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I am teaching Modern Physics this semester, a course I have taught three times before. The fun of re-teaching is many-sided: I get to have fresh insights into the material, the students push me with their questions [I always say students come to university to educate the professors; just don't ask me why they have to pay tuition to do that-:)], and I get to appreciate just how strange relativity and quantum mechanics are. Below I present an example from each of these categories: i) (Re-) Fresh (-ing) insight The first thing we learn in special relativity are the Lorentz transforms, which famously link position with time through the speed of light. The transforms for time (dilation) or space (contraction) intervals can be derived by considering two frames moving with uniform velocities with respect to each other and by assuming the velocity of light is the same in both frames. This is an exercise in geometry and algebra and takes several steps and some focus to execute. I wanted a more intuitive explanation of how the velocity of light joins space to time, an argument compact enough that I could carry it around 'in my pocket'. Here's one that I thought of, and maybe it is well known to some people, but I will share it nonetheless. Both in Newtonian and Einsteinian mechanics, velocity is given by the time derivative of position: v = dx/dt Now if space and time are allowed to vary independently, then dx and dt can take any values. Sure, dx and dt are small quantities from the point of view of calculus. But we can choose dt so much smaller than dx that v turns out to be even greater than the speed of light. But if we enforce the requirement that v cannot exceed the speed of light (c), then it follows immediately that dx cannot vary independently of dt. In other words, space and time are linked to each other through the constancy of the speed of light. ii) One-way speed of light I was not even aware that this was an issue until an undergraduate in my class pointed it out to me a week ago. There are contentions in the literature saying that measuring the one-way speed of light is dependent on the synchronization convention between the clocks at the start and finish points. The way to get around the synchronization problem is to use a mirror and reflect the light back to the clock at the starting point. This clock is obviously synchronized with itself. However, this configuration opens up the possibility of different velocities for light in different directions: what if the velocity was c/2 to the mirror and instantaneous back to the clock after reflection? What we would be measuring in that case was the average velocity of light. There is a YouTube video saying the one-way measurement cannot be done, as well as a Wikipedia article. However, a little digging revealed a cool classroom experiment that measured the one-way speed of light to be within 0.4% accuracy of the accepted value of c. The trick is to modulate the light intensity and to keep track of the relative phase between the modulator at the starting point and the detector at the end point. This relative phase changes as the path length for the light travel is varied. The time can be calculated from the relation phase = modulation frequency x time It is an elegant experiment which does not require absolute path lengths (x) or times (t) to be measured since only the slope of the graph is relevant: c = dx/dt! iii) How strange: mass is a form of energy In Newtonian mechanics, mass is conserved. In class I remind the students about this by considering two apples, then transforming them (on the white board) into apple pie, then into applesauce, and finally into apple juice. In all cases the mass is 2m_a where m_a is the mass of one apple. (Of course, we are working in the approximation where ingredients put in and fluids drained out are being ignored, for the picky people, this is just another 'I can carry it in my pocket' argument). In relativity mass is a form of energy that can be converted into other forms of energy (just as kinetic energy can be converted to potential energy in classical mechanics). For example a neutron and a proton have some of their rest mass converted into the potential energy of binding when they combine into a deuteron. So in relativity mass is not conserved, but total relativistic energy is. In case some of you are looking for a 'fruit'ful analogy for relativistic fundamental particles, you can try the fruit quark here -:).

