The physics giant who defended the molecular theory fell on the eve of dawn...

"He knew that he had the most intelligent mind of that era, which was his capital for arrogance, but his inferiority complex was also obvious. Once many people stood on the opposite side of him, he would become uneasy and repeatedly ponder whether he had made this or that mistake..."

— Albert Einstein

Written by Zheng Chao (Researcher at Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences)

Background

In our previous article not long ago, we talked about the ancient idea that "matter is composed of indivisible atoms", which originated from ancient Greece. In the early nineteenth century, Dalton jumped out of the barriers of philosophical speculation and proposed the modern atomic theory based on the problem of the chemical composition of matter. A stone stirs up a thousand waves. The idea of ​​understanding chemical reactions based on atoms contributed to the vigorous development of chemistry in the nineteenth century. In 1860, Cannizzaro spread Avogadro's molecular theory at the Karlsruhe Conference, further promoting the application of atomic and molecular concepts in chemical research. However, there is still a long way for atoms and molecules to go from scientific concepts to physical reality.

This article continues the story from the previous one…

The Blockade of the Activeists

Although Cannizzaro clarified many misunderstandings about the concepts of atoms and molecules at the Karlsruhe Conference, it was far from eliminating the doubts in the minds of chemists. Kekulé's statement in 1867 best reflects this contradictory mentality. He said that as a chemist, he "fully agrees that atoms and molecules are not only wise assumptions, but also indispensable needs"; but as a philosophical point of view, he "does not believe that atoms and molecules are the basic units of matter." After all, the chemical analysis methods at that time were very limited and far from enough to prove the existence of "the hard little balls invented by Dalton." In the eyes of quite a number of chemists, atoms and molecules are just a convenient model to characterize the composition of material elements. "If the east is not bright, the west will be bright." The battlefield for the debate on the existence of molecules quietly shifted from chemistry to another emerging discipline - thermodynamics and classical statistical mechanics in the second half of the 19th century.

In the 18th century, the first industrial revolution marked by the steam engine brought unprecedented great changes to human society. Thermodynamics was born and developed almost for the realistic goal of improving the working efficiency of steam engines, or more generally, heat engines. For capitalists, a greedy but extremely beautiful wish is to generate power continuously without consuming energy. However, physicists represented by Dalton's student JP Joule verified the conservation of energy through experiments, breaking the dream of the (first type) perpetual motion machine that "creates something out of nothing". Then, as a second choice, can all the heat input into the heat engine be converted into power to avoid any waste? French engineer N. Carnot proposed the Carnot cycle of the ideal heat engine, clearly pointing out that no matter how the working medium is changed or the mechanical structure is optimized, it is impossible to make the efficiency of the heat engine reach 100%. British physicist W. Thomson (later Lord Kelvin) further pointed out that it is impossible to absorb heat from a single heat source and use it all to do work without causing other effects, thus declaring the bankruptcy of the (second type) perpetual motion machine that "makes the best use of everything". German physicist R. Clausius extracted the concept of entropy (S) based on the Carnot cycle to describe the "energy degradation" in the thermodynamic process, and gave a mathematical expression of the second law of thermodynamics: the entropy of any isolated system never decreases, and reaches its maximum value in the equilibrium state.

ΔS ≥ 0 (4)

The concise formula (4) is like a flying arrow, marking the "direction" of the world of thermodynamics.

Although the birth of thermodynamics has a strong practical background, it soon developed into a sophisticated "phenomenological science". Thermodynamics is not concerned with the microscopic structure of the research object, but uses state functions such as internal energy, entropy and temperature to characterize the macroscopic properties of the system when it is close to equilibrium. Thermodynamics is so elusive that it can tell you the limit of "working hard" and inadvertently lure you into the philosophical trap of "heat death theory". Therefore, believers of atomic and molecular theories naturally hope to build the theoretical basis of thermodynamics (mechanical theory) based on the microscopic structure of matter. The problem they must solve is how to use statistical means to link the motion behavior of a large number of molecules with the macroscopic thermodynamic properties of the system, and the final result of this effort is classical statistical mechanics.

