Just a little under 2,000 years ago, Claudius Ptolemy was working in Alexandria. Probably from a Greek family, a citizen of Rome, he lived there for about eighty years (from roughly 85 AD to 165 AD). Although his personal life remains largely unknown, he wrote major works on optics, geography, astrology and astronomy, as well as a mathematical study of music. However, among these it is as a theoretical or mathematical astronomer he is best known today.
Around a thousand years before Ptolemy, Babylonian astronomers had started to address the prediction of the movement of the sun, moon and planets, which, in turn, allowed a better understanding of such events as eclipses and navigation at night. For them, the issue was simple. These objects moved in cycles, and the task was to describe the cycles. As it happens, the Babylonians didn’t assume that the cycles were all around the earth; it was only some hundreds of years later that the beginnings of a geocentric model began to emerge. The Babylonian astronomers used mathematics to develop simple formulae to explain their observations.
Ptolemy was the lucky inheritor of their observations and those of many others over at least 1,000 years. At the same time, there was increasing commitment to a cosmological model that placed the earth at the centre of the universe, all other objects circling around it. However, while these observations and the geocentric model seemed to make a great deal of sense, there were some irritating anomalies. Ptolemy’s great achievement, published in thirteen volumes, (in a book called the Almagest), was to come up with an analysis of motions of observable bodies in space, which was predictive, reasonably accurate, and yet fulfilled a philosophical preference for seeing the design of the universe predicated on simple geometrics, and the earth at the centre of the universe. His analysis was to last, essentially unchallenged, for 1,500 years.
His starting point was that the sun ‘circled’ the earth. Based on calculations of the seasons and the length of the year, he proposed a model for the sun, which followed a circular path around the earth. However, to make sense of all the observations, and especially the equinoxes, the centre of that circle was not the earth itself, but a point close by (called the eccentric). Next, he proposed a slightly more complex model for the moon. He proposed that the moon revolved around the earth following a circular path, but, as it followed that path it also went around a small circular path, an epicycle, the centre of which followed the larger circular path! It’s hard to explain in words, but his explanation was based on two key ideas: the earth is at the centre of the universe with objects like the sun and the moon that followed circular paths (focussed around a point close to the earth), and some, like the moon followed epicycles within these circles.
Once he had established that idea, he found it was possible to move on to explaining the apparently bizarre behaviour of the planets, which went in one direction most of the time, but them sometimes decided to travel in the opposite. Confused? It was confusing. Above is a (simple!) diagram explaining the motions of the sun, Mercury and Venus (any more planets, and it would require a massive sheet of paper). [i]:
Today, we can look at this diagram and smile. Why? Because the geocentric model has been abandoned, and we know the planets, including the earth, revolve around the sun, following simple elliptical orbits which centre on two foci, one of which is the sun.[ii]
My father was an astronomer, and he introduced me to the world of the paths followed by planets, which led him on to explain the brilliance of Kepler’s three laws of planetary motion.[iii] Poor Ptolemy! What he did was such an achievement at the time, but, as we review his complex models in the light of what we know today, we can say they were “kind of nuts”!
Now, I’d like to talk about another topic in physics, and this is the world of sub-atomic particles, something else my father had tried to explain to me. When I was young, it was all fairly simple. Atoms had three constituent parts – protons, neutrons and electrons. Electrons were a bit of a nuisance, because you couldn’t simultaneously pinpoint where they were and how fast they were travelling (the uncertainty principle). Odd, but for schoolboy physics, that was just fine.
Then there were photons and neutrinos. Photons were like little packets, particles travelling at the speed of light, but, inconveniently, also behaving like waves (waves of what??), with no mass. Neutrinos were truly glamourous: they travelled at the speed of light, but weighed nothing, and were zipping through us all the time. We might call this the ‘Babylonian’ phase of sub-atomic particles: they were observable (using clever devices), and more or less predictable, but scientists lacked an adequate theory to explain all their properties.
Since those days, things have gone rapidly downhill. It started with photons. Bad enough that they were simultaneously both particles and waves. That was demonstrated at the beginning of the 19th Century by Thomas Young. The essence of his experiment was simple: shine a light through two slits on to a screen, with each of the slits having a cover. If one of the slits is covered, then the light is shown as a simple image on the other side. Uncover both slits, and the two beams of light come together and form an interference pattern, (lines of light with dark in between). Simple and elegant; light has wave properties.
However, in the 20th Century, the experiment was repeated, but with better technology. Fire a single photon of light with both slits uncovered, and the photon will land on one of those areas where you would expect to see light (as a result of the interference effect, as above). Now fire a single photon with one slit covered, and the photon lands where previously it was dark. Somehow the photon ‘knew’ that only one slit was open, but how could that be? If you want to read more, I have always enjoyed Gary Zukav’s descriptions of the weird and wonderful world of physics [iv] Understanding the details is not important, however: the key point was that photons experimentally didn’t ‘behave’ as theory would lead us to expect. This turned out to be just one of many critical observations that didn’t appear to make sense.
