The Second Law and Cosmology - MITweb.mit.edu/keenansymposium/documents/MaxTegmarkLecture.pdfKeenan...
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Keenan Symposium Max Tegmark, MIT The Second Law and Cosmology
Transcript of The Second Law and Cosmology - MITweb.mit.edu/keenansymposium/documents/MaxTegmarkLecture.pdfKeenan...
Keenan Symposium
Max Tegmark, MIT
The Second Law and Cosmology
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)
Maximum: 10122 bits
What’s the entropy of our universe?
Observed: 1089 bits
Minimum: 0 bits
My talk will have two parts.
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?
Why is theentropy so
low?
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)
How did our solar system end up so far from thermal equilibrium?
(Cf. Dick Bedeau’s talk)
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)
?
Q: Why did it start out so uniform?
A: It didn’t! Inflation!
100dpi
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
Boomzoom
Gut
h &
Kai
ser
2005
, Sci
ence
Why is theentropy so
high?
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?
102 bits
How much of this information needs to go on the T-shirt?
Very little
How much of this information needs to go on the T-shirt?
Very little
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)
CmbggOmOl
Stan
dard
mod
el p
aram
eter
s:C
osm
olog
yPa
rtic
le p
hysi
cs
C = h = G
= kb =
qe =
1−
So what does goon the T-shirt?
MT,Aguirre,Rees &Wilczek2005
CmbggOmOl
The Standard Model Lagrangian
(From T.D. Gutierrez)
L=
So what does goon the T-shirt?
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
Q: Is all we observe all there is?
Our high entropy suggests no!
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.
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:
Sound toocrazy?
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
We’renot
takingthis guyseriouslyenough
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.”
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.”
Conclusion:
Despite its old age, the SecondLaw isn’t old and tired!
It’s alive and kicking, continuingto stimulate research.
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