Astronomy and Cosmologies
Wed.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/H
Hubble data for 5 galaxies
70
speed (10^3 km/s)
60
50
40
30
20
10
0
0.00
2.00
4.00
6.00
distance (10^8 pc)
8.00
10.00
12.00
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 + gravity
Kepler’s and Newton’s laws:
Jupiter’s moons and dark matter
Light!
Milky Way, galaxies, and the Universe
Big Bang and 3K background radiation
WMAP 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 = 4p2r3/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
BH
Wavelength l of mass M vs size R of black hole
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:
R
BH
Rgrav
* next year in Physics of Astronomy
GM
 2
c
2. Quantum mechanical size of a
Black Hole
Energy of photon  wavelength of particle
E
hc
l
 pc

p  Mc 
h
l
Solve for wavelength l in terms of mass M :
l  ____________
The deBroglie wavelength, l, 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
Schwartzschild radius  deBroglie wavelength
Rl
GM p
h

2
c
M pc
Solve for the Planck mass :
M p 2  ____________
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
hc
Substitute your Planck mass, M p 
, into either R or l :
G
GM p
R  2  ______________
c
h
l
 ______________
M pc
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.
5. Optional: calculate Planck length and
mass
Usethese fundamental constants :
h  6 x 10
34
2
3
kg m
8 m m
11 m
, c  3 x 10  s  , G  7 x 10
s
s
kg s 2
hc
to evaluatethe Planck mass, M p 
 _________________
G
hG
and the Planck length Lp 
 _________________
3
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 / tp
Solve for the Planck time tp:
Planck scales
You should find roughly these sizes for the:
Planck mass = M p  hc ~ 3 x 10-8 kg
G
Planck length Lp 
hG
c3
~ 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.)
Planck timet p 
hG
c5
~ 10-43 s
(At earlier times, our familiar laws of physics “break down”.)
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?