The molecule that was also a wave

According to the principles of quantum mechanics, you’re a wave – just like light is both a particle and a wave. It’s just that your wavelength is so small that your wave nature doesn’t matter, and you’re treated like a particle. The larger an object is, the smaller its wavelength, and vice versa. We’re confused about whether light is a particle or a wave because photons, the particles of light, are so small and have a measurable wavelength as a result. Scientists know that electrons, protons, neutrons, even neutrinos have the properties of a wave.

But while the math of quantum mechanics says you’re a wave, how can we know for sure if we can’t measure it? There are two ways. One, we don’t have any evidence to the contrary. Two, scientists have been checking if larger and larger particles, as far as they can go, exhibit the properties of a wave – and at every step of the way, they’ve come up with positive results. Both together, we have no reason to believe that we’re not also waves.

Such tests reaffirm the need for quantum mechanics to understand the nature of reality because the rules of classical mechanics alone don’t explain wave-particle duality.

On September 23, scientists from Austria, China, Germany and Switzerland reported that they had measured the wavelength of a group of molecules called oligoporphyrins. Specifically, they used “oligo-tetraphenylporphyrins enriched by a library of up to 60 fluoroalkylsulphanyl chains”. Altogether, they consisted “of up to 2,000 atoms”, becoming the heaviest object directly known to exhibit wave-like properties.

The molecule in question. DOI: 10.1038/s41567-019-0663-9

According to the scientists’ peer-reviewed paper, the molecules had a wavelength of around 53 femtometers, about 100,000-times smaller than the molecules themselves.

* * *

We have known since at least the 11th century, through the work of the Arab scholar Ibn al-Haytham, that light is a wave. In 1670, Isaac Newton propounded that light is made up of small particles, and spent three decades supplying evidence for his argument. His push birthed a conflict: was light wave-like or made up of particles?

The British polymath Thomas Young built on the 17th century Dutch physicist Christiaan Huygens to devise an experiment in 1801 that definitively proved light was a wave. It is known widely today as the Young’s double-slit experiment. It is so simple even as its outcomes are so immutable that it has become a mainstay of modern tests of quantum mechanics. Physicists use upgraded versions of the experiment to this day to study the nature and properties matter-waves.

(If you would like to know more, I highly recommend Anil Ananthaswamy’s biography of this experiment, Through Two Doors At Once; here’s an excerpt.)

In the experiment, light from a common source – such as a candle – is allowed to pass through two fine slits separated by a short distance. A sheet of paper sufficiently behind the slits then shows a strange pattern of alternating light and dark bands instead of just two patches of light. This is because light waves passing through the two slits interfere with each other, producing the famous interference pattern. Since only waves can interfere, the experiment shows that light has to be a wave.

An illustration of the double-slit experiment from ‘Though Two Doors At Once’ (2019).

The particulate nature of light would get its proper due only in 1900, when Max Planck stumbled upon a mathematical inconsistency that forced him to conclude light had to be made up of smaller packets of energy. It was the birth of quantum mechanics.

* * *

The international group’s test went roughly as follows: the scientists pulsed a laser onto a glass plate coated with the oligoporphyrins to release a stream of the molecules; collected them into a beam using collimators; randomly chopped the beam into smaller bits; passed each bit through diffraction gratings to split it up; then had the two little beams interfere with each other. Finally, they counted the number of molecules striking the detector while the detector registered the interference pattern.

They had insulated the whole device, about 2m long, from extremely small disturbances, like vibrations, to prevent the results from being corrupted. In their paper, the scientists even write that the final interference pattern was blurred thanks to Earth’s rotation, and which they were able to “compensate for” using effects due to Earth’s gravity.

A schematic diagram of the experimental setup. The oligoporphyrins move from left to right as the experiment progresses. The results of the counter are visible in a diagram above the right-most component. DOI: 10.1038/s41567-019-0663-9

To ascertain that the pattern they were seeing on the detector was in fact due to interference, the scientists performed a variety of checks each of which established a relationship between the shapes on the detector with the properties of the components of the interferometer according to the rules of quantum mechanics. They were also able to rule out alternative, i.e. classical, explanations this way.

For example, the scientists fired a laser through the cloud of molecules post-interference. Each molecule split the laser light into two separate beams, which recombined to produce an interference pattern of their own. This way, scientists could elicit the molecules’ interference pattern by studying the laser’s interference pattern. As they varied the laser power, they found that the visibility distribution of the molecules more closely matched with quantum mechanical models than with classical models, confirming interference.

