Quantum Fluctuations

Quantum fluctuations and the snark


A tribute to Professor Brian Josephson 


For me, a memorable launch of Professor Josephsons scientific journey dates back to his graduate student days. His findings on superfluid flow were hotly contested by the hugely influential double Nobel Prize winner, John Bardeen. The David and Goliath confrontation, which took place at Queen Mary College, resulted in a very surprising victory for Brian. I cant imagine a more intimidating start to his career. It has seen limitless progression since then.

Take a look at his website to see the breadth and depth of Professor Josephson’s thinking.


This is a modular sculpture where the physical limits of sandstone have been challenged to make it appear liquid. One small part of the sculpture is a bridge constructed in an artificial stone that I invented.  I challenge you to distinguish between the natural and artificial stone.

The difficulty with sculpting quantum fluctuations is that they cannot be visualized and, even if they could, the observer would affect the observed. Thus, while the very core of the sculpture is imaginary, it is these real force fields that give rise to matter itself. 

The problem with stone is that this stuff is heavy. Sandstone has a density of 2.3 g/cm3. This means that a 1 cubic meter of sandstone weighs about 2,300 kilograms. Consider that a 25 pound or 11 kg sack of potatoes is at the upper limit of one ordinary persons ability to easily lift. 

This has led me to several conclusions:

First, the basic units of my universe must be easy to handle. It would be very challenging to handle a 2,300 kg block without hoist machinery. Thus, the units should be not much more than 11 kgs each. This called for the modular design for large works.

Second, the classic technique of relief sculpting also applies to 11kg blocks, and treating the relatively thin slab as a canvas for a 3D rendition made sense to me. Instead of square blocks, I worked in slabs of relatively shallow depth. However, unlike traditional relief sculpting, both the face and the back are carved. This piece is a composite of several manageable slabs of sandstone that can be assembled and disassembled. 

Third, layered modules bring an unusual twist to stone sculpture. Many years ago, I had bought a beautiful and seemingly impossibly intricate wood carving in Hong Kong, as shown in this picture: 

It was only quite recently that I realized that it was not carved as a single block of wood, as the visual illusion suggested, but had been invisibly assembled as modules of separately carved motifs.  This very small epiphany is important for my current work.

Quantum Fluctuations was my first layered modular work in stone. It is composed of several separately carved elements; the backplate, the front plate, the two side plates, and the baseplate. The Snark and the Snark ghost on their respective stands, are sandwiched in this cage of quantum fluctuations. They are structural bolts that hold the entire montage firmly together.

Fourth, you may notice a truncated inscription around the edge of the sculpture. (The calligraphy is not my own, but was painstakingly carved by Alberto Martinez.

Finally, stone carving has parallels with traditional drawing and painting. In painting, we use variable line density to achieve depth, shadow and contrast, avoidance of surface repetition, perspective and shading. In stone carving, the effects are achieved by differential sanding, surface texturing and depth of image. You might see that reflected in the graded polarity of the quantum fluctuations.

Now, I will enumerate two prejudices that underpin this work.


It seems amply and intuitively obvious, to me at least, that the universe is deeply interconnected from the minute Planck scale to the intergalactic scale.  Perhaps, rather than being interconnected, it approaches an irreducible whole.

Life scientists, including humble biochemists, have been quite good at deconstructing the entirety of living things into its constituent parts, but reconstructing the fractured Humpty Dumpty has proved very challenging. indeed it has not been achieved.

More is different. There is something about an emergent whole that really does seem to be incomputable and ineffable. Deconstructing the stuff of matter seems to have followed a similar path.

Interconnectedness and emergent irreducibility. I am a long-time addict of rabbit holes, in no small part due to Lewis Carroll. It seems that upon descent into these labyrinthine tunnels they have a structure which can be seen as an emergent phenomena. It also seems that many of these rabbit holes are a labyrinth of interconnected tunnels.

Quantum fluctuations appear to be of this nature, smelling like the Holy Grail of the Theory of Everything. interconnectedness and emergent irreducibility. The sum being greater than the sum of its parts.


