Paul P. Mealing

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Friday, 20 November 2009

Science, Philosophy, Religion

In a not-so-recent discussion I had on Stephen Law’s blog, I had trouble convincing some of the participants that, not only is there a difference between science and philosophy, but the distinction is an important one.

In a comment on my last post, Timmo made a reference to Richard Feynman’s book, The Character of Physical Law, which got me re-reading it. You may wonder how these 2 issues are related. Well, in my last post I discussed some of Erwin Schrodinger’s philosophy, and the aforementioned Feynman’s book is probably his most philosophical. Together, they highlight the fact that Feynman’s philosophical musings probably couldn’t be more different than Schrodinger’s, yet I doubt that they would disagree on the science. The same is true of contemporary physicists. For example, Roger Penrose and Stephen Hawking, even though they have collaborated scientifically and even won a joint prize in physics, are philosophically miles apart on the nature of mind. In his book, Shadows of the Mind, Penrose actually invited Hawking to provide a counter-philosophical point of view, which, of course, he did. Likewise, Albert Einstein and Kurt Godel were very good friends, when they were both fellows at the Princeton Institute for Advanced Study, but held philosophically divergent views: Godel was a mathematical Platonist and Einstein was not; yet I’m sure they didn’t disagree on the mathematics of each other’s theories.

As a general rule, philosophy deals with questions, the answers for which are not certain, and in many cases, may never be; whereas science deals with questions, where the answers will decide the ultimate truth, and the limits of truth, for a particular theory. Bertrand Russell made the observation that, in philosophy, there may be no right or wrong answers, but the questions, when addressed in the right spirit, are the bulwark against dogmatism and the conservative resistance we find to genuine questing for knowledge. A corollary to this approach is to beware of those who claim they have answers of certainty to questions of profundity.

You may wonder where religion fits into all this. Well, religion is philosophy taken to the metaphysical extreme, but is often confounded by politics to the extent that some people don’t delineate one from the other. In fact, religion is often confounded with ideology, because, for many people, religion and ideology are unassailable truths. But truth is arguably the most elusive concept in the human world, and in this context is an abuse.

I have 2 ways of defining science. Firstly, a general definition is that science is the study of the natural world in all its manifestations. So this leaves out many aspects of knowledge that are human-based, or what is generically called the humanities: all the arts, and topics like ethics and justice. Arguably, psychology crosses the boundary, and I discussed this briefly in another post, Is psychology a science? (Nov. 08). But the topic of ‘mind’, that was raised by Schrodinger, certainly falls into a category where science, psychology and philosophy all merge, but I don’t want to get too far off the track, so I will return to ‘mind’ later. Interestingly, philosophy is generally considered a humanities subject.

The other definition, which is effectively a working definition, is that science is a dialectic between theory and experimentation or observation. Questions that can’t be answered by experimental analysis generally remain philosophical until they can. An example is AI (artificial intelligence). Will AI ever be sentient? Providing we can agree on a definition of sentience, this question will probably one day be resolved. Until that day, it will remain a philosophical question. But there are other philosophical questions that may never be decided by science. An example is the so-called multiverse (multiple universes) theory. If they exist, we may never find any evidence of them, though one should be careful of never saying never. Metaphysical questions like: does the universe have a purpose? (See my post on this topic, Oct. 07) is an example of a subtly different nature. This is a question that science can’t answer, although almost anyone who gives an answer, one way or the other, uses their scientific knowledge to support it. And this is why the distinction is important. Using science to support a philosophical point of view doesn’t turn philosophy into science, though many people, when lost in their own rhetoric, may infer that it does, whether intentionally or not.

On the subject of the dialectic in science, Feynman, in his book, The Character of Physical Law, gives excellent examples, whilst discussing the evolution of the Universal Theory of Gravitation: specifically, how astronomical observations forced changes to theory and then confirmed theory. In other words, without experimentation and observation, we would have just continued to bark up the wrong tree.

His opening chapter on The Law of Gravitation, an example of Physical Law provides one of the best expositions of this dialectic, including descriptions of the experiments that Galileo performed to show gravity’s universality on Earth. And how Tycho Brahe’s unprecedented accuracy in tracking planetary motion gave Johannes Kepler the key to his 3 laws, which ultimately led Newton to the Universal Theory of Gravity we have today. Yes, it’s been modified by Einstein, as Feynman explains, but Newton was able to marry Kepler’s laws to his calculus that not only clinched the theory but eventually led to predictions of another planet perturbing Neptune’s orbit. The ultimate test of a theory is when it predicts hitherto unobserved events.

