Over the last month I’ve acquired 3 books that are not entirely unrelated. Not surprisingly, they all deal with topics I’ve discussed before.
In order of acquisition they are: Physics and Philosophy by Werner Heisenberg; The Book of Universes by John D. Barrow; and MATHS 1001 by Richard Elwes. Of all these, Heisenberg’s book is probably the least accessible, even though it’s written more for a lay-audience than an academic one.
Elwes’ book is subtitled Absolutely everything you need to know about mathematics in 1001 bite-sized explanations. Under the subtitle is a mini-bite-sized blurb presented as an un-credited quote: ‘More helpful than an encyclopaedia, much easier than a textbook’.
Both of these claims seem unrealistic, yet the blurb is probably closer to the end result than the subtitle. I had this book whilst I spent a recent 4 day sojourn in hospital and it ensured that I never got bored.
But Barrow’s book is the most compelling, not least because he’s not just an observer but a participant in the story. Barrow covers the entire Western history of ‘cosmology’ from Stonehenge to String Theories. This is a book that really does attempt to tell you everything you wanted to know about theories of the universe(s). And Barrow’s book is certainly worth writing a post about, because he revealed things to me that I hadn’t known or considered before.
On the back fly cover, Barrow’s credentials are impressive: ‘Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, Fellow of Clare Hall, Cambridge, a Fellow of the Royal Society, and current Gresham Professor of Geometry at Gresham College, London.’ As an understatement, the citation continues: ‘His principal area of scientific research is cosmology…’. It’s rare to find someone, so highly respected in an esoteric field, who can write so eloquently and incisively for a lay audience. Paul Davies comes to mind, as does Roger Penrose, both of whom get mentioned in the pages.
Not surprisingly, even though Barrow’s narrative goes from Aristotle to Ptolemy to Copernicus then Galileo, Kepler and Newton, it resides mostly in the 20th Century, specifically post Einstein’s theories of relativity. Einstein’s field equations have really dictated all theoretical explorations into cosmology from their inception to the present day, and Barrow continually reminds us of this, despite all the empirical data that has driven our best understanding of the universe to date, like Hubble’s constant and the microwave background radiation.
One of the revelations I found in this text, is that Alan Guth’s inflationary hypothesis virtually guarantees that there is a multiverse. Inflation is like a bubble and beyond the bubble, which must always lie beyond the horizon of our expanding universe, are all the anomalies and inconsistencies that we expect to find from a Big Bang universe. The hypothesis contains within it the possibility that there are numerous other inflationary bubbles, many of which could have occurred prior to ours. Barrow also points out that, if there are an infinite number of universes, than any event with probability greater than 0 could occur an infinite number of times. Only mathematicians and cosmologists truly understand just how big infinity is and what its consequences are. Elwes’ book (MATHS 1001) also brings this point home, albeit in a different way. Barrow’s point is that if there are an infinite number of universes then there are an infinite number of you(s) doing exactly what you are doing now as well as an infinite number living infinitely different lives. The fact that they will never encounter each other means that they can exist without mutual awareness except as philosophical speculations like I’m doing now.
For most people the thought of an infinite number of themselves living infinitely variable lives is enough to turn them off the infinite multiverse hypothesis. It should also make one reconsider the idea of an infinite afterlife.
The other philosophical concept that Barrow discusses at length is the anthropic principle and how it is virtually unavoidable in the face of our existence. Another of his relevations (to me) was that we don’t live in one of the most ‘probable’ universes. He demonstrates that if we were to produce a bell curve of probable universes that our particular universe exists in the ‘tail’ and not at the peak as one might expect.
As he says: “Universes that don’t produce the possibility of ‘observers’ – and they do not need to be like ourselves – don’t really count when it comes to comparing the theory with the evidence.”
He then goes on to say: “This is most sobering. We are not used to the existence of cosmologists being a significant factor in the evaluation of cosmological theories.”
There is a link between this idea and quantum mechanics, which I’ll return to later. It was explored specifically by John Wheeler and discussed at length by Paul Davies in his book, The Goldilocks Enigma. People are often dismissive about the idea of why there is something rather than nothing. Recently, Stephen Law, in a debate with Peter Atkins, said that this was the wrong question without elaborating on why it was or what the right question might be. The point is that without conscious entities there may as well be nothing, because only conscious entities, like us, give meaning to the universe at all. To dismiss the question is to say that the universe not only has no meaning but should have no meaning. It’s not surprising (to me) that the people who insist our existence has no meaning also insist that we have no free will. I challenge both premises (or conclusions, depending how they’re framed).
Slightly off track, but only slightly; Barrow immediately follows this relevation with another of equal importance. Life in a universe requires both lots of time and lots of space, so we should not be so surprised that we live in such a vast expanse of space bookended by equally vast amounts of time. It is because life requires enormous complexity that it also requires enormous time to create it.
Again, to quote Barrow: “This is why we should not be surprised to find that our universe is so old. It takes lots of time to produce the chemical building blocks needed for any type of complexity. And because the universe is expanding, if it is old, it must be big – billions of light years in extent.”
