Our Place in the Universe

My latest book review:

The Copernicus Complex: Our Cosmic Significance in a Universe of Planets and Probabilities (Hardcover)
by Caleb Scharf

Nicolaus Copernicus is credited with the realisation that the Earth is not at the centre of the Universe, but orbits around the Sun. This was a key step in the development of the idea that we do not occupy a special place in the Universe, and that, by implication, there may be nothing special about us, cosmically speaking. In the late twentieth century, this led to the so-called “principle of terrestrial mediocrity”, which says that our place in the Universe is so ordinary as to be typical — that we live on an ordinary planet, orbiting an ordinary star, in an ordinary galaxy. Caleb Scharf argues that this approach, what he calls the “Copernicus complex”, has gone too far. The Earth, he says, is a rather unusual planet situated in a rather unusual location; this gives a different perspective on the likelihood of other life forms like us existing across the Universe, which he puts in context by comparing our Solar System with the hundreds of other planetary systems that have now been discovered.

In order to get to the meat of his argument, Scharf runs through a breezy historical introduction, name-checking all the usual suspects from Aristarchus to Newton, via Copernicus, Tycho, Kepler and Galileo. The story of the discovery of our place in the Universe is a familiar one, but neatly summed up in a sentence: “The Sun with all its worlds is like a single raindrop on a particular hour of a particular day in a specific cloud somewhere in the skies of Earth.” [ED: Quote from p 52, please check that it is in final book] It is by making a comparison with other “raindrops” — other planetary systems — that Scharf reaches a conclusion that would have surprised previous generations of astronomers.

Our Solar System is a relatively orderly place, with widely spaced planets following roughly circular orbits around the Sun. This has allowed the Earth to be undisturbed for billions of years while life has evolved on its surface. While ours was the only planetary system known, it was natural to think that this is a typical example. But with many other planetary systems now known, it is clear that this is not the case. In most other systems, orbits are more elliptical and planets are closer together, allowing interactions which make chaotic disorder common and make it impossible for a planet to stay in a stable orbit with the right conditions for life for billions of years. Scharf calculates that we are in a 2 or 3 per cent “club”. In other words, that 97 planetary systems out of every hundred do not allow for the existence of Earth-like planets in stable orbits, providing suitable homes for life forms like us. “Our solar system is at least somewhat unusual, and we have the numbers to back that up.” [ED quote page 125]

He then goes on to consider the chances of complex life forms like us evolving even on those planets in the 2 or 3 per cent club. This is a much tricker proposition, since, as with the case of planetary systems a few decades ago, we only have one example to guide us. But in explaining why this is such a tricky problem, Scharf provides the best explanation that I have ever seen for the non-specialist of the statistical technique known as Bayes’ Theorem. It is almost worth reading the book for this alone, for Bayesian techniques underpin much of our everyday lives, including the spell-checker that is correcting my words as I write, and the number plate recognition systems that identify cars caught in speed trtaps.

The key features of life, as other people have observed, are that it involves self-sustaining cycles of activity, feeding off a flow of energy (for example, sunlight) and that it exists on the border between orderly and disorderly extremes — on the “edge of chaos”, as it is sometimes referred to. One consequence of this is that life drives systems away from chemical equilibrium. The classic example is the difference between the atmosphere of the Earth, rich in highly reactive oxygen, and the atmosphere of Mars, composed of stable, unreactive carbon dioxide. This alone tells us that Mars is a dead planet today, whatever may have happened on its surface in its youth. Scharf discusses these ideas clearly, with a particularly informative account of the role played by bacterial organisms in the story of life on Earth, but, curiously, without mentioning Gaia theory, which is the most powerful presentation of this kind of argument.