The second prejudice that I hold is that life may not be an all or nothing phenomenon, but is spectral in nature. A little life” begins when fundamental particles transition to atoms, then atoms to molecules, and then chemistry transitions to biology. This journey finally arrives at full-blown emergent consciousness.

Consider this rather preposterous sentence: Since the big bang, atoms learned to talk.

The basis of this belief is very simple: biology evolved from chemistry. This evolution is probably still happening. It was not a one-off miracle event. This process of self-assembly, compartmentalization and advanced computation of complex systems permitted the extraordinary evolution of living things. Even the simplest being is many orders of magnitude more complex than, for example, our weather systems.

But, most biologists have remained stuck and have failed to grasp this important principle. Indeed, they are still quibbling about the definition of life!

To my knowledge, there is only one serious paper on the subject, in which Christophe Malaterre & Jean-François Chartier present a data-driven approach to assessing what they charmingly call lifeness.”

The American quantum physicist, Jonathan P. Dowling, forcefully expressed this same bias:

There is no such thing as life! There are interesting chemical reactions, like Stephen Hawking, and less interesting chemical reactions like salt crystals…There is no line, no breath of lifeseparating living from nonliving. That is a metaphysical bit of silliness. We should focus on interesting over boring chemical reactions and forget about this line that does not exist except in our own minds.”

This is almost straight out of John Wheelers It from Bitthat posits that  consciousness participates in creating reality.

This sculpture may seem to some to be animated in subtle ways. Some have commented that the quantum fluctuations seem like writhing eels or snakes. That is for the observer to decide. After all, the observer makes the reality.

But the stuff of matter does appear to have a shape-shifting anima to it. This is what the life science vitalists called Élan.

Élan vital or vital impetus, was coined by Henri Bergson to address the question of self-organization and the spontaneous morphogenesis of things in an increasingly complex manner. This smells to me like quantum fields becoming atoms, atoms becoming molecules, and chemistry becoming biology.

In 1998, David Bohm wrote Nature itself is a web of living energy, every object is a mirror made of a yarn of all that is”. (Wholeness and the Implicate Order)

Can it be that quantum fluctuations are a type of Élan, a type of prototypical lifeness?


Well, now that my confessions are over, and I may already have offended many of you, I want to shift my focus to “the quantum lunatic asylum”. In no way is this a biologists slur on quantum physics. Quite the reverse, it is a nod to how deeply complex nature has shown herself to be and how our brains appear poorly configured to grasp her mysteries.

117 years ago, Einstein published his theory of general relativity. This was one of a succession of near-mortal blows to contemporary thought including Heisenberg, Hubble, Freud and Darwin. This series of ideas shattered the calm model of an orderly, predictable universe.

The average person still is trying to digest these outlandish relativity ideas:

Time is an illusion
Things can be in two places at the same time
Contradictions can coexist as true
Particles are instantly interconnected over infinite time and distance
Distance is elastic
Space is not empty
Matter and energy are interchangeable
Everything is an uncertain probability curve
Matter derives from quantum fields
The observer affects the observed
Multiple dimensions
Parallel universes

Sheer madness!  Has the lunatic asylum has overtaken our best and brightest minds?

We seem not to know what stuff is. The more we search for its core, the more elusive it becomes. The Nobel biochemist Albert Szent-György wrote this same sentiment about the Élan of life:

My own scientific career was a descent from higher to lower dimension, led by a desire to understand life. I went from animals to cells, from cells to bacteria, from bacteria to molecules…On my way life ran out between my fingers”.

Is the stuff of matter also running out between quantum fingers as it flickers back and forth to energy at the Planck scale? Or, worse still, when it is two things at the same time, a particle and a wave?


As the search for the fundamental building block of stuff continues, it is evident that we have run out of words. Words have failed us. We need to look no further than the fact that we now assign extremely exotic descriptors including flavors, directionality, antiquarks, color, and spin to quarks. There are no adequate words to describe what we are trying to say.

This lack of language has confused everybody enormously.

Quantum field theories are by far the most complicated objects in mathematics, to the point where mathematicians have no idea how to make sense of them. Quantum field theory is mathematics that has not yet been invented by mathematicians.

