In the year of the Nobel Prize for Bell's inequality, remembering Bell's life

The 2022 Nobel Prize in Physics was awarded to three physicists who conducted experiments related to quantum entanglement. The "Bell inequality" was directly mentioned in the award reason, which brought the Northern Irish physicist John Bell back into people's attention. Bell is famous for his research on the foundations of quantum mechanics, especially the Bell theorem and Bell inequality. He told us that the microscopic world of matter follows unimaginable laws, which has now become the foundation of the field of quantum information. In fact, these achievements that made him go down in history were "amateur". He worked at the European Organization for Nuclear Research for a long time in his life, and also made outstanding contributions in accelerators, nuclear physics and elementary particles. He was also called the "saint of CERN". In the year when Bell's inequality won the Nobel Prize, we would like to commemorate Bell's extraordinary life.

Written by Liu Yuanxing (doctoral candidate at the School of Humanities, University of Chinese Academy of Sciences) and Guo Rongzhen (doctoral candidate at the Institute of Theoretical Physics, Chinese Academy of Sciences)

The 2022 Nobel Prize in Physics was awarded to three physicists, Alain Aspect, John F. Clauser and Anton Zeilinger, in recognition of their achievements in entangled photon experiments and Bell's inequality experiments. Bell's inequality is undoubtedly one of the most important foundations of these scientists' work. Who is Bell? He is not Alexander Graham Bell, the father of the telephone or famous for Bell Labs, but John Stewart Bell.

Figure 1 John Stewart Bell (July 28, 1928-October 1, 1990) Image source: Wikipedia

A turbulent but happy childhood

In 1928, Bell was born in Belfast, the capital of Northern Ireland, a city with a long history and a glorious past. In the 1760s, the Industrial Revolution emerged in Britain, and Belfast benefited from it. By the early 19th century, it became the world's largest producer of linen products. It also has the world's leading Harland and Wolff Shipyard, where the famous "Titanic" was cast. But after World War II, the city began to go downhill, and because of the issue of Northern Ireland's ownership, the city fell into great chaos, and both the economy and politics were hit. Bell was born in such an era.

Bell is the eldest son in the family. He has an older sister and two younger brothers (Figure 2). His father Jackie is an ordinary worker, and his mother Annie is a shop clerk. Both of Bell's parents received only very basic education. Bell's father's family was ordinary, while his mother came from a prominent family that had fallen on hard times. Bell's grandfather was once a very successful businessman. His grandfather had a profound influence on Bell's mother. Annie was good at managing the household. Even though she was living in poverty today, she was always able to save money and make the family live a fulfilling and happy life. She once bought a second-hand bicycle for the children and recalled that they were as fun to ride as new ones[1]. Through this incident, the author speculates that the reason why Bell loved riding motorcycles so much in his youth was not only influenced by the environment where he lived at the time (young men in the area all loved riding motorcycles[2]), but also by the "bicycle incident" in his childhood. Later, Bell always had a beard. It is said that he had a deep cut near his mouth due to a serious motorcycle accident[3], which he covered with a thick beard.

Bell was different from others since he was a child. His family believed in Anglicanism, and many people around him believed in Catholicism. However, Bell insisted on his pursuit of truth. Even though religion could bring practical benefits (for example, at school, Irish children have a higher chance of joining the football team [4]), he did not believe in any religion. However, he was a staunch vegetarian. According to Bell's wife, he became a vegetarian under the influence of the famous Irish playwright George Bernard Shaw [5]. Bell's mother Anne also recalled such a story: One Christmas, Bell smelled the smell of roast turkey and commented: "I smell a burning body." Perhaps this compassion for animals is another reason why Bell became a vegetarian.

Figure 2 A family outing: top row from left: Bell’s grandmother Mrs Brownlee, sister Ruby Bell and mother Anne Bell; bottom row from left: brother David, Bell and brother Robert. Image source: Reference [6]

Bell was very smart since childhood. He was proficient in playing cards and chess. He also loved to show off what he had learned. He always told his family and even strangers about his knowledge. Although not everyone liked his personality, his parents were happy that Bell was good at self-expression. In addition, Bell was also very good at hands-on work. He once used a mustard can that was painted black on the inside and had a small hole pierced on the top of the lid, and a piece of photosensitive paper to make a pinhole camera in a dim red-light darkroom (bathroom)[7].