Left: LE Boltzmann (1844-1906); Right: FW Ostwald (1853-1932), winner of the 1909 Nobel Prize in Chemistry

On the development path of classical statistical mechanics, Clausius was the first to realize that the internal energy of an ideal gas can be expressed as the sum of the kinetic energy of the random motion of all gas molecules. British physicist JC Maxwell derived the velocity distribution formula of ideal gas molecules in equilibrium at a certain temperature, from which the number of gas molecules in a given velocity range in equilibrium can be calculated. All preparations were ready, and the baton of history was passed to Austrian physicist LE Boltzmann in the 1870s. The theoretical framework of classical statistical mechanics will be laid in his hands, and this loner who believes in and defends the molecular theory will suffer for it.

Boltzmann's most important contributions to classical statistical mechanics include the statistical definition of entropy and the H theorem that describes the time evolution of the velocity distribution of ideal gas molecules.

The degree of disorder is determined by the random motion of a large number of molecules that make up the system. Boltzmann believed that due to the random motion of a large number of molecules that make up the system, each certain macroscopic state of the system must correspond to a huge number of different microscopic states. The macroscopic disorder of the system is precisely the manifestation of the diversity of its microscopic states. Therefore, the entropy S of a certain macroscopic state of the system must be related to the number W of the corresponding microscopic states, and the number of microscopic states corresponding to the equilibrium state with the largest entropy value must also be the maximum value. If it is assumed that the probability of each microscopic state occurring is equal, then the equilibrium state is the one with the highest probability of occurring among all possible macroscopic states of the system. In order to meet the requirement that entropy is an extensive quantity (the whole is equal to the sum of its parts), Boltzmann believed that the entropy of the system should be proportional to the natural logarithm of its number of microscopic states. This proportional relationship was later written by German physicist Planck (M. Planck) as an equation (Boltzmann formula) as shown in equation (5):

Boltzmann's formula provides a clear definition of what is difficult for beginners to understand.

The equilibrium state is the state that thermodynamics pays most attention to. Although Maxwell's formula gives the distribution law of molecular motion speed when the system is in equilibrium, it cannot tell us how the system evolves and why it can definitely evolve to the equilibrium state. Boltzmann used classical mechanics to describe the motion and collision of ideal gas molecules. Under the assumption that the molecules colliding with each other are independent and unrelated (molecular chaos), he derived the equation for the evolution of the molecular motion speed distribution f with time (generally called the Boltzmann equation), and its equilibrium state solution (satisfying the condition ∂f/∂t = 0) is exactly the Maxwell distribution. Boltzmann further defined a functional H about f (as shown in equation (6), where dΓ is the phase space volume element),

He also proved that the H function only decreases and never increases during the evolution of a thermodynamic system toward an equilibrium state, and reaches a minimum value at equilibrium (dH/dt ≤ 0), which is the famous H theorem. More importantly, the H function is linearly negatively correlated with entropy. The H theorem is therefore equivalent to asserting that entropy only increases and never decreases during the evolution of a thermodynamic system, and that the equilibrium state is the state with the maximum entropy (dS/dt ≥ 0). In other words, Boltzmann derived the second law of thermodynamics from the motion behavior of a large number of molecules that satisfy classical mechanics!

Figure 5. Boltzmann’s tombstone in Vienna’s Central Cemetery, with the statistical definition of entropy above it.

Boltzmann himself suffered as much criticism and questioning as his conclusions were shocking. The most significant logical "loophole" of the H theorem is the so-called "reversal problem". We know that the laws of classical mechanics have time reversal symmetry. If the movement of each molecule follows classical mechanics, then why does the collection of these molecules have a definite evolutionary direction? If the evolution of the system from state A to state B is an entropy increase process, then in state B, let the movement speed of all molecules take a negative value. According to time reversal symmetry, the system will evolve in the opposite direction to state A, and this reverse process must be a decrease in entropy! Boltzmann's explanation for this "paradox" is that the H theorem is not a mechanical law, but a statistical law. The evolution of the macroscopic system in the direction of entropy increase is the statistical average result of the motion behavior of a large number of molecules. Although there is still no satisfactory interpretation of the connotation of the H theorem to this day, this was not the most fatal challenge faced by Boltzmann at the end of the 19th century. Compared with the differences in understanding of mathematical formulas, the disputes with contemporaries on philosophical viewpoints and world views brought Boltzmann an unbearable burden.

