Understanding the Work of Einstein
On the Road to Quantum Entropy, Part 4
After visiting entropy and quantum mechanics, with a detour through simulated worlds, we will now change gears: let us explore the work of Albert Einstein, who is (spoiler alert) one of the greatest minds in history of physics.
This article is going to be be quite different than the usual treatment, so it may give you some food for thought even if you are familiar with his work.
Classical Picture
First, what was the state of Physics before Einstein? Let us try to understand a bit the picture of classical physics.
What Is Stuff Made of
Our starting point is going to be the same question that philosophers and other curious people have been asking since the beginning of time: what are things made of?
This question may seem pointless now, because everybody has known for centuries or even millenia that things are made of small particles called atoms, right? Not so fast. Hardly a hundred years ago scientists were still debating this issue. It can be instructive to look at it from our privileged perspective.
The Debate that Matters
First, what is regular matter made of? It is a simple enough question, but quite hard to answer. People have been worrying about it since antiquity. So how do you go about finding out the answer without modern instruments? There is only one way: using reason.
In Ancient Greece philosophers like Democritus and Epicurus imagined what it would like to divide any substances into smaller pieces, and found it hard to believe that this process could go on indefinitely without the substance losing its essence. So they concluded that all substances were made of small indivisible particles, a theory known as atomism. Not everyone agreed, most famously Aristotle: he thought that matter could be infinitely divided in an endless process. Since Aristotle’s opinions carried a lot of weight, the matter was more or less settled during the Middle Ages, not without some discordances. But we have to remember that most of Aristotle became dogma both to Islamic and to Christian authorities, and therefore most philosophers stayed within it.
After the Renaissance some thinkers like Descartes or Galileo became new proponents of atomism. But this time the debate was more solidly founded. Scientists were discovering the laws by which substances could be combined into others, and during the 18th century this study would lead to the foundation of chemistry. Since molecules like water or ammonia were created only in constant proportions, John Dalton concluded in 1808 that we were seeing elementary atoms combining always in the same ways. But the question was not really settled: many scientists still believed in substances that could be infinitely divided. In 1826 the reputed Humphry Davy insisted that the “atomic conjecture” should be ignored. During the 19th century both sides continued arguing without definite proof.
The Light Debate
Enough about matter for now. Let’s go to another question which is even more interesting: what is light made of?
The field of optics has been studied since antiquity. Epicurus already established that the speed of light (which he referred to as “rapidity of images”) is the fastest possible in the universe in this astounding paragraph:
It is useful, also, to retain this principle, and to know that the images have an incomparable thinness; which fact indeed is in no respect contradicted by sensible appearances. From which it follows that their rapidity also is incomparable; for they find everywhere an easy passage, and besides, their minuteness causes them to experience no shock, or at all events to experience but a very slight one, while a multitude of elements very soon encounter some resistance.
Other philosophers also argued about the nature of light. Around 1650 many giants were studying the field with a more mathematically-oriented approach: due to their propagation in a straight line Newton argued for particles, while other scientists like Huygens and Hooke formulated a wave theory. Given the tremendous weight of Newton in early Physics, his opinion could counteract the multitude of phenomena well explained by waves.
The debate was not settled until 1801, when Young came up with a wonderful double-slit experiment that clearly showed interference patterns, convincing physicists that light was indeed a wave. The crucial effect that he measured is diffraction: as we saw in our little simulator, waves can change direction when passing through a narrow opening. So does light, although its wavelength is so small that the effect is only appreciable at short distances.
So we reach the 19th century with a more or less clear picture: matter was made of atoms, light was made of waves.
Cracks in the Foundation
But this situation would not last for very long. The magnificent building of Classical Physics founded by Galileo Galilei, raised by Isaac Newton and perfected by other giants in the following two centuries started showing cracks in the very foundations at the end of the 19th century, first with the Michelson–Morley experiment and then by black body radiation. Both are very relevant to our story.
In Search of Ether
About light only one question remained: if it is a wave, then what exactly is waving?
Waves are a very particular phenomenon that happens when there is an oscillation in a substance. For instance, waves in water happen because its molecules wiggle up and down. If light is a wave and it can propagate even when there is no matter, then what is oscillating to create it? The answer given by scientists was ether: the intangible medium where waves of light were supposed to propagate. Of course its existence would create other problems: what properties did this mysterious ether have? And so scientists set about to detect it.
In 1887 Michelson and Morley were trying to find signs of its existence. This transparent substance had to permeate the whole of space so that light could propagate in the vacuum. And since our Earth is moving through space around the sun, it would navigate through the ether at different speeds depending on the time of the year. And so the famous Michelson–Morley experiment was designed. By making very precise measurements, a different speed of light in different directions should be measured. Also the experiment had to be repeated multiple times, if by any chance our planet was moving exactly along the ether at the moment of the first measurement.
Of course their very precise measurements found none of that nonsense: light seemed to travel at exactly the same speed at all times and in all directions. There was no ether to be found anywhere.