After going to school, Bell's grades were always among the best, and when he was 11 years old, he expressed his desire to become a scientist. But for children in Belfast, free compulsory education ended at the age of 14, and education after that had to pay a large amount of tuition. Bell's father came out to help the family earn money when he was only 6 years old, but the family was always poor. In addition, due to the influence of education policy, he naturally thought that Bell should leave school at the age of 14 to find another way to make a living [8], but his mother encouraged Bell to continue studying. Bell wanted to go to a self-funded secondary school several times, but the tuition fees became a stumbling block. In the end, he was successfully enrolled because of a scholarship provided by Belfast Technical High School [9]. Bell's sister Ruby was not so lucky. Although she also received a scholarship from the school, she was unable to continue her studies due to the concept of favoring boys over girls. Bell's other two brothers, David and Robert, also dropped out of school at the age of 14 to start earning money.

Studying, seeking employment and seeking love

At the beginning of middle school, Bell developed a strong interest in ancient Greek philosophy. After reading a large number of philosophy books, he was disappointed to find that the definition of a so-called "good philosopher" is just that they can refute other philosophers, and that philosophy is about solving very big problems. For Bell, there was no progress in solving these problems [10]. When he began to learn physics, he was pleasantly surprised to find that the progress of physics was significantly better than that of philosophy. From then on, Bell picked up his old dream again and gradually planted the seeds of becoming a physicist in his heart. However, he was not very satisfied with the rigid teaching of physics in school. Bell was an absolute top student in middle school, but he did not show any extraordinary talents.

After graduating from high school at the age of 16, Bell was unable to enter university because he was under the school enrollment age and could not afford the tuition. During this period, he began to look for a job that could temporarily support himself. He interviewed for many jobs, such as a handyman in a small factory and an entry-level job at the BBC, but ultimately failed. This was because the employers of these jobs thought Bell's conditions were too good, and when he started working, Bell's body language showed that he did not want to do the job.[11] Fortunately, the many practical skills Bell learned at Belfast Technical School helped him find a job as a technical assistant in the Department of Physics at Queen's University Belfast, and stayed to work under the head of the department, Karl George Emeléus.[12] During this period, he was also allowed to audit physics courses. After having a certain foundation in physics and saving enough tuition, he officially enrolled in Queen's University in 1945.

Bell still maintained his characteristic of liking to express himself during his college years, and he also liked to debate with others. He often participated in group activities at school. Bell was not only interested in physics, but also participated in discussions on philosophy, politics, etc.

In his early college years, Bell studied under Amelius and Robert Harbinson Sloane. In his first year of college, Bell passed the first-year course exams and entered the second year of study. Later, he studied quantum mechanics and related philosophical issues, and was deeply influenced by the book Natural Philosophy of Cause and Chance by the great German physicist Max Born[13]—he was deeply attracted by quantum mechanics, especially the strange wave function collapse of quantum mechanics, which fascinated him and became one of his research directions throughout his life. Bell got along very well with his two teachers most of the time, but whenever Bell asked his teachers questions about quantum mechanics, they always argued with each other and could not convince each other. Bell believed that the teachers' explanations could not help him better understand quantum mechanics, and the teachers also became impatient under Bell's questioning[14].

In his last year at Queen's, Bell had the opportunity to study under Paul Ewald, a physicist who had come to Ireland because of the political disaster in Germany. He was the president of the Technical University of Stuttgart and one of the founders of X-ray crystallography. This was also Ewald's last year in Belfast. Bell and Ewald had a subtle chemistry and they talked about everything. Bell left a deep impression on Ewald[15]. In his last year before graduation, Bell finally got his wish to start studying the quantum mechanics of long-chain molecules. When Bell was working on his thesis, Ewald suggested that he visit Rudolf Peierls, a top theoretical physicist who was also in exile in Germany. However, Bell was restricted by his family situation at the time and wanted to go to work directly, so he did not follow his mentor's advice. However, Bell's fate with Rudolf Peierls did not end, and the two would have intersections in the future. In 1947, Bell obtained a first-class degree in experimental physics and a year later obtained a first-class degree in mathematical physics.