The solid blue line indicates the quantum mechanical model and the dashed red line is a classical model, both scaled vertically by a factor of 0.93. The shaded areas on the curves represent uncertainty in the model parameters, and the dotted lines indicate unscaled theory curves. DOI: 10.1038/s41567-019-0663-9

What these scientists have achieved isn’t only a feat of measurement. Their findings also help refine the border between the classical and the quantum. The force of gravity governs the laws of classical mechanics, which deals with macroscopic objects, while the electromagnetic, strong nuclear and weak nuclear forces rule the microscopic world. Although macroscopic and microscopic objects occupy the same universe, physicists haven’t yet understood how classical and quantum mechanics can be combined into a single theory.

One of the problems standing in the way of this union is knowing where – and how – the macroscopic world ends and the microscopic world begins. So by observing quantum mechanical effects at the scale of thousands of atoms, scientists have quite literally pushed the boundaries of what we know about how the universe works.

Unusual third Van Allen belt explained

Remember that third Van Allen radiation belt that appeared in February and lasted for about a month? Scientists from the University of California, Los Angeles, have started to understand what it really was – a belt composed solely of electrons moving at almost light-speed – and why it occurred – because of a massive solar flare in September, 2012. Although these faster electrons aren’t unique, as they appear in the two original Van Allen belts as well, what scientists have to figure out now is what accelerates them to such high energies. My story on this development for The Hindu.

Bohr and the breakaway from classical mechanics

One hundred years ago, Niels Bohr developed the Bohr model of the atom, where electrons go around a nucleus at the center like planets in the Solar System. The model and its implications brought a lot of clarity to the field of physics at a time when physicists didn’t know what was inside an atom, and how that influenced the things around it. For his work, Bohr was awarded the physics Nobel Prize in 1922.

The Bohr model marked a transition from the world of Isaac Newton’s classical mechanics, where gravity was the dominant force and values like mass and velocity were accurately measurable, to that of quantum mechanics, where objects were too small to be seen even with powerful instruments and their exact position didn’t matter.

Even though modern quantum mechanics is still under development, its origins can be traced to humanity’s first thinking of energy as being quantized and not randomly strewn about in nature, and the Bohr model was an important part of this thinking.

The Bohr model

According to the Dane, electrons orbiting the nucleus at different distances were at different energies, and an electron inside an atom – any atom – could only have specific energies. Thus, electrons could ascend or descend through these orbits by gaining or losing a certain quantum of energy, respectively. By allowing for such transitions, the model acknowledged a more discrete energy conservation policy in physics, and used it to explain many aspects of chemistry and chemical reactions.

Unfortunately, this model couldn’t evolve continuously to become its modern equivalent because it could properly explain only the hydrogen atom, and it couldn’t account for the Zeeman effect.

What is the Zeeman effect? When an electron jumps from a higher to a lower energy-level, it loses some energy. This can be charted using a “map” of energies like the electromagnetic spectrum, showing if the energy has been lost as infrared, UV, visible, radio, etc., radiation. In 1896, Dutch physicist Pieter Zeeman found that this map could be distorted when the energy was emitted in the presence of a magnetic field, leading to the effect named after him.

It was only in 1925 that the cause of this behavior was found (by Wolfgang Pauli, George Uhlenbeck and Samuel Goudsmit), attributed to a property of electrons called spin.

The Bohr model couldn’t explain spin or its effects. It wasn’t discarded for this shortcoming, however, because it had succeeded in explaining a lot more, such as the emission of light in lasers, an application developed on the basis of Bohr’s theories and still in use today.

The model was also important for being a tangible breakaway from the principles of classical mechanics, which were useless at explaining quantum mechanical effects in atoms. Physicists recognized this and insisted on building on what they had.

A way ahead

To this end, a German named Arnold Sommerfeld provided a generalization of Bohr’s model – a correction – to let it explain the Zeeman effect in ionized helium (which is a hydrogen atom with one proton and one neutron more).

In 1924, Louis de Broglie introduced particle-wave duality into quantum mechanics, invoking that matter at its simplest could be both particulate and wave-like. As such, he was able to verify Bohr’s model mathematically from a waves’ perspective. Before him, in 1905, Albert Einstein had postulated the existence of light-particles called photons but couldn’t explain how they could be related to heat waves emanating from a gas, a problem he solved using de Broglie’s logic.

All these developments reinforced the apparent validity of Bohr’s model. Simultaneously, new discoveries were emerging that continuously challenged its authority (and classical mechanics’, too): molecular rotation, ground-state energy, Heisenberg’s uncertainty principle, Bose-Einstein statistics, etc. One option was to fall back to classical mechanics and rework quantum theory thereon. Another was to keep moving ahead in search of a solution.