This post is meant for the parents of high school students who often approach me, ostensibly to discuss, for their children, the prospect of choosing physics as a major in college. The use of the word 'ostensibly' will be clarified below. For the purpose of this post, I would like to classify physics students coming in from high school to college in the US, broadly into three loose categories: 1. Children of parents who are professionals in education or research: These include children of academics (university professors or school teachers), of researchers in industry and government labs, of program managers at funding agencies, of doctors, etc. These students have usually clearly made up their mind to go in for physics, are backed solidly in their choice by their families, and do not consult me. 2. Children of parents who are employed in areas outside of education and research and have college as their highest degree: The parents in this case could be in business, industry, law, entertainment, or other fields. They strongly believe in sending their children to college, but prefer to avoid educating them beyond college. The motivation behind this kind of thinking is that the parents would like their children to be 'settled' and financially secure as soon as possible, whereas a higher degree is perceived as not yielding RoI (return on investment); delaying a real job, income, savings, and promotions; and is even correlated to social disconnection, (relative) poverty and celibacy. Sometimes the children of such parents are fascinated by what they hear from and read in the media about physics - black holes, dark matter, extra dimensions, time travel, quantum computers, the metaverse, Oppenheimer - it's a wild and fascinating world out there. They may also have very good physics teachers in high school. (I have any number of students who are non-physics majors, such as the engineering, computer science, and imaging science students taking my Modern Physics course this semester, come into my office, and swear up and down that physics has always been their favorite subject). When they start clamoring to their parents about their interest in physics, the parents, not wishing to seem like autocrats by forbidding such a risky career move, hire me to do their dirty work for them. Here's how it works (this is based on about 10 meetings over 10 years): I meet with both parents and children, and after the initial excitement generated by the topic of physics, the parents turn on me, vocalizing their doubts about physics being a useful major for landing a job after college, being a dangerous option as an undergraduate degree as it lures students into graduate school (to be avoided for reasons mentioned above), being ultracompetitive, and not being as sensibly identifiable as majors like engineering, bioinformatics, data science, etc. In short, they voice all the misgivings which they do not wish to state directly to their children, but which can without any guilt be heaped upon a physics professor, albeit in the presence of the said children. The thing then for the professor is to back down and issue a stern warning to all and sundry against choosing physics as a major unless one is totally crazy or has a death wish: mission accomplished. (Usually the hint to the professor will be given via trick questions such as:" Is there any one course in the physics major that will turn my daughter into a genius?" The obvious answer is no; which is followed by the response: "Then why bother with physics? Why not do something useful?") After briefly considering the remaining category of incoming students, I will give some advice (below) to these parents. 3. Children who are the first generation to attend college: They are pioneers in some sense, who have hewed their path into education. They usually have thoughtful and genuine questions for me, as do their parents. Advice to parents from category 2. above: i) I appreciate your concern for your children. If you have decided they should not pursue physics, please tell them so yourself. If they end up pursuing physics nonetheless, they will do so on their own steam, not because of my opinions. (I know many colleagues who have become physicists in this way).  In other words, I do not need to be consulted. ii) Physics is undoubtedly a competitive subject and attracts some of the brightest minds (think Einstein). This is the beauty and terror of the subject. But the fact that people like me can survive in the field should give anyone plenty of hope. iii) Physics is a wonderful training ground for developing analytical skills and a great first degree for any kind of profession (I know Wall street quants, weather experts, oil prospectors, lawyers, doctors, writers,...who have first degrees in physics). For more extensive information, including salaries, please visit the Careers in Physics page of the American Physical Society. iv) I am always available for an honest consultation. * I am posting this a day early as I am traveling tomorrow.

Cloning in Biology Cloning in the life sciences is a fascinating and controversial topic. Dolly the sheep was the first mammal to be cloned and CC the first pet (it was a cat). Currently, a large number of countries only allow therapeutic cloning - the production of stem cells used for understanding and treating disease. Human cloning is forbidden and has never been carried out as far as we know. Concerns about cloning of live organisms include susceptibility to defects in organs and the immune system, premature aging, diminution of diversity in the gene pool, etc. Cloning in Quantum Physics In this context, it is also fascinating to note that in physics, a famous theorem forbids cloning of a quantum state. This is the No-Cloning Theorem, which takes only a few lines of linear algebra to prove, and which says that one cannot produce exact copies of an arbitrary quantum state. Practical Implications One of the important consequences of the No-Cloning Theorem is that it prevents the redundancy-based correction of errors in a quantum computer. In classical computers we can make multiple copies of a bit and take a majority vote if we think one or more of them have become corrupted (say one bit has flipped its value). This works to correct errors nicely as long as the probability of errors happening is small - usually the case - so the majority of the bits do not change from their fiducial value. In a quantum