For postwar scientists, more "practical" physics could undoubtedly earn more money than theoretical physics. Even though Bell loved quantum mechanics very much, he knew that it could only be his hobby and not his full-time job. Against this background, in 1949 Bell chose to find a job at the British Atomic Energy Research Establishment (AERE) in Harwell. Bell's resume was not impressive. He did not have a doctorate degree and did not graduate from a prestigious university. Compared with others, he was not very competitive. Fortunately, he met his mentor Klaus Fuchs here, who arranged for Bell to study reactors in the theoretical physics department [16]. A few months later, Fuchs was arrested for espionage, and Bell followed another person who appreciated and cared about him very much, Bill Walkinshaw, to Malvern College, 80 miles away from Harwell, to participate in the design of linear accelerators. Bell's initial research was on medical linear accelerators. Here, Bell's deep understanding of basic physics and strong mathematical talent played a crucial role in his accelerator theory research. Walkinshaw once said of Bale:

"There once lived a young man of extremely high ability, who could quickly and independently choose a subject for research, with a particular interest in particle dynamics. His mathematical ability was profound and extraordinary." [17]

Bell's talent was finally put to good use here. He published many articles in the fields of accelerator physics and high-energy physics. He even pointed out the huge mistakes made by scientists many years later[18]. We will introduce this later.

For Bell, another lifelong event also came. Here he met his work partner and future wife Mary Rose. Mary was born in Scotland. Her father was a clerk. Her mother was a primary school teacher. In addition to Mary, she had two older sisters at home. Their family was all vegetarians. Mary showed great interest in mathematics and physics when she was a child, and her parents were very supportive of her studies. After receiving a scholarship, she chose to study mathematics and physics at the University of Glasgow. Later, due to the war, she was seconded to the Telecommunications Research Establishment in Malvern in 1944 to do radar-related research[19]. After obtaining a doctorate in physics and mathematics, she returned to Harwell in 1947 and came to Malvern to work again in 1950[20]. Whether it was because they were attracted by each other's talent and rigorous work attitude at work, or because they were both vegetarians, sparks of love flew between them. At that time, someone asked Bell which one was Mary, “The fat one, the tall one…” Bell replied, “No, the pretty one” [21]. Bell also wrote in the preface of his book Speakable and Unspeakable in Quantum Mechanics, “When I look back at these articles, Mary’s figure is everywhere” [22]. They were not only bosom friends in life, but also partners in scientific research (Figure 3).

Figure 3 Mary and John Bell at Stonehenge[23]

A "hobby" that stirs up a thousand waves

In 1952, thanks to the policy of AERE at the time to support young people to obtain higher degrees, Bell decided to further his education - to study for a doctorate. At first, Bell wanted to study field theory, and he set his sights on the University of Glasgow and the University of Birmingham. He finally chose to come to Birmingham and study under Rudolf Peierls, whom he had never been able to visit. Although Peierls clearly opposed Bell's basic theoretical research in quantum mechanics, Bell was always obsessed with the problems in quantum theory that troubled him, so he chose quantum field theory as his research direction. In the end, he obtained a doctorate from the University of Birmingham in 1956.

In Bell's mind, quantum mechanics has always been a knot that cannot be untied. He has been tracking and thinking about the development of quantum mechanics just like in his student days. Bell has long been dissatisfied with the interpretation of quantum mechanics he has come into contact with.

The first thing that came into question was the “shut up and calculate” teaching method. The quantum mechanics lectures he attended were highly instrumental courses—giving out the Schrödinger equation, solving wave functions, solving for energy levels, solving for spectra—and Bell was deeply puzzled by this. These mathematical operations were all well and good, but didn’t quantum theory need philosophy? What is our actual perception of the material world? What is behind these equations?[24]

Later, the uncertainty principle became the source of Bell's confusion about quantum mechanics. Bell's biggest confusion about the uncertainty principle was: in real physics, before the observer makes any measurement, what determines how accurate the existence of momentum and position is? With this question in mind, Bell read one quantum mechanics book after another, but neither Born's Atomic Physics nor Paul Dirac's The Principles of Quantum Mechanics could answer his confusion.

