Schrodinger and Cheshire Cats

The Copenhagen Interpretation of Quantum Mechanics performs some highly complicated mathematical calculations on the assumption that everything is ambiguous until a human experimenter makes a measurement.  This copes with the awkward fact that subatomic particles fitted neither the classical idea of particles nor the classical concept of waves.  Light can behave as an obvious wave, as shown by interference patterns when light passed through two slits.  But light is also made up of individual particles called photons, as shown by the photoelectric effect, which made sense only in terms of photons striking atoms and knocking electrons out of them.  There were many more such oddities.

Maths using this assumption does allow for very accurate predictions of what was actually measured.  But what does it mean in the wider world?  That was the issue behind the famous and widely misunderstood matter of Schrodinger’s Cat.  As the man himself put it:

“One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

“It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a ‘blurred model’ for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.”

There is in fact a simple common-sense solution – the quantum uncertainty vanishes when the Geiger counter makes the measurement, if it does.  This was the view of Niels Bohr, the leading thinker in the development of the Copenhagen interpretation.  This common-sense notion was later expanded by a few theorists to include the specific suggestion that quantum uncertainty lasts only for as long as the force of gravity is insignificant.  This might plausibly be so, since when it comes to individual atoms, gravity is vastly weaker than the other known forces.  (Strong Nuclear, Electromagnetic and Weak Nuclear, with the weakest of them a hundred million million million million times as strong as gravity.)

One could also say that the quantum equations make sense if you view them as accurate forecasts of what is likely to happen.  Not as statements of what has actually happened.

Let’s do an analogy.  Let’s imagine someone who has a bad gambling habit.  They use an on-line betting system. They place a large bet on a particular horserace, using the quoted odds that are indeed an accurate forecast of several different possible outcomes, allowing for bookie’s profits.  Then they visit China, where gambling is banned.  They find they cannot check the result, because the website is blocked. But they can look at their on-line bank account. They can figure that if they won, a large payment will in due course appear. That’s to say, they will only have knowledge of the event some time after it happened.  But the event has still happened, and is definite.

Of course horse races are clearly real and definite events, even when we lack knowledge of the outcome.  Quantum events might be, if there are ‘hidden variable’ that we still need to discover.  But there is also nothing too odd about quantum events being uncertain, provided they resolve themselves before rising to interact with the normal world.  Once the Geiger counter measures a decay and the cat is killed, there is no more uncertainty.  Likewise if it does not happen.  The equations merely gave a forecast.  The human experimenter has to open the box to discover the outcome.

There are no great threats to common sense – and few opportunities for philosophical pretentiousness – if we assume that the subatomic realm follows an alien logic.  That it instantly loses these features as it builds up into the familiar world.  Once we start talking about real objects, even microscopic objects, the nuclear forces stop being relevant and electromagnetism largely cancels out.  Gravity dominates, and current theories of gravity imply certainty at least about past events.

I say ‘certainty about past events’, because the post-Newton Newtonian view of a deterministic cosmos turns out to be false.  Newton himself believed in an active interventionist God.  When he noticed that observed shifts in the orbits of Jupiter and Saturn were not compatible with Classical Greek observations of those planets in very similar orbits, he assumed that God must occasionally step in to stop the system out of balance.

The work of later scientists showed that the observed shifts were actually long-term cycles which restored the status quo.  One could expect broad stability lasting for far longer than humans had been observing the planets.  There were several contributors, but the French astronomer and mathematician Laplace did the most important work and showed that the solar system needed no outside hand to keep it stable.  There is a popular story that when asked about God, he said ‘I have no need of that hypothesis’.  This is probably not literally true, but it is a fair summary of what he found.  The system solidified into Newtonianism, a belief that everything might in principle be known.  Both Adam Smith and Karl Marx were trying to be the Newton of economics, and both failed.

The Newtonian view dominated until well into the 20th century.  Then the discovery of Chaos Dynamics changed everything.  This included lurking instabilities in the solar system that could in the future lead to the expulsion of one of the existing planets, with Mercury and Mars most at risk.  It is also possible and even likely that our solar system once contained additional planets, though the notion of the asteroid belt as debris from some ancient collision between entire planets has long been discredited.  Asteroid are remnants of early building-blocks that never did form a planet.

Anyone trying to understand the universe should be familiar with at least the basics of Chaos Dynamics.  The best place to start is still James Gleick’s Chaos: Making a New Science.  It was written nearly 30 years ago, but no better popular guide has so far been produced.

