Today’s question: When we see the structure of an atom, what should we conclude?
Very interesting question. Atom: the most basic element in the universe. Atom is the smallest union into which matter can be divided without the release of electrically charged particles. One of the most fascinating things in our nature is the existence of a highly organized atom. Ancient Greeks could only imagine it. For millennia, we doubted the existence of atoms. We told ourselves that the idea of atoms is nothing more than a speculative imagination. But in our age, we can see it using devices like Scanning Tunneling Microscopes (STMs).
Atoms amazes us. The atom is about 10⁻¹⁰ meters in size. How could something so tiny could exist with a structure of its own? All the technology we see is based on the structure of atoms. When we see a periodic table, it shows the orderliness of atoms in nature. When we see a chemical reaction, we see the meticulousness of atomic functions. When we see an atomic clock showing us time with exquisite precision, we wonder about their perfection.
Atoms also scare us. When we hear that so and so nation tested a hypersonic missile tipped with an atomic bomb, the images of Hiroshima, Nagasaki, Chernobyl, Fukushima, Three Mile Island nuclear disasters flash in our minds and we are reminded of the destructive power of atoms.
The discovery of atoms is a trump of physics and of mathematics. In fact, if we look into history, we see how beautifully physics and mathematics intertwine as they integrate in the pursuit of scientific knowledge. Physics became a highly sophisticated mathematical science. Physics and mathematics are knit together in the fabric of nature.
Eugene Wigner received the Nobel Prize in Physics in 1963. He was a pioneer in the mathematical formulation of quantum mechanics. In 1960, he wrote a piece titled ‘The unreasonable Effectiveness of Mathematics in the Natural Sciences’. It boggled his mind that mathematics leads us to incredible discoveries of nature which are completely surprising, unpredictable and even unfathomable. It took him into a sort of mysticism.
If you look into the history of science, this wonderment at the elegant interwovenness of physics and mathematics is not a new or modern tradition. Go back to the time of Pythagoras. Five hundred years before Christ. Pythagoras believed that the planets move according to mathematical equations. His Pythagorean theorem tremendously impacted philosophy. Geometry is not just about angles and triangles. It is about the laws woven into the fabric of the universe. Greeks thought mathematics could lead them to understand the fundamental building blocks of matter. Greek philosopher Democritus formulated an atomic theory of the universe.
For millennia, atoms were only seen as speculative opinions of philosophers who had so much free time on their hands. A scientific understanding of atoms became a reality only in the modern times.
Let us start with Isaac Newton. The mathematical view of the natural world was firmly established by the work of Isaac Newton. He wanted to thoroughly examine the relationship between physics and mathematics. His greatest work was titled the Mathematical Principles of Natural Philosophy. In this masterpiece, he laid out the mathematical foundation of the natural world. He invented calculus to deal with his new system of mechanics.
Newton’s teacher in mathematics was Isaac Barrow. In 1663, Barrow became the first Lucasian Professor of Mathematics in the University of Cambridge, England. Then in 1669, Newton himself became the Lucasian Professor. Three hundred years later, in 1979, Stephen Hawking became the Lucasian Professor of mathematics. If you look at the list of these professors, you will find famous figures like Charles Babbage, who is called the father of the computer and Paul Dirac, who predicted the existence of antimatter. Dirac’s equations not only proved the existence of atoms, but went further establishing the presence of subatomic particles like positrons. From Democritus to Dirac, we see a highway on which mathematics shed its light leading the physicists towards the discovery of atoms and its constituents.
After Newton, a paradigm was set in motion which led science to this day: if you want to understand the fundamental nature of reality, you must start with a mathematical model of any given phenomenon. From a highly mathematical viewpoint, Newton predicted the existence of atoms.
Then comes Joseph Priestly (1733 – 1804). He was a Dissenting Calvinist. Who were these Dissenters? They were questioners. They simply did not go with the flow. They questioned established traditions in Christian religion. They formed their own beliefs based on scripture and reason. Many dissenters turned into great scientists. Priestley was one of them.