Bell was also deeply disturbed by the special status of measurement in the Copenhagen interpretation. He certainly recognized that in science, measurement plays the most important role. In order to understand a particular physical quantity, we must measure it. But Bell's view was that when we measure a physical quantity in the scientific sense, we must be trying to obtain a value that existed before the measurement. He believed that the subject matter of science should not be limited to the results of measurement - it should study what exists in the absence of measurement. It is for this reason that Bell declared himself to be a "follower of Einstein" - he was a staunch realist[25].

Finally, Bell was not interested in the elaborate “parables” that Niels Bohr often used in his discussions of fundamental problems in quantum mechanics. Compared to those speculative words, Bell was more concerned with solid mathematics and factual evidence.[26]

Bell's dissatisfaction with the Copenhagen interpretation spurred his thinking. Finally, in 1952, the opportunity came. He read David Bohm's 1952 article on hidden variables - at this time, he gradually focused his attention on John von Neumann and the EPR paradox.

In fact, the EPR problem was not as eye-catching as we would like to think today. Although this was the paper led by Einstein, Bohr's response was also very quick. At this time, the general understanding in the academic community was that the Copenhagen School had already solved the thorny conceptual problems in quantum mechanics, and Einstein's criticism of the EPR problem could only be regarded as his own failure to adjust his cognition to embrace the new theory. According to Bell's friend Leslie Kerr, Bell's first contact with the EPR problem was not directly from the original EPR paper, but from Bohm's famous book "Quantum Theory".

Bell himself was deeply attracted by this problem[27]—Bohm’s account of the book not only took into account the exploration of the problem of physical reality, but also discussed the technical details in a concise way. At the same time, Bohm himself made many useful advances in the theory of hidden variables. From this perspective, Bohm can be regarded as a guide for Bell in the study of quantum mechanics.

After reading Bohm's 1952 paper, Bell was very excited. As Mary said, "In his own words, 'This paper was like a revelation to me.'" [28] He carefully digested Bohm's paper and actively asked questions when Bohm came to give a report. Attendees recalled that Bell's questions clearly showed that he had studied Bohm's paper very carefully. This also guided him to understand von Neumann's work in depth, because Bohm's writing had always expressed doubts about von Neumann's book's falsification of the existence of hidden variables, but Bohm himself failed to find a way to strictly prove his point. This was accomplished by Bell several years later.

In 1960, Bell and Mary joined the European Organization for Nuclear Research (CERN). They had many interactions with CERN when they worked in Malvern before. Bell was attracted by particle physics, so they officially joined CERN. Bell worked in the theoretical department, while Mary joined the accelerator research group [29]. Bell's main work was particle physics and accelerator research, but he never stopped thinking about his "hobby" - the basic theory of quantum mechanics. In 1963, Bell and his wife got a vacation opportunity, and he devoted himself to the study of quantum mechanics. He also visited Stanford University, the University of Wisconsin, and Brandeis University. While working as a short-term visiting scholar at Stanford University, Bell completed his first interim paper - "On the problem of Hidden Variables in Quantum Mechanics". In this article, Bell pointed out sharply that there were loopholes in the mathematical assumptions used in von Neumann's classic book "Mathematical Foundations of Quantum Mechanics" to disprove the existence of hidden variables:

"Any real linear combination of two Hermitian operators is an observable, and the expectation of any real linear combination of two Hermitian operators is just the real linear combination of the expectations of the two Hermitian operators."

Bell's argument for this was also very simple. He used a particle with a spin of -1/2 and considered constructing the most general Hermitian operator on its state space. He found that at least some hidden variable theories that could be simply constructed did not satisfy von Neumann's assumptions, thus providing a simple and powerful counterexample. In addition, a paper jointly published by Josef-Maria Jauch and Constantin Piron and a paper by Andrew Gleason had similar problems [30]. Due to problems with the editor of the journal, Bell's paper was not published until 1966. He also stated in the paper that his thinking on this issue could be traced back to 1952 [31]. Bell successfully proved that the hidden variable interpretation was not completely refuted.