String Theory is an example of a theory without the dialectic, so we have innumerable variants of which none can be validated by reality. String Theory is not exactly philosophy either – it’s a mathematical adventure. I would describe it as a mathematical model looking for an experiment to make it a scientifically valid theory. I’m not an expert on the subject, but I provide a review of Peter Woit’s book, Not Even Wrong, in a post I wrote earlier this year (Nature’s Layers of Reality, May 09).

And this leads to the significance of mathematics. No one who discusses physics and philosophy can avoid discussing the role of mathematics, and this includes Feynman. In the edition of Feynman’s book that I have (1992), Paul Davies has written an Introduction. He not only acknowledges Feynman’s influence, unorthodoxy and brilliance as a communicator, but relates a dialogue he once had with him on the philosophy of mathematics.

“…Feynman had an abiding suspicion of philosophers. I once had occasion to tackle him about the nature of mathematics… whether abstract mathematical laws could be considered to enjoy an independent Platonic existence. He gave a spirited and skilful description of why this indeed appears so but soon backed off when I pressed him to take a specific philosophical position. He was similarly wary when I attempted to draw him out on the subject of reductionism.”

Feynman devotes an entire chapter (lecture) to the topic, The Relation of Mathematics to Physics, describing it as a language with reasoning, and sees it as an intellectual construct based on axioms. He doesn’t address Godel’s Incompleteness Theorem, because it’s not strictly relevant to his topic: mathematics in physics. He refers to Newton’s calculus as an ‘invention’, whereas Platonists would call it a ‘discovery’.

But more relevant to this discussion is that he describes 3 different ways of looking at the Universal Theory of Gravity, even though they are all mathematically equivalent. One is ‘action at a distance’ or force mediated by the inverse square law; two is by a ‘potential field’; and three is by the ‘least action’ principle, which is Feynman’s personal favourite, and I discuss it in 2 other post ( Nature’s Layers of Reality, May 09 and The Laws of Nature, Mar.08). The point is that these are philosophical interpretations that would determine how a scientist may investigate a phenomenon further. Feynman prefers the ‘least action’ principle because it applies to the refraction of light as well, and therefore suggests a universal principle.

So there is philosophy within science as well as philosophy outside of science, and, once again, I think the distinction is important. Philosophy within science is more likely to be eventually resolved because it generally leads to new avenues of investigation. Feynman says of this: “…every theoretical physicist who is any good knows six or seven different theoretical representations of exactly the same physics.” By ‘exactly the same physics’ he means the mathematics is equivalent (this will become more evident when I discuss quantum mechanics). In other words, it contributes to the dialectic between theory and empirical evidence. Philosophy outside of science is generally removed from the dialectic, which is why it remains philosophy and not science. Philosophy within science remains philosophy until it can evolve into theory. In quantum mechanics (as I discuss below) theory is effectively deadlocked and has been for many decades. At least, that is the impression I get from what I’ve read on the subject by people who know it.

As an aside, the abovementioned quote was once construed by a philosophical writer (Michael Frayn in The Human Touch) as evidence that theoretical physicists effectively make things up because "nature doesn’t have six or seven different ways to represent itself, or even one." But it’s obvious to me that, even though Feynman referred to theories as ‘guesses’ in his usual cavalier manner, he didn’t doubt the validity of nature’s laws. In the cases he’s referring to, the mathematics is solid, but the philosophical interpretations are not (I elaborate on this below).

Elsewhere in the book, Feynman alludes to a view that we will eventually understand all the laws of physics. This is a philosophical position and one I’ve argued against in the past. My reason is history. We never know what we are going to discover and every resolution of a mystery in science has only revealed more mysteries. I find it hard to imagine that this will ever stop, but I also admit that I don’t want it to stop. Feynman, on the other hand, argues that we will eventually run out of finding new laws: either, because of the limit of our ability to reveal them or the limit of their actual existence. He believes that the 20th Century was a golden age of discovery in physics, and no one can deny that. But each age has uncovered new intellectual territory and nature appears far from revealing all its secrets.

On a related note, I quote Feynman in my post, Nature’s Layers of Reality, (cited by Peter Woit, Not Even Wrong) where he is scathing about String Theory. I’m not in a position to judge String Theory, but I don’t think it’s the scientific Holy Grail as some commentators do, and it does reveal how much we still don’t know. String Theory is an example of where people hope to find a ‘Theory of Everything’. It’s one of the reasons I’m a sceptic, but I could be proven wrong.