Note also that no one has yet cracked the problem of ‘Quantum Gravity’, a theory that would sensibly combine Quantum Mechanics with General Relativity.  One out of the cluster of theories known as ‘String Theory’ might well do this, if it turns out to be true.  But nothing has so far been testable by any experiment humans can perform.  One out of the cluster of theories known as Supersymmetry would be a huge step forward.  But the Large Hadron Collider has so far been unfavourable, failing to find particles that the simpler versions of Supersymmetry had predicted.  The issue is still open: something may turn up to vindicate Supersymmetry, with the Large Hadron Collider having been re-started in 2015 with higher power.  But there are valid alternatives to both Supersymetry and String Theory.

Given the amount of uncertainty about the basics, the apparent oddities of the quantum realm might sensibly be dismissed as a product of our lack of knowledge.  Sadly, theorists are fond of startling new ideas and hate to admit ignorance.  The bizarre favourite is the Many-Worlds idea, which requires an entire new universe for each quantum event, which seems excessive.  What’s much more popular among non-scientists is the notion that quantum events are only real when we notice them.  This is one way of understanding the Copenhagen interpretation of Quantum Mechanics – but as I mentioned earlier, Niels Bohr did not accept it.  Bohr assumed that the simple act of measurement by a Geiger counter would be enough to settle the fate of Schrodinger’s Cat.

There are also valid alternatives to the Copenhagen interpretation, the ‘Pilot Wave’ or De Broglie–Bohm theory.  These restore determinism, at the cost of perhaps suggesting a mysterious connection between distant objects.  Some founders of quantum physics – notably Louis de Broglie – championed an alternative interpretation, known as ‘pilot-wave theory’, which posits that quantum particles are borne along on some type of wave. According to pilot-wave theory, the particles have definite trajectories, but because of the pilot wave’s influence, they still exhibit wavelike statistics.  There is no necessity to believe that human observation is a key part of the process, which the Copenhagen interpretation seems to suggest.

Having thought a lot about the matter, I suddenly found myself composing a relevant poem:

  • Where is the song of a stuffed bird?
  • How does a grilled fish swim?
  • How can I tell who belled Schrodinger’s Cat?
  • And why are observers surprised?
  • Why was the muon like nothing they ordered
  • In the orderly physicist’s world?
  • Why does a rainbow bring joy to my heart
  • While a melon is simply to eat?
  • Why do I speak of this joy of my heart
  • When I know that it’s only a pump?
  • Should I decide that my joys ought to fade
  • And just sharpen my logic instead?
  • Ask a computer and it won’t say ‘Yes’
  • Nor say ‘No’, since there’s no one at home:
  • Ask one who programs (and I was one such)
  • And they’ll tell you “you fell for our tricks”
  • “We wrote the code and it blindly obeys –
  • “Though we shouldn’t say ‘blindly’ these days”.

Why should a subatomic event need our observation to be real?  This is incompatible with a vast mass of evidence that both the Earth and the wider universe had an enormously long pre-human history. And the Earth itself formed from a random scatter of materials about two-thirds of the way through the universe’s history.  So if we find contradictions in theories that never the less make surprising and accurate predictions, it’s most likely that our observations are giving us a very incomplete picture of what’s really going on.

A stuffed bird won’t sing, because the process of catching, killing and stuffing it has massively altered its nature.  But before being caught and given such a cruel re-working, it should have sung nicely enough, according to its species.  A human who claimed that the bird only sang because it later ended up in the human’s collection of stuffed birds would not be taken seriously.  It also seems safe to assume that birds sang very nicely long before there were humans around to notice, even the more respectful sort of human who just wants to listen to the song and maybe record it.

Songbirds are believed to have originated some 50 million years ago, long before there was anything human to hear them – though our remote primate ancestors would have heard and perhaps enjoyed that song.  The song of extinct birds is lost; but if some unobtrusive alien observers were there to record them, they could be said to still exist.  In any case, such lost songs were real at the time, even if there were no such aliens and the specific sounds are lost beyond recovery.

There is a further muddle in popular understanding, in which the passive act of observation is treated as if it depended on the will or knowledge of the observer.  People think that Quantum Mechanics means that if you believing something to be so, you make it so.  A convenient and rather lazy notion, since it relieves you of any obligation to study objective reality.  You can dismiss it as just someone else’s preferred beliefs, as President-Elect Trump has been doing with Climate Change.

