entropy in cosmology

27
Keenan Symposium Max Tegmark, MIT The Second Law and Cosmology

description

considering the entropy evolution of the universe

Transcript of entropy in cosmology

Page 1: entropy in cosmology

Keenan Symposium

Max Tegmark, MIT

The Second Law and Cosmology

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

It’s remarkable that the 2nd law and the arrow oftime have anything to do with cosmology!

(As Dick Bedeau &Charles Bennettmentioned)

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Maximum: 10122 bits

What’s the entropy of our universe?

Observed: 1089 bits

Minimum: 0 bits

My talk will have two parts.

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Maximum: 10122 bits

What’s the entropy of our universe?

Observed: 1089 bits

Minimum: 0 bits

1) Why is the entropy so low? 2) Why is the entropy so high?

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Why is theentropy so

low?

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

What I mean by entropy:• I’ll use the microscopic definition

• I’ll measure it in bits (kB=1)

• I’ll use it loosely to refer to algorithmic complexity

(We have severe problems to even define entropy in cosmology)

“Nobody knows what entropy really is, so in a debateyou will always have the advantage.”John von Neumann (1949)

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How did our solar system end up so far from thermal equilibrium?

(Cf. Dick Bedeau’s talk)

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

2nd law in cosmology:

2nd law without gravity:

clumpy => uniform:

uniform => clumpy:

(formation movies: universe, galaxy, star)

e-H/kT (as per Dick Bedeau)

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?

Q: Why did it start out so uniform?

A: It didn’t! Inflation!

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100dpi

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

Boomzoom

Gut

h &

Kai

ser

2005

, Sci

ence

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Why is theentropy so

high?

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Maximum: 10122 bits

What’s the entropy of our universe?

Observed: 1089 bits

Minimum: 0 bits

1) Why is the entropy so low? 2) Why is the entropy so high?

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102 bits

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How much of this information needs to go on the T-shirt?

Very little

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How much of this information needs to go on the T-shirt?

Very little

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

Generic outcome: 101100100011001001110…(Just our address in Hilbert space - not specified on T-shirt)

Quantum random number generatorbased on Stern-Gerlach apparatus:

(Charles Bennett just discussed quantum mechanics)

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CmbggOmOl

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eter

s:C

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C = h = G

= kb =

qe =

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So what does goon the T-shirt?

MT,Aguirre,Rees &Wilczek2005

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CmbggOmOl

The Standard Model Lagrangian

(From T.D. Gutierrez)

L=

So what does goon the T-shirt?

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

Q: Is all we observe all there is?

Our high entropy suggests no!

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If what we observe… …requires more bits todescribe than…

…a completemathematical description

of the world…

…then we’re in a multiverse!

1089

bits?103

bits?

So if you’re lookingfor a simple

mathematical TOE,you’re looking for amultiverse theory.

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

Why is the entropy so low?

Because inflation happened.

Why is the entropy so high?

Because we’re in a multiverse.(Inflation predicts this too)

In cosmology, the the 2nd law gives intriguing hints, bothrelated to inflation:

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Sound toocrazy?

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

We’renot

takingthis guyseriouslyenough

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

The strongest form of the anthropic principle:

“The Universe must be such that we like it.”

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Max TegmarkDept. of Physics, MIT

[email protected] Symposium

October 4, 2007

The strongest form of the anthropic principle:

“The Universe must be such that we like it.”

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Conclusion:

Despite its old age, the SecondLaw isn’t old and tired!

It’s alive and kicking, continuingto stimulate research.