Roger Penrose on entropy: How did he calculate that?

 

One of the fine-tuning arguments frequently used is the low entropy state of the universe at the Big Bang.  This was calculated by Roger Penrose to be 1:10¹⁰¹²³.  How does he do this?  He explains it in his book, The Emperor’s New Mind.  Here is the section of the book that discusses it.   Penrose uses the Bekenstein-Hawking formula for the entropy of a particle in a black hole to determine the entropy of a particle at the singularity of the Big Bang as if the entire universe were a giant black hole.  He calculates this to be 10⁴³.  There are estimated to be 10⁸⁰ particles in the observable universe. 

 

10⁸⁰ x 10⁴³ = 10¹²³ . 

Entropy is on a logarithmic scale, so that is how he arrives at 10¹⁰¹²³. 

V = total phase-space volume available

W = original phase-space volume

V/W = 10¹⁰¹²³

 

Therefore, the accuracy of the low entropy value was 1:10¹⁰¹²³.  Penrose says,

“This is an extraordinary figure. One could not possibly even write the number down in full, in the ordinary denary notation: it would be `1' followed by 10<sup>123</sup> successive `0 's! Even if we were to write a `0' on each separate proton and on each separate neutron in the entire universe-and we could throw in all the other particles as well for good measure-we should fall far short of writing down the figure needed. The precision needed to set the universe on its course is seen to be in no way inferior to all that extraordinary precision that we have already become accustomed to in the superb dynamical equations (Newton's, Maxwell's, Einstein's) which govern the behaviour of things from moment to moment.”

 

If there are more particles in the universe than 10⁸⁰ (like an infinite number), all the more extraordinary!!

Sean Carroll pointed out in his debate with William Lane Craig that this low entropy value was not a requirement for life to exist and, therefore, should not be considered finely tuned by a creator.  As I discussed here, Robin Collins addresses this in his paper claiming that without a low entropy at the Big Bang, we would not know that our universe had a beginning and some of our fundamental laws of physics would not have been discovered.