Like Newton, Priestly believed that God created our observed world and by examining it and studying it rationally we can understand the nature of reality. He was a minister and a scientist. Who said science and religion are enemies? While studying the Bible on one hand, Priestly discovered oxygen on the other hand. His laborious experiments led to the discovery of oxygen. He also studied electricity, putting him in touch with Benjamin Franklin.
Priestley discovered 10 new gases, including oxygen. Here is oxygen, which is continuously replenished by photosynthesis. Priestly thought, ‘this God of nature is not a vengeful God of his Calvinist youth. He is a benevolent God who kept a process like photosynthesis in nature to recycle noxious gases into life giving oxygen’. Priestley’s discovery of oxygen unleashed a chemical revolution in science further taking us towards the discovery of atoms.
Then comes John Dalton(1766 – 1844), an English chemist. Born into a Quaker family, he was also a dissenter like Priestley. He noticed some mathematical regularities in how chemical compounds are formed. He formulated the law of multiple proportions based on his observations. Let me give you an example.
-100 grams of tin combined with 13.5 grams of oxygen formed tin oxide
-100 grams of tin combined with 27 grams of oxygen formed tin dioxide
13.5/27, that is the ratio of one to two.
Oxygen as it bonds with tin is following a fixed ratio. There must be discrete units of oxygen to make this possible. Nature is using simple ratios of counting numbers. Dalton thought, maybe elements are made up of countable bits. He formulated his atomic theory of matter based on this thinking. Remember how it all started: observing mathematical regularities in chemical reactions.
Then comes Robert Brown (1773 – 1858). He was a Scottish botanist. The quest for atoms moves from gases to plants. He was spending a lot of time around his microscope, studying plants, flowers and their tiny parts. In 1827, he found something interesting while looking through his microscope. Minute particles from the grains of pollen of a plant were making jittery motion in water. It is called Brownian motion. It was observed also in gases like motes in sunlight. For the next 78 years, nobody was able to explain this curious, seemingly erratic motion of tiny particles suspended in a fluid or in a gas. It fell on Einstein to explain the Brownian motion.
James Clerk Maxwell
Before we talk about Einstein, we should look at another giant of science named James Clerk Maxwell (1831 – 1879). His mathematics not only took us in the direction of the reality of atoms but also helped us know what is inside the atom. Maxwell was born in Edinburgh on the 13th of June 1831. His mother encouraged him to “look up through Nature to Nature’s God”. She advised him to memorize the Bible. From his childhood, he knew the Bible by heart. At eight years of age, Maxwell could repeat the whole of the 119th Psalms. “His knowledge of Scripture, from his earliest boyhood, was extraordinarily extensive and minute; and he could give chapter and verse for almost any quotation from the Psalms.”
His father John Maxwell took him to attend lectures in physics and mathematics. Maxwell started to apply mathematics to the natural phenomena around him. He was fascinated by Newton’s mathematical theory of gravity. A humble and gentle person, he was described as ‘the most perfect example of a Christian Gentleman’ by his physician, Dr.Lorraine.
I thought Maxwell was another run of the mill physicist. But when I went over some of the books on the history of science, I realized the scientific revolution he brought up in our world. In the 1860s, Maxwell had a series of papers designed to show that matter consisted of what he called molecules. His equations led to the discovery of radio waves. They predicted the speed of light. If the 18th century belongs to Newton and the 20th century belongs to Einstein, the 19th century must belong to Maxwell.
In 2004, Philosopher Robert P.Crease had conducted a survey asking physicists to vote for the greatest equations of all time. Most physicists voted for Maxwell’s Equations as the greatest equations in the history of science.
In “The Greatest Equations Ever”, Philosopher Robert P.Crease explains the importance of Maxwell’s equations: “Although Maxwell’s equations are relatively simple, they daringly reorganize our perception of nature, unifying electricity and magnetism and linking geometry, topology and physics. They are essential to understanding the surrounding world. And as the first field equations, they not only showed scientists a new way of approaching physics but also took them on the first step towards a unification of the fundamental forces of nature”.
