Philosophic Issues in Cosmology 2: Relativistic Theories for the Origin of the Universe

There was a young lady named Bright,Whose speed was far faster than light;She started one day In a relative way, And returned on the previous night. A.H.R. Buller, Punch 

This is the second of 7 (or maybe 9) posts, from articles on the Magis Facebook Site, 2010.   They attempt to summarize George Ellis's fine article, Issues in the Philosophy of Cosmology. 

The usual exposition of Einstein's General Relativity Field Equations is very forbidding, full of Greek subscripts and tensor notation;  a clear, simplified version has been given on the web by John Baez, and is appropriate for considering the Big Bang.  The standard general relativity model for cosmology is that given by Friedmann-LeMaitre-Robertson-Walker,  usually designated by  FLRW. The FLRW model proceeds from the following simplifying assumptions: a) the universe is isotropic (looks the same in every direction, from every point in space);  b) there is a constant amount of matter in the universe;  c) on a large scale (hundreds of times the distance between galaxies) the universe has a homogeneous matter density (matter is spread evenly throughout space);   d) the effects of “pressure” (from radiation or the vacuum) can be neglected.

With these simplifying assumptions, the equation for the “size” of the universe, its radius R, becomes simple, and looks just like the equation of motion for a particle traveling under an inverse square law, like that of gravity.  (Note:  this is not to say the size of the universe is really given by some value R;  the universe might possibly be infinite—more about that later—but to show how space is expanding.)    The universe might expand and then contract in a “Big Crunch” (like a ball falling back to earth), corresponding to positively curved spacetime (like a sphere); it might expand with a constant velocity of expansion (like a projectile going into orbit), corresponding to flat space-time (like a plane); or it might expand with an accelerating velocity of expansion (like a projectile achieving escape velocity), corresponding to a saddle-shaped curvature of space-time.     It should also be emphasized that the FLRW solution to the Einstein General Relativity equations is by no means unique, nor is it the only solution with a singularity.   It is a model, however, that is in accord with measured data (red shift, COBE microwave background radiation).

The assumptions stated above do not apply rigorously.   Observations have shown a filament or bubble-like structure to the universe with clusters and meta-clusters of galaxies. (A theoretical picture for this filament structure has been proposed.)  In the early stages of the universe radiation pressure was very likely significant.  More recently, measurements have shown that the expansion rate is increasing, which is presumed due to “dark energy”, possibly a pressure due to vacuum energy.    Moreover, at some point in the expansion the scale of the universe gets so small that classical physics does not apply and quantum mechanics has to be used for theory.   Unfortunately quantum mechanics and general relativity have not  yet been reconciled into one general theory, so there is a fundamental difficulty with this melding of the two theories.

The simple solution above for FLRW models gives an acceleration of R proportional to 1/R^2, which signifies that there is a singularity at R=0, that is to say, if you try to plug in R=0 you'll get infinity.   This would be the same as the infinity at the source for other forces proportional to 1/R^2, coulomb attraction or gravity.   Ellis has this to say about the significance and existence of the  FLRW singularity:

“the universe starts at a space-time singularity ...This is not merely a start to matter — it is a start to space, to time, to physics itself. It is the most dramatic event in the history of the universe: it is the start of existence of everything. The underlying physical feature is the non-linear nature of the EFE  (Einstein Field Equation): going back into the past, the more the universe contracts, the higher the active gravitational density, causing it to contract even more....a major conclusion is that a Hot Big Bang must have occurred; densities and temperatures must have risen at least to high enough energies that quantum fields were significant, at something like the GUT (Grand Unified Theory) energy. The universe must have reached those extreme temperatures and energies at which classical theory breaks down.”  (emphasis in original).

Ellis is saying that even though we can't observe the universe at that time when it was so small  and temperatures were so high that quantum properties would have been significant, we can infer that this was the case theoretically,  that is to say that there was a “Hot Big Bang” at  the beginning of the universe with extremely high temperatures (energies)and an extremely small volume.

Thus, given the contracting size of the universe as one goes back to the origin, there will be a time such that quantum effects must come into play.  However, there are some basic limitations to using quantum mechanics as a theory for the origin of the universe.  As Ellis points out:

“The attempt to develop a fully adequate quantum gravity approach to cosmology is of course hampered by the lack of a fully adequate theory of quantum gravity, as well as by the problems at the foundation of quantum theory (the measurement problem, collapse of the wave function, etc.)”

(Added later:  The Hawking-Penrose Theorems shows that a class of solutions to the General Relativity equations have a singularity in the solution.   Also, the Borde-Guth-Vilenkin Theorem shows that under conditions of universe average expansion,  there is a beginning point.    Since all such solutions are non-applicable at the singularity because quantum gravity enters the picture, the relevance of such theorems is perhaps questionable.)

See "Philosophic Issues in Cosmology 3: Mathematical Metaphysics--Quantum Mechanical Theories in Cosmology, for the ways physicists apply quantum mechanics to deal with theories of origin (or non-origin) of the universe.