Radiating Black Body
Another important sign that classical physics was not the whole picture was the investigation of black body radiation. A hot chamber (“black body”) was supposed to radiate energy of all frequencies, and the classical theory predicted that this energy was supposed to grow without bounds as the wavelength increased. This was called the ultraviolet catastrophe, since it would have caused the destruction of the world as we know it. The “light as waves” picture was not working.
In 1900 Max Planck proposed his quantisation of radiation to solve the problem. The implication was that light was not a constant vibration of a substance, but instead was sent as particles (“packets” or “quanta” in technical talk). So in a strange twist of fate, we are back to light as particles! Nobody could make any sense of the situation at this point: was light waves, or was it particles? Remember that the picture for matter wasn’t even settled yet.
Enter Einstein
In 1905 an obscure employee of the Swiss patent office called Albert Einstein published a series of four scientific articles that would change Physics forever. Not in vain this was called his annus mirabilis or wonder year: in essence he solved the most important mysteries in Classical Physics, and opened many, many more questions.
Light Particles
In his first paper Einstein used quantisation to explain the photoelectric effect, by which certain materials emitted a current when hit by light. He assumed that light was composed of particles, which we now call photons.
Along the way he derived that the energy carried by any individual photon is proportional to its frequency, using the same constant used by Planck for the black body. This opened the way for quantum mechanics in all its glory: it was a valid approach for every day problems.
By the way, the explanation of the photoelectric effect is what won Einstein the Nobel prize in 1921, despite his most famous achievements.
Relativity Is Born
In another 1905 paper Einstein introduced to the world the theory of special relativity: how to understand the propagation of light without an underlying medium. First, the speed of light in a vacuum had to be defined as a constant, and also to be the maximum speed possible in the universe (as suspected by Epicurus). The weird outcomes were that:
- light is a combination of electric and magnetic fields propagating in a vacuum,
- moving objects contract in the direction of movement,
- kinetic energy grows without limit when approaching the speed of light,
- and time passes more slowly for fast-moving objects.
All these strange consequences would be completely validated in further experiments. The picture that emanated was perfectly coherent but very different from our everyday experience with clocks and moving objects. The mind-bending ideas behind the theory were revolutionary, and it would take many decades for other physicists to study and deeply understand their consequences.
It would be very easy to blow the contributions of Einstein out of all proportion by saying that he came up with special relativity all on his own. We would thus be ignoring all of the geniuses that had tried to answer the same questions: Hendrik Lorentz had postulated the contraction of objects in the direction of movement, Henri Poincaré discovered relativistic velocity transformations, while Hermann Minkowski later formulated the four dimensions of space-time as a coherent space.
But believing that Einstein’s work was just a trivial rehash of previous work would be just as wrong. In fact, Einstein created a coherent version of Maxwells’ equations of electromagetism that worked in all conditions and circumstances, and that required no ether; and he derived the correct equations of movement for objects at any speed.
In a separate paper Einstein would derive the famous equation
E = mc² which explains the transformation of matter into
energy and viceversa.
Atoms Are Real
Not happy with solving these two long-running mysteries, Einstein set out in his second 1905 paper to settle the debate on atomism. In a study on Brownian motion he explained why little particles of pollen seemed to jiggle when viewed through the microscope.
The solution was a very elegant derivation of statistical mechanics using a random bombardment of water molecules. He also correctly derived the number of molecules in a mole, which is called by chemists Avogadro constant. In essence Einstein counted the number of atoms in matter, finding out the mass of each atom in the process.
Later Contributions
The biggest mystery left was: how did gravity work in this new world of constant speed of light? In 1915 Einstein did it again, publishing his theory of general relativity: how the presence of energy curves space-time itself, made even more interesting because this curvature generates even more energy.
It would be too long to delve into the details of this complex theory, and I’m not even sure I know how to explain it. Let us just state that it is essential to understand cosmology and astrophysics. General relativity has resisted all efforts of quantization so far, and it is the best explanation that we have for how gravity works more than a century later.
Einstein had a long and illustrious career in physics after 1915, and his many contributions would reinforce the pillars of the new physics that he pioneered. The picture that he left us can be summarized as: light and matter are made of particles. So how can we make sense of all phenomena that are explained by waves? Quantum mechanics would bring the answers. Einstein helped refine this theory through his multiple criticisms: for instance, he was instrumental in finding out about quantum entanglement when he co-created the Einstein-Podolsky-Rosen paradox.
The great thinker tried and failed to extend his relativistic field equations in a unified field theory, that also included quantum mechanics. But to be honest nobody has succeeded yet in this search.
Conclusion
As we have seen, Albert Einstein took a classical world and quantized it, creating a coherent picture that left out any mysterious substances. He also helped us understand how such a world made of particles could work, doing pioneering work in many branches of Physics (and opening up a few others).
We will soon continue our journey exploring quantum entropy.
Acknowledgements
Thanks to Carlos Santisteban for the encouragement to write this article.
Published on 2021-11-07, modified on 2021-12-05. Comments, suggestions?
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