We are also reaching the place where numbers fail us. For who can describe the new physics beyond the event horizon of a black hole, or in pulsars, magnetars, strange matter planets or antimatter stars? This cosmos is much more exotic and dynamic than the silent black vacuum portrayed in the Stanley Kubriks 2001: a Space Odyssey.

Where words fail, language becomes ambiguous. This leads me to my first misappropriation. Lewis Carrolls Alice’s Adventures in Wonderland, published in 1865, has been described as as “a descent into the dark world of the subconscious”. But, today we can apply that topsy-turvy contrarian world of Alice to the quantum world, where up is down, black is white and flavors have synesthetic colors. It has all the mutually co-exiting contradictions of subconscious dreams.  A new seemingly nonsensical language.

Nonsense is the apparent absence of sense, reason or logic. From Wim Tigges, comes this tantalizing suggestion:

Everything follows logic within the rules of the fantasy world; the nonsense world, on the other hand, has no comprehensive system of logic, although it may imply the existence of an inscrutable one, just beyond our grasp.”

This suggests that what may seem like nonsense is effectively a new type of logic. The quantum physicist Bohr introduced the idea of complementarity, where apparent contradictions can coexist without defying logic. Isnt this the wave-particle duality?

In 1873, Lewis Carroll, suffered the loss of his beloved uncle. This uncle had the rather exotic job of being the inspector of lunatic asylums. His responsibilities, among other things, were to check thimbles, forks, and soap. Carroll used this theme as the repetitive chorus line for his epic poem, The Hunting of the Snark:

You may seek it with thimbles—and seek it with care;

You may hunt it with forks and hope;

You may threaten its life with a railway-share;

You may charm it with smiles and soap

Might this also serve as our repetitive chorus for the lunatic asylum of the particle zoo? A nonsense rhyme with an inscrutable logic that is just out of reach, in need of a new language. These are, no doubt, risky questions.


For Lewis Carroll, the hunting of the Snark was not an adventure without risks:

For, although common Snarks do no manner of harm,

Yet, I feel it my duty to say,

Some are Boojums

And Boojums were much to be feared. Just as Don Quixote tilted at windmills in his crazed folly, so careers have been jettisoned in the pursuit of illusive Snarks. Tenures have been scuttled and troubles brought upon otherwise wise and honorable people. It is a graveyard of the triumph of hope over experience. The source of common-room snickers and tittle-tattle. As the fearless Cambridge Astronomer Professor Fred Hoyle, who followed scientific and intellectual trails wherever they led, discovered – this was not for the feint of heart.

Tilting at Boojum windmills is to venture forth blindfolded, armed only with a map that is but a blank sheet of paper (like the crew in the Carroll poem), a well sharpened pencil, and an ample wastebasket. Such is the adventure of intrepid quantum physicists: Hunting The Snark.

Using new logic, new words, inventing new ways to permit simultaneous contradictions to be equally true. This is the task.


Now we take the first of several steps to thread the needle to sew these disparate pieces together.

As big misappropriations go, the seconding of Boojams by the superfluidity physicists takes the biscuit. These Boojams, named by physicists, describe the exotic state that occurs in two isotopes of helium at cryogenic temperatures that result in the beautiful geometric patterns on the surface of one of the phases of superfluid helium-3:

These fascinating patterns are a macroscopic manifestation of the underlying microstructure. Under the surface, hidden from view. Just out of reach.


This is where the rabbit hole enters the labyrinth below the surface.

The unusual properties of helium-3 superfluid are largely due to quantum tunneling of quantum entangled Cooper Pairs of electrons (pairs of electrons with opposite spins that are bound together) and result in the exotic superconductivity of Boojam fluids.

Quantum tunneling has also been identified in the eyes of migrating birds, respiratory systems, and photosynthesis.  Are these quantum fields migrating to Élan?

Cooper pairs of electrons can undergo constructive and destructive wave interference giving the following beautiful constructive and destructive patterns:

Quantum interference in a Cooper pair splitter: The three sites model 

Cooper Pairs are at the heart of Professor Josephson’s Nobel winning discovery: The Josephson Effect causes the beautiful geometric patterns and quantum interference.


