Does Physics Find Only Holes Within Holes?

In a hole in a hole dwelt a nothingness.  Not a comfortable sort of hole, and not a comfortable nothingness either.  This was a scientific sort of nothing, and that means intellectual discomfort.

For those who don’t recognise it, I am parodying Tolkien’s famous opening to The Hobbit.  I do this mostly for my own amusement, and in the hope of getting across some complex ideas with a dash of humour.  Tolkien wonderfully described the comfortable hole that Bilbo the hobbit lived in before being sent off to confront first the loathsome Gollum and then the fierce and alarmingly clever dragon Smaug, each with his own hole that he comfortably dwells in.  And you too should also be able to imagine a comfortable nothing, as in ‘nothing wrong’.  Or as in ‘Nothing to report: spectre no longer haunting Room 13: “We haven’t had that spirit here since 1969”, says manager of the Hotel California‘.  (That’s another parody, this time of a strange and famous pop song.)

The notion that science had found ‘a hole inside a hole through a hole’ comes from SF author James Blish.  A knowledgeable man with a successful popular writing style, Blish also coined the useful term ‘gas giant’, which has migrated from science fiction to real astronomy.  His notion of matter as hollow is part of the dismal vision in a dismal book called A Case of Conscience.  It starts out as Space Opera, and raises some interesting moral questions.  Sadly, it ends with the extermination of the alien race who have dared to be successfully virtuous without religion – all too similar to real history.

The ‘a hole inside a hole through a hole’ is Blish’s interpretation of what subatomic physics had found.  And is true up to a point: gaps between atoms are typically huge compared to the atoms themselves; atoms are mostly empty with a tiny nucleus at the centre; the nucleus is made up of protons and neutrons.  Blish wrote in 1958, before the realisation that tiny particles called quarks were the subcomponents of protons, neutrons and various exotic particles (including pions but not muons).  But SF writers had long speculated about such things.  Before World War Two, E. E. ‘Doc’ Smith in his ‘Skylark‘ SF adventure novels had his fictional scientists discovering many layers of sub-components within electrons.  No one has yet found evidence that electrons have sub-components. but the possibility is not absurd.

So do we have ‘a hole inside a hole through a hole’?  A complete nothingness within that?  Not really.  What science actually found is atoms where most of the mass is in something small and hugely substantial.  That’s not so dismal, though scientist don’t help by mostly using dry emotion-free imagery.  They are often self-defeating by being hostile to the popularisations that win them whatever mass support that they possess.  Few of them will accept the world of Science Fiction as useful, even though a lot of them read it.

The language used is also often unhelpful.  To speak of the atomic nucleus as ‘a fly in the cathedral’ does give a good impression of the actual sizes.  But speaking of ‘a wren in the cathedral’ would have sounded much more human and connected with the normal world.  And would reference Sir Christopher Wren, who designed London’s St. Paul’s Cathedral

So how did we get to this modern vision?

Ancient peoples wondered a lot about the universe.  Some of them had good insights.  From Classical Greece and Ancient India, we have fragmentary records of thinkers who believed that the most basic component of matter would be what the Greeks called an atom, an ‘uncuttable’, ‘indivisible’ or ‘unbreakable’.  In Greece, at least, this view tended towards materialism and atheism – though since we mostly know about them from what their enemies wrote, this may have been exaggerated or misunderstood.  There were also bitter objections in Western philosophy and theology to the notion of a void between atoms.  It was said to imply atheism, though I can see no logical connection, even if the same people happened to assert both.  In Hinduism, where religion is happy to co-exist with unfathomable mysteries, there were orthodox schools of Hindu thought that accepted atoms.  In any case, the pathetically small fragments we have of early materialist and atomistic beliefs in Pagan Greece and Pagan Rome seem quite close to modern science.

Sadly, these good beginnings lost out to the more mystical and dogmatic beliefs of Plato and Aristotle.  These in turn hybridised with some strands of early Christianity to produce the Official Christianity that Emperor Constantine imposed on the whole Empire.  But knowledge of this early science survived, mostly in the form of Plato and Aristotle’s criticisms.  A style of thinking that was capable of being revived as one of many strands of thought within the European Renaissance, like a long-dormant seed sprouting to brilliant new life.

By stages, the modern scientific method was developed.  This insists that truth comes mostly from observations of the world, not the niceness of arguments or from how comfortably the explanations sits with existing social or religious ideas.  Observations can include experiments, but Popper was wrong when he claimed that real science has to be falsifiable.  Real science merely has to look sensible when tested against the real world.  A theory that ties together a number of disconnected facts has to be taken seriously, though it will be unconfirmed science until it successfully predicts something new.  And if it then fails, it still might have been a reasonable idea.