Finally, he looks at the Universe at large, which emerged from a Big Bang just under 14 billion years ago and is now expanding ever more rapidly, so that in billions of years time no other galaxies will be visible from the confines of our Milky Way. About 95 per cent of all the stars that will ever exist have already come into being, and for the rest of eternity galaxies will fade away as the stars age. “We exist during what may be the only cosmic period when the universe’s nature can be correctly inferred by observing what is around us.” [ED page 211]

The bottom line of the book is that planets like Earth in systems like our Solar System are rare, but not unique. That the particular kind of complex life forms that we represent may be unique, but that other forms of complex life may have evolved elsewhere along different pathways. “We end up with this: Our place in the universe is special but not significant, unique but not exceptional.” We could, says Scharf, “be special yet surrounded by a universe of other equally complex, equally special life forms that just took a different trajectory.” [ED both from page 221]

Which leaves us with the biggest question of all. If intelligent life is common in the Universe, why can we see no trace of it? In particular, why hasn’t it visited us? Dubbed the “Fermi paradox”, after the physicist Enrico Fermi who first pointed out how easy it would be, given the age of the Milky Way galaxy, for spacefarers to send probes to every Sun-like star, this is still the most powerful argument against the existence of extraterrestrial civilizations. On balance, it seems to me that Scharf is wrong; but I hope he is right!

John Gribbin

is a Visiting Fellow in Astronomy

at the University of Sussex

and author of

Deep Simplicity: Chaos, complexity and the emergence of life (Random House)

A version of this review appeared in the Wall Street Journal

Aspects of reality

Spooky Action at a Distance and the Bell Inequality

It is 50 years since John Bell published a paper on the nature of reality which is often quoted but also often misunderstood.  This may clear up some of the confusion.

The paper was titled “On the Einstein-Podolsky-Rosen Paradox”, and begins by noting that the so-called EPR argument was advanced in support of the idea that “quantum mechanics could not be a complete theory but should be supplemented by additional variables.  These additional variables were to restore to the theory causality and locality.”  Bell says that “in this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics.  It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.”  In other words, if there is a real world out there independent of our observations (if the Moon is there when nobody is looking at it), then the world is non-local.  Equally, though, if you insist on locality, then you have to give up the idea of reality and accept the literal truth of the “collapse of the wave function” as envisaged by the Copenhagen Interpretation.  But you cannot have both — you cannot have local reality.

But the most dramatic feature of Bell’s discovery is often overlooked, even today.  This is not a result that applies only in the context of quantum mechanics, or a particular version of quantum mechanics, such as the Copenhagen Interpretation or the Many World Interpretation.  It applies to the Universe independently of the theory being used to describe the Universe.  It is a fundamental property of the Universe not to exhibit local reality.

I do not intend to go into the details of Bell’s calculation, which can be found in a detailed but accessible presentation by David Mermin in his book Boojums All The Way Through.  It happens that Mermin presents these ideas within the framework of the Copenhagen Interpretation, accepting locality but denying a reality independent of the observer; my own preference is to accept reality and live with non-locality, but this just emphasises the point that whichever interpretation you use Bell’s result still stands.  The crucial point is that Bell found that if a series of measurements of the spins of particles in a version of the EPR experiment is carried out, with various orientations of the detectors used to measure the spin, then if the world is both real and local the results of one set of measurements will be larger than the results of another set of measurements.  This is Bell’s inequality.  If Bell’s inequality is violated, if the results of the second set of measurements are larger than the first, it proves that the world does not obey local reality.  He then showed that the equations of quantum mechanics tell us that the inequality must indeed be violated.  Since then, other similar inequalities have been discovered; they are all known as Bell inequalities, even though he did not discover them all himself.  The whole package of ideas is known as Bell’s theorem.

Bell’s conclusion is worth quoting:
In a theory in which parameters are added to quantum mechanics to     determine the results of individual measurements without changing the     statistical predictions, there must be a mechanism whereby the setting of     one measuring device can influence the reading of another instrument,     however remote.  Moreover, the signal involved must propagate instantaneously.

It’s noteworthy that Bell did not expect to reach such a conclusion when he started out down this path.  His instinct was to side with Einstein and assert that local reality must be the basis on which the world works.  As he later wrote to Nick Herbert:
I was deeply impressed by Einstein’s reservations about quantum mechanics     and his views of it as an incomplete theory.  For several reasons the time was ripe for me to tackle the problem head on.  The result was the reverse of what I had hoped.  But I was delighted — in a region of wooliness and obscurity to have come upon something hard and clear.

