Spooky Action at a Distance
or Alice & Bob — a love story
Part One: Uncertainty Abounds
1. In any formal system that is written to express mathematics, there will exist a proposition that is undecidable. Neither it, nor its negation can be proved.
2. One of the things that cannot be proved in a formal system is the consistency of that theorem.
— Gödel’s Incompleteness Theorems.
Amid the wreckage of war-torn Europe in the 1920s, David Hilbert, the most influential mathematician of his time, sought to prove the consistency of mathematics. From the ruins of the present, he saw this project as a vehicle to a golden era. He put out a call to colleagues and scholars from the famed Vienna Circle, most of whom were certain that mathematics and logic were provably consistent.
So it might have come as a considerable blow to this ideal when a shy doctoral student, Kurt Gödel, declared that this ambition might be unattainable. In a mumbled presentation, the last at the Koenigsberg conference in 1930 held to celebrate the success of Hilbert’s quest, he presented his now infamous incompleteness theorems.
It might have come as a shock, but in fact the significance of his findings were largely ignored, due to Gödel’s halting delivery. It was John Von Neumann, known for his contribution to computer science (the Von Neumann Model for computer architecture is still the basis of the majority of modern computers, and he also worked on the Manhattan Project. Due to his charm, wit and fondness of the heady social life of Californian Academia in the 1950s he came to be known as Uncle Johnny) who realised the importance of Gödel’s two theorems, which in a generalised formulation are written above.
It might be useful at this point to describe the two theorems by way of analogy. Let’s look at the first theorem: In any formal system that is written to express mathematics, there will exist a proposition that is undecidable.
A nice way to visualise this is to imagine building a hypothetical mathematical box — precisely conceived and formalised using arithmetic logic. In this box, we wish to permanently confine a cat (also formally defined, using the same absolute logical rules we used to build the box).
We’re happy with the logic of our box and we trust our cat will be forever trapped by the rigour of the logically consistent rules we used to create the two entities. But according to Gödel, there will always be the possibility of the cat escaping even our most clever and fiendish designs.
It turns out our cat is far more crafty than Schrödinger’s — the cat who continues to live and die a million lives in the famous thought experiment that takes its name.
But that’s nothing compared to the second theorem: One of the things that cannot be proved in a formal system is the consistency of that theorem.
This tells us is that when we have built our box and cat — if we have the nerve to then open the box, what we find might not be a cat at all — it could just as well be a chicken, or a marine cephalopod, or a recipe for paella… anything at all. It could quite as easily be a neutron bomb connected to a timer reading 00:00:00:05.
So, despite the best efforts of these great mathematicians and philosophers, uncertainty remains untouched at the heart of logic, just out of reach.
There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.
— Lord Kelvin, c1900.
We might hope that the stuff that makes up the real world can be known with certainty, even if the abstract games of arithmetic cannot. After all, since Newton, the world could be described as an eternal clockwork machine, deterministic and forever reliable. As Kelvin’s quote shows, towards the end of the nineteenth century, some were so confident of this that they declared the pursuit of physics was effectively at an end.
Lord Kelvin uttered these words just before the foundations of physics were profoundly shaken by the twin revelations of general relativity and quantum mechanics. What quantum mechanics revealed was that uncertainty in physics was not due to an epistemological lack of detail, nor any deficiency in our measuring apparatus — it lay at the very heart of these theories and was an unavoidable and essential component, central to the workings of nature.
This essential ambiguity — embedded in reality, not our understanding of it — is enshrined in Heisenberg’s famous Uncertainty Principle. This states that there is a fundamental limit to the precision with which we can be know the physical properties of a pair of particles, such as their position and momentum. The more accurate our knowledge of one property, the fuzzier
is our knowledge about the other.
So in physics too, we fail to corner and catch uncertainty. Instead, it seems, we must start living with it. Maybe its time we all stopped worrying and learned to love the [uncertainty] bomb.
Part Two: Entanglement, with Diamonds
So, it turns out humanity’s ongoing quest for certainty continues to be foiled. Since the first awakenings of human cognition, culture and society, we have sought to give sense and meaning to the seemingly random vagaries of an uncaring and sometimes vicious universe —the inevitable calculus of who lives and who dies, which one prospers and which one fails.
We have built temples and churches and sacred monuments in our attempts to propitiate the gods, placate nature, and bring some certainty into a random universe. We have raised huge stone circles to both celebrate and try to understand those things in the world that at least seem to embody certainty — the daily appearances and journeys of the sun and moon, and the movements of the heavens.
Since the Enlightenment ushered in the so-called Age of Reason, we have built monuments of a different sort, and never more so than in the twentieth century. Grand telescopes have been raised to gaze at the heavens; incredibly complex and delicate spacecraft have been sent to look far back to the creation — the beginnings of time and space itself.