computer redundancy cannot be used in this naive way as the No-Cloning Theorem does not allow us to copy the (quantum) information. Peter Shor found a way around this problem, and thus made quantum computation realistic, by implementing redundancy using a resource from quantum mechanics called entanglement. Entanglement is the existence of correlations - that cannot be explained classically - between two or more objects. In quantum error correction, the information in a single qubit (the quantum analog of the bit) is shared in a highly entangled state of 9 (some ancillary) qubits. This sophisticated enactment of redundancy allows for a tolerable fidelity of transmission of quantum information through a noisy channel. Giving up Perfection Interestingly, physics does allow for the imperfect cloning of a quantum state. In a pioneering paper, Buzek and Hillery came up with the design of a Universal (i.e. input-state-independent) Quantum Copying Machine (UQCM) which they showed could copy quantum states with a maximum fidelity of 5/6. Quite close to unity! Imperfect cloning is nowadays used to simulate eavesdropping on quantum cryptography networks. Two bonus remarks i) A short proof of the No-Cloning Theorem: Heisenberg's uncertainty principle says that the position and momentum of a state cannot be determined precisely at the same time. But if we could clone the state, one copy could be used to measure the position exactly and the other the momentum. This would violate the uncertainty principle, and hence cannot be possible. (I find this proof a bit slick). ii) It can be shown that if perfect quantum cloning is allowed then signals can be sent faster than light between two objects. In fact 'superluminal signaling' occurs for any fidelity of cloning greater than 5/6! This bound on cloning fidelity maintains peace between quantum physics and relativity [1]. [1] N. Gisin, Quantum cloning without signaling, Physics Letters A 242, 1 (1998).

Posing the Question It is well known that in physics research (and probably other areas as well, but I am not qualified to talk about them) asking the right question is often the crucial step to solving a problem. Einstein famously obtained his insights into special relativity by wondering what it would be like to ride on a light beam. The mother of the physicist I. I. Rabi, who later won a Nobel prize, used to ask him every day, not if he had answered questions in class, but if he had asked a good question. I have known researchers step back from a problem saying "We weren't asking the right questions." However, it seems to me that the art of questioning is perhaps not taught as much as the art of answering. We learnt how to complete homework problems, take tests, sit for exams, etc. where someone else has performed the difficult and subtle task of framing the question (for those who like this sort of thing the Clay Mathematical Institute offers a significant sum of money for solving one of their posted problems). We are only responsible and rewarded for answering. In the physics curriculum we are taught a great number of formal techniques for finding solutions. We are of course, encouraged to ask questions in class, but rarely taught formally how to frame questions. Implications for Research One of the consequences of this approach is that it defines a type of student as 'good' who might not be suitable for research. I have seen on many occasions, students with good classroom grades flounder in the research environment, where the framing of questions can be a crucial skill. I have also seen the reverse where a student who takes three tries to pass the academic qualifying exam ends up with a strong research resume and several good publications (part of the reason many universities are doing away with GREs; they have low correlation to research success). Another example, which I found quaint when I first came across it, was talking to a colleague from a different field (high energy physics) where perhaps the questions posed by Nature are well known to all practitioners of the field, and the only interest is in solving them (which is not something that I am trivializing). This person asked me once what the main questions in my field (atomic, molecular and optical physics) were. I was taken aback because I did not know the answer. I was not aware of any such agenda set by my field - other than that of cooking up interesting questions, each of which had set off an unexpected revolution. And nobody knew what the next interesting question would be - that was part of the excitement. Here are two examples of such questions: Can you build a laser? Can you cool the motion of atoms with lasers? When the first laser was built, no one was trying to solve a grand problem with it; in fact it famously became known as a 'solution looking for a problem'. Of course, many uses for lasers were eventually found. Today there is a 20 billion USD worldwide laser market. When laser cooling of atoms was first realized, it was not the result of widespread competition; only three research groups were working in this then obscure area. Later, two Nobel prizes and atomic clocks for the GPS came out of this research. A Possible Solution - I mean - Question I am not formally trained in the techniques of pedagogy, though I do teach for a living, and try to follow best practices. So what I am about to suggest is very crude, but I think it involves the right philosophy. For example a freshman mechanics question which could perform the required exercise might be: A diver jumps off a cliff and into a lake. We would like to know with what velocity she hits the water. Neglect friction due to air. What information do you need to solve this problem? Give a stepwise account of the process by which you will arrive at the answer. In answering this question, the student participates more in its framing than they would if numerical values of the relevant quantities (initial velocity, acceleration due to gravity, time the diver spends in the air) were supplied. In fact, some students might find a different way to pose and solve the problem (using initial velocity, acceleration due to gravity and height of cliff). This can be used to show them that different procedures can be devised to determine the same physical quantity. A few questions like this - I'm only asking for maybe 10% market share here - would help train students in sharpening questions, in addition to finding answers.