In the words that Arthur Conan Doyle put unto the mouth of Sherlock Holmes, in The Sign of Four, Bell had eliminated the impossible — local reality.  What was left, however improbable, had to be the truth.

But it is one thing to prove mathematically that the world is either unreal or non-local, and quite another to prove it by experiment.  Bell realised this; at the end of his paper he said “The example considered above has the advantage that it requires little imagination to envisage the measurements involved actually being made.”  Little imagination, but a great deal of experimental skill.  Astonishingly it was less than ten years before the first such experiments were carried out by a team headed by Alain Aspect.

The essence of the experiments to test Bell’s theorem is that photons from a single source fly off in opposite directions, and that their polarizations at various angles across the line of sight are measured at detectors as far away as possible from the source.  The angle of polarization being measured can be chosen by setting one detector — a polarizing filter — at a particular angle, and the number of photons passing through the filter (let’s call it filter A) can be compared with the number of photons passing through a filter set at another, carefully chosen, angle on the other wing of the experiment (let’s call it filter B).  The results of first-generation experiments, notably those of John  Clauser, showed that the setting of filter A affected the number of photons passing through filter B.  Somehow, the photons arriving at B “knew” the setting of A, and adjusted their behaviour accordingly.  This is startling enough, but it does not yet prove that the communication between A and B is happening faster than light (non-locally), because the whole experimental setup is determined before the photons leave the source.  Conceivably, some signal could be travelling between A and B at less than the speed of light, so that they are in some sense coordinated, before the photons reach them.  This would still be pretty spooky, bit it would not be non-local.

John Bell expressed this clearly, in a paper first published in 1981.  After commenting that “those of us who are inspired by Einstein” would be happy to discover that quantum mechanics may be wrong, and that “perhaps Nature is not as queer as quantum mechanics”, he went on:
But the experimental situation is not very encouraging from this point of     view.  It is true that practical experiments fall far short of the ideal, because     of counter inefficiencies, or analyzer inefficiencies, [or other practical difficulties].  Although there is an escape route there, it is hard for me to believe that quantum mechanics works so nicely for inefficient practical set-ups and yet is going to fail badly when sufficient refinements are made.      Of more importance, in my opinion, is the complete absence of the vital time factor in existing experiments.  The analyzers are not rotated during the flight of the particles.  Even if one is obliged to admit some long range influence, it need not travel faster than light — and so would be much less     indigestible.  For me, then, it is of capital importance that Aspect is engaged     in an experiment in which the time factor is introduced.

That experiment bore fruit soon after Bell highlighted its significance.  But it had been a long time in the making.

Alain Aspect was born in 1947, which makes him the first significant person in this story to be younger than me (just by a year).  He was brought up in the southwest of France, near Bordeaux, and had a childhood interest in physics, astronomy and science fiction.  After completing high school, he studied at the École Normale Supérieure de Chachan, near Paris, and went on to the University of Orsay, completing his first postgraduate degree, roughly equivalent to an MPhil in the English-speaking world and sometimes known in France as the “little doctorate”, in 1971.  Aspect then spent three years doing national service, working as a teacher in the former French colony of Cameroon.  This gave him plenty of time to read and think, and most of his reading and thinking concerned quantum physics.  The courses he had taken as a student in France had covered quantum mechanics from a mathematical perspective, concentrating on the equations rather than the fundamental physics, and scarcely discussing the conceptual foundations at all.  But it was the physics that fascinated Aspect, and it was while in Cameroon that he read the EPR paper and realised that it contained a fundamental insight into the nature of the world.  This highlights Aspect’s approach — he always went back to the sources wherever possible, studying Schrödinger’s, or Einstein’s, or Bohm’s original publications, not secondhand interpretations of what they had said.  It was, however, not until he returned to France, late in 1974, that he read Bell’s paper on the implications of the EPR idea; it was, he has said “love at first sight”.  Eager to make a contribution, and disappointed to find that Clauser had already carried out a test of Bell’s theorem, he resolved to tackle the locality loophole as the topic for his “big doctorate”.