By finding loopholes in von Neumann's rigorous mathematical derivation, Bell gained full confidence to attack the non-locality problem of quantum mechanics. Bell's second interim achievement paper was his most famous paper "On the Einstein-Podolsky-Rosen paradox". In this paper, Bell focused on Bohm's version of the EPR paradox.

Unlike the EPR paradox based on particle spin that we are generally familiar with, the entangled quantum state in Einstein's original paper is the position state of the two particles. Later, Bohm converted it into the entanglement of spin states that we are familiar with today. This treatment has a lot to do with the initial confrontation between Bohm and Einstein. Einstein's original idea was that the measurement problem of two-particle entanglement they constructed could imply that particles can have a definite position and momentum at the same time, so Bohr's response was to reiterate the uncertainty relationship that was almost a consensus under the Copenhagen School. However, the real key to the EPR problem is not here, but the fact that when the observer knows the state of one of the entangled particle pairs, the state of the other particle is immediately determined, that is, the problem of locality. Einstein himself later clarified his views again, but Bohr did not seem to notice this. Bohm's transformation pointed out the original EPR problem in a clearer and more operational way.

In Bell's view at the time, although the hidden variable theory proposed by Bohm could reproduce many predictions of traditional quantum mechanics, it itself had a very distinct non-local feature. The EPR paradox directly pointed out the locality problem, but Bohm believed that the non-locality problem of quantum mechanics pointed out by EPR would be overcome by the hidden variable explanation. The combination of the two seemed to imply that there was a local hidden variable theory that could both reproduce the important predictions of quantum mechanics and overcome the disturbing non-local features of the EPR paradox. However, Bell proved that no local hidden variable theory could reproduce all the statistical predictions of quantum mechanics, a statement that later became known as Bell's theorem[32].

Bell's theorem shows that the difference between local hidden variable theory and quantum mechanics is not just purely speculative, but they must have measurable differences - people can rely on specific experiments to make a final judgment on the two. Bell quickly found the specific means of operation based on the original EPR experiment and the revision of Bohm's version. Bell found that in Bohm's modified EPR experiment, the measurement of the spin components of the two particles was always in the perpendicular direction. This is derived from the original EPR paper, because the position-momentum relationship and the relationship between the spins in the perpendicular direction considered by Einstein have the same algebraic origin in quantum mechanics. The work of predecessors has indeed proved that if the measurement in question is always limited to the spin components in the same direction or perpendicular to each other, the measurement results of quantum mechanics are no different from the measurement results of local hidden variables. However, once the spin measurement in any direction is introduced, the difference between the two can no longer be concealed. The Bell inequality derived by Bell describes the commonality of such measurement results under any local hidden variable theory, and the measurement results of traditional quantum mechanics will definitely not satisfy this inequality. Therefore, designing experiments to test whether Bell's inequality is valid or not becomes a fair judge of two theories or even two worldviews.

Although Bell’s original intention in writing Bell’s inequality was to prove that Einstein was right, it was used to prove that Einstein was wrong. In an era when the Copenhagen interpretation was successfully explaining countless microscopic phenomena, it would have been impossible to do such work without feeling uneasy about its philosophical implications. However, when Asper’s experiment was successful, Bell also made a fair comment, “This experiment shows that Einstein’s worldview is untenable.”[33]

An interesting point here is that when Bell was at Stanford University, it would have been natural for him to choose Physical Review during the submission process. However, Physical Review charged a high publication fee, and Bell thought it was very rude for a visiting scholar to ask Stanford University for this fee.[34] Therefore, Bell chose to submit the article to Physics, a relatively unknown magazine that was only published until 1968.

Classics in accelerator physics

Although Bell is well-known for his research in quantum mechanics, quantum mechanics was just his hobby after all, while accelerator physics and high-energy physics were his main occupations.