In previous posts (specifically Quantum Mechanical Philosophy, Jul.09) I describe how the philosophical implications of quantum mechanics are not resolved, yet as a meta-theory, it is arguably the most empirically successful ever. Paul Davies makes exactly the same point in The Goldilocks Enigma. Quantum mechanics demonstrates, more strikingly than any other endeavour, the fundamental differences that lie between science and philosophy. Philosophically, there is the Copenhagen interpretation (Neils Bohr), the Many Worlds interpretation (Hugh Everitt) and the Hidden Variables interpretation (David Bohm). And there are variations amongst these, which I discuss to some extent in the aforementioned post. These are not just different theories; they all have philosophical implications on how we perceive reality. Epistemologically, it can’t get more serious than that.

The Copenhagen interpretation is generally considered to be the conventional interpretation, but as Feynman says in his book: “…I think I can safely say that nobody understands quantum mechanics”. What he means is that no one can explain quantum phenomena in plain language without creating cognitive or logical contradictions. Schrodinger created a thought experiment, popularly known as Schrodinger’s Cat, that encapsulates this conundrum perfectly, where, theoretically, a cat can be dead and alive at the same time. Ironically, Schrodinger also created (he would say discovered) the mathematical equations that have made quantum mechanics the most successful theory ever.

Mathematically, there are no contradictions or conundrums – Schrodinger’s wave mechanical equations and their derivatives, especially the famous Dirac equation, have not only confirmed existing observed phenomena but predicted new ones. Dirac’s equation not only prescribed quantum electron ‘spin’ as an inherent feature of the equation, but predicted the electron’s anti-particle (the positron) and therefore anti-matter. As Feynman says, the best theories, by far, are those where we get more out than what we've put in. More relevant to this discussion, quantum mechanics demonstrates explicitly that science deals in answers and philosophy deals in questions, and sometimes one is not resolved by the other as we might expect.

And now I must come to ‘mind’ because it’s the one topic that really does cross boundaries (including religion). Feynman doesn’t discuss it, because it’s not relevant to his lectures on physics, but Schrodinger did (see previous post), and so does Penrose, who has written 3 books on the subject that I have read. I haven’t read Daniel Dennett’s Consciousness Explained but I’ve read John Searle’s Mind, and it’s the most accessible I’ve found on the subject thus far. I’ve discussed this in previous posts (Subjectivity: The Mind’s I, June 09) and of course in my last post on Schrodinger. I think Schrodinger makes a couple of salient points, which I’ve alluded to previously. In particular, that there is a subjective aspect to consciousness that makes it ontological as well as epistemological. Searle makes this point as well, in his aforementioned book, as does the Dalai Lama in his book, The Universe in a Single Atom.

Schrodinger, in particular, explains how phenomena like light and sound can be measured and analysed by instruments, and we can even analyse how they are transcribed into nerve impulses in our bodies, but all the instruments and analysis in the world can’t describe or explain the actual experience we have of light and sound. This is a contentious point, but people forget that this is what consciousness is, first and foremost: an experience. And if each and every one of us didn’t have this experience, science would no doubt tell us that it doesn’t exist, in the same way that science tells us that free will doesn’t exist. It is still the greatest enigma in the universe, and is likely to remain that way, possibly for ever.

And this leads to Schrodinger’s second salient point: without ‘mind’ the universe would be meaningless. In an earlier post (The Existential God, Sep.09) I reviewed Don Cupitt’s book, Above Us Only Sky, who goes further and says that without language, there would be no meaning and no ‘truth’. I won’t revisit Cupitt, but one should not confuse meaning with reality, nor ontology with epistemology. To quote Einstein: “The most incomprehensible thing about the universe is that it’s comprehensible.” There are various ways one can interpret that statement but mine is: The greatest mystery of the universe is that it created the ability to understand itself. Paul Davies takes this head-on in The Goldilocks Enigma and elaborates on a philosophical premise proposed by John Wheeler. Wheeler effectively argued that the universe exists as the result of a cosmological-scale quantum loop. Because we observe it, it exists. I’m not going to argue one way or the other with Wheeler, but I agree with Schrodinger that without ‘mind’ there is no point to the universe’s existence, and Davies makes a similar point. At the end of The Goldilocks Enigma he summarises all the philosophical viewpoints that are in currency (including ID, the multiverse and the ‘absurd universe’, probably better known as the accidental universe) ending with Wheeler’s, which he calls The self-explaining universe. To quote: “I have suggested that only self-consistent loops capable of understanding themselves can create themselves, so that only universes with (at least the potential for) life and mind really exist.”

In a way I’ve returned to a point I alluded to much earlier: does the universe have a purpose? This is a philosophical question, as I said, but it leads into religion and religious belief. Paul Davies obviously believes it does, and says so, but he’s quick to point out that this does not axiomatically lead to a belief in God. Feynman, whom I’m almost certain was an atheist, makes only one reference to God in his book, when he discusses the hierarchical nature of nature. He explains how the laws of physics can have consequences at a higher level that are unforeseeable yet totally necessary for the universe’s existence as we know it. The example he gives is Hoyle’s and Salpeter’s prediction concerning carbon 12, which arises from the unlikely combination of 3 helium atoms creating a specific new energy level that allows the rest of the elements in the periodic table to exist. Feynman doesn’t make anything metaphysical of this, but he makes the point that nature’s laws at one level have consequences at a higher level of existence that are not readily apparent.