We build gigantic particle accelerators with which we peer deep into the depths of the building blocks of nature that make up everything we know (but not everything there is, as we have discovered in the last few decades) and we construct apparatus that can detect movements a thousand times smaller than the size of a proton to hear the sound of black holes colliding, many millions of light years away in space and time. Lawrence Krauss, a cosmologist and Professor of Physics at Arizona State university, considers these projects the ‘gothic cathedrals of our age’ — bringing together the efforts of thousands of people, labouring for years with a singular purpose.
By using these monuments to science, we may have conceded in our quest for absolute certainty, but in quantum mechanics, we have our most reliable and tested theory of reality yet. In fact, so successful has the theory been, the period following it’s discovery and refinement has sometimes been called the ‘shut up and calculate’ era. The central weirdness and uncertainty of quantum mechanics was ignored as we used it to build the modern world, of which there is little that exists that is not fundamentally built on the theory.
One of these weirdnesses is the quantum mechanical notion of entanglement. There are many complicated explanations for the ideas around entanglement, but in essence it can be explained quite simply.
Let’s take two particles, and bring them close together. We let them interact — let them feel each other a little bit. We have now entangled our pair of particles — they are now linked in a fundamental and special way.
One of the properties of our of entangled pair is that when we change
the state of one particle, the state of the other changes too. This is called complementarity. This will happen however far you move the particles
away from each other. This is strange — how can they signal each other
over a distance? But what is stranger — much stranger — is that this
change happens instantly.
Einstein’s theories of relativity tell us that there is a cosmic speed limit — that nothing can travel faster than the speed of light. But our pair of particles undergo their changes simultaneously and instantaneously over an arbitrarily large distance — even if the particles were at opposite ends of the universe.
Einstein didn’t like quantum mechanics. He particularly didn’t like complementarity and entanglement. He called it Spooky Action at a Distance. Even though his analysis of this spookiness has shone light onto whole new areas of physics including quantum teleportation, cryptography and computing, he never quite got on with QM.
INTERMISSION: Research Methodology
So… if perhaps, by now, we’re getting a little tired of all this uncertainty, it is in entanglement that we might find some relief. We might be feeling a little jaded by all this talk of maths and physics too. Maybe we need a story. Something with a little drama, maybe some romance. Space travel (no FTL!) and inter-galactic themes. And diamonds. Definitely diamonds.
But who could tell such a story? And how could it be told?
Part Three: Alice, Bob and Quantum Gravity
One of the grand challenges of modern physics is the quest to unify the two theories that describe the word we live in — the theories of relativity and quantum mechanics — the very large with the very small.
Very recent research into quantum gravity (one approach to this challenge) sees the whole of space being entangled in a very special way. Leonard Susskind, professor of theoretical physics at Stanford University and director of the Stanford Institute for Theoretical Physics is at the forefront of this research. And from his theories, we can can tell our story.
This story is set in sometime in the future, around tea-time. The heroes of our story, Alice and Bob [1], are deeply in love and have recently wed. Because they are both particle physicists and foresightful women, familiar with Susskind’s theories of entangled space, they ensured that the Graff diamond rings they exchanged on the occasion of their engagement were made entirely from entangled particle pairs… just in case.
Shortly after our story begins, however, our couple are separated, both ordered on separate missions which take them to far-flung reaches of the galaxy, many light-years apart.
Then disaster strikes. Due to the right switch being pulled at the wrong time in the control room of CERN’s new planet-circling particle accelerator, a black hole is created that destroys the galaxy and everything in it. Mysteriously, only Alice and Bob survive… Can they ever get back together?
Well, Leonard Susskind says yes, they can. If Alice and Bob follow his theories, they can be reunited. All they need to do is compress their still-entangled diamond rings so much as to create a pair of entangled black holes. Due to the Susskind’s notion of complexly entangled space, the two entangle black holes are connected by an Einstein-Rosen Bridge — more commonly called a wormhole — through which they can travel and meet.
Alice and Bob are once again together, entangled, and still madly in love.
Part Four: Entangled Artefacts
Is the story of Alice and Bob a flight of fantasy? Well of course it is. There are many flaws in the tale, but the conclusions from the physics at the heart of the story are sound. As always, the devil is in the doing. We can easily entangle particles, with the right equipment. Quantum computation is based on creating and shepherding pairs of entangled electrons. But getting them to remain entangled (at a distance, at larger scales, at any temperature above absolute zero) is an altogether trickier business.
Leo Kouwenhoven, Professor of Quantum Transport might be able to help. Along with the DiCarlo Group at TUDelft have shown that even certain molecules can be entangled, and therefore effectively occupy two places in space at once. He demonstrates entanglement at the millimetre scale at room temperature. So this idea of entangling diamonds doesn’t seem quite so impossible after all.
