Polar opposite: From a series of drawings of fast disappearing animals
In my last post about sub-atomic particles and drawing, I was hedging around having to try and explain what is normally called quantum theory. So once again I’m going to have a go at trying to communicate what I think a complex scientific principle is and explain how I am trying to use my personal awareness of it (awareness rather than understanding, because I don’t think I have a hope in Hell of really understanding it), to inform my approach to making and thinking about drawing.
Quantum theory sets out an explanation of the nature and behaviour of matter and energy on the atomic and subatomic level. Its history is very interesting because as different scientists have attempted to explain it, our understanding of things such as energy, radiation, mass and matter have needed to change.
Right at the beginning of the twentieth century the physicist Max Planck first developed a quantum theory. He had set out to understand why radiation from a glowing body changes in colour as it gets hotter. We have all seen this when heating metal, it gets red, then orange, then yellow and then if you can heat it up far enough, it can get to be a blue colour. Think of our sun, this emits radiation and it’s yellow, but if we are in in the DC fictional universe, Superman comes from Krypton, a planet that circles a red sun that must have been cooler. But what is radiation? In Planck’s time it was thought to be a constant electromagnetic wave, but he couldn’t get the maths right when applying that idea to the reason for the change in colours. So he decided to think about the emission of individual units of energy, which he called ‘quanta’. Quanta being a term that covers all sorts of energy, a photon being a quantum of the electromagnetic radiation that we associate with light. (‘Quanta’ is the plural form of ‘quantum’) What had been sorted out during the previous century was that electricity, magnetism and light were all different sorts of electromagnetic radiation and we are now aware that there are waves of energy moving all around us in the form of TV and audio transmissions, gamma radiation from space, light and heat in the atmosphere, x-rays etc. Scientists understand them all as electromagnetic radiation, their waves of energy being called electromagnetic because they have oscillating electric and magnetic fields.
But we need to go back in time a little to sort out how these what appear to be very different things were seen to be all related.
But first of all there is that diagram that I’m sure many of you have seen before that shows how the various types of electromagnetic field are related. The visible light spectrum is enlarged because it is the one most important to us.
Electromagnetic spectrum
It was James Clark Maxwell who first unified the fields of electricity, magnetism and optics. He described light as a propagating wave of electric and magnetic fields. My understanding of propagating is that it refers to something’s ability to transmit something, or bring something forth (like a new plant) in this case light, through a medium. So this particular wave carries light, whilst others carry for instance radio waves. But I also think this is a problem with words, I cant see how a field can also be a propagating wave through a medium, unless the field is its own medium, within which the photon moves.
I think it is reasonably easy to visualise the relationship between electricity and magnetism because we have all seen experiments such as the moving of a magnet over a wire to induce an electric current. The one seems to be caused by the other and vice versa.
Maxwell relied on Faraday’s visualisation of magnetic and electrical forces as being like fields that extend into space. These fields allow for the transmission of forces to other charges. Such as in a magnet positively charged elements will head towards a negative charge.
Faraday visualised electric charges as producing fieldsthat extend through space and which transmit electric and magnetic forces to other distant charges. But he had to visualise a field, so I can sort of see another word based problem. I think of farmers’ fields as extending to two dimensions, but these ‘fields’ must be far more complicated than that. So how did Faraday think of fields? The term was originally used in mathematics to represent any physical quantity whose value changes from one point in space to another. So and I’m sure I will have got this wrong, if I want to measure the average temperature of lets say a brick, there would be lots of different temperatures to measure, all of which would be contributing to something I could call the overall temperature. For instance a point in shadow near the brick’s surface might be cooler than another point in full sunlight, but colder than a point near the bottom of the brick. This would mean that I am specifying a distribution of numbers, one for each spatial point. The temperature “field” would therefore be an accounting of those numbers. As a visual person, I could visualise this as a three-dimensional graph, having x, y and x axes. In this way I could think about a field as an expression of the spatial coordinates. The temperature would however be constantly changing, the brick being much colder at night, so the field would also vary with time. If a field is expressed as a function of spatial coordinates together with time it would look like this as an equation; T(x, y, z, t), where T is the temperature field, x, y, and z are the spatial coordinates, and t is the time. But electrical fields flow and bricks don’t.
