Phase-Space volume V - Roger Penrose

[bobsmith76]

I've heard a lot about fine tuning but Roger Penrose on this website
http://www.ws5.com/Penrose/
which is an excerpt from his book the Emperor's New Mind

claims that the phase-space volume must be accurate to within 10^10^123. I can't understand the following lines. If someone could make them clear that would help but don't worry because I need to study more physics anyway and I don't think I'm ready to reach this level. I just want to know if this is true, and if so why does no one talk about this amazing bit of fine-tuning? I've a few articles on fine tuning but I've seen only one other person talk about this.


However, we are considering a closed universe so eventually it should recollapse;

and it is not unreasonable to estimate the entropy of the final crunch by using the

Bekenstein-Hawking formula as though the whole universe had formed a black

hole. This gives an entropy per baryon of 10^43, and the absolutely stupendous

total, for the entire big crunch would be



10^123.



This figure will give us an estimate of the total phase-space volume V available

to the Creator, since this entropy should represent the logarithm of the volume of

the (easily) largest compartment. Since 10^123 is the logarithm of the volume, the

volume must be the exponential of 10^123, i.e.



V = 10^10^123.



in natural units! (Some perceptive readers may feel that I should have used the

figure e^10^123, but for numbers of this size, the a and the 10 are essentially

interchangeable!) How big was the original phase-space volume W that the Creator

had to aim for in order to provide a universe compatible with the second law of

thermodynamics and with what we now observe? It does not much matter whether

we take the value

W = 10^10^101 or W = 10^10^88

given by the galactic black holes or by the background radiation, respectively, or a

much smaller (and, in fact, more appropriate) figure which would have been the

actual figure at the big bang. Either way, the ratio of V to W will be, closely



V/W = 10^10^123.



This now tells us how precise the Creator's aim must have been: namely to an

accuracy of one part in 10^10^123.

 

[bobsmith76]

I'm really looking for some help for this one. I don't need to understand it, I'm not at that level anyway, I just want to know if this is true and if it is why does no one talk about it.

 

[yenchin]

I don't have time to go over the details right now, I hope someone else get to reply you. Those are some long paragraph. Which part do you not understand specifically?

Sure people do talk about this, for example, see the papers below. They may be somewhat technical but maybe you can learn something from it. The second and third paper are quite readable.

1. Does Inflation Provide Natural Initial Conditions for the Universe?, http://arxiv.org/abs/gr-qc/0505037
2.The Arrow Of Time In The Landscape, http://arxiv.org/abs/0711.1656
3. Is Our Universe Natural? http://arxiv.org/abs/hep-th/0512148