Einstein’s Special Theory of Relativity

Einstein’s Special Theory of Relativity

• Your description of physical reality is the same regardless of the velocity at which you move.

• Regardless of your speed or direction, you always measure the speed of light to be the same.

• So what?• The length of an object decreases as its speed increases• Clocks passing by you run more slowly than do clocks at rest• An object approaching the speed of light becomes infinitely

massive.• Concept of spacetime (time is another dimension, like

space)

Einstein’s General Theory of Relativity predicts black holes• Mass warps space resulting in light

traveling in curved paths

Is General Relativity right?• The orbit of Mercury is explained

by Relativity better than by Kepler’s laws

• Light is measurably deflected by the Sun’s gravitational curving of spacetime.

• Extremely accurate clocks run more slowly when being flown in airplanes

• Some stars have spectra that have been gravitationally redshifted.

If we apply General Relativity to a collapsing stellar core, we find that it can be sufficiently dense to trap light by its

gravity.

The final fate of the cores of stars

Several binary star systems contain black holes as

evidenced by X-rays emitted

Cygnus X-1 must

have a mass of about 7 times that of the Sun

Other black hole candidates include:

• LMC X-3 in the Large Magellanic Cloud orbits its companion every 1.7 days and might be about 6 solar masses

• Monoceros A0620-00 orbits an X-ray source every 7 hours and 45 minutes and might be more than 9 solar masses.

• V404 Cygnus has an orbital period of 6.47 days which causes Doppler shifts to vary more than 400 km/s. It is at least 6 solar masses.

Supermassive black holes exist at the centers of

most galaxies

Supermassive black holes exist at the centers of

most galaxies

Primordial black holes may have formed in the early universe

• The Big Bang from which the universe emerged might have been chaotic and powerful enough to have compressed tiny knots of matter into primordial black holes

• Their masses could range from a few grams to more massive than planet Earth

• These have never been observed• Mathematical models suggest that these

might evaporate over time.

How big is a black hole?RSch3 M

Where the Schwarzschild radius RSch is in km, M is in solar masses

So… a 5 M black hole has a radius of about 15 km

Matter in a black hole becomes much simpler than elsewhere in the

universe• No electrons, protons, or neutrons• Event horizon

• the shell from within light cannot escape• Schwarzschild radius (RSch)

• the distance from the center to the event horizon• gravitational waves

• ripples in spacetime which carry energy away from the black hole

• The only three properties of a black hole• mass, angular momentum, and electrical charge

Roy Kerr(1934- )

Karl Schwarzschild(1873-1916)

Schwarzschild and Kerr found solutions to Einstein’s equations of General Relativity for black holes

Schwarzschild (Nonrotating) Black Hole

In the Erogoregion, nothing can remain at rest as spacetime here is being pulled around the black hole

Structure of a Kerr

(Rotating) Black Hole

Falling into a black hole is an infinite voyage as gravitational tidal forces pull spacetime in

such a way that time becomes infinitely long

Only to an outside observer! It would seem like ashort trip indeed to someone falling into the black hole.

Hawking proved that black holes evaporate

One of a pair of virtual particles can be trapped in a black hole as its counterpart escapes

Galaxies

Whirlpool Nebula (M51)

Cepheid variable stars help determine the

distances to galaxies

What does the Milky Way look like?

Looking towards the center of the Milky Way

galaxy

(through a rare region that is almost dust-free)

Distance measurements to globular clusters define the

location of the galactic center • Globular clusters form a

sphere around the center of the Milky Way .

• In 1917, Harlow Shapley determined distances to globular clusters by finding variable stars and used the period-luminosity relationship.

• The center of this distribution shows the location of the galactic center.

The center of the distribution of globular clusters shows the location of the Milky Way’s

center• globular clusters• galactic nucleus• nuclear bulge• spiral arms• disk• note position of

the Sun, just over half way out.

• Looking for 21-cm wavelengths of light …• emitted by interstellar

hydrogen• as we look along the disk

of the Milky Way (from inside), we see 21-cm photons Doppler shifted varying amounts

• this allows the interstellar hydrogen to be mapped

Radio observations help map the galactic

disk

What does the Milky Way look like from outside the galaxy?

The galaxy is rotating as stars orbit the center of

mass• Differential rotation gives spiral

arms their characteristic “whirlpool” appearance

Differential Rotation of the Galaxy

The Sun orbits at 230 km/s or about 500,000 mph

The Galaxy’s Rotation Curve

Most of the matter in the Galaxy has not yet been

identified• According to Kepler’s

Third Law, the farther a star is from the center, the slower it should orbit

• Observations show that speed actually increases with distance from the center

• This could be due to gravity from extra mass we cannot see - called DARK MATTER.

The galactic nucleus is also still poorly understood because dust

obscures our view• The center is located near the

constellation of Sagittarius.

Next week (hopefully): Telescope observations

• 8 pm Tuesday, May 20, last hour of night class (telescopes on the roof)

• Weather permitting• Attendance not required, but

strongly recommended and will be for credit

• If you can’t make it, see me for an alternate assignment

Total Lunar Eclipse This Thursday!

Moonrise:Sunset:

Total Eclipse Begins:Mid-Eclipse:

Total Eclipse Ends:Partial Eclipse Ends:

Moon Leaves Penumbra:

8:00 pm8:07 pm8:14 pm8:40 pm9:06 pm10:17 pm11:15 pm

Assignments• Study for quiz next week (Chapters

10-13)• Read Essentials IV,

Chapters 14-15• 5 points extra credit for eclipse

observations handed in to me next week (sketch, describe color & appearance of moon, and record times of observation)