There was no possible experiment that could have confirmed Copernicus’s revival of the Ancient Greek notion that had the Earth orbiting the sun.  At least not until the space age, when it had long ceased to be disputed.  (Though I have a hazy memory of a television program about the Jain religion, which includes one of their theologians having a crisis of faith because a satellite was in orbit: this was not reconcilable with their vision of a flat earth centred on an immense world-mountain.)  Regardless, there were a mass of observations that made the sun-centred view overwhelmingly likely, particularly when people followed Galileo’s lead and used telescopes to study the planets and stars.  Sadly, in Italy the religious authorities decided to silence any scientific or mathematic thinker who dared come up with discoveries that did not sit nicely with existing social or religious ideas.  It wasn’t just Galileo: it also applied to some new mathematical insights that later allowed Newton to work out that gravity applied in the heavens as well as down here on Earth.

Theologians who had the power to give their dogmas the force of law successfully extinguished original thinking in Italy, and everywhere else where the Catholic Church had full intellectual hegemony.  In Catholic France, the monarchs were happy to allow free-thinking on matters that didn’t appear to challenge royal authority, which meant that a great deal of excellent science was produced.  This also applied in Protestant countries, even though Protestant theologians strongly denounced Galileo’s re-assertion of Copernicus’s view.  Copernicus had been ignored by Catholic theologians in his own time, partly because his published work included the qualification that his sun-centred system was just a mathematical trick and not reality.  Protestant theologians disliked sun-centred systems, but the political authorities did not allow them power of suppression over anything that wasn’t an overt challenge to popular faith.

At the same time as the sun was being made the centre, chemistry made progress by initially refusing to tie itself to any one theory.  The early ‘sceptical chemists’ concentrating on finding out the details of what actually existed.  By weighing and other exact measurements, a body of reliable data was slowly built up.  It was realised that ‘air’ was actually a mix of several ‘airs’, soon re-named gases.  And deduced by stages that these were somehow associated with particular liquids or solids.  Some of these gases were lighter than air, and some heavier.

It was realised that everything made sense if distinct chemical elements existed, and kept their identity through whatever chemical violence might be thrown at them.  And that the chemical elements were each composed of a distinct type of atom, with definite rules for how these atoms combined.  Combinations that mostly made molecules very different from their constituent atoms.

One simple example: common salt is sodium chloride, and essential to life.  Pure sodium is a metal which reacts violently with water.  Chlorine is a green and poisonous gas.  In a salty solution, sodium chloride exists as a slew of separate sodium and chlorine ions: but the ionisation (gain or loss of electrons) will have changed the atoms so that the violent reactivity of the un-ionised elements is lost.  Indeed, the violent reactivity is based on having a spare electron that the atom can readily lose (sodium) or an outer shell of electrons with a free spot for one more (chlorine).  Ionisation makes them safe and suitable to be part of organic life.

Most gases (but not helium, neon, argon etc.) are composed of atoms combined as molecules.  Helpfully for the progress of chemistry, it was found by careful measurements that a given volume of gas at a given temperature and pressure would contain the same number of atoms or molecules.  Physicists took this idea and developed Kinetic Theory, which assumed that molecules in a gas were relatively small and bounced off of each other at random.  The maths was complex, but the results were a strikingly good match for what experimenters had already found as unexplained empirical laws.

Understanding atoms also made sense of the traditional ‘elements’ of Greek philosophy: Earth and Fire and Air and Water.  It turned out that these were not elemental entities, but simply different relationships of atoms:

  • ‘Air’ is a mix of gases, with molecules or atoms freely bouncing off each other.
  • ‘Water’ is the best-known and most common of many molecules that are liquid at temperatures comfortable to humans. Molten metals are also liquids.  Mercury happens to be ‘molten’ within the human range of comfort.  Liquids are more densely packed molecules or atoms than gases, and these may also be significantly attracted to each other.  But they are also constantly shifting their combinations.  The shape of a liquid is ever-changing, even though its volume is constant at a particular temperature and pressure.
  • ‘Earth’ is a collection of various solids. Liquids become solid when they are cold enough, as with water becoming ice.  Solids mostly melt when hot enough, with even iron flowing in a really hot fire.  In solids, ‘Earth’, molecules form permanent bonds and resist being set asunder.
  • ‘Fire’ is a product of some chemical reactions that release a lot of energy. Fires have to keep on taking in new material, or else burn out.
  • ‘Aether’ or Quintessence is a fifth element that later thinkers added to the original Greek system. It is actually a mixed bag of things seen in the sky above the clouds.  The sun and other stars are plasma, much hotter than any gas.  The EarthMoon, Mars and Mercury are rock.  For the other planets, we see just clouds.  Venus has a solid surface beneath its clouds.  Jupiter and the other giant planets are believed to have solid cores, but very deep down and invisible to us.