From 1893, Boltzmann taught at the University of Vienna in Austria and the University of Leipzig in Germany. It was at these two schools that he met the strongest opponents of molecular theory and statistical mechanics: FW Ostwald of the University of Leipzig and E. Mach of the University of Vienna. Although Ostwald was a chemist, his research was quite alienated from the "mainstream" in the German chemical community at that time - organic chemistry. He never discovered or synthesized any new substance in the laboratory, but paid special attention to using physical methods to solve the "grand" problems in chemical research. Ostwald is recognized as the founder of the discipline of "physical chemistry". He was awarded the 1909 Nobel Prize in Chemistry for his basic theories on chemical equilibrium and reaction rate, as well as his outstanding contributions in the field of catalysis. When Ostwald came to teach at the University of Leipzig in 1887, he delivered a speech entitled "Energy and Its Transformation" and has since devoted himself to the study of "energetics". Ostwald was deeply impressed by the great power of thermodynamics in physical chemistry research. This made him believe that all phenomena in nature can be explained only by the concept of energy. The fundamental constituent element of the universe is energy in various forms, and the laws of nature are the laws governing the flow and transformation of energy; atoms and molecules are just mathematical fictions, and matter is not the carrier of energy, but the manifestation of energy; the principle of energetics can provide a more solid and clear foundation for chemistry and other sciences than molecular theory. Ostwald further raised the idea of ​​energetics to a philosophical level, and gradually formed the worldview of "energeticism" or "energy monism". Although Ostwald maintained a good personal relationship with Boltzmann, and even helped Boltzmann get a teaching position at the University of Leipzig when he was in trouble. However, at the meeting of natural philosophers held in the northern German port city of Lübeck in 1895, Ostwald openly opposed the molecular theory and had a fierce debate with Boltzmann. The molecular theorists and energetic theorists, led by Boltzmann and Ostwald respectively, refused to give in to each other, and their debate lasted throughout the last decade of the 19th century.

Mach was an influential experimental physicist and philosopher in the late 19th century. He achieved a series of important results in the study of optics and fluid mechanics. The term "Mach number" (a dimensionless number representing the ratio of fluid velocity to the local speed of sound) that is now familiar to people in the aviation field is named after him. Mach severely criticized the molecular theory from the philosophical point of view of empiricism. He believed that if molecules are tiny entities that cannot be directly perceived or observed, then it is unfounded to assume that their motion obeys the laws of classical mechanics that describe macroscopic objects. Therefore, Mach believed that Boltzmann's conclusion based on "the motion and collision of molecules can be described by classical mechanics" was at most a useful mathematical model, far from being evidence of the existence of molecules. In the face of the defense of the molecular theorists, Mach often threw out the "killer weapon": Have you seen one molecule? At this time, the molecular theorists could only retreat in disappointment and admit that they could not do this (for the time being). After all, from an empirical point of view, opposing the molecular theory did not contradict people's experience and logic at the end of the 19th century.

Boltzmann had a strong and sensitive personality, and his continuous debate with opponents of molecular theory caused serious damage to his mental state. In addition to long-term depression, Boltzmann in his later years also suffered from insomnia, angina pectoris and asthma. In 1901, Boltzmann left Leipzig and returned to his alma mater, the University of Vienna, to take over the teaching position vacated by Mach after his retirement. Although he escaped from the stronghold of energeticism, the music capital did not bring enough comfort to Boltzmann, who was good at piano. In September 1906, Boltzmann and his family went on vacation to Trieste, a coastal city in northeastern Italy. On the last day of the holiday, Boltzmann, who was out of control, took advantage of his wife and daughter going to the beach to swim and hanged himself in the hotel room. Boltzmann was buried in the Central Cemetery of Vienna, and the statistical definition formula of entropy named after him was engraved on his tombstone.

History is so sad. If Boltzmann could live two more years, he would have seen decisive experimental evidence that confirmed the objective existence of molecules. Whether this could heal Boltzmann's mental trauma, we will never know, but Ostwald did change his mind because of it. In 1909, Ostwald admitted in the preface of his famous textbook "Introduction to General Chemistry" (third edition): "We have recently mastered experimental evidence that proves the discontinuous nature of matter." Mach, who was already in his twilight years, still adhered to his philosophical views. In 1913, he published the book "Principles of Physical Optics". In the preface, Mach clearly stated: "I reject today's belief in atomic theory."

Figure 6. (Left) Ostwald's Introduction to General Chemistry (third edition, English translation) preface page; (Right) Mach's Principles of Physical Optics (English translation) preface page. The blue lines in the figure mark the source of the text quoted in the text.