He invokes God (metaphorically, as he’s quick to point out) as either the progenitor of the laws or the ultimate end result; at opposite ends of reality. In an uncharacteristically poetic moment, in another part of the book, he says: “Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.” He’s indirectly invoking the implication in the title of the Dalai Lama’s book on science and religion The Universe in a Single Atom. The laws of nature are the threads and the tapestry is the universe in all its complexity.

There are no objective religious truths, contrary to what fundamentalists tell us, but there are mathematical truths. And the more we learn about the universe, the more mathematics plays a role. Every book I’ve read on nature’s laws illustrates this fundamental premise. Feynman, Einstein and Hawking would suggest that the mathematics is human reason, but others, like Penrose, Schrodinger and Godel, would argue that mathematics is independent of human thought, albeit we only know it through human thought. Pythagoras and Plato might have argued that God exists in the mathematics and Schrodinger might have argued that God is the ultimate unity of mind (refer my last post). Like Feynman’s metaphorical attribution, they represent opposite ends of reality. At the end of the day, God becomes a metaphor and a projection for what we don’t know, whichever end of reality we posit that projection.

Religion is mind’s quest to find meaning in its own existence. If we were to accept that simple premise without the urge to create an edifice of mythology and political ideology around it, maybe we could all accept each other’s religion.

Sunday, 15 November 2009

Schrodinger’s philosophy (absolutely nothing to do with cats)

I mentioned in my last post, a recent acquisition: What is Life? by Erwin Schrodinger. This is a book that I’d heard about on more than a few occasions, so expectations were high, and I can honestly say it doesn’t disappoint. It says a lot that the copy I have is the eighteenth edition published in 2008, and it was originally published in 1944.

It started off as a series of lectures for the Dublin Institute for Advanced Studies at Trinity College, Dublin in February 1943. He then added an epilogue, On Determinism and Free Will. This segues into another essay (book really) called Mind and Matter which is another set of lectures delivered at Trinity College, Cambridge in 1956. The collection is bookended by a one-page Forward written by Roger Penrose in 1991, and Autobiographical Sketches, written as a virtual appendix by Schrodinger himself in November 1960.

Erwin Schrodinger is most famously known for the set of equations that bear his name, formulated in 1925/6 and for which he was awarded a Nobel Prize in 1933. They are the fundamental equations for quantum mechanics, arguably no less important than Einstein’s equations of relativity that I discussed in my previous post.

This collection is essentially a book on philosophy, that starts off by explaining the role of statistics in physics, then the role of quantum mechanics in evolutionary biology, then a philosophical discourse on mind that leads to a discussion on religion and finally epistemology. It’s a slim volume, a little over 150 pages long (leaving aside his autobiographical sketches). Yet I would recommend that all philosophers and students of philosophy should read it. To quote Paul Davies on the back cover:

“In these little books [Schrodinger] set down … most of the great conceptual issues that confront the scientist who would attempt to unravel the mysteries of life. This combined volume should be compulsory reading for all students…”

According to Penrose’s Forward, this book influenced J.B.S. Haldane and Francis Crick. Considering that it’s over 60 years old and was written before the discovery of DNA, it gives a remarkable insight into the role of mutations in evolutionary biology. Not only that, but Schrodinger explains the role of quantum mechanics in creating mutations. But he begins by explaining how virtually all of physics is statistical, giving examples ranging from Brownian motion, to the physics of magnetism, to radioactivity. His salient point is that, in each of these cases, no one can say when an individual element (atom) might change or react, but statistically they all follow strict mathematical rules. This is a mystery that struck me when I studied physics in high school, and here is a Nobel Prize winning physicist confirming what I thought then: it’s a facet of nature that defies our intuitive logic yet it’s been proven in virtually every arena of physics. We can’t predict the outcome of an individual element but we can predict the overall outcome with preternatural accuracy. He also explains the role of scale: the magnitude of numerical atoms or molecules that make up the smallest physical entities, which is what gives statistical power to many of nature’s dynamics.

Schrodinger then addresses the fundamentals that make life unique, including the fact that every cell contains the ‘code’, effectively the ‘blueprint’ that determines every facet of an organism like us. Remember, this is decades before the structure of DNA was discovered, yet Schrodinger explains how ‘isomers’ can create a code analogous to the way Morse code can be created by just dots and dashes, and this code determines how a life form functions, appears and grows.