In human terms, you can imagine a gas as a crowd in which no one knows each other and each goes their own way.  A liquid like a party in which people stop to talk but then circulate.  A solid is like a military formation in which everyone has their place, or like a crowd who have linked arms and intend not to be moved.  Fire is like a stampede, a destructive force.  All very explicable: but I remember my father telling me that university students on the arts side would come to believe in these ‘elements’ as real after being taught them as an aid to understanding ancient literature.

It is worth adding that the ancient Chinese had a completely different system of ‘elements’: Wood, Earth, Water, Fire, and Metal.  This ignores air, but does correctly recognise the fundamental difference between metals, inorganic non-metals and everything organic.  It has also been argued that these were never seen as ‘elements’ in the Western sense: not fundamental components.  In any case, it was another dead end.  Part of a pattern of ingenuity within a traditional Chinese culture that existed across at least 3000 years, but never moved towards real science.  As I’ve explained elsewhere, Traditional China did produce several vital inventions that were almost certainly necessary to allow Europe’s spectacular rise.  These included printing, gunpowder and the magnetic compass, which Francis Bacon (Lord Verulam) noted as major advances that Classical Europe had known nothing of.  But the same traditional culture that made China the best pre-industrial society also smothered the possibility of something radically new.  Only Marxism as a ‘Fourth Wave’ creed derived from first principles allowed Chinese to truly grasp the modern world.  The European Enlightenment and European Liberalism were full of assumptions about the world: notions that were true for European culture, but mostly not valid for humans in general.

A world made of atoms was much closer to the deep truths of the world than a world made of four elements, or five elements, or made of whatever you chose to think it was made of.  But towards the end of the 19th century, it was gradually realised that atoms could occasionally be broken apart and were actually composed of smaller units.  First they found the electron.  Then Ernest Rutherford showed that the mysterious energy that seemingly came from nowhere in radioactivity was actually caused by atoms breaking down and changing into other atoms, different chemical elements.  Which was not a wildly new idea: as far back as 1815, it had been suggested that the hydrogen atom was the fundamental unit and that other atoms were made by combinations of this unit.  A lot of elements had atomic weights that were close to being multiples of the atomic weight of hydrogen, so the idea was plausible.  But only in 1919 did Rutherford shoot alpha particles into pure nitrogen and demonstrate that he had created oxygen and hydrogen.  This confirmed what he already suspected: that the different chemical elements were composed of something more fundamental.  And the basic one-for-hydrogen unit became known from 1920 as a proton.

Separately from this, researchers guided by Rutherford had discovered in 1911 that atoms had an immense concentration of positive charge at their core.  J. J. Thomson had discovered the electron back in 1897, and had proposed the ‘plum pudding model’ of the atom: electrons set in a sea of positive charge.  Rutherford had the idea of shooting alpha particles at gold foil, to test this.  Unexpectedly, some of these were deflected at very large angles.  Detailed measurements showed that the atomic nucleus was a tiny thing compared to the atom, sometimes compared to a fly in a cathedral.  As I said earlier, a wren in a cathedral would have been a better image.

Does this mean that solids are not really solid?  Actually no.  Solids are solid because their atoms link to other atoms by strong chemical bonds.  Both solids and liquids are hard to compress, because atoms normally have a definite size and there is no spare space between them, as there is in a gas.  The nucleus of an atom hangs on very strongly to most of its electrons, which have a definite structure.  Simplifying a little, each atom has an outermost shell containing from one to eight electrons.  Carbon has four in the outer shell, while oxygen has six, so a carbon atom can share two electrons each with a pair of oxygen atoms to make carbon dioxide.  But when oxygen is scarce, carbon can also form a different sort of bond to form carbon monoxide.  This is much more reactive, burning in air to make carbon dioxide.  It is also poisonous, forming a strong bond with the blood’s haemoglobin and so stopping the normal transport of oxygen round the body: ending organic life for humans and other animals.

