Astronomy and CosmologiesWed.18.May 2005, last lecture, Spring 2005, Zita

• Age of the universe – finish H workshop

• Your questions on Cosmology and the Early Universe

• Summative lecture

• Black holes and Planck time

• Questions for your generation

• Looking ahead

Age of the Universe

In the Hubble workshop, you:• found the recession speed and distance to 5 galaxies• plotted speed vs distance

Next, find the• slope = v/d = Hubble constant = H (km/s/Mpc)• age of the universe T = 1/H

Discuss:• assumptions• results using Wendy Freedman’s improved H=71

H=v/d and T=1/HHubble data for 5 galaxies

0

10

20

30

40

50

60

70

0.00 2.00 4.00 6.00 8.00 10.00 12.00

distance (10^8 pc)

spee

d (

10^

3 km

/s)

Your questions on Cosmology and the Early Universe

WMAP data reveal fundamental characteristics of the universe:

Cosmological parameters

Shape of the universe

Fate of the universe?

You have learned this quarter:

Solar system + gravityKepler’s and Newton’s laws:

Jupiter’s moons and dark matter

Light!Milky Way, galaxies, and the Universe

Big Bang and 3K background radiationWMAP yields cosmological parameters:

shape, density, fate? of universe

You learned about ancient and modern observing techniques,

and cosmologies across cultures.

You learned: Gravity holds the solar system together

Eclipses … size of the Earth, Moon, and Sun …

You learned: Newton’s 2d law explains why Kepler’s 3d law works

F=GmM/r2 yields period2 = 42r3/GM

Precession of the equinoxes … Heliocentric model …

You found Jupiter’s mass from its moons’ orbit,

and discovered dark matter from the motion of stars in our Galaxy

You learned: Light and spectra reveal the temperature, composition, brightness,

motion, magnetic fields… of stars

You learned: Our Sun is one of billions of stars in the Milky Way Galaxy

You learned: Our galaxy is one of billions of galaxies in the universe

You learned: The 3K microwave background supports the Big Bang…

… and shows the origin of structure in the universe, and the shape, density, and fate of the universe

BUT - how did the universe begin?

Quantum fluctuations in the vacuum?One universe? (Anthropic principle)Multiverses? (Lucky chance)Bouncing between Big Bangs and Big Crunches?

Limits of understanding

Looking out: WMAP and high-Z supernovae

Looking back: earliest moment = Planck time

Quantum Mechanics vs Gravity

Wavelength of mass M vs size R of black hole

BH

1. Gravitational size of a Black Hole

We can use energy conservation* to find the size (Rgrav=Schwartzschild radius) of the event horizon of a black hole with mass M:

BH

* next year in Physics of Astronomy

2grav

GMR

c

R

2. Quantum mechanical size of a Black Hole

in :

____________

Energy of photon wavelengthof particle

hc hE pc p Mc

Solve for wavelength terms of mass M

The deBroglie wavelength, , describes the smallest region of space in which a particle (or a black hole) of mass m can be localized, according to quantum mechanics.

3. Find the Planck mass, Mp

2

2

:

____________

p

p

p

Schwartzschild radius deBroglie wavelength

R

GM h

c M c

Solve for the Planck mass

M

If a black hole had a mass less than the Planck mass Mp, its quantum-mechanical size could be outside its event horizon. This wouldn’t make sense, so M is the smallest possible black hole.

4. Find the Planck length, Lp

These both yield the Planck length, Lp. Any black hole smaller than this could have its singularity outside its event horizon. That wouldn’t make sense, so L is the smallest possible black hole we can describe with both QM and GR, our current theory of gravity.

2

, , :

______________

______________

p

p

p

hcSubstitute your Planck mass M intoeither R or

GGM

Rch

M c

5. Optional: calculate Planck length and mass

2 3

34 8 112

3

:

6 10 , 3 10 , 7 10

, _________________

_________________

ms

p

p

Usethese fundamental constants

kg m m mh x c x G x

s s kg s

hctoevaluate the Planck mass M

G

hGand the Planck length L

c

These are smallest scales we can describe with both QM and GR.

6. Calculate the Planck time

Consider the time it would take for light to cross the Planck length:

Speed = distance / time

c = Lp / p

Solve for the Planck time p:

Planck scales

You should find roughly these sizes for the:

Planck mass = ~ 3 x 10-8 kg

~ 4 x 10-35 m

(A black hole smaller than this could be outside its own event horizon, so QM and gravity are not both consistent at this scale.)

~ 10-43 s

(At earlier times, our familiar laws of physics “break down”.)

p

hcM

G

3p

hGPlanck length L

c

5p

hGPlanck time

c

Outstanding cosmological questions

What physics operated before the Planck time?

What is gravity? Higgs? Graviton? Other?

What is dark matter? Neutrino mass? Wimps?

What is dark energy? Why does universe’s expansion accelerate?

How to unite gravity with QM? Loop quantum gravity? Superstrings? D-branes? Supersymmetric particles?