His book is full of these little treasures – so obvious when he points them out – yet never really contemplated by most of us. One name that keeps appearing throughout this volume is Ludwig Boltzman, whom Schrodinger considered of no less significant to our knowledge of physics than Planck or Einstein. He explains the contribution that Boltzman made to thermodynamics, and entropy in particular, including the simple mathematical equation that encapsulates it. He also explains the role this has on the ‘arrow of time’. Few people appreciate that entropy determines the direction of time in physics, not relativity nor quantum mechanics. This was first pointed out to me by Penrose, in his book The Emperor’s New Mind. But Schrodinger covers it better still (only in the second part on Mind). He explains it by evoking statistical outcomes and the very simple analogy of shuffling a pack of cards. How many times would you need to shuffle a pack to get it in the right order. In effect this is entropy, and it’s like trying to reorganise the molecules of a broken egg to return it to its unbroken state.

On the subject of life and entropy, he addresses the fact that life alone seems to defy the second law of thermodynamics (actually, it doesn’t, otherwise we wouldn’t die). Nevertheless, life has a dynamism unlike non-organic molecular structures that defies our intuition. Schrodinger introduces the term, ‘negative entropy’, to explain how organisms increase the entropy of the environment; effectively the expense they impose for keeping themselves alive, whether they be primates like us, or bees, or trees in a forest.

In his short treatise on Determinism and Free Will, which he writes as an ‘Epilogue’ to the first set of lectures, he ventures, without apology, into the metaphysical, and acknowledges an influence by Aldous Huxley, specifically his The Perennial Philosophy. Early in this essay he says: “…I wish to emphasize that in my opinion , and contrary to the opinion upheld in some quarters, quantum indeterminancy plays no biological relevant role … except perhaps by enhancing their purely accidental character in such events as meiosis, natural and X-ray-induced mutation and so on…”

I find this a strange declaration, since he had just elaborated at length on the role of quantum mechanics in mutations, which are the causal factors in evolutionary biology, with natural selection being nature’s scythe so to speak. In the previous passage to the one quoted, Schrodinger emphasises that quantum mechanics is ‘statistico-deterministic’, which means that determinism is not completely eliminated by quantum phenomena as many people seem to believe. However, mutations are purely chance and, importantly, rare events, which Schrodinger explains in detail in the body of his lectures, so biological evolution is far from deterministic at its root cause.

It’s impossible in the space I’ve allotted myself here, to do justice to Schrodinger’s book, but whilst it’s full of gems from the opening pages, it’s towards the end that it becomes truly philosophical. Schrodinger tackles the problem of mind in a way that one rarely finds. For a start, he points out that we tend to ignore ‘the elephant in the room’, though, of course, he doesn’t use that phrase, whereby it’s only through mind that the universe has any meaning at all. And that, when we examine the universe - exactly in the way he has throughout the book - we effectively pretend that mind is not part of it. I’ve attempted to address this myself in a previous post on Subjectivity: The Mind's I (June 09). Schrodinger uses the term ‘objectivation’ which he’s obviously coined himself to highlight this point. He alludes to religion (specifically the Eastern religion of the Upanishads) by postulating that there is ‘one mind’ not many, without which the universe would not exist, not because it requires a God to create it, but because, there would be no reason for it to exist without mind. I may not be doing him justice here, so I would beg you read his words yourself, but that’s how I interpret him. I can actually see his point, and I’ve made similar arguments myself: without consciousness there is no point to the universe at all. I need to point out, by the way, that Schrodinger rejected orthodox religion early in his life, and he makes almost no reference to God, except, at one point, to acknowledge: "when God is experienced.. he must be missing in the space-time picture" just like our minds are.

He talks at length about 3 philosophers he considers significant: Plato, Kant and Einstein, all relating to epistemology. In regard to Plato, he gives easy-to-follow examples in both geometry and arithmetic to demonstrate “...true relations whose truth is not only unassailable, but is obviously there forever; the relations held and will hold irrespective of our inquiry into them. A mathematical truth is timeless, it does not come into being when we discover it.”

Then he proceeds to Kant, giving one of the best accounts I’ve read concerning Kant’s controversial views on space and time, which leads to the discussion on the ‘arrow of time’ (and Boltzman’s resolution that I referenced earlier). “He [Kant] would show plainly that space was necessarily infinite and believed firmly that it was in the nature of the human mind to endow it with the geometrical properties summarized by Euclid.”

This leads to Einstein who revealed that space and time are not independent as Kant thought, and is not Euclidean either. However, Schrodinger makes the following point: “Einstein has not – as you sometimes hear – given the lie to Kant’s deep thoughts on the idealization of space and time; he has, on the contrary, made a step towards its accomplishment.”

