The Arrow of Time. LeCosPA Group Meeting 19 October 2010. The Arrow of Time. The past is different from the future. E.g. We don’t remember the future. [ Duh ?] Entropy tends to increase in a closed system [2 nd Law of Thermodynamics]. The Arrow of Time.
19 October 2010
“So far as we know, all the fundamental laws of physics, such as Newton’s equations, are reversible. Then were does irreversibility come from? It comes from order going to disorder, but we do not understand this until we know the origin of the order. Why is it that the situations we find ourselves in every day are always out of equilibrium?”
Fluctuation in Equilibrium
“There must then be in the universe, which is in thermal equilibrium as a whole and therefore dead, here and there relatively small regions of the size of our galaxy (which we call worlds), which during the relatively short time of eons deviate significantly from thermal equilibrium. Among these worlds the state probability increases as often as it decreases.” (1895)
Early Universe [Thermal gas]:
Approximate by CMB photon energy density: S ~ N
If all matter is made into a black hole:
The Initial Condition
Sean Carroll and Jennifer Chen, Gen. Relativ. Gravit. (2005) 37(10): 1671–1674
Cosmology, Time’s Arrow, and That Old Double Standard, Huw Price, gr-qc/9310022v1
The arrow of time, T. Gold, American Journal of Physics30, pp. 403–410, doi:10.1119/1.1942052.
Since inflation doesn’t solve the problem, let’s push it further back!
We accept that the entropy was low at Big Bang, but deny the Big Bang was the beginning of the universe – and look for explanation of low entropy before then.
Gasperini and Veneziano, 1993.
Cyclic Universe: Steinhardt and Turok, 2007.
Perhaps the very far past is not different from the far future: they are both high-entropystate. If so, the hot, dense state we have been calling “the early Universe” is actually not the true beginning of the Universe but rather just a transitional state between stages of its history.
The universe is time symmetric by having high entropy at both ends. [c.f. Gold Universe]
But why does the entropy is so low in the middle?
In essence, as gravity is turned on, the system is forced from a region of large entropy (with respect to the non-gravitational dynamics) into a region with low entropy (with respect to gravity)
Smooth Initial Conditions from Weak Gravity, Brian Greene, Kurt Hinterbichler, Simon Judes, Maulik Parikh, hep-th/0911.0693v1.
Arrow of Time in String Theory,
Brett McInnes, Nucl.Phys.B782:1-25,2007
Hirosi Ooguri, Cumrun Vafa, Erik Verlinde, Hartle-Hawking Wave-Function for
Flux Compactifications: The Entropic Principle, Lett.Math.Phys. 74 (2005) 311,
What about torus?
Thus torus must be in class Z.
String theory allows for a very large variety of possible universes, brought into existence by the birth of baby universes. This ensemble of many universes is called the String Landscape. The Landscape is actuallyvery small:there is no hope whatever of finding a universe like ours in the Landscape by mere chance.
The Arrow Of Time In The Landscape, Brett McInnes, To appear in R. Vaas (ed.): Beyond the Big Bang. Springer: Heidelberg 2008, arXiv:0711.1656v2 [hep-th].
Baby universe, by definition, are not “creation from nothing”!