Possibly one of the most memorable quantum animations on the web is this one, which lies at the very core of our story. It is this very image that I have tried to reduce to liquid stone in my sculpture:

We dive now into hierarchical nested Russian dolls.

The quantum interference causing the geometric patterns in the ultra-cold superfluid helium-3 is key to the quantum tunneling that occurs in the Josephson Effect.

This, in turn, relates to the fundamental particle, the quark.

Quarks, in turn, are implicated in quantum fluctuations and are deeply tied to Heisenbergs Uncertainty Principle, which is at the very heart of quantum physics.

And so, it seems to me, these threads suggest how the very fabric of reality is deeply interconnected in nested hierarchies, where the numerous underground tunnels meet beyond the eye and beyond our grasp.


As we continue to thread the needle, these beautiful geometric patterns of the superfluid Boojams are stunning similar to the dynamic calcium-triggered rhythmic pulsations seen in biological slime mold aggregates, almost certainty a form of communication to the colony.

Slime molds are those strange fungal community structures that can solve maze problems better than humans, while lacking not only a brain but any semblance of a nervous system. This superior group intelligence, like that found in fish shoals, bird flocks and ant hills, is considered an emergent phenomenon of individually simple agents.

And here are actual photos of the calcium-triggered geometric pulsations of the slime mold:

You might notice that the Snark in the sculpture is decorated with these slime mold patterns, reminiscent of the quantum Boojams. If a quantum Snark were ever to be physically visualized, (of course, without the observer affecting the observed) my guess is that it would be an organically morphing shape with energy tendrils probing the space around it – not unlike the form of the slime mold.


Finally, you may notice a truncated inscription around the edge of the sculpture.

In full, it reads, the charges of matter are the energy debts of light”, and it is a poetic rendition of the Dirac equation by my friend, John Gowan Jr. He summarized his fanciful lines as follows:

In our asymmetric universe (which is missing all its antimatter, as noted by Paul Dirac) the original antimatter is registered as charges, which act to return our massive system to its original massless symmetric state of energy, light. (Personal communication).

Even the august figure of the Nobel quantum physicist, Neils Bohr was prone to such philosophical musings!

For a more detailed dive into John’s Gowen’s work, I suggest you look at.

So to summarize our tour of the labyrinth.

Lewis Carrolls The Hunting of the Snark –> dangerous Snarks being called Boojams –> Boojams are the Cooper Pairs which underly the Josephson Effect showing exotic geometry and quantum interference –> quantum interference is related to Quarks –> Quarks are at the heart of Heisenbergs Uncertainty Principle –> a Quark might well look like a slime mold with their exotic geometry –> is a dangerous Snark called a Boomjam?

And so in this circular geometric nonsense we have all descended into the lunatic asylum singing the chorus:

You may seek it with thimbles—and seek it with care;

You may hunt it with forks and hope; 

You may threaten its life with a railway-share; 

You may charm it with smiles and soap


I conclude this dedication of the sculpture with some lines from The Prelude by William Wordsworth in which he talks of when he stole a small boat and rowed across a lake at night.

When, from behind that craggy steep till then

The horizons bound, a huge peak, black and huge,

As if with voluntary power instinct,

Upreared its head. I struck and struck again,

And growing still in stature the grim shape

Towered up between me and the stars, and still,

For so it seemed, with purpose of its own

And measured motion like a living thing,

Strode after me. With trembling oars I turned,

And through the silent water stole my way

Back to the covert of the willow tree;

There in her mooring-place I left my bark, –

And through the meadows homeward went, in grave

And serious mood; but after I had seen

That spectacle, for many days, my brain

Worked with a dim and undetermined sense

Of unknown modes of being; oer my thoughts

There hung a darkness, call it solitude

Or blank desertion. No familiar shapes

Remained, no pleasant images of trees,

Of sea or sky, no colours of green fields;

But huge and mighty forms, that do not live

Like living men, moved slowly through the mind

By day, and were a trouble to my dreams.

And upon that note of unknown modes of being”, especially as it relates to The Hunting of the Snark in the particle zoo, with the addition of quantum fluctuations, I rest my case.

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