How to plot a vector within three dimensional axes
Plotting velocities using vectors
Using vectors to visualise changes in a fluid
If you want to work out the mathematics of things that move, you use vectors, because if things are moving they don’t have a fixed position, but they do have magnitude and direction at each point in space as they move. When measuring the temperature of the brick we were using a scalar method or way of measuring a fixed single measurable entity. A bit like using bit maps to draw with on a computer instead of vector graphics. Vector graphics are comprised of paths, which are defined by start and end points. (See this earlier post) Because they are not made up of a specific number of dots, they can be scaled to a larger size and not lose any image quality. I know it might feel that I’m drifting off the point here but bare with me, because from what I can see so much of what science at this level is about is metaphor, trying to grasp something by thinking about something else, so I’m following my nose again and thinking about something else. Unlike raster graphics, vector images are not resolution-dependent. But I feel that I am resolution dependent, in the sense that my scale sits between the tiny sub atomic and the vast operation of stars like the sun. Vector images have no fixed intrinsic resolution, they display at the resolution capability of whatever output devices (monitors or printers) are rendering them. So are vector images a way of thinking about how electromagnetic and other energy fields can operate at both microscopic and cosmic scales? Am I in effect when I try to think of my day to day operation in the world as I think I see it, more like a raster graphic, having to hold on to the contents of millions of tiny bits of information, rather than being shaped by an idea of an energy field, an idea that can be applied at both macro and micro levels. Is this why everything around me gets fuzzy edges when I begin to look closely at them?
“It’s not what it is but where it is”, was a favourite phrase of myself and other drawing tutors during the time I was teaching students to draw from observation. Drawing accurately was about searching for points in space. Drawing with an attention to your perceptual awareness within this process was about recognising how eye and body movement caused a constant repositioning of relationships, therefore all you could actually draw was the record of the search for something that could by definition never be found. When you are looking to measure movement in space, a vector can deal with speed, as well as direction, something that I had not really thought about when undertaking those now distant drawing classes. The speed of the two eyes’ sweep through a space and of their scan of the objects and their relationships was not something we considered, it was simply taken for granted that a constant oscillation of movement was the actual state within which the situation of looking existed. We did not treat the world as something that consisted of static lumps, but we did ask questions, such as how can mass be visualised on a flat surface? Giacometti was the artist often cited as being someone who understood these things.
Going back to the world of mathematics, if instead of the brick we decide to measure the changing temperatures of a fluid in motion, such as in a flowing stream, or going back to that old life studio, changes in temperature in the air in a room, we would need to use vectors.
Giacometti
Going back to the world of mathematics, if instead of the brick we decide to measure the changing temperatures of a fluid in motion, such as in a flowing stream, or going back to that old life studio, changes in temperature in the air in a room, we would need to use vectors.
What I find interesting at this point is that by trying to understand what is going on I’m becoming more aware of how important it is that I’m always in motion, and if I step back from the world a little, I can see that everything else is in motion too. There is a wonderful Sam Taylor Wood video of a still life that reveals that a still life is in fact never still.
Sam Taylor Wood: Still life
Sam Taylor Wood’s ‘still-life’ is of course about time and the reality is that time is a dimension that non scientists rarely think about at a quantum level. It could be that time is an emergent phenomenon resulting from entanglement, in which different quantum particles effectively share an existence, even though physically separated, so that the quantum state of each particle can only be described relative to the other entangled particles. This entanglement, does seem to keep re-occurring, just as a photon is not a separate particle, it is a flux in an energy field, it is what happens when I take away things and let processes take over.
A never stillness seems to lie behind the way to think about everything, so I think I need to return to science again. The relationship between optics and electromagnetism is a fundamental one and central to what it means to be a visual artist because vision is itself something that would never have developed if light had not existed. On Earth light from the sun provides energy for all living things, it fact it could be argued that we are just a very strange physical form of the Sun's energy. So how does the Sun produce light?