Under the French system at the time, this could be a large, long-term project provided he could find a supervisor and a base from which to work.  Christian Imbert and the Institute of Physics at the University of Paris-South, located at Orsay, agreed to take him on, and as a first step he visited Bell in Geneva early in 1975 to discuss the idea.  Bell was enthusiastic, but warned Aspect that it would be a long job, and if things went wrong it could blight his career.  In fact, it took four years to obtain funding and build the experiment, two more years to start to get meaningful results, and Aspect did not receive his big doctorate (“doctorat d’état”) until 1983.  But it was worth it.

Such an epic achievement could not be carried out alone, and Aspect led a team that included Philippe Grangier, Gérard Roger and Jean Dalibard.  The key improvement over earlier tests of Bell’s theorem was to find, and apply, a technique for switching the polarizing filters while the photons were in flight, so that there was no way that relevant information could be conveyed between A and B at less than light speed.  To do this, they didn’t actually rotate the filters while the photons were flying through the apparatus, but switched rapidly between two different polarizers oriented at different angles, using an ingenious optical-acoustic liquid mirror.

The photons set out on their way towards the polarizing filters in the usual way, but part of the way along their journey they encounter the liquid mirror.  This is simply a tank of water, into which two beams of ultrasonic sound waves can be propagated.  If the sound is turned off, the photons go straight through the water and arrive at a polarizing filter set at a certain angle.  If the sound is turned on, the two acoustic beams interact to create a standing wave in the water, which deflects the photons towards a second polarizing filter set at a different angle.  On the other side of the experiment, the second beam of photons is subjected to similar switching, and both beams are monitored; the polarization of large numbers of photons is automatically compared with the settings of the polarizers on the other side.  It is relatively simple to envisage such an experiment, but immensely difficult to put it into practice, matching up the beams and polarizers, and recording all the data automatically — which is why the first results were not obtained until 1981, and more meaningful data in 1982.  But what matters is that the acoustic switching (carried out automatically, of course) occurred every 10 nanoseconds (1 ns is one billionth of a second), and it occurred after the photons had left their source.   But the time taken for light to get from one side of the experiment to the other (a distance of nearly 13 metres) was 40 ns.  There is no way that a message could travel from A to B quickly enough to “tell” the photons on one side of the apparatus what was happening to their partners on the other side of the apparatus, unless that information travelled faster than light.  Aspect and his colleagues discovered that even under these conditions Bell’s inequality is violated.  Local realism is not a good description of how the Universe works.

Adapted from my book Computing with Quantum Cats.

Black Holes — the truth

There has been a flurry of daft stories recently claiming that “black holes do not exist”.  This is my attempt to put these claims in  perspective.