Stephen Hawking recently created a minor furor when he claimed the entire universe could have arisen from nothing. People who should know better, or should simply read more, were derisive of the statement, believing he was giving fundamentalists ready-made ammunition by kicking an own goal. Back in the 1980s, Paul Davies in his book, God and the New Physics (covers much the same material as Dawkins’ The God Delusion, only in more depth) quotes Alan Guth that “the Universe is the ultimate free lunch”. Barrow also points out that gravity in the way of potential energy (therefore negative energy) can exactly balance all the positive energy of mass and radiation (through E=mc2) so that the energy balance for the entire universe can be zero.
Heisenberg’s uncertainty principle allows that matter (therefore energy) can and is produced all the time (via ‘quantum fluctuations’) albeit for very short periods of time. The shorter the time, the higher the energy, via the relationship of Planck’s constant, h. So a quantum mechanism for producing something from nothing does exist. That it can happen on a cosmological scale is not so improbable if all the principle forces of nature: gravitation, electromagnetic, electroweak and strong nuclear; can all meet as equal magnitude in the crucible we call the Big Bang. In his discussion on ‘grand unification’ Barrow leaves gravity out of it. I’ve glossed over this for the sake of brevity, but Barrow discusses it in detail. He also gives a rational explanation for the asymmetry between matter and anti-matter that allows anything to exist at all.
Another revelation I found in Barrow’s book was his discussion of string theories, now collectively called M theory, and the significance of Calib-Yau spaces or manifolds, of which there are over 10500 possibilities (remember 1 billion is only 109). Significantly, all these predict that gravity can be expressed by Einstein’s field equations. So Einstein still dominates the landscape, though what he would make of this development is anyone’s guess.
This means that our quest for a ‘Theory of Everything’ has led to a multitude of universes of which ours is one in 10500. But Barrow goes further when he explains “There are an infinite number of possible universes. The number is too large to be explored systematically by any computer.”
But Barrow’s best revelation is left to the next to last page when he claims that he and Douglas Shaw have recently postulated that the cosmological constant (which ‘adds an additional equation to those first found by Einstein’) is given by the relationship (tp/tu)2 where tp is Planck’s fundamental time, 10-43 sec, and tu is the current age of the universe, 4.3x1017 sec. tp is the smallest quantity of time predicted by quantum mechanics, so is effectively the basic unit of time for the whole universe. By postulating the cosmological constant as a squared ratio dependent on the age of the universe it gives a rational reason, as opposed to a mystical one, why it is the value we observe today of 0.5x10-121. What’s more, their postulate makes a prediction that the curvature of the universe is -0.0056. Current observations give between -0.0133 and +0.0084, but more accurate maps of the microwave background radiation should ‘be able to confirm or refute this very precise prediction’.
There is an intriguing connection between the anthropic principle and quantum mechanics. The Copenhagen interpretation, led by Bohr and given support by Heisenberg, attempts to bridge the gap between the classical world and the quantum world, by stating that something becomes manifest only after we’ve made a ‘measurement’. I think Bohr took this literally and John Wheeler, who was a loyal disciple of Bohr’s, took it even further when he extrapolated it to the cosmos. Paul Davies explores John Wheeler’s thesis in The Goldilocks Enigma, whereby Wheeler proposes a reverse causal relationship, a cosmological quantum loop in effect, between our observation of the universe and its existence. Most people find this too fantastical to entertain, yet it ties quantum mechanics to the anthropic principle in a fundamental way.
Elwes’ book also discusses quantum mechanics and explicates better than most I’ve read, when he expounds that the wave function (given by Schrodinger’s equation) ‘is no longer a valid description of the state of the particle. It is difficult to avoid the conclusion that whenever someone (or perhaps something) takes a measurement, the quantum system mysteriously jumps from being smoothly spread out, to crystallizing at a specific position.’ (italics in the original)
One can’t help but compare Heisenberg’s book (Physics and Philosophy) with Schrodinger’s (What is Life?), which I reviewed in November 2009. Both men made fundamental contributions to quantum theory, for which they were both awarded Nobel prizes, yet they maintained philosophical differences over its ramifications. Schrodinger’s book is a far better read, not least because it’s more accessible. Both impress upon the reader the significance of mathematics in fathoming the universe’s secrets. Schrodinger appealed to Platonism whereas, to my surprise, Heisenberg appealed to the Pythagoreans, who influenced Plato’s Academy and its curriculum of arithmetic, geometry, astronomy and music – Pythagoras’s quadrivium. In particular, Heisenberg quotes Russell on Pythagoras: “I don’t know of any other man who has been as influential as he was in the sphere of thought.”
Quantum phenomena suggests to me that everything is connected. Why do radioactive half lives follow a totally predictable rule statistically but individually are not predictable at all? It’s like the decay exists at a holistic level rather than a unit level. Planck’s constant gives an epistemological limit to our ability to predict or know. At the other end of the scale, the universe exists for us at a time when we can make sense of it. Barrow, along with Douglas Shaw, entails Planck’s constant as a fundamental unit of time in an equation that suggests we understand it only because we are here at this specific time in its history. There is no other explanation, and maybe there is no other explanation required.
Addendum 1: Scientific American (through Paul J. Steinhardt) have a for-and-against discussion on the merits of Alan Guth's 30 year old inflationary theory, and include a reference to Roger Penrose's ideas that I discussed in a post last January.
Addendum 2: Yes, I've changed the title (Sep 2017).