I’m not sure I agree with Schrodinger on this particular point. Space and time do exist outside the human mind – in fact, space-time is arguably the very fabric of the universe – which, on the surface, does put the lie to Kant’s interpretation as I’ve read it in his Critique of Pure Reason. Having said that, Schrodinger does argue that it is only mind that sees time as past, present and future, and that is an insight that is undeniable as it is obvious. It brings us back to the question: what meaning does the universe have without mind? Einstein showed that time is (relativistically) dependent on the observer, and to that extent, one could say relativity theory supports Kant’s contention of time being internal.

Lastly, Schrodinger touches on a point that is at once obvious, yet rarely, if ever, contemplated, which he calls: “The Mystery of the Sensual Qualities”. In particular, he discusses colour and sound, and he discusses both of them in depth, explaining that, whilst they are both frequency-dependent, the means in which we perceive them and they are propagated are entirely different. For example, colours of quite different frequencies can be mixed to produce a new colour of a frequency that is identical to a single colour of the same frequency and we can’t sense the difference. On the other hand, when sounds of different frequencies are mixed, as in music, we have no trouble in delineating them. But that’s not the main point he is making. The main point is that, whilst we can perform experiments with instruments to give ‘objective’ analysis of colours and sounds, we can’t objectively identify the sensing of them – that is entirely a ‘subjective’ affair. I’ve made this point myself in other posts. It’s why I argue that AI will never ‘sense’ colours and sounds like we do. In fact, it’s why I argue that AI will never have ‘mind’. Schrodinger argues this point better than any other author I’ve read. Of course, he makes no mention of AI, even though Turing had already set that ball rolling in Schrodinger’s own time.

In his autobiographical notes, Schrodinger explains how he learnt English (from an Aunt) even before he had learnt to write German. (He also mentions in passing that his mother’s Aunt had ‘six Angora cats’, which is the only reference to cats in the entire volume.) He was conscripted in the first World War, but spent World War 2 in Dublin; in fact, from 1939 through to 1956, for which he considered himself very fortunate. He called it “My Long Exile, but without the bitter association of the word, as it was a wonderful time.”

Schrodinger’s transcribed lectures are provocative, erudite and articulate. He makes you think deeply about topics and philosophical issues that are common place yet are fundamentally and inexplicably profound. It is one of the best philosophical books I’ve read and I’m surprised it’s not a prescribed text, though perhaps it is in some parts of the world. I know I will read it again.

Many people, in fact most, whether they be scientists, philosophers or theologians, will disagree with Schrodinger. But that’s not the point. The point is that he makes you think about issues you believe you have resolved when you almost certainly haven’t.

Sunday, 8 November 2009

Einstein’s Code and Kerr’s Solution

When I started this blog, over 2 years ago now, I never anticipated picking up ‘followers’ and now I feel the need to maintain some sort of standard. For those who do follow this blog, it is obvious that I don’t comment on a regular basis (although I do on other people’s blogs) but that I only write when something especially attracts my attention. It’s becoming increasingly a blog where I want to share rare intellectual discoveries rather than express my opinions, though I do that as well.

Two recent such discoveries, are Cracking the Einstein Code by Fulvio Melia and What is Life by Erwin Schrodinger. The second book is a classic that I’ve wanted to read for a long time, while the first was an unexpected discovery. This post will focus on Melia’s book, subtitled, Relativity and the Birth of Black Hole Physics, and Schrodinger’s tome will probably be a subject for a future post.

Melia’s book is largely concerned with a little-known aspect of Einstein’s General Theory of Relativity (yes, it deserves capitals): a Kiwi called Roy Kerr, in 1963, unlocked the code inherent in Einstein’s 6 field equations that gave a description of space-time for a rotating body, which is the normal reality for massive bodies in the universe, from planets like ours to entire galaxies.

Now I need to say at the start, that whilst I write on esoteric topics, my knowledge is limited in the extreme, unlike the authors whom I read. Anyone following recent comments on this blog will notice that a generous intellect, called Timmo, has made critical comments on 2 of my former posts (Quantum Tunneling, Oct. 09 and Nature's Layers of Reality, May 09). I wish to acknowledge Timmo’s contribution and I welcome someone who really does know what they’re talking about when it comes to physics.

What I especially like about Melia’s account is that he acknowledges all the other people who contributed to the success of relativity theory (specifically, the General Theory), most of whom I’d never heard of. Like many people, I thought that Einstein’s theory had come effectively fully-fledged from his own mind. I wasn’t aware that there was a history of significant contributions from its conception right up to 1963, almost a decade after Einstein’s death.