Historian Basil Mahon explains the importance of James Clerk Maxwell in his book, The Man Who Changed Everything,
“The influence of James Clerk Maxwell runs all through our daily lives. His electromagnetic waves bring us radio and television and provide the radar that makes safe air travel possible. Colour television works on the three-colour principle that he demonstrated. Pilots fly aircraft by control systems which derive from his work. Many of our bridges and other structures were designed using his reciprocal diagrams and photoelastic techniques.
Even more significant is his influence on the whole development of physical science. He started a revolution in the way physicists look at the world. It was he who began to think that the objects and forces that we see and feel may be merely our limited perception of an underlying reality which is inaccessible to our senses but may be described mathematically.
He was the first to use field equations to represent physical processes; they are now the standard form used by physicists to model what goes on in the vastness of space and inside atoms. He was also the first to use statistical methods to describe processes involving many particles, another technique which is now standard. He predicted, correctly, that light was a wholly electromagnetic phenomenon and that its speed was simply the ratio between the electromagnetic and electrostatic units of charge. His equations of the electromagnetic field were the chief inspiration for Einstein’s special theory of relativity and, along with his kinetic theory of gases, played a part in Planck’s discovery of the quantum of energy.”
Mathematician Robyn Arianrhod explains pioneering genius of Maxwell:
“He was the first physicist to embrace deliberately the ambiguous relationship between language and reality; the first to accept that in a very real sense, language is reality. He showed that the structure of mathematical language seems to reflect hidden physical structures, so that in the unseen realms of the world, such as the heart of atoms, radio waves and black holes – ‘the hidden, dimmer regions where thought weds fact’, as he put it – the closest we may ever come to perceiving physical reality directly is to imagine it mathematically.”
Little over a hundred years before Maxwell’s birth, Irish clergyman Jonathan Swift wrote the Gulliver’s Travels. In the third voyage of Gulliver’s Travels, we see a flying island traveling in the air supported by a giant magnet. People on this island literally have their heads in the clouds. They are obsessed with abstract mathematics.
Maxwell would unleash a world led by triumph of abstract mathematics. His mathematics not only took us closer to the reality of the atoms, but also made more delightful endeavors become possible. You can peer inside the atoms.
Then comes Albert Einstein. Einstein admired Maxwell so much that he placed a photograph of Maxwell on his study wall. While Maxwell brought together electricity and magnetism into a single coherent theory of electromagnetism, Einstein integrated mechanics and Maxwell’s electrodynamics into a single coherent theory of special relativity.
Robert Brown and James Maxwell – the fruits of their work had come to ripen in the hands of Einstein. In 1905 he published a paper titled, “On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat”. Using a mathematical model, he showed that Brownian motion was caused by the minute particles being hit by water molecules. Einstein wrote,
“It will be shown in this paper that, according to the molecular-kinetic theory of heat, bodies of microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitude that these motions can be easily detected by a microscope.”
Note the year: 1905. It is called Einstein’s Miraculous Year, because that year he published five great papers that changed the face of physics. His paper on the Brownian motion is the second paper of the year. Einstein opined that if the water were made up of molecules, which react to temperature, they could create random movements of the grains or dust.
The word ‘random’ is important to notice. The randomness in the Brownian motion later extended to fluctuations in the stock market, ballots in an election, genetic drift, coin flipping and gave birth to the science of probability. This ‘randomness’ in nature disturbed the deterministic worldview of Einstein that he later bemoaned, ‘God does not play dice with the universe’. To which, physicist Niels Bohr responded with, ‘Einstein, who are you to tell God what to do?’ Stephen Hawking went further and said, “God not only plays dice, but sometimes throws them where they cannot be seen.” It is so fascinating to see how determinism and randomness come together in nature.
