Science, maths and computers.
This photograph represents something truly incredible - the coming together of 29 of the greatest minds of the early 20th century, to discuss and debate the ins-and-outs of the newly formulated matrix mechanics, or what we now call quantum mechanics.
Einstein, Curie, Heisenberg, Schrödinger are names which are now embedded in common parlance. It’s impossible to complete a physics degree without hearing about most of the people in this photograph - the Pauli exclusion principle; Dirac notation; Brillouin zones; Debye length; Compton scattering; the Langevin equation… I could go on. Indeed, more than half of the people in this photograph became Nobel laureates.
As a physicist, it’s pretty humbling to look at this photo and think about how each of the dour faces staring right back at me has shaped human knowledge to such a degree.
The Fifth conference, on ‘Electrons et Photons’ became one of the most famous of the early Solvay conferences. It was the venue for one of the more infamous (and controversially misinterpreted) exchanges between Einstein and Bohr, where Einstein - a critic of Heisenberg’s Uncertainty Principle - famously asserted ‘God does not play dice’ to which Bohr replied ‘Einstein, stop telling God what to do.’
Here is the complete list of names in the photograph:
P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;
I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson
A couple of years ago I had the enormous privilege to attend a TEDx lecture by mathematician and cosmologist Roger Penrose. Unfortunately at the time I was only a beginner in physics, and his talk, Before the Big Bang, largely went over my head. What stuck with me though was his incredible hand-drawn slides. Rather than being dry Arial bullet points peppered with the occasional whimsical clip-art, they displayed a great deal of Penrose’s effort to put across to the audience what he was trying to say in a visually appealing and stimulating manner.
Here are a couple of slides from another one of his talks, this one on his controversial Orch-OR theory. Him and a colleague, Dr Stuart Hameroff independently came across and later co-developed a theory for brain computation and consciousness. While the neuron has long been assumed to be the fundamental computational unit of the bran - analogous to a transistor in a microchip - Hameroff and Penrose suggest that something much smaller is actually responsible: the microtubule.
Microtubules are self-assembling polymers found in the cytoskeleton of cells and made up of many repeated units of the peanut-shaped protein dimer tubulin. Each can be in one of two internal states denoted by black and white in the picture below. States can propagate along microtubules like cellular automata.
The idea introduced by Penrose is that each dimer is described as being in a quantum superposition of both states (right, below), evoking language from quantum computing, making individual tubulin proteins represent ‘qubits’ rather than ‘bits’.
Hameroff and Penrose express many concerns with the idea that neurons act as the fundamental unit of computation. One such concern is the apparent wealth of cognitive functions available to micro-organisms that lack a nervous system. For example, single cell organisms such as the Paramecium can swim, search out food, learn, remember and procreate, all without the help of neuronal computation.
Penrose and Hameroff cite certain experiments which show that different parts of the brain communicate faster than electro-neurochemistry should allow. Furthermore, Penrose has spent two books trying to prove that certain ‘non-computable’ (or Gödelean) thought displayed by humans proves that consciousness cannot be explained in terms of the brain being a classical Turing machine.
They claim that quantum computation through microtubule channels neatly alleviates these concerns.
However, for this theory to work, a few alterations must be made to physics… The ‘OR’ part of Orch-OR stands for ‘objective reduction’, which is an even more fundamental theory of Penrose’s, concerning the nature of quantum physics, general relativity and the nature of spacetime itself, in particular one of the most fundamental aspects of nature: the collapse of the wavefunction.
For Orch-OR and the theory of microtubule computation to hold, a great deal of physics first needs to be revolutionised, and so it is no wonder that Hameroff and Penrose have come under heavy criticism for their theory. Many cite non-predictive and untestable claims made by Orch-OR as well as fundamental flaws in the nature of how quantum states can propagate through matter.
Don’t get me wrong: it truly is a fantastic, and imaginative idea, but that doesn’t make it correct. It has a long way to come before it’s close to being acceptable as a working theory, but what it is successful at is making us question our most fundamental assumptions, which I think can only be a great thing in science.
