29 September 2012

Happy with the Big Bang? Me neither.

Religion is not fond of science, which has reduced it to some niche of human thought where it sits anxiously awaiting the next blow. There is one exception: the Big Bang. Ah, the Big Bang, how beloved it is! An infinitely dense, infinitely hot singularity from which the whole universe has evolved, and where the equations of physics break down: who could better describe Divine Intervention? At last, science agrees with God creating the universe, be it 14 billion instead of 6000 years ago. (Here one example among many. Don't forget to include the logical inconsistencies carelessly left behind by the Creator, and the popular misconceptions about the Big Bang.) God has even provided a befitting icon:

his humble servant abbé Lemaître, a catholic priest and scientist, among the founding fathers of the Big Bang. Clearly, Intelligent Design is at work here. Now, what I dislike about the idea of a Big Bang is precisely that it's so pre-copernican. The human species —an insignificant and short-lived self-reproducing carbon structure having evolved in some remote speck of one of the billions of galaxies, bound to disappear with the solar system— would miraculously live in the (unique) universe having started with the most singular event imaginable? Come on. Were is the modesty learnt since Copernicus and Darwin? The Big Bang, as it is generally conceived today, cannot be the whole story. There must be a wider setting. Recently, I found comfort in this pocket size 31 pages booklet issued by Scientific American.

Yes, there are alternatives to the Unique-Big-Bang-Singularity, and questions like What happened before the Big Bang do make sense. I was happy to read that in String Theory

What we call the big bang may have been 
the collision of our universe with another one

(p.22, referring to The myth of the Beginning of Time, May 2004). In another theory, Loop Quantum Gravity, the Big Bang may actually have been triggered by a previous universe collapsing. LQG excludes big-bang-like singularities, and provides a natural (not ad hoc) explanation for the early period of acceleration known as cosmic inflation. I favour it because it is a discrete theory of spacetime. In this kind of approach, space and time cannot be divided indefinitely; at some point, you attain an indivisible atom of space or time, the finest grain in a grainy universe. (Here or here a synopsis.) Continuity is an illusion, much like continuity in a movie is an illusion.

If space and time are continuous, i.e. indefinitely divisible, you cannot understand how an object in rest ever gets moving. The Greek philosopher Zeno (the marble one above) had already shown some logical difficulties arising from the assumption that space and time can be divided indefinitely. Don't think you can easily refute his paradoxes. If you have an easy answer, you have probably answered a different question, not Zeno's. (And don't think to impress those Greeks by throwing in series or integrals. Archimedes invented this stuff, yet went to great lengths not to fall into Zeno's traps.) Galileo thought about it, and postulated there is no such thing as "rest", only movement so small as to give the impression of rest. Newton also did. In his system, (unaccelerated) motion is the natural state. He was much aware of the discrete vs. continuous problem. When using discrete models (for instance, a 'curve' consisting of separate points) he begs the reader to translate them for himself into the 'proper' geometrical language. (Principia Mathematica, Cambridge University Press 1934, p.38, here or here.) Yes, continuous models with integrals and differential equations are easier to work with than discrete ones with sums and difference equations. Most of the time, the results are equivalent, one being infinitely close to the other. Yet, for problems at the most fundamental level, they may not be. In mathematics, Dirac's delta function (introduced for the needs of quantum mechanics) is a famous example. As a continuous object, its intended definition immediately leads to contradictions, which in mathematics means it does not exist. (Physicists don't care.) Make it discrete, and it becomes simple and consistent. I was happy to read in Bojowald's Follow the Bouncing Universe (p.28 in my booklet, more here and here —also here) that the same happens in Loop Quantum Gravity, whose difference equations capture fundamental features lost in differential equations. Support for an old conviction of mine: if difference equations and differential equations disagree, the former are right.