.38x10-7]

= 1 +5.2x10-10;

therefore per day, clock in satellite is

faster by

(5.20 x10-10)(8.64x104) = 45.3 x10-6s per

day*, as measured on the ground

So must correct for both Special and

General effects for GPS to have a chance

of working!

*See also discussion at

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

More accurate calc. gives 45 x 10-6 s for General

GPS

Sat.

Earth

R = 6.38x103 km

Better scale drawing:

r1

r2

Relativity and GPS systems (cont’d.)

General relativity:

Experimental verifications:

4. Precession of

the perihelion

of Mercury:

Distortion of

spacetime

due to Sun’s

gravity

MOSTLY DUE TO INFLUENCE OF OTHER PLANETS--NEWTONIAN

Newtonian mech. predicts ~ 5557

arcseconds/century = 5557/3600

= 1.6°/century, which is ~43

arcsec/century = 0.011°/century

smaller than observed.

5. Gravity

waves?

General relativity-

-Experimental

verifications:

Physics Today,

1993

http://www.ligo.caltech.edu/LIGO_web/about/brochure.html

Video: http://www.ligo.caltech.edu/cit_local.html , with link to: Einstein's messengers

The LIGO experiment, just getting underway: Interferometric measurements

of gravity waves = gravitational distortion of space time: Two labs, CA and

WA, 1900 miles apart. No gravity waves observed to date. Upgraded

measurements in 2015…maybe.

Number 771 #1, March 29, 2006 by Phil Schewe and Ben Stein Black Hole Merger Movie Accurate calculations of the gravitational waveforms emitted during the collision of black holes can now be made. A new computer study of how a pair of black holes, circling each other, disturbs the surrounding space and sends huge gusts of gravitational waves outwards, should greatly benefit the experimental search for those waves with detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the planned Laser Interferometer Space Antenna (LISA). The relative difficulty of computer modeling of complicated physical behavior depends partly on the system in question and on the equations that describe the forces at work. To describe the complicated configuration of charges and currents, one uses Maxwell's equations to determine the forces at work. In the case of black-hole binaries, the equations are those from Albert Einstein's theory of general relativity. Black holes encapsulate the ultimate in gravitational forces, and this presents difficulties for computations attempting to model behavior nearby. Nevertheless, some physicists at the University of Texas at Brownsville have now derived an algorithm that not only produces accurate estimates of the gravity waves of the inspiraling black holes, even over the short time intervals leading up to the final merger, but also is easily implemented on computers (see figures and movie at Physics News Graphics). "The importance of this work," says Carlos Lousto, one of the authors of the new study, "is that it gives an accurate prediction to the gravitational wave observatories, such as LIGO, of what they are going to observe." The new results are part of a larger study of numerical relativity carried out at the University of Texas, work referred to as the Lazarus Project. Campanelli, Lousto, Marronetti, and Zlochower, Physical Review Letters, 24 March 2006 Contact Carlos Oscar Lousto, lousto@phys.utb.edu, 956-882-6651 Figures and movie at Physics News Graphics Back to Physics News Update

http://www.aip.org/png/2006/256.htm

General relativity- Gravity waves from the biggest shows possible:

two black holes colliding

See Section 15.5 of textbook, and http://sfgate.com/cgi-bin/article.cgi?f=/c/a/2004/04/05/MNG0K60C151.DTL&type=news http://einstein.stanford.edu/

6. Frame dragging

Consequences:

Light (photons) attracted by gravity→black holes

and gravitational lensing”seeing” dark matter

Time contraction or dilation between clocks at

different points in gravitational potential (planes, GPS)

Motion of Mercury orbit (perihelion)

Gravity waves? Probably observed, but LIGO looking

more directly

Frame dragging? Now observed