That was then, but it’s been getting worse. There is a very strange thing called ‘entanglement’.[v] Measuring the physical properties on certain pairs of particles shows they are entangled. What does this mean? Suppose we have a pair of entangled particles whose total ‘spin’ is known to be zero, and one particle is found to have clockwise spin on a certain axis, the spin of the other particle, measured on the same axis, will be found to be counterclockwise; this is to be expected due to their entanglement.[vi]
However, if we take any measurement of the property of just one particle, the result will be that measurement will change the original quantum property. In the case of entangled particles, such a measurement will be on the entangled system as a whole. In other words, one particle of an entangled pair “knows” what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances. Some recent research suggests this ‘impossible’ transfer of information may also take place over time in such a way that the two particles are not simultaneously in existence.[vii]
Hey, we just slipped by that stuff about ‘spin’. Physicists list of elementary particles has three types: quarks, leptons and bosons (as well as the Higgs Boson of recent fame). Showing a sense of humour, scientists suggest quarks come in six ‘flavors’ – ‘up, down, bottom, top, strange and charm’; there are six types of leptons – electron, electron neutrino, muon, muon neutrino, tau, tau neutrino; and twelve varieties of boson – the photon, the three W and Z bosons of the weak force, and the eight gluons of the strong force. Charmed? I’m sure you’re better informed now!
One final complication? Many physicists like to consider elementary particles as if they are like minute (really minute!!) rubber bands, oscillating in space. This is the topic called string theory. In order to make sense of this theory, the mathematics has become very complex moving beyond the four dimensions with which we are familiar (depth, height and width, if you like, with time added as the fourth – thanks Einstein!), to ten dimensions. Some mathematicians have moved on to 24-dimension mathematics. [viii] All this recent thinking has two very interesting consequences.
First, there is the challenge of ‘reality’. These multi-dimensional analyses are proving very rewarding for mathematicians. However, from the fifth dimension on, there is nothing that is being described in mathematical terms that corresponds to our sensory reality (except, of course, in way out television programs and SF films). There are many theories about what these other dimensions might be, but no real basis beyond speculation. Are they ‘real’? That question makes us ask ‘what is meant by ‘real’?. Can something be real if it can’t be sensed?
The second consequence is that several theoreticians have become very interested in the ‘multiverses’ concept. This has two competing models right now. One has been proposed by Lisa Randall and Raman Sundrum, who argue there is a fifth dimension on the cosmological scale, the scale described by general relativity. According to their theory what we normally call our universe might be embedded in a vastly bigger five-dimensional space, a kind of super-universe. Within this super-space, ours might be just one of a whole array of co-existing universes, each a separate 4D bubble within a wider arena of 5D space.[ix] Makes my head ache!
The other is the idea there are “many worlds”. This theory implies that all ‘possible’ alternate histories and futures are real, each representing an actual ‘world’ (or ‘universe’). In other words, there is a very large, even infinite, number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes. You drop a cup and it breaks; at that moment, there is another world created in which you drop that cup and it doesn’t break, and that world evolves independently from the one where it did. We can blame Hugh Everett for this one. [x] Seems a long, long way from our lived-in world.
I think we are at the Ptolemaic phase of understanding elementary particles. In case you didn’t get the point, it doesn’t make sense because it’s “kind of nuts”!! Instead of cycles and epicycles we have strings and many worlds. If you’re concerned about this crazy stuff, no need to worry: we just have to wait for the Copernicus of elementary particles to turn up! Just hope it’s soon ..,
[i] James Ferguson (1710-1776), engraved for the Encyclopaedia by Andrew Bell. – Encyclopaedia Britannica (1st Edition, 1771; facsimile reprint 1971), Volume 1, Fig. 2 of Plate XL facing page 449
[ii] Yes, it has got a bit more complex as astronomers have had to include variations in these elliptical orbits for each planet as a result of the gravitational impact of all the other planets: however, remarkably simple compared to Ptolemy’s model.
[iii] These are well explained in Wikipedia: <https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion>. Did I say well explained? I got lost half-way through!!
[iv] Gary Zukav, The Dancing Wu Li Masters, Rider, 1979: see pages 84-88 for the dual slit experiments.
[v] <https://en.wikipedia.org/wiki/Quantum_entanglement>
[vi] Please don’t ask me what ‘spin’ is: let’s just accept it for the moment!
[vii] Again, this is well explained in an article: <https://aeon.co/ideas/you-thought-quantum-mechanics-was-weird-check-out-entangled-time>
[viii] <https://aeon.co/essays/how-many-dimensions-are-there-and-what-do-they-do-to-reality>
[ix] For a completely unintelligible summary for a non-mathematician like me, see <https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model.
[x] You, another Wikipedia reference, for which I make no apology. It’s a good starting point: < https://en.wikipedia.org/wiki/Many-worlds_interpretation.