Historical figures

In the 19th century, the debate on the existence of molecules shifted from chemistry to thermodynamics and statistical mechanics, and it dragged on for decades without a final conclusion. One important reason was the lack of an effective method to directly observe molecules. If the size and mass of a certain molecule could be measured, or the number of molecules contained in a certain amount of macroscopic matter could be calculated, the situation would inevitably change. Where can we find such a method? Readers may still remember that when high school chemistry classes introduced the concept of molecules, they would introduce a method called "using the oil film method".

On the water surface, a thin monomolecular oil film is formed. If the volume V of oleic acid used (such as 4 × 10^(–5) cm^3) and the area A of the oil film formed (such as 1.65 × 10^2 cm^2) are measured, the linear dimension of the oleic acid molecule d = V/A can be estimated (approximately 4 × 10^(–5) cm^3 / 1.65 × 10^2 cm^2 = 2.42 × 10^(–7) cm).

It is a very common phenomenon that grease spreads on the water surface to form a film. In 1773, Franklin (B. Franklin), one of the founding fathers of the United States, wrote a letter to a friend in which he described in detail an experience he had 16 years ago: in a fleet sailing on the sea, there were one or two ships with no obvious tracks at the stern, and the hull seemed to glide on the sea surface. An experienced captain told Franklin that this must be because the cook on the ship was dumping swill, and the grease lubricated the bottom of the boat. Franklin conducted an experiment in Clapham, south of London. On a lake wrinkled by the wind, Franklin poured oil into the water. Although the amount of oil was only a small spoonful, the rapidly spreading oil film immediately calmed down several square yards of the water surface. Since then, he often hid a small pot of oil in a bamboo cane, and performed the trick of "calming the water" to his friends whenever he had the chance. Although Franklin the Magician often won plaudits, given his life period (Franklin died in 1790) and the timeline of the development of molecular theory, it is impossible for Franklin to use the oil film method to estimate the number or size of molecules.

The first person in history to estimate the size of air molecules and the number of molecules contained in 1 cm^3 of air under standard conditions (0 °C, 1 atmosphere) was the Austrian physicist JJ Loschmidt. He was also Boltzmann's teacher when he was studying at the University of Vienna. Loschmidt's calculations were based on Avogadro's law and the molecular kinetic theory of ideal gases. Starting from Clausius's formula for the mean free path of gas molecules (the average distance that molecules move between two adjacent collisions), he assumed that air molecules were spheres and derived that their diameter s and mean free path l satisfy the following simple relationship:

s = 8εl (7)

(7) In the formula, ε = Nπs^3/6, called the compressibility coefficient of the substance, represents the volume actually occupied by the N spherical molecules contained in a unit volume of gas. Macroscopically, it is approximately equal to the ratio of the liquid density of the substance to the gas density under standard conditions (assuming that the liquid molecule spheres are tightly connected). There were many studies on the mean free path of air molecules at that time, and the value used by Loschmidt was 1.40 × 10^(–7) m. If the diameter of air molecules is to be obtained, the compressibility coefficient of air ε must be known. Unfortunately, in the 1860s, people had not yet achieved the liquefaction of air, and it was impossible to determine the density of liquid air through experiments. Loschmidt regarded air as a "compound" composed of 77% nitrogen and 23% oxygen. Based on the atomic constant determined by H. Kopp, he cleverly estimated the density of liquid air and then obtained the compressibility coefficient of air to be 8.66× 10^(–4). Therefore, the diameter of the air molecule can be calculated to be 8 × 8.66 × 10^(–4) × 1.40 × 10^(–7) m = 9.69 × 10^(–10) m (about one-third of the linear dimension of the oleic acid molecule estimated above, which is much larger than the actual nitrogen and oxygen molecules). Based on this value, the number of molecules contained in 1 cm^3 of air under standard conditions is 1.83 × 10^18, a value sometimes called the Loschmidt constant (Loschmidt believed that his calculations might have an order of magnitude error, and the modern value of this constant is about 2.7 × 10^19). Loschmidt's results were not reliably verified by experiments at the time, so their influence was relatively limited. If you want to calculate the number of molecules accurately, such as the number of molecules contained in each "gram molecule" of a substance (gram molecule is the mass of a substance in grams, and its value is equal to its molecular weight. For example, the molecular weight of hydrogen is 2, and 1 gram molecule of hydrogen is 2 grams of hydrogen), you need to focus your eyes under a microscope. It was the random movement of pollen particles on the water surface that eventually brought a heavy Nobel Prize and a string of numbers that went down in history.