Philosophic Issues in Cosmology--I. Introduction*

"The Ancient of Days", William Blake

 "The heavens declare the glory of God; and the firmament sheweth his handywork." Psalm 19A (KJV).

"The laws of nature themselves tells us that not only can the universe have popped into existence like a proton and have required nothing in terms of energy but also that it is possible that nothing caused the big bang," Professor Steven Hawking (Discovery Channel broadcast).

"But contrary to what Hawking claims, physical laws can never provide a complete explanation of the universe. Laws themselves do not create anything, they are merely a description of what happens under certain conditions."  Professor John Lennox (Mathematics and Philosophy of Science, Oxford University). 

 "I think that only an idiot can be an atheist!  We must admit that there exists and incomprehensible power or force with limitless foresight and knowledge that started the whole universe going in the first place." Professor Christian Anfinsen (Nobel Prize for Chemistry), quoted in Cosmos, Bios and Theos.

There has been much heat, and only some light after the publication of Hawking's and Mlodinow's The Grand Design, a work that claimed the universe started from nothing because of gravity.   I'm not going to recapitulate the excellent rebuttals of the Hawking/Mlodinow thesis (including a fine one by Stacy Trasancos) , but rather expand on the proposition given in the quote by Professor Lennox above.    What can science tell us about Creation, and what can it not?

Let's first inquire what science is about.   Fr. Stanley Jaki maintains in "The Limits of a Limitless Science" that science requires quantitative, empirical verification (or rejection) of predictions based on theory.   Although this restricts true science to the so-called "hard" discipline (physics in particular, chemistry and other sciences insofar as they are quantitative), I concur.   This quantitative verification requirement then puts  assertions that cannot be empirically verified (or falsified) into the realm of metaphysics--thus M-theory, most interpretations of quantum mechanics and many assertions about creation should be judged as propositions in philosophy/metaphysics.

This condition applies especially to cosmology--the scientific discipline that deals with our Universe as an entity.  l'll expand on this, taking material from an article previously posted on the Magis Facebook site,*  which in turn summarized a review article by George F.R. Ellis .

What are the conditions that require cosmology to have a philosophic base?
  Intrinsic limitations on scientific cosmology studies:

• We can't step outside the universe or duplicate it as an experimental object;
• We explore the universe by electromagnetic radiation (from radio to gamma rays),  which limits the distance out and, correspondingly, the past time for which measurements can be made.  This limitation is of two types.  
• The first is a time horizon due to the coupling of matter and radiation at times before the universe was about 380,000 years old, giving an opaque barrier at distances/times corresponding to less than 380,000 years from the beginning.   This means that there is a time horizon--we cannot see further back in time than 380,000 years after the origin. 
• The second limitation is a distance horizon—if the universe expansion is uniform, such that the further a point is from us (and, correspondingly, the further back in time), the faster it is moving—then there will be a distance d, such a star at that distance d will be moving away from us at the speed of light, or faster.   This means that we cannot communicate at distances greater than d, since communication can only take place at the speed of light.

An important consequence of the time horizon is that we have to infer what happened before the 380,000 years from the properties of the universe we determine after that time.  So theories about singularities, quantum origins, inflation can only be tested (if at all) by  predictions about  the state of our universe at times greater than or equal to 380,000 years from the origin.

An important consequence of the distant horizon has to do with causality.   Two events cannot influence each other (since interactions cannot travel faster than the speed of light)  if they are further apart than the distance horizon.  This is one of the reasons that “inflation” is invoked in the very early life of the universe. (See below.) The  early universe was larger than the horizon distance d (speed of light times age of the universe), so the question is how was a causal relation retained between different parts of the early universe to give the same temperatures and densities  (approximately) for parts of the universe that were not causally connected.

There is also a practical limitation, a physics horizon.   The energies in the early stages of the Big Bang are so high that there is no way that these could be duplicated in the laboratory, despite occasional claims of popular science writers to the contrary.

Thus, as George Ellis emphasizes “Testable Physics cannot explain the initial state and hence  the specific nature of the universe.” (Issues in the Philosophy of Cosmology)   Accordingly, cosmology rests on philosophy, on metaphysical assumptions.    Two of the most important of these assumptions are, according to Ellis:

THESIS A1: The universe itself cannot be subjected to physical experimentation. We cannot re-run the universe with the same or altered conditions to see what would happen if they were different , so we cannot carry out scientific experiments on the universe itself.

THESIS A2: The universe cannot be observationally compared with other universes.  We cannot compare the universe with any similar object, nor can we test our hypotheses about it by observations determining statistical properties of a known class of physically existing universes.   George Ellis, Issues in the Philosophy of Cosmology

We'll explore these issues in greater detail in further posts here.

*This will be the first of seven posts, taken in part from previous posts on the Magis Facebook site.