This idea merges easily with an acceptance of lying as almost the same of truth.  Always a popular notion, since an individual who lies cleverly will have some strong immediate advantages over truth-speakers.  But a belief in objective reality would also suggest that liars tend to get caught, as indeed they do.  Tells you that an acceptance of lies will in the long run poison any society that allows it, as indeed it does.  But with subjectivism, you could feel quite relaxed about the matter.  Any bad thing that happens is ‘just one of those things’.  Not the foreseeable consequences of your own selfish and dishonest behaviour.

In the social world, there are indeed many circumstances where believing something can indeed make it so:

  • Financial panics can be caused by nothing more than a belief that there is about to be a panic.
  • The current UK flag is commonly called the Union Jack, even though this probably began as a term just for the naval version.
  • ‘Computer’ was originally a term for humans who were did long repetitive arithmetic. Devices initially known as ‘electronic computers’ soon made this human function obsolete.  Those electronic devices then became known just as computers.
  • ‘Tandem’ is a Latin word that means ‘at length’. But it was applied to a rather long bicycle with two riders lined up rather than side by side.  A Tandem bicycle may in fact have more than two riders.  But the word is also used more widely and abstractly as ‘in tandem’, two working together.

These last three cases are historic changes.  The older meanings remain objective facts, though dropped from current usage.


To get back to particle physics, Schrodinger’s Cat gets vast attention, despite several easy solutions that allow the quantum maths to mesh with observed reality.  Mostly overlooked is a much worse oddity: how can identical atoms of an unstable isotope have different lifetimes?  There is no known external cause, but the process is far from random.  For a decent-sized mass of a given isotope, one can make a very accurate and reliable prediction of the ‘half life’; the time for half of the atoms to have decayed.

Each isotope is a unique combinations of protons and neutrons.  Carbon-12 is six protons and six neutrons.  It is stable, and is the normal form of the carbon that is a major part of our own bodies and everything else alive, as well as coal and diamonds and chalk and cheese.  But it’s not the only possible carbon.  Carbon-13 is 1.1% of all natural carbon on Earth, and is only marginally different from Carbon-12.   It is another matter with Carbon-14, an unstable isotope formed by cosmic rays and which then slowly decays.  Carbon-14 can give us important truths, since it is used in archaeology for dating organic materials.  It has eight neutrons, six protons and a half-life of over 5700 years.

All this is familiar and used routinely – yet it raises a logical problem that I’d see as much more significant than Schrodinger’s Cat.  A million atoms of an unstable isotope like Carbon-14 are all identical, as far as we know.  But some will undergo radioactive decay and others will not, for no apparent reason.  Yet this will happen at a wholly predictable rate, with roughly half a million gone when the known half-life has elapsed.  Just how can this happen?

One explanation is ‘Hidden Variables’ – the atoms are not truly identical, even though we can not measure the differences.  This certainly operates in the familiar world – insurance companies make very accurate predictions of death rates in human populations, even though each death has a cause, mostly known and sometimes obvious.

The only other answer I can see is that atoms of an isotope are not really separate entities; just expressions of something more basic.  That would require a total rethink of what we currently suppose that we know about the universe.  But mainstream science is confident that the universe began as a single interconnected entity in the first infinitesimal moments of the Origin Event or Big Bang.  That it only later became cool enough for individual atoms to emerge.  So perhaps a correct understanding of physics lies beyond the realms we know.

I said earlier that the Cheshire Cat from Alice In Wonderland may have inspired Schrodinger’s Cat.  I’ve not seen anyone else say this.  The similarity suddenly occurred to me for no very obvious reason – a classic inspiration.  I then checked and found that Schrodinger was indeed in Oxford at the time he floated the idea.  Lewis Carroll (Charles Dodgson) spent most of his life in Oxford, and wrote his books there.  The inspiration for the fictional Alice was Alice Liddell, daughter of the dean of Christ Church.  Dodgson held the Christ Church Mathematical Lectureship for much his life, while Schrodinger was a highly mathematical physicist.  They also had a shared interesting in underage girls, though Schrodinger was less innocent than Dodgson is presumed to have been.  So it seems likely that Schrodinger knew the Alice stories, including the enigmatic Cheshire Cat.  Another topic that an historian of science might find it useful to look into.