In 1827, British botanist R. Brown used a microscope to observe pollen particles suspended in water. He found that these particles were constantly moving, and their trajectories were chaotic. At first, Brown thought this might be a manifestation of the vitality of pollen as a living organism. However, when he used dead pollen particles or powders of inanimate substances (such as coal, rock, and metal), he could see the same phenomenon; and the intensity of the movement increased with the decrease in particle size, liquid viscosity, or the increase in temperature. This never-ending movement was named Brownian motion. In the second half of the 19th century, molecular theorists gradually believed that Brownian motion was caused by the continuous unbalanced collisions of particles with the surrounding liquid molecules. Just as cathode rays were the clue to JJ Thomson's discovery of electrons, Brownian motion is likely to become evidence of the existence of molecules. However, this evidence is far from being generally accepted, and it still lacks a quantitative theory and a set of controlled experimental tests.

Left: A. Einstein (1879-1955), winner of the 1921 Nobel Prize in Physics; Right: JB Perrin (1870-1942), winner of the 1926 Nobel Prize in Physics

In 1905, Albert Einstein, who had just received his doctorate in physics from the University of Zurich, welcomed his "miracle year". He published four papers in the German journal "Annals of Physics", which greatly promoted the construction of the foundation of 20th century physics. Among them, the article "The Motion of Suspended Particles in a Still Liquid Required by the Molecular Kinetic Theory of Heat" provided the first complete explanation for Brownian motion. Einstein believed that because Brownian particles were very small (linear dimensions were about 10^(–4) cm), they could not be completely offset by the impact of liquid molecules from different directions. What is observed under a microscope is the average displacement of Brownian particles due to frequent impacts of molecules within the macroscopically resolvable time, which is a fluctuation phenomenon under statistical laws. Einstein derived the differential equation for the diffusion of Brownian particles and the distribution formula for the displacement of particles in a certain direction within a given time. It can be seen that the average displacement λ of Brownian particles is proportional to the square root of time t.

(8)

In the expression of the proportionality coefficient of λ and t^(1/2) in equation (8), apart from the universal gas constant R, and observable quantities such as absolute temperature T, the internal friction coefficient k of the liquid, and the effective radius P of the Brownian particle, the only unknown quantity left is the number of molecules N contained in each gram of the substance! Einstein's formula points out a way to calculate the number and size of molecules starting from the observable quantities of Brownian motion.

Three years later, French physicist JB Perrin took the last step to prove the objective existence of molecules. Perrin studied at the École Normale Supérieure in Paris in his early years, and later taught at the Sorbonne University in Paris for a long time. In 1895, Perrin proved the existence of negatively charged particles in cathode rays, laying the foundation for Thomson's discovery of electrons. In 1908, inspired by Einstein's theory of Brownian motion, he experimentally determined the number of molecules contained in each gram of molecular substance (i.e., N in formula (8)). In order to commemorate Avogadro, the founder of the molecular theory, Perrin suggested naming this value Avogadro number, denoted as NA. The key to Perrin's experimental design is to change the direction of testing the Brownian motion effect from horizontal to vertical; abandon natural (uncontrollable) Brownian particle systems such as pollen particles, and use specially prepared monodisperse (standardized) emulsions as research objects. Perrin believed that due to the combined effects of gravity (sedimentation) and Brownian motion (diffusion), particles in the emulsion have a difference in number density distribution in the vertical direction (the number of particles at high altitudes is less than that at low altitudes in equilibrium), just as the density of the atmosphere gradually becomes thinner with increasing altitude. He further derived the formula for the vertical number density distribution of emulsion particles:

(9)

Where R and g are the universal gas constant and gravitational acceleration. Assuming that the mass m and density D of the particles in the emulsion, the liquid density d, and the ambient temperature T are known, and the number of particles n' and n on two horizontal planes with a height difference of h in the emulsion are experimentally measured, the Avogadro number NA can be calculated.

