Sunday, April 24, 2016

Worlds without End:
The Conformal Cyclic Cosmology of Roger Penrose

The Conformal Cyclic Cosmology of Roger Penrose
At the left is our universe; at the right the mapped "Aeons"
The mapping takes the zero Big Bang to the finite red circle;
and the infinite end (at infinite time) to the finite blue circle.
See the text for a fuller explanation.
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." Albert Einstein
Ah, past the plunge of plummet,
In seas I cannot sound,
My heart and soul and senses,
World without end, are drowned.  
A.E. Housman, "A Shropshire Lad"
"Perhaps the best argument in favour of the thesis that the Big Bang supports theism is the obvious unease with which it is greeted by some atheistic physicists.    At times this has led to scientific ideas, such as continuous creation or an oscillating universe, being advanced with a tenacity which so exceeds their intrinsic worth that one can only suspect the operation of psychological forces lying very much deeper than the usual desire of a theorist to support his/her theory [emphasis added].    Chris Isham, "Creation of the Universe as Quantum Process"in Physics, Philosophy and Theology--A Common Quest for Understanding.

INTRODUCTION

In a previous post I mentioned that the conformal cyclic cosmology (CCC) proposed by Roger Penrose deserves an article, "nay, a chapter" on its own.  Although  there are several cosmology theories that propose multiple universes (see here and here),  the CCC is perhaps the only one that might be subject to experimental tests.   And if such tests were to confirm Penrose's hypothesis, what then would be the consequences for Catholic teaching?    We'll address that question below.

CCC, CONFORMAL CYCLIC COSMOLOGY--AN OVERVIEW

This will be a summary of Penrose's thesis;  for a fuller account go to his 2005 paper, Before the Big Bang: an Outrageous New Perspective ..., his 2013 paper, On the Gravitization of Quantum Mechanics 2: Conformal Cyclic Cosmology, or his book, Cycles of Time.    For the last link Peter Woit (author of Not Even Wrong, a critique of String/Brane theory) has written a better and more comprehensive review than I ever could.

The starting point for this theory is the puzzle of the Second Law of Thermodynamics.   Why does entropy increase for the universe?   In one of his other books, The Road to Reality, Penrose poses this question, that appears to contradict a prime principle of physics, time reversibility of physical processes. Why is the Universe so ordered at the moment of the Big Bang?  (He estimates the relative volume of phase space into which the universe expands as 10^(10^123), a number greater than all the particles in the universe.)

Penrose's answer is that gravitational degrees of freedom are not activated in the very early universe, and it's gravitational effects that give rise to the increase in entropy:
"The answer lies in the fact that the high entropy of the microwave background refers only to the matter content of the universe and not to the gravitation field, as would be encoded in its space-time geometry in accordance with Einstein’s general relativity. What we find...is an extraordinary uniformity, ... interpreted as gravitational degrees of freedom ...being not excited at all.... the entropy rises as the initially uniform distribution of matter begins to clump, as the gravitational degrees of freedom begin to be taken up.  This allows stars to be formed, which become much hotter than their surroundings. ....and finally this gravitational clumping leads to the presence of black holes (particularly the huge ones in galactic centres), which represent an enormous increase in entropy." Roger Penrose, "Before the Big Bang, an Outrageous Perspective."
So, where does "conformal"* enter into the picture?*    By means of a mathematical transformation of spacetime coordinates, the zero--the singularity at the origin-- can be transformed into a finite boundary, as shown in the diagram above.   Further, the infinity--the singularity at the end of the universe--can also be transformed into a finite boundary.   Penrose's "outrageous perspective" is to assume that these transformations are more than mathematical devices, but portray reality.   Moreover, not only are these mathematically transformed beginnings and ends real, they are conjoined:  the end of one universe is the beginning of the next.

An important way in which Penrose's cosmology differs from other proposals is that it can (in principle) be tested experimentally.   Symmetry requirements enable particles with integral spin (which include photons) to cross the boundary between the nth and (n+1)th universe, but not particles with half-integral spin (mass particles such as electrons and protons).  

Accordingly there might be signals from a preceding universe shown in the microwave background radiation, COBE.   Penrose and Gurzadyan claimed to have found such by concentric circles in the background radiation, presumed to be due to gravity waves formed by collisions between massive black holes in the preceding Aeon.
Circles in COBE from Penrose
and Gurzadyan via Sean Carroll

However this "evidence" has been challenged by several authors who claim that intrinsic structure that can be deduced by statistical manipulation is part of the natural variation of the COBE radiation.  In fact, one group showed that statistically significant equilateral triangles could also be deduced by appropriate manipulation.

Other objections have been raised to the CCC thesis: for the conformal mapping at the end of the universe to be physically significant, it is required that no matter be left in the universe.    Protons have a finite lifetime (albeit very long--their decay has not yet been observed), but electrons do not.    So, unless all electrons in the universe were to be annihilated by positron-electron collisions (or some other interaction), the massless condition would not hold, nor would it hold if neutrinos continued to exist.


THEOLOGICAL SIGNIFICANCE OF THE PENROSE COSMOLOGY

Catholic theologians breathed a huge sigh of relief (presumed) when Abbe LeMaitre's primordial atom thesis ("The Big Bang") was confirmed by galactic red shift measurements and became scientifically acceptable.   Indeed, Pope Pius XII argued that this scientific theory validated Catholic teaching.   LeMaitre himself was not inclined to such a strong view;  rather he disassociated the science from theology with this statement:

 “As far as I can see, such a theory remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being… For the believer, it removes any attempt at familiarity with God… It is consonant with Isaiah speaking of the hidden God, hidden even in the beginning of the universe.” Abbe Georges LeMaitre, S.J., "The Primeval Atom Hypothesis and the Problem of Clusters of Galaxies"

St. Thomas did not say that reason could prove a universe beginning in time; although reason could prove a First Cause--God--for the origin of the universe (possibly as an eternal entity, since God is eternal);  it is an article of faith to believe a universe created in time.   The Big Bang notion is consistent with Creation at t=0, but does not prove it.    If we believe God is the author of all, a First Cause, then He can create an infinity of universes, as in the bubble universe hypothesis of Lande or in the parallel worlds given by some interpretations of quantum theory.     Economy of effort is not required of God.

Accordingly, faith trumps science in this.   Revelation gives us reason to believe, and despite the efforts of non-believing scientists to trash a strong confirmation of God's creative power, the Big Bang, we still can remain confident in that power as the source of being.   Such a position is not "fideism", an adherence to Catholic teaching in the face of empirical evidence to the contrary.   It is a recognition of the limits of science, and the authority of theology and philosophy in final verdicts on truth.

*"Conformal mappings" or transformations are defined as those that preserve angles but not distances; see this link for examples.
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About Me

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Retired, cranky, old physicist.   Convert to Catholicism in 1995.   Trying to show that there is no contradiction between what science tells us about the world and our Catholic faith.   Intermittent blogs and adult education classes to achieve this end (see http://rationalcatholic.blogspot.com/   and http://home.ptd.net/~rkurland)

Extraordinary Minister of Communion volunteer to federal prison and hospital; lector, EOMC.
Sometime player of bass clarinet, alto clarinet, clarinet, bass, tenor bowed psaltery for parish instrumental group and local folk group.

And, finally, my motivation:
“It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking.
Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.”
St. Augustine of Hippo, The Trinity I,8.