Many other chemical possibilities exist.  Carbon can also link to itself, sharing one electron each with four other carbon atoms.  Each of these in turn can form a bond to three more carbon atoms, creating an immensely strong lattice known to us as diamond.  And diamonds aren’t for ever: one early chemical experiment used a magnifying glass to focus a burning beam of sunlight onto a small diamond.  The diamond vanished completely, and left behind carbon dioxide.  But chemical bonds don’t break easily, and that’s what keeps solids as solids.  And it is very much harder to strip an atom of those electrons it possesses below its outermost shell, even though a lot of the atom would count as empty if you count electrons as point particles.  Electrons are negatively charged, protons are positive.  Their link is enormously strong.

It is however possible for extreme gravity to crush an atom and remove most of the spare space.  The fly quits the cathedral and moves into a matchbox, if you like.  This happens in White Dwarf Stars, which were recognised from 1910 onwards as extremely small but enormously massive.  A matchbox full of white dwarf material would have a mass of about 250 tonnes, the weight of a wide-body passenger aircraft.  It was later found that one could go further: dissolve the atoms entirely and have a ‘sea’ of protons and neutrons in an ultra-compressed body known as a neutron star.  A matchbox containing neutron-star material would have a mass of some 5 billion tonnes, the weight of a cubic kilometre of typical Earth rock.

Protons and neutron are not the lowest level.  Particle physicists in the early 1960s collided protons with protons at high speeds, even higher than the cosmic-ray collisions I mentioned earlier.  They found them bouncing off each other in ways that suggested that each proton contained three much smaller units.  Units that were given the name of quarks, from a stray remark in James Joyce’s Finnegans Wake.

(Which arguably ought to have been called Finnegan’s Wake: or Finnegans’ Wake if more than one Finnegan had diedBut when it comes to slogans and book titles, English grammar sometimes gets relaxed.  I’ve seen jokes about someone telling California’s Hells Angels that they really should have an apostrophe.  It is indeed Hell’s Angels in the title of Howard Hughes’s 1930 drama about the First World War.  But the film shows the slogan, and I’m sure I saw both forms used.  And there was considerable irritation when book-chain Waterstones chose to waste a lot of money becoming Waterstone’s: money better spent on keeping some low-turnover books on the shelves.  So on this matter (though on very little else) I find myself ‘on the side of the Angels’.)

Getting back to quarks.  Things get very strange at that level of existence: no one has managed to detect a free quark.  There are now sensible theories to explain why they could not exist, except under very special conditions.  It could be that some radically different theory will be needed, but more likely not.

Quarks were a major part of the existing Standard Model of particle physics.  This was put together in the 1970s and has been wonderfully successful in predicting new particles and their energies.  It was completed recently with the discovery of the Higgs Boson.  Theories claiming to go beyond this all still need quarks, as far as I know.

Not that neutron-star matter is necessarily the limit.  It is believed that things could go still further, with a mix of extreme gravity and temperatures producing a quark–gluon plasma, also known as quark soup.  An experiment in 2005 is generally believed to have made a sample.  It may exist at the core of neutron stars, and there might also be ‘quark stars’.  This remains speculative.

Even more speculative is ‘String Theory’, which has now mostly moved from ‘string’ to membranes as the ultimate basis for everything.  Black holes alarm physicists, because theory implies that some of them could contain a singularity, a point of infinite density, which would not make sense.  It is even feared that a naked singularity could exist, a point of infinite density that was not hidden respectably behind the event horizon of a black hole.  But it has also been suggested that matter could be reduced below ‘quark soup’ and down to the level of ‘string’, which would be interesting but not alarming.

That’s what matter is reckoned to consist of.  The central reality isn’t a ‘hole within a hole’.  Packages containing ultra-dense matter would be a better summary.  If the atomic nucleus is a ‘fly in the cathedral’, it is also a fly that outweighs the cathedral by a very large margin.

Solid matter as we know it consists of this mix of voids and ultra-dense objects.  Ordinary matter is incapable of passing through these voids.  Air and other gases are easy to pass through, because the molecules or atoms are only very weakly linked to each other.  But the atoms that make up molecules mostly hang together very strongly.  Water and other liquids offer resistance, because the molecules keep on making and then abandoning links.  Solids stay solid until broken or torn or shattered, because the atoms or molecules make individual links that are very hard to break.

