entropy in cosmology
DESCRIPTION
considering the entropy evolution of the universeTRANSCRIPT
![Page 1: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/1.jpg)
Keenan Symposium
Max Tegmark, MIT
The Second Law and Cosmology
![Page 2: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/2.jpg)
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)
![Page 3: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/3.jpg)
Maximum: 10122 bits
What’s the entropy of our universe?
Observed: 1089 bits
Minimum: 0 bits
My talk will have two parts.
![Page 4: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/4.jpg)
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?
![Page 5: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/5.jpg)
Why is theentropy so
low?
![Page 6: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/6.jpg)
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)
![Page 7: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/7.jpg)
How did our solar system end up so far from thermal equilibrium?
(Cf. Dick Bedeau’s talk)
![Page 8: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/8.jpg)
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)
![Page 9: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/9.jpg)
?
Q: Why did it start out so uniform?
A: It didn’t! Inflation!
![Page 10: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/10.jpg)
100dpi
![Page 11: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/11.jpg)
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
Boomzoom
Gut
h &
Kai
ser
2005
, Sci
ence
![Page 12: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/12.jpg)
Why is theentropy so
high?
![Page 13: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/13.jpg)
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?
![Page 14: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/14.jpg)
102 bits
![Page 15: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/15.jpg)
How much of this information needs to go on the T-shirt?
Very little
![Page 16: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/16.jpg)
How much of this information needs to go on the T-shirt?
Very little
![Page 17: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/17.jpg)
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)
![Page 18: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/18.jpg)
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
![Page 19: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/19.jpg)
CmbggOmOl
The Standard Model Lagrangian
(From T.D. Gutierrez)
L=
So what does goon the T-shirt?
![Page 20: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/20.jpg)
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
Q: Is all we observe all there is?
Our high entropy suggests no!
![Page 21: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/21.jpg)
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.
![Page 22: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/22.jpg)
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:
![Page 23: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/23.jpg)
Sound toocrazy?
![Page 24: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/24.jpg)
Max TegmarkDept. of Physics, MIT
[email protected] Symposium
October 4, 2007
We’renot
takingthis guyseriouslyenough
![Page 25: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/25.jpg)
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.”
![Page 26: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/26.jpg)
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.”
![Page 27: entropy in cosmology](https://reader033.vdocuments.net/reader033/viewer/2022051322/5464cf5eb4af9f4e3f8b4d4a/html5/thumbnails/27.jpg)
Conclusion:
Despite its old age, the SecondLaw isn’t old and tired!
It’s alive and kicking, continuingto stimulate research.