Sometime in the not too distant future, a jeweller such as Graff might be able to entangle the diamonds in their engagement range. Entanglement is quite the apt metaphor to use for items meant to further entangle their wearers in eternal romantic bliss — however far apart they may be, their diamonds are always in the same place. Certainly worth a pitch to the marketing team.
This rather frivolous and frothy chain of thought is a bit of fun, and not particularly consequential, buy it might lead one to think a little deeper about how people are entangled, and how one might be able experiment with this idea of spooky action at a distance. How might it be possible to maintain contact, not through dry text, or even voice — just the knowledge of the presence and proximity of another, however far apart in space. An analogue, qualitative impression, with all information felt, not spoken. A tele-haptic intervention perhaps.
Touch at a distance
Touch between one another is common to us all, and conveys magnitudes. To investigate the idea of touch at a distance, it is sensible to start perhaps one of the basic atoms of touch — pressure. Could we mediate the pressure of touch over the network, at a distance? Would it ‘translate’?
The image below shows an experimental prototype of what such a device might look like. It consist of two pairs of components, equally matched, but having opposite behaviour. These matched machines can in theory be separated by any distance, being connected through the network.
The paired devices would need four main components — something to afford and invite touching; a sensor to deliver real-time data; a micro-controller to make sense of this data and send it to its twin; and a motor to react to the users touch and pressure.
As one person pushes on the touch-pad, the pressure of her finger will cause the motor on her device to move away from her, at a speed that depends on the pressure of her finger. It will also cause the motor on the other device to move in the opposite direction.
It’s not quite so simple though. Someone may also be pressing on the touch-pad — across the table, in another room, or perhaps in Hong Kong or Sydenham, Karachi or DesMoines. The pressure from their touch will of course impede the motion of the other user. In this way, it may be possible to sense the presence of a real person at the other end of the line — real touch, in [almost] real time.
It’s that almost that is of concern. The network is fast, but like anything else, it can only transfer data below the speed of light. And when we’re dealing with much more complex tele-haptics and tele-presence over distances, the amount of that needs to be sensed, collected, processed, transferred, processed a second time, to be finally transformed into movement by actuators at the other end… the speed of light is way too slow.
Mischa Dohler, Professor in Wireless Communications at King’s College London has thought a lot about this problem. With his experience in telecommunications he is well placed to find ways to beet the speed of light.
The problem is in the time it takes to send the big data-streams needed to enable fully real-time tele-haptics. The solution is to send only small amounts of data, and do a lot of pre-processing at either (or any) node. Dohler and his colleagues at the Centre for Telecommunications Research, King’s College London, intend to leverage the speeds and features of the 5G network to allow only the optimum amount data to be sent over the network, while predictive machine learning models will handle all the sense data and actuator movement at either end of the tele-haptic connection.
Further iterations
multi-touch
The most basic module described above can be thought of as being a geometrically two dimensional object — a line in space between the furthest extents of the two touch-pads. It could be greatly expanded in its ability to transmit touch by adding a third dimension. By using a touch-pad that could sense pressure over many points on the plane, and increasing the number of motors we use, we might be able to mimic the touch and pressure of a hand — pressure from all the points on the palm, fingers and thumb.
Below is an image showing how this might work. The multi-touch-pad senses the pressure of the hand in a 16x19 grid — low resolution, but it might be enough to give the impression of more complex human touch. This is then sent to a micro-controller, which translates this data into linear movement data and transmits this to the motor controllers. This raises and lowers individual rods attached to the motors in accordance with the pressure readings from the multi-touch-pad. A sheet of flexible material is stretched between all points n the 16x9 grid of actuator rods.
heat
Another vital component of human touch is temperature. We can transform our pressure data into changes in temperature using the peltier elements — simple ceramic squares which will either become warmer or cooler depending on the amount of current they receive. This could be felt by the hand of another person, either in real-time or offline. It could also be visualised using a heat resistant material. The tiny handprint left by a child as he leaves to go to school could be seen and felt by his father when he arrives at his office.
These objects are entirely not intended to be product prototypes in the usual sense of the word. They are meant to be experimental and inquisitive interventions, questioning and attempting to understand the most basic sense of touch at its most simple level. It also asks questions about the truth of our senses — is someone really there at the other end, or is this just a simulation of touch and movement, being played out in blind algorithmic reaction to our touch, but entirely dark, unconscious, un-present. And could we tell the difference?
[1] Alice and Bob are fictional characters commonly used as placeholder names in cryptology, as well as science and engineering literature. The Alice and Bob characters were invented by Ron Rivest, Adi Shamir, and Leonard Adleman in their 1978 paper “A method for obtaining digital signatures and public-key cryptosystems.”[1] Subsequently, they have become common archetypes in many scientific and engineering fields, such as quantum cryptography, game theory and physics.[2] As the use of Alice and Bob became more popular, additional characters were added, each with a particular meaning.