The caption to this image is:
“Symmetrized density-density correlation function for 4 electrons in a graphene quantum dot. Four-fold symmetry, typical of a one-dimensional Wigner crystal, is seen.”
WOAH SCIENCEGASM! Those were a lot of words, none of which truly describe how awesome what this picture represents is.
We all know what the toy depiction of crystals are: balls of atoms connected by sticks in some regular cubic or hexagonal fashion. For some reason we’re quite comfortable with the idea that atoms can be stacked like cannonballs and to a good approximation this is true: atoms tend to arrange themselves in exactly the same way that a fruitseller will arrange oranges to fit as many possible in his tray.
Now, our concept of what electrons look like is far different. Instead of being static and inert solid spheres we think of them as tiny, charged, dynamic particles ‘whizzing’ around the nucleus of an atom (Though I’ve already discussed how this isn’t quite true).
How then can one explain the strange fact that under certain conditions, electrons can crystallise in just the same way that atoms do? This goes vastly against our intuition, but it’s another example of how awesome quantum physics can be.
The image above is (sort of) an image of just that - the observation of crystallised electrons (so called Wigner crystals) in graphene.
What’s amazing is that the electrons also follow the same stacking procedure as oranges, cannonballs and atoms despite being far from inert, solid, or static. Though they’re arranged relative to one another in this way, the actual spacing between electrons in such a crystal is roughly 2 million times their radius! Imagine a pyramid stack of marbles where each marble was shrunk by a factor of 2 million while staying in the same place - that’s what these electrons seem to be doing.
That’s not even as weird as it gets… ‘Holes’ are what we call spaces left behind by electrons when they escape an atom. In a sea of electrons, holes are like bubbles that move as independent particles in a solid. In fact they behave almost exactly like electrons but opposite in many respects (like how a bubble behaves like an ‘upside down’ water drop). Now, these holes (which are really nothing, just an absence of an electron) also, under the right circumstances, form crystals just like electrons do. In the image above, you can see how the red holes form a square lattice in a sea of yellow electrons.
In related news, I have a Crystal Physics exam tomorrow.
TL;DR: Things that stack like hard spheres:
This amazing gif by xverdxse is close to my idea of what an atom looks like. Far from the schoolbook picture of a clump of snooker ball protons and neutrons encircled by hoops of electrons the real picture of an atom is more like a vibrating cloud. A cloud? Yeah, a specific type of cloud called a probability density function. Woah maths alert! WEEOO-WEEOO, code red, code red!
A probability density function (PDF) is just a measure (function) of how likely it is (probability) to ‘find’ the atom in a given region of space (density). The thickness of the cloud in a small region is proportional to the likelihood of finding the atom centered within that region. In the image above, it is most likely to be found in the center of the black region, and the likelihood of it being found further away gets smaller and smaller until it’s nearly zero outside.
Every frame of this image corresponds to making a single measurement of it’s position. If it weren’t on a loop and we waited long enough, we should expect it to sooner or later make a large jump to a grey or even white area.
This is how quantum tunneling works: a particle confined to a domain will at any given time have a small but finite probability of being found outside its confinement region! Even a tennis ball has a finite (but astronomically tiny) probability of tunneling through a solid wall.
So what do atoms actually look like? Well, they don’t. They area collection of volumeless point-particles that don’t have any physical shape that you can draw on a piece of paper. However they have an effective shape that is described by (amongst other things and depending on what kind of measurements you make) the PDF.
If you take a step back from your screen and look at the above ‘atom’, you can kind of consider it as a single solid entity even though it is an amorphous cloud of pixels. This is all we can say about the ‘true’ shape of the atom and is a visual approximation we have to make if we want to try to understand what atoms look like and not chew off our own faces in philosophical frustration.
A great article by David Javerbaum describing the non-Newtonian politics of Mitt Romney:
“…Mitt Romney’s political viewpoints can be expressed only in terms of likelihood, not certainty. While some views are obviously far less likely than others, no view can be thought of as absolutely impossible. Thus, for instance, there is at any given moment a nonzero chance that Mitt Romney supports child slavery…”
Read the whole article here.
(Pictured: A Feynman diagram of an encounter between a Romney and an anti-Romney)