Sunday, March 16, 2014

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 10123 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.

Friday, March 7, 2014

The Fine-Tuning for Discoverability


The recent debate with Sean Carroll and William Lane Craig on February 21, 2014 had a different format than most debates.  Craig and Carroll debated on a Friday night, but then each brought two other people with them to write companion paper’s to support/refute the various positions and give a talk the following morning.  Sean Carroll brought Tim Mauldin and Alex Rosenberg.  William Lane Craig brought Robin Collins and James Sinclair.  I haven’t had time to look at the debate in depth yet, but on the surface it was a great exchange with lots of scientific details.  Sean Carroll held his own quite well, and holding your own against WLC is almost a default victory.  Not all of the videos are posted yet.  I can say the talk Tim Mauldin gave was a snooze….a giant ‘we don’t know anything and don’t need God either’. 

William Lane Craig
Sean Carroll

 
 
 
 
 
 
 
 
One of the arguments Craig uses that points to an intelligent creator is the fine-tuning for life.  Carroll claims we have no evidence to suggest the universe is fine-tuned for life.  An example he uses is Roger Penrose’s staggering calculation for the minimum entropy value at the Big Bang….1:1010123.  You could put a zero on every particle in the observable universe with more to spare.  It’s an unfathomably small number!!!  Carroll claims that the entropy of the early universe did not need to be that low for life to form, so it is actually an argument against the fine-tuning by a creator.  Queue Robin Collins.



Robin Collins
Robin Collins is an expert in the fine-tuning of universe.  His talk is not out on video yet, but he has published his companion paper called “The Fine-Tuning for Discoverability”.  He calls it the Discoverability Thesis.
 

“Discoverability Thesis: This thesis is that the universe is non-accidentally structured in such a way as to be highly discoverable.”

 
 
In other words, not only is the universe fine-tuned for life, but it is also finely tuned to allow for intelligent agents to be able to understand it.  Many of the fundamental constants and early universe conditions are not necessary for life, but are necessary if we are to be able to learn about the universe and life.  Collins claims to have found at least a dozen examples of fine-tuning for discoverability.

The low entropy condition at the Big Bang is one of them.  Carroll is correct in saying that the entropy could be higher and still support life, but having a low entropy helps our discoverability in two ways:

1)     A low entropy allows us to see other galaxies and a larger universe.  Without a low entropy, we would only see our galaxy.  We wouldn’t know that the universe was expanding or that it had a beginning.

2)    Without a low entropy in the beginning, the universe would not have a uniform distribution.  We wouldn’t be able to discover some of the fundamental laws that govern the universe, like General Relativity which assumes a uniform distribution throughout the universe.

The beginning of the universe points to a transcendent cause.  A universe that follows laws and can be rationally understood indicates a rational mind formed those laws. 

Another example of tuning for discoverability is the constant, α, that governs the electromagnetic force. 

“A small increase in α would have resulted in all open wood fires going out; yet harnessing fire was essential to the development of civilization, technology, and science – e.g., the forging of metals….. Going in the other direction, if α were decreased, light microscopes would have proportionality less resolving power without the size of living cells or other microscopic objects changing (when measured in atomic units).”

So a larger α means no open wood flames and a smaller α means we would not be able to examine living cells, both of which are very significant to discoverability and technological advancement.

Another example of fine-tuning discoverability is radioactive decay compared to the strength of gravity.  This allows us to study geology, archeology, and paleontology….all crucial in learning about life, the Earth, and history.

“the ability to use radioactive dating – which plays a crucial role in geology, archeology, and paleontology -- depends on the density of radioactive elements in the crust of the planet on which observers evolve. As the strength of gravity is decreased (e.g., as measured by the force between two protons a unit distance apart), the density of radioactive elements must decrease to keep the number of volcanoes per unit area from increasing, which would decrease livability.”

Some atheists, including Carroll, have claimed that extra, unnecessary particles show that the universe was not created by an intelligent agent since a designer would not include such unnecessary features.  This is merely a “Naturalism of the gaps” argument….. ‘I don’t know why a creator would do this, so there is no creator’.  One example is the muon.  Collins argues that the muon has played a very important role in our ability to learn about our universe and other particles.  He sites this article in Symmetry Magazine:

“The muon is one of 16 fundamental particles that make up everything—all matter, all forces, all energy—in the visible universe….The muon’s puzzling appearance and subsequent identification as a unique and autonomous particle perplexed scientists and revolutionized the field of particle physics. It was the precursor to the three generations of matter and opened the door for the discovery of quarks and other particles.”

“Today scientists can manipulate the muon and use it as a tool not only for particle physics research but also for cosmology, archeology and public safety. They have used muons to test special relativity and time dilation and to probe the interiors of pyramids for secret chambers. Today scientists use muons to image novel materials such as high-temperature superconductors, to study chemical reactions, to look for hidden nuclear weapons and even to determine things as delicate as the size of a proton.”

There is even talk of building a muon collider.  For an unnecessary particle, a lot has been learned because of it and this isn’t the end of what we will learn from the muon! 

Collins goes on to discuss the cosmic microwave background radiation and the dark energy coincidence problem, but that will have to be another post.  Needless to say, his paper is full of good info!!

How does the discoverability point to an intelligent creator?  If the entropy were higher, we would not know that our universe had a beginning and required a transcendent cause.  We also would not know some of the fundamental laws that govern our universe, which a rational universe provides evidence for a rational creator.  If the constant that governs the electromagnetic force, α, were higher, we wouldn’t have fire or anything that results from fire.  If α were lower, we would not be able to see living cells in a microscope.  If you want to know why that points to an intelligent mind, see Steven Meyer’s video on the cell.  Radioactive decay has allowed us to study geology, archeology, and paleontology….all crucial in learning about life, the Earth, and history.  The muon has opened the door to understand our universe at the particle level.

The more I learn, the more Romans 1 amazes me.  God truly has revealed his existence through what he has made.