Explaining the Brownian motion, Einstein convinced many physicists of the existence of atoms. In 1913, French physicist Jean Perrin did experiments and proved the accuracy of Einstein’s predictions. He won a Nobel Prize for proving the existence of atoms. In the 1920s, Norbert Wiener gave a more rigorous mathematical treatment of Brownian motion.
The 20th century witnessed more stunning developments in our journey to understand the atom: the discovery of electrons, of protons, of neutrons, even subatomic particles like quarks, leptons and muons. Scientists like J.J.Thompson, Ernest Rutherford, Niels Bohr, Paul Dirac, Werner Heisenberg, Erwin Schrodinger changed the face of atomic theory of matter. quantum theory successfully predicted the properties of atoms, subatomic particles and their forces. Now we are talking about what is inside protons and neutrons.
In 1989, scientists at IBM took individual xenon atoms and arranged them to spell out the company’s name. Looking through a microscope, now you can see the beauty of an individual atom that evaded human curiosity for millennia.
Mathematics of atoms also paved the way to understand the universe at large. When you look at a galaxy, you will see millions of stars. Their gravitational interactions can be mind boggling. A mathematical analysis of those interactions led to the prediction of dark matter. Once again, we will see the amazing power of Maxwell’s equations. We came to know more shocking facts about nature: Atoms make up only about 5% of the cosmos. The remainder is made up of dark matter and dark energy.
From Democritus to Dirac and beyond, we see the triumph of mathematics in the discovery of atoms. Einstein wondered , ‘How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably appropriate to the objects of reality?’
Einstein watched his words carefully because he was living in a world rapidly progressing into the age of secularism. But Newton has no such qualms. He wrote in the General Scholium:
“It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always and everywhere. Whence also he is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act, but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us. As a blind man has no idea of colors, so have we no idea of the manner by which the all-wise God perceives and understands all things.”
Newton firmly believed that our external reality is a mathematical structure because it was designed by God himself. Historian Paul Wood explains how Newton’s biblical view of God influenced his physics.
“Newton’s God was the personal, all-powerful Pantocrator of the Bible. Concomitant with his Hebraic and profoundly biblical view of God, is Newton’s characterization of God as a deity of unchallenged sovereignty, power and dominion. Newton’s God governs the world directly through general and particular providence, and bears a constant relationship to His creatures and creation. It is not difficult to see how this conception of God could profoundly affect Newton’s natural philosophy.”
Then Mr.Wood goes further to show the influence of Christianity on Newton’s mathematics.
“It is likely that Newton’s God of dominion even impinged on his mathematics, because his method of fluxions (calculus) depends on the continuous flow of absolute time, which Newton associated with God, whose eternity and omnipresence is said in the General Scholium to be coextensive with time (duration) and space.”
We also saw how this pursuit of mathematics as the language of God’s design helped Maxwell to build on his mother’s advice to “look up through Nature to Nature’s God”. He told his friend Professor Hort, “The only desire which I can have is like David to serve my own generation by the will of God, and then fall asleep.” Maxwell saw science as a calling from God to understand and glorify God’s created order in the universe.
Inspired by Maxwell, physicist Isidor Isaac Rabi (1898 – 1988) made groundbreaking studies in the magnetic resonance of crystals, which earned him a Nobel Prize in physics. His achievements led to the discovery of nuclear spin of atoms and the development of MRI technology we use in medical diagnosis. Later in his life, when his physician sent him for an MRI, he marveled at the beauty of his science. He said, ‘I saw myself in that machine’.
Atoms still amaze us by throwing surprising secrets at us. When an unexpected lepton called muon was discovered, Rabi is said to have exclaimed “Who ordered that?”
Maxwell would have answered him with one word, ‘God’. The Bible says that God is not a God of confusion (1 Corinthians 14:33). All our great discoveries are fruits of the mathematical order He established in nature.
My answer to your question is, when we see the wonderful structure of the atom, it points us to the amazing wisdom of our great God, Lord Jesus Christ. Amen.