Black Holes
A concentration of matter which has a gravitational field strong enough to curve spacetime completely round upon itself so that nothing can escape, not even light, is said to be a black hole.  This can happen either if a relatively modest amount of matter is squeezed to very high densities (for example, if the Earth were to be squeezed down to about the size of a pea), or if there is a very large concentration of relatively low mass material (for example, a few million times the mass of our Sun in a sphere as big across as our Solar System, equivalent to about the same density as water).
The first person to suggest that there might exist “dark stars” whose gravitation was so strong that light could not escape from them was John Michell, a Fellow of the Royal Society whose ideas were presented to the Society in 1783.  Michell based his calculations on Isaac Newton’s theory of gravity, the best available at the time, and on the corpuscular theory of light, which envisaged light as a stream of tiny particles, like miniature cannon balls (now called photons).  Michell assumed that these particles of light would be affected by gravity in the same way as any other objects.  Ole Romer had accurately measured the speed of light a hundred years earlier, and Michell was able to calculate how large an object with the density of the Sun would have to be in order to have an escape velocity greater than the speed of light.
If such objects existed, light could not escape from them, and they would be dark.  The escape velocity from the surface of the Sun is only 0.2 per cent of the speed of light, but if you imagine successive larger objects with the same density as the Sun the escape velocity increases rapidly.  Michell pointed out that such an object with a diameter 500 times the diameter of the Sun (roughly as big across as the Solar System) would have an escape velocity greater than the speed of light.
The same conclusion was reached independently by Pierre Laplace, and published by him in 1796.  In a particularly prescient remark, Michell pointed out that although such objects would be invisible, “if any other luminiferous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones”.  In other words, he suggested that black holes would most easily be found if they occurred in binary systems.  But the notion of dark stars was forgotten in the 19th century and only revived in the context ofAlbert Einstein’s general theory of relativity, when astronomers realised that there was another way to make black holes.
One of the first people to analyse the implications of Einstein’s theory was Karl Schwarzschild, an astronomer serving on the eastern front in World War I.  The general theory of relativity explains the force of gravity as a result of the way spacetime is curved in the vicinity of matter.  Schwarzschild calculated the exact mathematical description of the geometry of spacetime around a spherical mass, and sent his calculations to Einstein, who presented them to the Prussian Academy of Sciences early in 1916.  The calculations showed that for any mass there is a critical radius, now called the Schwarzschild radius, which corresponds to such an extreme distortion of spacetime that if the mass were to be squeezed inside the critical radius space would close around the object and pinch it off from the rest of the Universe.  It would, in effect, become a self-contained universe in its own right, from which nothing (not even light) could escape.
For the Sun, the Schwarzschild radius is 2.9 km; for the Earth, it is 0.88 cm.  This does not mean that there is what we now call a black hole (the term was first used in this sense only in 1967, by John Wheeler) of the appropriate size at the centre of the Sun or of the Earth.  There is nothing unusual about spacetime at this distance from the centre of the object.  What Schwarzschild’s calculations showed was that if the Sun could be squeezed into a ball less than 2.9 km across, or if the Earth could be squeezed into a ball only 0.88 cm across, they would be permanently and cut off from the outside Universe in a black hole.  Matter can still fall in to such a black hole, but nothing can escape.
For several decades this was seen simply as a mathematical curiosity, because nobody thought that it would be possible for real, physical objects to collapse to the states of extreme density that would be required to make black holes.  Even white dwarf stars, which began to be understood in the 1920s, contain about the same mass as our Sun in a sphere about as big as the Earth, much more than 3 km across.  And for a time nobody realised that you can also make a black hole, essentially the same as the kind of dark star envisaged by Michell and Laplace, if you have a very large amount of matter at quite ordinary densities.  The Schwarzschild radius corresponding to any mass M is given by the formula 2GM/c2, where G is the constant of gravity and c is the speed of light.
In the 1930s, Subrahmanyan Chandrasekhar showed that even a white dwarf could be stable only if it had a mass less than 1.4 times the mass of the Sun, and that any heavier dead star would collapse further.  A few researchers considered the possibility that this could lead to th formation of neutron stars, typically with a radius only one seven-hundredth of that of a white dwarf, just a few kilometers across.  But the idea was not widely accepted until the discovery of pulsars in the mid1960s showed that neutron stars really did exist.
This led to a revival of interest in the theory of black holes, because neutron stars sit on the edge of becoming black holes.  Although it is hard to imagine squeezing the Sun down to a radius of2.9 km, neutron stars with about the same mass as the Sun and radii less than about 10 km were now known to exist, and it would be a relatively small step from there to a black hole.