However, this decision didn’t have to be taken because the field of physics itself had started to move ahead in different ways, ways which would become ultimately unified.

Leaps of faith

Between 1900 and 1925, there were a handful of people responsible for opening this floodgate to tide over the centuries old Newtonian laws. Perhaps the last among them was Niels Bohr; the first was Max Planck, who originated quantum theory when he was working on making light bulbs glow brighter. He found that the smallest bits of energy to be found in nature weren’t random, but actually came in specific amounts that he called quanta.

It is notable that when either of these men began working on their respective contributions to quantum mechanics, they took a leap of faith that couldn’t be spanned by purely scientific reasoning, as is the dominant process today, but by faith in philosophical reasoning and, simply, hope.

For example, Planck wasn’t fond of a class of mechanics he used to establish quantum mechanics. When asked about it, he said it was an “act of despair”, that he was “ready to sacrifice any of [his] previous convictions about physics”. Bohr, on the other hand, had relied on the intuitive philosophy of correspondence to conceive of his model. In fact, even before he had received his Nobel in 1922, Bohr had begun to deviate from his most eminent finding because it disagreed with what he thought were more important, and to be preserved, foundational ideas.

It was also through this philosophy of correspondence that the many theories were able to be unified over the course of time. According to it, a new theory should replicate the results of an older, well-established one in the domain where it worked.

Coming a full circle

Since humankind’s investigation into the nature of physics has proceeded from the large to the small, new attempts to investigate from the small to the large were likely to run into old theories. And when multiple new quantum theories were found to replicate the results of one classical theory, they could be translated between each other by corresponding through the old theory (thus the name).

Because the Bohr model could successfully explain how and why energy was emitted by electrons jumping orbits in the hydrogen atom, it had a domain of applicability. So, it couldn’t be entirely wrong and would have to correspond in some way with another, possibly more successful, theory.

Earlier, in 1924, de Broglie’s formulation was suffering from its own inability to explain certain wave-like phenomena in particulate matter. Then, in 1926, Erwin Schrodinger built on it and, like Sommerfeld did with Bohr’s ideas, generalized them so that they could apply in experimental quantum mechanics. The end result was the famous Schrodinger’s equation.

The Sommerfeld-Bohr theory corresponds with the equation, and this is where it comes “full circle”. After the equation became well known, the Bohr model was finally understood as being a semi-classical approximation of the Schrodinger equation. In other words, the model represented some of the simplest corrections to be made to classical mechanics for it to become quantum in any way.

An ingenious span

After this, the Bohr model was, rather became, a fully integrable part of the foundational ancestry of modern quantum mechanics. While its significance in the field today is great yet still one of many like it, by itself it had a special place in history: a bridge, between the older classical thinking and the newer quantum thinking.

Even philosophically speaking, Niels Bohr and his pathbreaking work were important because they planted the seeds of ingenuity in our minds, and led us to think outside of convention.

This article, as written by me, originally appeared in The Copernican science blog on May 19, 2013.

Bohr and the breakaway from classical mechanics

Niels Bohr, 1950.
Niels Bohr, 1950. Photo: Blogspot

One hundred years ago, Niels Bohr developed the Bohr model of the atom, where electrons go around a nucleus at the centre like planets in the Solar System. The model and its implications brought a lot of clarity to the field of physics at a time when physicists didn’t know what was inside an atom, and how that influenced the things around it. For his work, Bohr was awarded the physics Nobel Prize in 1922.

The Bohr model marked a transition from the world of Isaac Newton’s classical mechanics, where gravity was the dominant force and values like mass and velocity were accurately measurable, to that of quantum mechanics, where objects were too small to be seen even with powerful instruments and their exact position didn’t matter.

Even though modern quantum mechanics is still under development, its origins can be traced to humanity’s first thinking of energy as being quantised and not randomly strewn about in nature, and the Bohr model was an important part of this thinking.

The Bohr model

According to the Dane, electrons orbiting the nucleus at different distances were at different energies, and an electron inside an atom – any atom – could only have specific energies. Thus, electrons could ascend or descend through these orbits by gaining or losing a certain quantum of energy, respectively. By allowing for such transitions, the model acknowledged a more discrete energy conservation policy in physics, and used it to explain many aspects of chemistry and chemical reactions.

Unfortunately, this model couldn’t evolve continuously to become its modern equivalent because it could properly explain only the hydrogen atom, and it couldn’t account for the Zeeman effect.

What is the Zeeman effect? When an electron jumps from a higher to a lower energy-level, it loses some energy. This can be charted using a “map” of energies like the electromagnetic spectrum, showing if the energy has been lost as infrared, UV, visible, radio, etc., radiation. In 1896, Dutch physicist Pieter Zeeman found that this map could be distorted when the energy was emitted in the presence of a magnetic field, leading to the effect named after him.