People will be familiar with nets and metal mesh fences.  These are mostly just air, but are clearly impossibly to walk through unless you have the force to break them.  Just as you could walk through a wall made of paper, or break a soap-bubble with a light touch.  But the dismal vision of living in a universe made up of ‘holes within holes’ is a simple misunderstanding.  As is the related idea that one might walk through walls: most of the solid matter is void, but those voids are well protected by electromagnetic ties between objects of extreme density.

Considering the very large as well as the very small, I notice a more general pattern: density within voids.  The sun makes up the vast bulk of the mass of the solar system.  The planets make up most of the rest, with Jupiter having more mass than the rest of them put together.  The apparently-crowded asteroid belt is actually almost empty: no spacecraft has yet encountered an asteroid that it was not aiming for.  Isaac Asimov notes somewhere that from almost all asteroids, an observer would not see any other asteroid as more than the occasional point of light.  Put together, they would not be more than a thousandth of the mass of the Earth.  Other solar systems seem to be broadly similar, except some of them consist of two or more stars, some with shared planets revolving round them both.  Other binaries have a separate set of planets for each star.  But always, the bulk of the mass is in the star or stars.

Stepping up, the Milky Way galaxy is much denser at its core than in its disk (and the disk is where we live).  The spiral arms of some galaxies are not in fact coherent objects, and not much denser than the gaps between the arms.  There is a black hole at the centre of our galaxy, with a mass of several million suns – not an enormous concentration in a galaxy with at least two thousand million stars.  The movements of the stars throughout the galaxy also suggests that the bright stars are set in a much larger disk of Dark Matter.  This remains controversial, but the only alternative that can explain the known movements of stars and galaxies is to re-write the law of gravity.  A system called Modified Newtonian Dynamics is the best candidate, but still very much a minority view.

Stepping up again, the Milky Way and the Andromeda Galaxy are the heavyweights of a collection of more than 50 galaxies known as the Local Group.  Andromeda is the ‘boss’, with at least twice the mass of our galaxy.  It also has a much bigger black hole at the core, part of a double structure that remains mysterious.  It is known that galaxies can and do swallow up and absorb other smaller galaxies, but majority opinion among astronomers is now against the double structure being the original core plus a remnant of a swallowed galaxy.

Local groups similar to our own are reckoned to be common throughout the universe, though we only see nearby examples.  Much more impressive are Galactic Clusters, made up of thousands of galaxies and with gigantic elliptical galaxies at their centres.  The Virgo Cluster has more than a thousand galaxies, and is centred on a galaxy called Messier 87, which has more than 200 times the mass of the Milky Way.  But it is only one of several large galaxies in the cluster, and does not dominate it in the way the sun dominates the solar system or the nucleus dominates the atom.  And these Galactic Clusters seem to be the largest real objects in the universe – ‘objects’ in the sense that their mutual gravity is strong enough to bring them together despite the continuing expansion of the universe.

Beyond Clusters are Galactic Superclusters.  It used to be believed that Superclusters were coherent objects.  That our own Local Group was destined to become part of a more concentrated version of an existing Virgo Supercluster.  Further measurements suggest not, particularly now that we know that the expansion of the universe is accelerating.  Superclusters are now believed to be loose associations of many Galactic Clusters and Local Groups that will each eventually go its own way.  It was also realised in 2014 that the ‘Virgo Supercluster’ was just one of four components of a truly gigantic Laniakea Supercluster.

Superclusters in turn make up still vaster walls and filaments, with voids between them that contain very few galaxies.  This was discovered in the 1980s and was a considerable surprise.  In 1989 they found something called the ‘Great Wall’, over 500 million light-years long, 300 million light-years wide and 16 million light-years thick.  It is now known to be one of several such structures, and has been renamed the ‘CfA2 Great Wall’.  (Astronomers have a way of choosing dull and awkward names for their most astonishing discoveries.)

Nor is the Great Wall the largest thing in the known universe.  Even larger concentrations of galaxies have been found, and we are part of one of the larger groupings, the Pisces–Cetus Supercluster Complex.  It is a thousand million light-years long, but the current record-holder is ten times bigger.  Even vaster structures may be found as we continue to map the universe.

It remains puzzling that these gigantic structures exist.  Objects up to the scale of Galactic Clusters or Local Groups can be presumed to have pulled themselves together by mutual gravity, but beyond this?  That’s the realm of speculative cosmology, the attempt to work out in detail what happened in the Origin Event (Big Bang).

This is a from a much longer and more diverse article, Physics and the Nature of Reality.  It also has relevant references