The Sun mainly consists of plasma. Plasma is sometimes called the forth state of matter, (solid, liquid, gas and plasma) and is called plasma because Irving Langmuir who was the first scientist to name it, thought it reminded him of "the way blood plasma carries red and white corpuscles and germs". The Latin word plasma was taken from the Greek and meant 'something formed', 'a mouldable substance' or 'jelly', and although I have to keep reminding myself of how words trap you into thinking about things in a certain way, I think this is a useful metaphor to hold on to. In our blood it is the carrier for vital ingredients such as cells and proteins around the body. In the Sun, plasma is in constant movement and acts as both a carrier and emitter of radiation.
In the Sun’s core energy is produced by hydrogen atoms being converted into the nuclei of helium. This is actually what is happening when plasma, which occurs when an ionized gaseous substance, in this case hydrogen, becomes highly electrically conductive to the point that long-range electric and magnetic fields dominate the behaviour of the matter. This is possible thanks to the extreme pressure and temperature that exists within the core. The fusion of four protons (hydrogen nuclei) into one alpha particle, two protons and two neutrons bound together into a particle that is identical to a helium nucleus, releases two positrons, as well as two neutrinos (which changes two of the protons into neutrons), and energy. This energy is electromagnetic and works its way through the Sun’s outer layers getting less powerful as it does so, finally getting to the surface, where it leaves the Sun in the form of radiation. I.e. energy travelling as rays.
The sun emits all of the different kinds of electromagnetic radiation, (see the chart above) 99% of its rays are though in the form of visible light, ultraviolet rays, and infrared rays (what we call heat). Energy waves travel out from their source in straight lines, which is why they are also called rays. (These are Maxwell’s travelling harmonic waves) The confusion is that energy is sent out as a wave, even though it travels in straight lines, this is called the rectilinear propagation of light. But now I think it gets hard to think about. I have tended to think of photons as being particles of light, but now understand that there are no such things as particles, just bundles of energy, so a photon would bethe quantum of the electromagnetic field, or the force carrier or mover within the electromagnetic force. But it looks as if the scientists want to deal with it as both a particle and a wave. Again it’s a problem with words, if the situation is thought of as a certain moment in a series of events we call light, perhaps it’s easier to reconcile, but this does mean including time as a constant factor and therefore movement, in the way we think of everything.
It is as if our way of ‘knowing’ is being challenged, and my guess is that it has always been the case, because if there are so many energy states interpenetrating my existence, including the energy state that is myself, there must be a sort of built in awareness that allows me to navigate life, because I am just one example of a species that has developed out of many other species over millions of years. This could be very similar to the way that some birds navigate by being able to detect the nonlocal quantum signature of electromagnetic waves. The protein that apparently allows this to happen, it has been theorised, can be found in all living creatures that have evolved to move over distances. Perhaps this is something we have lost the ability to use, but which occasionally trips into our awareness. This could be why we hear echoes of things that aren’t there, intimations of other presences, or portents that drive us to make decisions about which we have no real understanding as to why, things that Janice Radway points to in her introduction to Avery F. Gordon’s ‘Ghostly Matters’, whereby she makes the point that we need to develop a way of negotiating between what we see and what we know and I would add what we feel or tacitly grasp to be the case. This shadow world is usually associated with the subconscious but perhaps this is the way things are, the subconscious being like the awareness of subatomic electromagnetic fields, more to do with being a process than a thing.
But here is the maths, here is the stuff that I’m also suspicious of, because of the way I think it suggests its own answers. In copying this information from the web I’ve tried to leave in the hyper-links so that you can follow the detail.
What Maxwell did was to show that electromagnetic waves describe propagating oscillations in the strengths of electric and magnetic fields. Maxwell’s wave equation showed that the speed of the waves, labeled c, is determined by a combination of constants in the laws of electrostatics and magnetostatics. This is the equation that demonstrates that this is the case:
Where ε0, the permittivity of free space, has an experimentally determined value of 8.85 × 10−12 square coulomb per newton square metre, and μ0, the magnetic permeability of free space, has a value of 1.26 × 10−6 newton square seconds per square coulomb.
The calculated speed, about 3 × 108 metres per second, agreed with the known speed of light, and led Maxwell to conclude that, light itself—including radiant heat and other radiation, is an electromagnetic disturbance in the form of waves propagated through the electro-magnetic field according to electro-magnetic laws.