Theoretical studies show that a black hole has just three properties that define it  its mass, its electric charge, and its rotation (angular momentum).  An uncharged, non-rotating black hole is described by the Schwarzschild solution to Einstein’s equations, a charged, non-rotating black hole is described by the Reissner-Nordstrom solution, an uncharged but rotating black hole is described by the Kerr solution, and a rotating, charged black hole is described by the Kerr-Newman solution.  A black hole has no other properties, summed up by the phrase “a black hole has no hair”.  Real black holes are likely to be rotating and uncharged, so that the Kerr solution is the one of most interest.
Both black holes and neutron stars are now thought to be produced in the death throes of massive stars that explode as supernovas.  The calculations showed that any compact supernova remnant with a mass less than about three times the mass of the Sun (the Oppenheimer-Volkoff limit) could form a stable neutron star, but any compact remnant with more than this mass would collapse into a black hole, crushing its contents into a singularity at the centre of the hole, a mirror image of the Big Bang singularity in which the Universe was born.  If such an object happened to be in orbit around an ordinary star, it would strip matter from its companion to form an accretion disk of hot material funneling in to the black hole. The temperature in the accretion disk might rise so high that it would radiate X-rays, making the black hole detectable.
In the early 1970s, echoing Michell’s prediction, just such an object was found in a binary system.  An Xray source known as Cygnus X1 was identified with a star known as HDE 226868.  The orbital dynamics of the system showed that the source of the X-rays, coming from an object smaller than the Earth in orbit around the visible star, had a mass greater than the Oppenheimer-Volkoff limit.  It could only be a black hole.  Since then, a handful of other black holes have been identified in the same way, and in 1994 a system known as V404 Cygni became the best black hole “candidate” to date when it was shown to be made up of a star with about 70 per cent as much mass as our Sun in orbit around an Xray source with about 12 times the Sun’s mass.  But such confirmed identifications may be much less than the tip of the proverbial iceberg.
Such “stellar mass” black holes can only be detected if they are in binary systems, as Michell realised.  An isolated black hole lives up to its name  it is black, and undetectable.  But very many stars should, according to astrophysical theory, end their lives as neutron stars or black holes.  Observers actually detect about the same number of good black hole candidates in binary systems as they do binary pulsars, and this suggests that the number of isolated stellar mass black holes must be the same as the number of isolated pulsars.  This supposition is backed up by theoretical calculations.     There are several hundred active pulsars known in our Galaxy today.  But theory tells us that a pulsar is only active as a radio source for a short time, before it fades into undetectable silence.  So there should be correspondingly more “dead” pulsars (quiet neutron stars) around.  Our Galaxy contains a hundred billion bright stars, and has been around for thousands of million of years.  The best estimate is that there are around four hundred million dead pulsars in our Galaxy today, and even a conservative estimate would place the number of stellar mass black holes at a quarter of that figure  one hundred million.  If so, and the black holes are scattered at random across the Galaxy, the nearest one is probably just 15 light years away.  And since there is nothing unusual about our Galaxy, every other galaxy in the Universe must contain a similar profusion of black holes.
They may also contain something much more like the kind of “dark star” originally envisaged by Michell and Laplace.  These are now known as “supermassive black holes”, and are thought to lie at the hearts of active galaxies and quasars, providing the gravitational powerhouses which explain the source of energy in these objects.  A black hole as big across as our Solar System, containing a few million solar masses of material, could swallow matter from its surroundings at a rate of one or two stars a year.  In the process, a large fraction of the star’s mass would be converted into energy, in line with Einstein’s equation E = mc2.  Quiescent supermassive black holes may lie at the centres of all galaxies, including our own.     In 1994, observers using the Hubble Space Telescope discovered a disc of hot material, about 150 thousand parsecs across, orbiting at speeds of about two million kilometers per hour (about 3 x 107 cm/sec, almost 1 per cent of the speed of light) around the central region of the galaxy M87, at a distance of about 15 million parsecs from our Galaxy.  A jet of hot gas, more than a kiloparsec long, is being shot out from the central “engine” in M87.  The orbital speeds in the accretion disk at the heart of M87 is conclusive proof that it is held in the gravitational grip of a supermassive black hole, with a mass that may be as great as three billion times the mass of our Sun, and the jet is explained as an outpouring of energy from one of the polar regions of the accretion system.
Also in 1994, astronomers from the University of Oxford and from Keele University identified a stellar-mass black hole in a binary system known as V404 Cygni.  The orbital parameters of the system enabled them to “weigh” the black hole accurately, showing that it has about 12 times as much mass as our Sun and is orbited by an ordinary star with about 70 per cent of the Sun’s mass.  This is the most precise measurement so far of the mass of a “dark star”, and is therefore the best individual proof that black holes exist.

Adapted from my book Companion to the Cosmos