It was only in 1925 that the cause of this behaviour was found (by Wolfgang Pauli, George Uhlenbeck and Samuel Goudsmit), attributed to a property of electrons called spin.

The Bohr model couldn’t explain spin or its effects. It wasn’t discarded for this shortcoming, however, because it had succeeded in explaining a lot more, such as the emission of light in lasers, an application developed on the basis of Bohr’s theories and still in use today.

The model was also important for being a tangible breakaway from the principles of classical mechanics, which were useless at explaining quantum mechanical effects in atoms. Physicists recognised this and insisted on building on what they had.

A way ahead

To this end, a German named Arnold Sommerfeld provided a generalisation of Bohr’s model – a correction – to let it explain the Zeeman effect in ionized helium (which is a hydrogen atom with one proton and one neutron more).

In 1924, Louis de Broglie introduced particle-wave duality into quantum mechanics, invoking that matter at its simplest could be both particulate and wave-like. As such, he was able to verify Bohr’s model mathematically from a waves’ perspective. Before him, in 1905, Albert Einstein had postulated the existence of light-particles called photons but couldn’t explain how they could be related to heat waves emanating from a gas, a problem he solved using de Broglie’s logic.

All these developments reinforced the apparent validity of Bohr’s model. Simultaneously, new discoveries were emerging that continuously challenged its authority (and classical mechanics’, too): molecular rotation, ground-state energy, Heisenberg’s uncertainty principle, Bose-Einstein statistics, etc. One option was to fall back to classical mechanics and rework quantum theory thereon. Another was to keep moving ahead in search of a solution.

However, this decision didn’t have to be taken because the field of physics itself had started to move ahead in different ways, ways which would become ultimately unified.

Leaps of faith

Between 1900 and 1925, there were a handful of people responsible for opening this floodgate to tide over the centuries old Newtonian laws. Perhaps the last among them was Niels Bohr; the first was Max Planck, who originated quantum theory when he was working on making light bulbs glow brighter. He found that the smallest bits of energy to be found in nature weren’t random, but actually came in specific amounts that he called quanta.

It is notable that when either of these men began working on their respective contributions to quantum mechanics, they took a leap of faith that couldn’t be spanned by purely scientific reasoning, as is the dominant process today, but by faith in philosophical reasoning and, simply, hope.

For example, Planck wasn’t fond of a class of mechanics he used to establish quantum mechanics. When asked about it, he said it was an “act of despair”, that he was “ready to sacrifice any of [his] previous convictions about physics”. Bohr, on the other hand, had relied on the intuitive philosophy of correspondence to conceive of his model. In fact, only a few years after he had received his Nobel in 1922, Bohr had begun to deviate from his most eminent finding because it disagreed with what he thought were more important, and to be preserved, foundational ideas.

It was also through this philosophy of correspondence that the many theories were able to be unified over the course of time. According to it, a new theory should replicate the results of an older, well-established one in the domain where it worked.

Coming a full circle

Since humankind’s investigation into the nature of physics has proceeded from the large to the small, new attempts to investigate from the small to the large were likely to run into old theories. And when multiple new quantum theories were found to replicate the results of one classical theory, they could be translated between each other by corresponding through the old theory (thus the name).

Because the Bohr model could successfully explain how and why energy was emitted by electrons jumping orbits in the hydrogen atom, it had a domain of applicability. So, it couldn’t be entirely wrong and would have to correspond in some way with another, possibly more succesful, theory.

Earlier, in 1924, de Broglie’s formulation was suffering from its own inability to explain certain wave-like phenomena in particulate matter. Then, in 1926, Erwin Schrodinger built on it and, like Sommerfeld did with Bohr’s ideas, generalised them so that they could apply in experimental quantum mechanics. The end result was the famous Schrodinger’s equation.

The Sommerfeld-Bohr theory corresponds with the equation, and this is where it comes “full circle”. After the equation became well known, the Bohr model was finally understood as being a semi-classical approximation of the Schrodinger equation. In other words, the model represented some of the simplest corrections to be made to classical mechanics for it to become quantum in any way.

An ingenious span

After this, the Bohr model was, rather became, a fully integrable part of the foundational ancestry of modern quantum mechanics. While its significance in the field today is great yet still one of many like it, by itself it had a special place in history: a bridge, between the older classical thinking and the newer quantum thinking.

Even philosophically speaking, Niels Bohr and his path-breaking work were important because they planted the seeds of ingenuity in our minds, and led us to think outside of convention.