Most of Bell's accelerator research in the 1950s was done at AERE, which provided mathematical methods for building linear accelerators, and these methods can still be used as the starting point for large-scale computer programs today.[35]

The mathematical method referred to here is to establish a general theory of the movement of particle beams under the strong focusing system, which is important in the principle of accelerators. The so-called strong focusing system relies on two types of magnets with different properties - focusing magnets and defocusing magnets. Under the specific arrangement and combination of focusing magnets and defocusing magnetic fields, charged particles can make the particle beam more and more concentrated while maintaining the stability of the particle beam, just like the performance of a light beam under a convex lens and a concave lens group. When dealing with the strong focusing problem at the beginning, everyone naturally adopted the traditional method, that is, to analyze the trajectory of the particle beam based on the equation of motion. However, for the most general design, the analysis based on differential equations is too cumbersome and cumbersome, and the most convenient way is to use matrices. In 1953, Bell wrote the article "Basic Algebra of the Strong Focusing System", which detailed the matrix processing method under the strong focusing problem and introduced the important invariant in this system, which is now generally called the Courant-Snyder invariance. It is important to emphasize that Bell’s work was conducted independently of Ernest D. Courant. Phil Burke and Ian Percival wrote in their biographical memoirs that Bell’s article was “extremely influential… read by all accelerator designers of the time”[36].

Another important work of Bell during this period was the article "Linear accelerator phase oscillations" published in the AERE report in 1954. This article was also a representative work carefully selected by Bell's wife Mary for his research during this period when she participated in compiling Bell's paper collection, showing her admiration for Bell's work. The main "opponents" of this article were two heavyweights in accelerator physics, Robert Serber and 'Pief' Panofsky. (By the way, this name in quotation marks was given to Panofsky by his relatives and friends because they felt that his original name was too difficult to pronounce.)

In a linear accelerator, the acceleration of electron beams is carried out in a waveguide by relying on a periodically changing electric field. Based on simple electrodynamics, we know that the electric field in a waveguide is composed of a combination of several different Fourier modes. So when studying the acceleration of this type of electron beam, do we only need to consider the influence of a mode of a certain basic frequency, or do we need to consider the contribution of all modes? John C. Slater's article in 1948 supported the former, while Seiber and Panofsky's studies in 1948 and 1951 respectively believed that the influence depends on the specific form of the accelerating electric field. Bell's article supports the former view.

Bell's calculations were directly carried out for arbitrary acceleration fields. The mistake of the two experts was that they made inappropriate approximations in their specific calculations. How to make a good approximation in physics is an extremely profound problem, and the handling of approximations can reflect the ability of physicists. As Mary said, Bell's article is based on the Hamiltonian form of relativistic particle dynamics under arbitrary acceleration fields in linear accelerators. More deeply, the analysis of Bell's article is still based on the use of Courant-Schneider invariants. The original Hamiltonian form protects important dynamical invariants and therefore protects dynamical evolution. This also confirms Bell's profound understanding of the basic theory.

However, the article was not submitted to a journal for publication, but was instead published as an internal report of the institute. Mary said that later scientists were still making the same mistakes that Bell pointed out in the article.[37]

In the 1980s, Bell's interest returned to the field of accelerator physics. As the energy and brightness of accelerators increase, the impact of quantum fluctuations on the particle beams in the accelerator will become more and more significant. In the 1950s, an accelerator designer could still rely on his familiarity with classical theory to carry out his work with ease - just like Bell mentioned above - but in the 1980s, people had to treat quantum effects systematically and seriously in traditional accelerator research. At the same time, CERN in the 1980s was also conducting research and development of many accelerator-related projects, such as the Initial Cooling Experiment (ICE) and the Large Electron-Positron Collider (LEP, which was dismantled at the end of 2000). Both the research interest in physics and the research needs of his unit eventually prompted Bell to return to his main research business in the 1950s.

In terms of ICE, Bell's research mainly focuses on the research of particle beam cooling technology. There is an important physical concept in the research of particle beams, called emittance, which refers to the area occupied by the particle beam in the phase space. The lower the emittance, the more concentrated the spatial distribution of the corresponding particle beam, and the more consistent the momentum distribution, which means that the particle beam has better quality. The cooling of particle beams refers to the technology of reducing the emittance of particle beams. Bell has in-depth research on several important technical directions of this technology, such as electron cooling, stochastic cooling and radiation damping. It is particularly worth emphasizing that when studying radiation damping as a particle beam cooling technology, Bell once again - just like in the strong focusing problem - relied on his deep physics foundation to develop a generalized formal theory. This time his theoretical tools are Lagrange brackets and Lagrange invariants.