It is easier said than done. Although the experimental principle is not complicated, it takes a lot of hard work to get a conclusive result. Using the centrifugal method, Perrin spent several months sorting out dozens of grams of highly uniform particles of gamboge (a kind of painting pigment) and frankincense (a kind of natural resin) (particle size less than 0.5 μm), and accurately measured their mass and density. He cleverly constructed a 0.1 mm high emulsion sample on the microscope slide, and used a high-power lens with a very shallow depth of field to observe the single layer of particles in the emulsion. In order to overcome the interference of the Brownian motion of the particles itself on the observation, Perrin managed to limit the field of view of the microscope to an area the size of a needle tip, and used the naked eye to observe the number of particles that appeared in this area at a certain moment through the microscope. After counting thousands of times, the number of particles n at a certain height of the emulsion can be calculated. The way is simple, and the heavy sword has no edge. Perrin used this ingenious and simple method to conduct a large number of repeated observations of emulsions of different types, particle sizes and viscosities at different temperatures, and calculated the value of NA to be 6.5~7.2 × 10^23 according to formula (9). Perrin and his student M. Chaudesaigues also used a microscope to directly observe the average displacement λ of the Brownian motion of emulsion particles, and calculated the value of NA to be in a narrow range of 5.5~8.0 × 10^23 according to formula (8). If the experimental error is deducted, it can be considered that NA is a constant for different substances, and the Avogadro number can therefore be upgraded to the Avogadro constant.

Figure 7. Perrin’s microscope photo of garcinia emulsion particles in a state of sedimentation-diffusion equilibrium. Image source: Advances in Colloid Science (left); Stud. Hist. Phil. Sci. 2008, 39, 312–322 (right)

Perrin's observation of the emulsion of garcinia and frankincense did not require the existence of molecules in advance, but his observation results, especially the highly consistent values ​​of NA calculated using different methods, proved the correctness of Einstein's theory of Brownian motion, thus demonstrating the objective existence of molecules. Unlike phenomenologists who only accept experimental phenomena that can be directly perceived and observed, Perrin pointed out that his work established a causal relationship between complex phenomena visible to the naked eye and simple principles that cannot be directly touched (… to explain the complications of the visible in terms of invisible simplicity). After Perrin's experiment, Ostwald, the leader of energeticism, accepted the existence of molecules. The great French scientist H. Poincaré, who previously believed that molecules were just an insignificant mathematical hypothesis that could be abandoned at any time, like Mach, highly praised Perrin's work, saying: "Perrin determined the number of molecules (contained in a certain amount of matter), and this outstanding work announced the victory of molecular theory." In 1926, Perrin was awarded the Nobel Prize in Physics for his contributions to "the discontinuous structure of matter" and "the discovery of sedimentation equilibrium." It had been 123 years since Dalton wrote the first atomic weights table, 66 years since Cannizzaro spread Avogadro's molecular theory at the Karlsruhe Conference, and 20 years since Boltzmann committed suicide.

At the beginning of the 20th century, the emergence of more experimental evidence and characterization methods about the microscopic world, as well as the great changes brought about by quantum mechanics, made the objective existence of atoms and molecules no longer a controversial issue, but gradually became common knowledge that the general public had some knowledge of. In 1971, the 14th General Conference on Weights and Measures abolished the "gram molecule" and redefined the "mole" (abbreviated as mol) as the unit of the amount of substance (mole thus became one of the seven basic units in the International System of Units):

Atoms and molecules have gone from speculation to science, and have experienced a pursuit that spans a century. As time goes by, people today seem to take atoms and molecules for granted, and no longer care about their historical evolution. When I was reading materials about Dalton, Avogadro, Gay-Lussac, Berzelius and others, I felt alienated and difficult to understand the issues they were concerned about, the methods they used, and the terms they invented. This is probably the result of my 20 years of training in contemporary chemistry! But in any case, the real "from zero to one" explorations of the senior scientists, even the mistakes they made and the disputes they had, are all worth our careful appreciation. Those painful and happy journeys that were achieved only after going through hardships in the dark can probably be best described by a passage from the British mathematician A. Wiles:

"When you first enter a completely dark room, you will stumble around everywhere. In the process, you gradually become familiar with the location of each piece of furniture. Finally, perhaps after six months of groping, you find the switch of the chandelier. When you turn on the chandelier, everything in the room is illuminated in an instant, and all the furnishings confirm your guess. In joy, you open the door to the next dark room without hesitation..."

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Acknowledgements

The authors would like to thank Academician You Shuli from the Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Researcher Cao Zexian from the Institute of Physics, Chinese Academy of Sciences, Professor Zhang Shaodong from Shanghai Jiao Tong University, and Researcher Liu Jinyan from the Institute of the History of Natural Sciences, Chinese Academy of Sciences for their valuable comments on this article.

About the Author

Dr. Zheng Chao is a researcher at the Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, and a recipient of the National Natural Science Foundation of China Excellent Young Scientist Fund Project. His research interests are physical organic chemistry and chiral synthesis.

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