So here we have the bringing together of a whole series of things that previously were separate, and more recently
Thinking of dualities the 'is light a particle or a wave?' issue became even more problematic when Heisenberg proved that precise, simultaneous measurement of the position and momentum of a subatomic particle was impossible. The more precisely one value is measured, the more flawed will be the measurement of the other value. This is the uncertainty principle, which became a very important part of what we now know as quantum theory.
The two interpretations of quantum theory that develop the implications of the uncertainty principle are the Copenhagen interpretation and the many-worlds theory. Niels Bohr proposed the Copenhagen interpretation of quantum theory, which asserts that a particle is whatever it is measured to be (for example, a wave or a particle), but that it cannot be assumed to have specific properties, or even to exist, until it is measured. Bohr was therefore suggesting that objective reality does not exist. This translates to a principle called superposition that claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check. The analogy of Schrodinger's Cat is often used to illustrate this idea. Place a live cat in a thick lead box, inside of which is an unbroken glass cyanide capsule and seal the box. We can’t know if the cat is alive or if the cyanide capsule has broken and the cat has died. Since we do not know, the cat is both dead and alive, according to quantum law, it is in a superposition of states. It is only when we break open the box and see what condition the cat is in that the superposition is lost, and the cat must be either alive or dead.
Schrodinger's bears
The second interpretation of quantum theory is the many-worlds or multiverse theory. It holds that as soon as a potential exists for any object to be in any state, the universe of that object transmutes into a series of parallel universes equal to the number of possible states in which that the object can exist, with each universe containing a unique single possible state of that object. Furthermore, there is a mechanism for interaction between these universes that somehow permits all states to be accessible in some way and for all possible states to be affected in some manner.
This seems to me to be scientists trying to avoid the problem, perhaps what they are really saying is, 'we don’t know the answer'. The fact that all of this stuff only applies to the 5% of the universe that we can access, also suggests that when and if we begin to understand what the other 95% of dark matter and dark energy consists of, we may well find that everything is interconnected and that a common belief in ghosts and other such phenomena has roots in those somethings that we just feel are there but cant experience empirically.
Quantum vanitas
Which brings me back to drawing and drawing’s ability to take us places where logic doesn’t go. I’m not going to argue that drawing in some way taps into other possible worlds or existences, but I will suggest that what drawing can do is allow you to take flight, allow you to become lost in the absorbsion of doing and in that absorbsion perhaps you might be able to tap into fields of energy, in a way unavailable to words or mathematical equations. After all if bees, like dolphins can understand the concept of zero and use what seems like maths to solve problems, we may well have over estimated our skill base. Perhaps what we are missing is simply that bees are more perceptually attuned to magnetic or other fields and from their point of view we are bee-blind.
Diagram from an article looking at the map-like spatial memory of a bee, suggesting that a bee dance is like a drawing whereby they are mapping territory.
In my own work I often find I am wondering through space directed by something I'm unsure of. I believe that I am magnetically charged and in that charge sometimes I find a form.
Drawing in a quantum library
Artists looking to develop structures based on the implications of mathematical forms as indicated by this type of investigation often move into animation. Equilibrium by Memo Akten is a good example of this type of controlled response to the implications of mathematical possibilities.
References
If you want to read about birds and their ability to tap into magnetic fields, this is one of several articles on the subject: A Pauls, James & Zhang, Yiteng & Berman, G & Kais, Sabre. (2013). Quantum Coherence and Entanglement in the Avian Compass. Physical review. E, Statistical, nonlinear, and soft matter physics. 87. 062704. 10.1103/PhysRevE.87.062704.
Honey bees navigate according to a map-like spatial memory: Find the article on honey bees here: Randolf Menzel, Uwe Greggers, Alan Smith, Sandra Berger, Robert Brandt,Sascha Brunke, Gesine Bundrock, Sandra Hülse, Tobias Plümpe, FrankSchaupp, Elke Schüttler, Silke Stach, Jan Stindt, Nicola Stollhoff, SebastianWatzl Proceedings of the National Academy of Sciences Feb 2005, 102 (8) 3040-3045; DOI:10.1073/pnas.0408550102
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