Firstly, there is David Hilbert (who is extraordinarily famous in mathematics) and who had a correspondence with Einstein and helped him to develop his field equations. In fact, according to Melia, Hilbert actually published the equations on 20 November 1915, 5 days before Einstein, which led to an argument over priority. However, Einstein wrote a letter of reconciliation on 20 December in the same year, which Melia quotes from.

But even Hilbert “could not overcome a serious problem – how to demonstrate that energy is conserved in Einstein’s theory.” From a conceptual point of view, this had always troubled me about relativity, and it wasn’t until I read Feynman’s account in Six Not-So-Easy Pieces, that I believe I understood it. What I didn’t know, before reading Melia’s account, is that a woman, Emmy Noether, who worked with Hilbert at Gottingen University, was the one who resolved this issue by introducing symmetries in connection with conservation laws, specifically conservation of momentum and energy. To paraphrase Melia, Newton’s second law relates changes in momentum to a force; Noether’s Theorem shows how a change in our frame of reference and Newton’s second law are effectively the same thing. (Different frames of reference refer to different observers moving about at different velocities – with no absolute frame of reference, conservation of energy and momentum becomes an issue.)

Einstein’s General Theory of Relativity is premised on the ‘Principle of Equivalence’. Standing in a stationary elevator car in earth’s gravity is equivalent to being accelerated in an elevator car ‘vertically’ in gravity-free space (vertical, in this context, means being pulled from above our heads so our feet are pressed against the floor of the car). Gravity is felt as a force, by us on earth, only because we are stopped from falling. In free fall, no one feels a force being exerted on them, whether they are in a space ship orbiting the earth or jumping off a cliff. This is the key conceptual point to grasp about Einstein’s theory of gravity (which is the General Theory of Relativity). In free fall there is no force, even though this is counter-intuitive when you are earth-bound, because we rarely experience free-fall for any meaningful period of time without dying.

I don’t claim to understand Noether’s Theorem, but I understand its significance. Noether died relatively young in America at age 53, 2 years after escaping Nazi Germany, and Einstein wrote a moving tribute to her in the New York Times (1935). Melia quotes physicists, Leon M. Lederman and Christopher T. Hill, from their book, Symmetry and the Beautiful Universe: “..certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics…” And I had never even heard of her.

Likewise, I’d never heard of Roy Kerr before reading Melia’s book, yet his contribution to relativistic physics is arguably no less significant. According to Melia, Kerr’s Theorem is the fundamental methodology used to investigate black holes (theoretically) to this day.

Kerr completed his undergraduate course at Canterbury University in Christchurch NZ (enrolling at the age of 16 and going straight into 3rd year mathematics). Canterbury is also where Ernest Rutherford started his academic career (Rutherford uncovered the secrets of the atom: that it was mostly empty space, amongst other things). Kerr then went on to Cambridge to study pure mathematics. His doctoral thesis supervisor was Professor Philip Hall, “one of the century’s greatest mathematicians”, according to Melia, and “Britain’s greatest algebraist”. Hall realised that Kerr’s abilities were singularly impressive but his knowledge incomplete. He set him 3 problems in ‘group theory’, including the ‘Axiom of Choice’, which is a fundamental component of ‘set theory’. Kerr dealt with this and the second problem with relative ease, but the third problem, called the ‘Burnside Conjecture’ was beyond him. Following his admission of defeat, Hall apparently lectured him on the subject for an hour but didn’t tell him that the problem had never been solved. In fact, a decade later, someone managed to prove that the conjecture was false by counterexample.

Unaware of this (at the time), Kerr decided that pure mathematics wasn’t his forte and so went into applied mathematics instead, specifically relativistic physics. It is well known (amongst people who take an interest in physics) that Karl Schwarzschild was the first to provide a solution to Einstein’s field equations for the simplest, idealised scenario of a completely symmetrical sphere in a vacuum. He was a Professor of Potsdam University but formulated his solution whilst serving on the Russian front in WW1. He became ill soon after and died after returning home, but his name remains forever associated with black holes, which are a natural theoretical consequence of his solution.

Kerr’s solution (known as Kerr’s Theorem) was not realised until 1963 when he was at the University of Texas, Austin, which had major ramifications for relativistic physics, in particular black hole physics, that are still with us today. Kerr’s monumental breakthrough was overshadowed by the discovery of quasars, a source of radio waves of unprecedented energy. In 1963, the Parkes radio telescope (in Australia) was used to employ a method postulated by British astronomer, Cyril Hazard. His method was simple but ingenious: to use the moon eclipsing the radio signal to exactly pinpoint the source in the night sky. This allowed astronomers to locate the ‘light’ source of the radio waves and thus use spectroscopy to determine its distance from us.