In response to LEP, Bell conducted in-depth research on radiation damping and quantum bremsstrahlung in the accelerator. Due to his experience with linear accelerators[38], Bell was able to directly calculate the radiation damping of the storage ring orbit in the accelerator through a very simple formula, while the traditional method is to use complex orbit calculations to achieve this[39]. Another very eye-catching work in Bell's research related to LEP is related to the Unruh Effect, an extremely important effect in the quantum field theory of curved spacetime. The Unruh Effect is an effect in which an accelerating observer finds that his vacuum is filled with thermal radiation. It is closely related to the famous Hawking radiation. However, the thermal background temperature generated by the Unruh Effect is extremely low, so that to this day, how to detect the Unruh Effect is still a controversial topic in academia. On this issue, Bell gave his own detection idea - observing the characteristics of the accelerated electron beam in the accelerator. In the title of Bell's own article, "The electron is an accelerated thermometer." Bell systematically studied the impact of the Unruh Effect on many observable effects of the electron beam. This is also a microcosm of Bell's dual identity as an outstanding theoretical physicist and experimental physicist.

In addition, Bell's profound understanding of classical mechanics and classical field theory made me accidentally capture another interesting "little thing" in Bell's academic career: Bell participated in translating the English version of the famous "Landau Ten Volumes" published by Lev Landau and EM Lifshitz, the "Course in Theoretical Physics" series. The parts that Bell participated in translating include "Mechanics", "Quantum Mechanics: A Non-relativistic Theory", "Electrodynamics of Continuum Media" and "Quantum Electrodynamics" (the earliest version was titled "Relativistic Quantum Theory"), which just correspond to Bell's most proficient research field.

A generalist in high-energy physics

Bell's main research direction throughout his life was high-energy physics. In terms of research methods, it includes research on particle physics phenomenology and quantum field theory. In terms of research objects, Bell's research breadth almost covers a series of studies that have had a profound impact on high-energy physics in history: CPT theorem, beta decay, phenomenological models of nuclear physics, neutrino physics, parton models, quantum chromodynamics, K mesons and CP violation problems, current algebra, light hadron spectroscopy and light hadron structure, hadron spectroscopy including heavy quark hadrons, gauge field theory, unstable particles in quantum field theory, σ-model, solitons in quantum field theory, quantum anomalies... We are unable to introduce Bell's achievements in each direction, so we will only select a few of them for introduction.

First of all, Bell's outstanding contribution in the CPT theorem. The CPT theorem is one of the most important theorems in quantum field theory. It points out that for any local quantum field theory that satisfies Lorentz invariance and whose Hamiltonian has Hermitian properties, the theory after three different discrete transformations - charge conjugation (C), space inversion (P) and time inversion (T) - is the same as before. With the help of the CPT theorem, many important inferences can be obtained, such as positive and negative particles must have equal masses, etc. Bell's paper proving the CPT theorem, "Time Reversal in Field Theory" was published in the Proceedings of the Royal Society (A) in 1955. But Bell's luck was a little worse. When he completed this paper, Gerhard Lüders and Wolfgang Pauli had reached the same conclusion almost at the same time before Bell (Bell's doctoral thesis was published in 1954, which actually included the content of the proof of the CPT theorem). However, Bell's paper gave a more general proof[40]. Moreover, Bell's proof was simpler and clearer, and very different from Luders's proof. This is the fundamental reason why Bell's paper was still published in the Proceedings of the Royal Society after Luders's paper was accepted. And to this day, Bell's work may be more meaningful than the axiomatic field theory argument developed by Luders later, as Martinus JG Veltman said[41]. In fact, the problem of time reversal invariance has always attracted him, and can even be considered one of the themes of his lifelong research. Therefore, he later studied the CP violation problem in K meson decay.