The phrase ‘grinning like a Cheshire Cat’ is a traditional saying.  The logic behind the phrase is unknown, though it may be related to the abundance of milk and cream in Cheshire’s dairy industries.  Cats cannot grin, of course.  Humans see them as humourless and serious, yet also slightly mystical.  ‘Enough to make a cat laugh’ is a standard phrase for something truly absurd.  Dogs are presumed to laugh, and it seems they really can do so.  So do our close relatives among the apes.  So do rats, surprisingly enough.

Laughing apparently began as a generalised pleasure-sound for some mammals, though not cats.  It is now associated with humour by humans, only because humour gives us pleasure.  (I’ll say more in a future article about why humour may exist as one aspect of a useful pattern of thinking.)  For cats, the pleasure-sound is the purr, so laughter would indeed be alien to them.  So we assume they have no sense of humour, while supposing that dogs share something of our own sense of humour.

For a cat to grin as the Cheshire Cat does is for a cat to cease to be a cat and become a chimera, a mix of human and animal elements.  A small relative of the dragon, in fact.

And what about hidden variables?  The quarks that compose protons and neutrons are stranger than is normally realised:

“We’ve known for half a century that protons and neutrons are not fundamental particles, but made of smaller constituents called quarks.  There are six types of quark: up, down, strange, charm, bottom and top.  The proton has a composition of up-up-down, while the neutron is up-down-down.

“Down quarks are slightly heavier than up quarks, but don’t expect that to explain the neutron’s sliver of extra mass: both quark masses are tiny.  It’s hard to tell exactly how tiny, because quarks are never seen singly…, but the up quark has a mass of something like 2 or 3 MeV, and the down quark maybe double that – just a tiny fraction of the total proton or neutron mass…

“Electrically charged particles can bind together by exchanging massless photons.  Similarly, colour-charged quarks bind together to form matter such as protons and neutrons by exchanging particles known as gluons.  Although gluons have no mass, they do have energy.  What’s more, thanks to Einstein’s famous E = mc2, that energy can be converted into a froth of quarks (and their antimatter equivalents) beyond the three normally said to reside in a proton or neutron.  According to the uncertainty principle of quantum physics, these extra particles are constantly popping up and disappearing again…

“To try and make sense of this quantum froth, over the past four decades particle theorists have invented and refined a technique known as lattice QCD.  In much the same way that meteorologists and climate scientists attempt to simulate the swirling complexities of Earth’s atmosphere by reducing it to a three-dimensional grid of points spaced kilometres apart, lattice QCD reduces a nucleon’s interior to a lattice of points in a simulated space-time tens of femtometres across.  Quarks sit at the vertices of this lattice, while gluons propagate along the edges.  By summing up the interactions along all these edges, and seeing how they evolve step-wise in time, you begin to build up a picture of how the nucleon works as a whole.

“Trouble is, even with a modest number of lattice points – say 100 by 100 by 100 separated by one-tenth of a femtometre – that’s an awful lot of interactions, and lattice QCD simulations require a screaming amount of computing power.  Complicating things still further, because quantum physics offers no certain outcomes, these simulations must be run thousands of times to arrive at an “average” answer.  To work out where the proton and neutron masses come from, Fodor and his colleagues had to harness two IBM Blue Gene supercomputers and two suites of cluster-computing processors…

“The calculation suffered from a glaring omission: the effects of electrical charge, which is another source of energy, and therefore mass.  All the transient quarks and antiquarks inside the nucleon are electrically charged, giving them a “self-energy” that makes an additional contribution to their mass.  Without taking into account this effect, all bets about quark masses are off.”

Could some of the particular configurations of the ‘froth of quarks’ (and gluons) within protons and neutrons be the ‘hidden variables’ that explain quantum uncertainty and radioactive decay, at least for particles composed of quarks?  The explanation as to why seemingly identical free neutrons will have different lifetimes, yet all conform to a general rule about their half-life?  The decay might be hitting one of more unstable configuration within the froth, or one that can generate an electron that is then ejected.  (And likewise for the variable behaviour of individual atoms of unstable isotopes.)

The article I quoted does of course say that the variations are also caused by quantum uncertainty.  But these might be influenced randomly by slight interactions with nearby charged particles.  It would be like the Butterfly Effect in weather forecasting: arising from definite causes but in practice unpredictable.

I’m aware that uncertainty also applies to electrons.  But the fact that quarks have very exact fractions of the charge of the electron suggest that electrons too are composed of something more basic.

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