Spectroscopy analyses the exact wavelengths of light emitted by a distant star, and from the Doppler shift we are able to determine how fast they retreat from us and thus how far away they are. There is a direct proportional relationship between how fast stars retreat and how far away they are using Hubble’s constant, named after Edwin Hubble who first discovered this phenomenon.

The first quasar, 3C273, was discovered by Maarten Schmidt at the Palomar Observatory in California, but because they were only seen as radio sources, spectroscopic analysis was not possible until a light source could be found to be directly associated with the radio source. Hence Hazard’s brilliant idea, subsequently employed at Parkes, to pinpoint quasar 3C273. And it was Schmidt who did the spectroscopic analysis, revealing that the light was red-shifted by an enormous 16% making it much further away then anyone had imagined.

During the 1960s, Australia was at the forefront of radio astronomy, and I remember in 1966, when satellites first linked up to produce the world’s first global televised transmission, the Beatles sang All You Need is Love to a worldwide audience simultaneously. Australia’s major contribution was to show the furthest known object in the universe being tracked by the Parkes’ radio telescope. This telescope featured in the movie The Dish, an Australian-made comedy starring another Kiwi, Sam Neill, which was a comedic rendition of Parkes’ role in broadcasting the first pictures from the moon landing in 1969. It also played a role in the Apollo 13 rescue mission, being the means to communicate the time to fire its retro rockets which allowed the astronauts to return to earth rather than bouncing off the atmosphere or diving too deep and burning up. The angle of descent was critical to their survival, and the ‘dish’ played a small, and little-known, but crucial role. (Unlike the rest of this exposition, nothing in this paragraph comes from Melia's book)

The curious aspect of Schmidt’s discovery is that, at the very first Texas Symposium on Relativistic Astrophysics in 1963, Kerr gave a 10minute lecture on his Theorem, which was virtually ignored because all the participants were far more interested in the recently discovered quasar. Yet Kerr’s Theorem gave the only relativistic solution to spinning black holes, which is exactly what quasars are.

Melia is meticulous in his coverage of all the people who contributed to our understanding of relativistic physics, both theoretically and experimentally. Not only the well known ones like Karl Schwarzschild, John Wheeler, Roger Penrose and Stephen Hawking, but unknown heroes like Noether and Kerr. He also mentions an Australian, Brandon Carter, who used Kerr’s Theorem to show that a ‘time loop’ (or 'time machine') could theoretically be generated beyond the event horizon of a rotating black hole. (But it only works in a vacuum, which makes it a catch-22 time machine.)

The significance of Kerr’s solution is that every significant physical body we know of in the universe is rotating, so Schwarzschild’s solution would almost certainly never be applicable to reality. Kerr’s solution reveals that there are, in fact, 2 event horizons for a rotating black hole. The event horizon is where the escape velocity from a black hole becomes the speed of light so nothing can escape from it. But a spinning black hole literally drags space-time around with it, which creates an inner and outer event horizon – don’t worry, I don’t understand it either. When a body crosses the first event horizon, the parameters of space and time are reversed: space becomes time-like and time becomes space-like. This is because time freezes at the event horizon for an outside observer and the external time becomes infinite from the inside. Time becomes space-like in that it becomes static and infinite, if I interpret it correctly. When an object crosses the second event horizon they reverse again so that ‘inside’ a spinning black hole, space and time become theoretically normal again. Of course, no one knows how true this really is. The other problem is that these theoretical considerations all assume a vacuum which is not the case if something is actually ‘crossing over’. To this day, there are no solutions to Einstein’s field equations for a non-vacuum – that is, for example, inside an object like the earth or the sun – only for outside in space.

That effectively is the limit of my understanding of this subject, even after reading Melia’s book. The story of Kerr himself is no less interesting. One gets the impression that, despite his obvious talents, he was not cut out for high level academia. He did not publish everything he uncovered, and he was not competitive in the sense that he sought to outdo his rivals at every opportunity, nor was he one for self-promotion. He left America in 1971 to take up a position of Head of Mathematics in the University of Canterbury in Christchurch, New Zealand. After his close friend and associate, Alfred Schild, died in 1977, Kerr virtually stopped visiting the US. He received the Hughes Medal from the Royal Society in 1984, the highest accolade he has received.

Roy Kerr writes his own afterward in Fulvio Melia’s book (they are good friends), in which he talks about the difficulties in attempting to get the advanced education he badly needed in 1950s New Zealand. But after going to Cambridge in the UK and the University of Texas in Austin, he believes he was fortunate in that he never had any mentors, as they would have undoubtedly led him away from the path that led to his groundbreaking discovery.