Bell's connection with CPT symmetry may be even more inspiring to us. Bell's mentor Peierls once read news about a particle physics experiment that seemed to have discovered a negatively charged particle that was stable and lighter than a proton. The participants in the experiment asked Peierls if the particle was an antiproton. At the time, particle physicists generally believed that particles and their antiparticles should have the same mass. But Bell expressed doubts about this. Bell was naturally averse to assuming the correctness of a view just because it was widely held [42] - Bell wanted to prove it. And this problem, as Peierls said, soon became a thorn in Bell's side. Bell also chose it as the research topic for his doctoral thesis.

Another thing that needs to be emphasized is Bell’s contribution to quantum anomalies. Noether’s theorem in classical physics, that is, the correspondence between continuous symmetry and conservation laws, is well-known. So when a classical theory is quantized, can the original symmetry at the classical level still be preserved in quantum field theory? Although there is still the Ward-Takahashi Identity caused by symmetry in quantum field theory, things are not that simple - quantum anomalies indicate the destruction of classical symmetry at the quantum level. Bell’s important example of quantum anomalies in gauge field theory, namely the Adler-Bell-Jackiw anomaly in quantum electrodynamics (QED), is still a classic in gauge field theory [43]. This anomaly refers to the fact that after considering the single-loop correction of QED, the electron axial vector flow that is conserved under classical electrodynamics cannot be guaranteed to be conserved. The ABJ anomaly is the first quantum anomaly discovered in academia, and its importance is self-evident. This has important implications for general quantum gauge theory, whether it is field theory in high-energy physics or field theory in condensed matter physics [44]. In a sense, in the study of high-energy physics, Bell's research on quantum anomalies may be more influential than his research on the nonlocality of quantum mechanics. An example is that on Inspire HEP, a commonly used search website for high-energy physics, the number of citations of the ABJ anomaly paper is greater than the sum of the citations of Bell's two papers on basic problems in quantum mechanics.

The death of CERN's saint

Bell worked at CERN for a total of 30 years. He was known as the "Saint of CERN"[45]. Many colleagues, whether they knew him or not, would ask Bell questions of various kinds, and he would always answer the key questions in one sentence. Bell often said that "CERN is like a train station with many passers-by"[46]. He could meet new friends and solve new problems every day. His colleagues were all impressed by Bell's passion for science and his pursuit of truth. Bell also maintained an old British tradition at CERN - 4 o'clock tea, which was also the time for him to chat with his friends. He not only talked about physics, but also about politics, philosophy and even art, and let his thoughts fly.

Bale suffered from migraines throughout his life. The problem disappeared for a few years, but in the last days of his life, he still had migraines for a few short periods of time.[47] However, he did not take it seriously. Bale's friend Reinhold Bertlmann also recalled that when he met Bale in Paris in 1990, Bale did not look in good health.[48] Bale also died of a sudden cerebral hemorrhage in the same year.

Bell's life was as short as a meteor. In these short 62 years, he left behind a very rich physical legacy. He spent his whole life pursuing the most profound and difficult questions in physics, and was willing to use this as a basis to start his work, without fear of walking alone on a lonely road. As a highly skilled theoretical physicist, he always maintained a close relationship between theory and experiment, and was willing to devote himself to solving specific experimental problems, while always working hard for the experimental verification of theory. It was the dual pursuit of theory and experiment, the deep integration of specific problems and philosophical thinking, and the equal competition of the wisdom of predecessors and self-reflection that enabled him to take an epoch-making step in the exploration of basic problems in quantum mechanics.

If we regard a scholar's lifelong research as a landscape, then Bell's landscape is not a forest of one tree, not a hundred flowers in full bloom, not a mountain of clouds and mist, not a sea of ​​rivers, but a garden with well-arranged layouts and mutual reflections. Although it is not a wonder of divine work, nor a magnificent sight of the creation of the world, his ingenuity has transformed his understanding of the world into the layout of a garden. Whenever you and I walk by, we will express our sincere admiration - how lucky you and I are to be able to appreciate such a scenery.

According to legend, in the year of Bell’s death, he was nominated for the Nobel Prize in Physics that year[49], and there is no doubt that he should be awarded the 2022 Nobel Prize in Physics, which may be a kind of compensation for Bell in some way.

References

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[6] Andrew Whitaker. John Stewart Bell and twentieth-century Physics: Vision and integrity[M]. UK: Oxford University Press, 2016: 4. Photo slightly cropped.

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