Physics of Astronomyweek 8 Thus. 25 May 2006

Crisis in Cosmology

Planck Time

Candidate solutions

Looking ahead

Astrophysics in crisis

Black holes:what do you know?

Big Bang: You’ve heard that “the laws of physics break down” in the earliest moment.

Black holes can help us understand what that means.

Evidence for the Big Bang

The 3-degree background radiation reveals the origin of structure in the universe

More evidence for the Big Bang

Expansion of the universe: further galaxies are receding faster

Primordial abundances of Hydrogen, Helium and metals

3K radiation: universe has cooled to the present

Inflation: solution of horizon and flatness problems

Questions about the Big Bang

What happened in the first tenth of a millionth of a billionth of a billionth of a billionth of a billionth of a second (10-43 sec)?

The universe was very small, so ask Quantum Mechanics.

The universe was very massive and dense, so ask General Relativity (theory of gravity).

Current paradigms in physics

Quantum Mechanics explains the very small

General Relativity explains the very massive (theory of gravity)

http://fusionanomaly.net/quantummechanics.html

http://www.phys.lsu.edu/dept/gifs/quantum.gif

How big was the universe in the beginning?

R

General Relativity (gravity)The early universe was a singularity –

mathematically like a black hole.

Event horizon R = distance inside which everything (including light) is contained

BH

R

Quantum Mechanics

The early universe was very small – a point.

Small quantum objects have an uncertain size R or wavelength

R=

Problem: the early singularity could be outside its own event horizon?!

“Laws of physics break down”

R

R=

Calculating the Planck scales:

1. Use energy conservation to find the GRAVITATIONAL size of a black hole, the Schwartzschild radius R.

2. Next, use the energy of light to calculate the QUANTUM MECH. size of a black hole, De Broglie wavelength .

3. Then, equate the QM size with the Gravitational size to find the PLANCK MASS Mp of the smallest sensible black hole.

4. Finally, substitute M into R to find PLANCK LENGTH Lp

5. and then calculate both Mp and Lp, and the Planck time.

6. These are the smallest scales that we can describe with both GR and QM. At smaller scales, GR and QM are mutually inconsistent.

1a. Gravitational size of a Black Hole

We can use energy conservation to find the size of a black hole. First, find the escape velocity (v) from an object with mass M and radius R:

Kinitial + Uinitial = Kfinal + Ufinal

½ mv2 – GmM/R = 0 + 0Solve for v:

M

Rm v

m

v→0, r→0

1b. Gravitational size of a Black Hole

For a black hole with mass M, the escape velocity v=c at the

event horizon r = Rgrav = Schwartzschild radius

BH 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 termsof massM

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 deBrogliewavelength

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 Mp 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 Ror

GGM

Rch

M c

5. Calculate the Planck length and mass

2 3

34 8 112

2

:

6 10 , 3 10 , 7 10

, _____________

_________________

ms

p

pp

Usethese fundamental constants

kg m m mh x c x G x

s s kg s

hctoevaluate the Planck mass M

G

GMand 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? Neutrinos? 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?

We need a new theory of “quantum gravity”

String theory? Loop quantum gravity?http://www.columbia.edu/cu/record/archives/vol23/vol23_iss18/28c.gif http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html

Will one of these resolve the crisis and become our ultimate GUT?

How to choose which model?

Criteria: * New model answers

old Q* Predictions pass tests* New puzzles solvable* Simplicity, beauty* More?

My generation articulated this problem. Your generation will solve it.

Looking ahead

Research posters tomorrow at Science Carnival

Research reports Tuesday

Summative lecture Tuesday

Final Thursday

Research reports

Approx. 5 pages – concise and clear

+ annotated bibliography

+ appendices: calculations and figures

+ reference sources at end of each sentence!

TEAMS: make it clear what each team member contributed, to the work and to the writing

Each team member should demonstrate his or her understanding INDEPENDENTLY

MAKE IT YOUR OWN – unique and original