This is a big and debated question, what with rising costs of education in several countries (parents often ask me about the ROI* for sending their children to college in the US), counter examples like Bill Gates and Steve Jobs who were hugely successful (in some sense) in spite of having dropped out of college, and people like Elon Musk saying that there is no need to have a college degree. I'm going to consider higher education from the postdoctoral degree downwards till college, so we know what lies ahead for every level. My discussion will be physics-biased, since that is what I am limited to by my experience. Postdoctoral degree This degree applies to disciplines like STEM (Science, Technology, Engineering, Mathematics, Computer Science and Healthcare), though my experience is limited to a specific subfield of physics. What is the use of a postdoc degree? The disciplines mentioned above often require such a degree; in a quarter century of academic experience I have only heard of one or two physicists who were hired into faculty positions without any postdoctoral experience. Some of this is due to the recognition that the PhD, which precedes postdoctoral experience, is a training degree, and the individual needs to demonstrate that they can perform research at another place, independently of their advisor, and perhaps even in a slightly different field. Some of it, especially the lengthening of the postdoctoral years (to about 6 across all fields in physics) is due to supply-and-demand economics. Every year there are a couple thousand physics PhDs produced in the United States. Partly due to the the fact that there is no mandated retirement age for academics in the US, this demand cannot be accommodated (when I complained to one of my professors around 2010 that the academic job market was bad, he remarked wryly that it had been bad since 1970). So people keep doing postdocs, or eventually seek non-academic jobs. The postdoctoral experience can help convince even the non-academic employer that the candidate can function independently (the years are counted as leadership experience) and sometimes commands a higher salary than the fresh PhD (but sometimes not). Doctoral degree Why get a PhD ? The years are long and exhausting (a Dean once told me when I was a grad student that the PhD is awarded for stamina), the pay is low (essentially half a decade or more of lost income), and the job market very tight (at least for academic positions). Of course, this degree is unavoidable for those who have set their aims on becoming academic researchers. I know of only one physics professor in the recent past who did not have a PhD, and he was a mathematical prodigy (Freeman Dyson). A doctoral degree is required or preferred for many positions even in industry. PhD-degree-holders are usually better paid compared to workers with a lower level of education. I often encounter physicists with masters degrees returning to academia from industry to obtain their doctorates, to become eligible for promotion possibilities, such as being a team leader. Of course there are other professions that require degrees in higher education: law school typically takes three years after college in the US; medicine four years of medical school, one year of internship, and at least three years of residency (whew). College degree Generally speaking, college education is a good ROI; specifically though, the outcome depends on the details. For example, STEM degrees tend to attract higher salaries as compared to liberal arts. Again, generally college graduates earn more and have lower unemployment rates than those who only have a high school diploma. In the US the cost of undergraduate education can total up to low hundreds of thousands of dollars. Those who take loans to pay for college take so long to pay it off that the ROI shows up only after they have worked about 15 years (!). Again, this number varies by discipline. College is pretty much unavoidable for those who wish to proceed to graduate school. There are, however, a number of students who avoid college (other than famous dropouts like the ones listed above). These may have family business they can find employment with directly; or prefer to go to trade school which gives them a diploma in less than two years (electricians, plumbers, chefs, etc do this). In general, college provides a much broader education and more career options. In the US, though, it is very expensive. *Return On Investment

Theoretical physics consists of building mathematical models of physical systems. All such models are approximate to varying degrees, since they cannot take everything into account. Still, there is some difference between finding an approximate and an exact solution of the (necessarily approximate) model. In this post, I will discuss both these outcomes. Approximate Solutions of Approximate Models By a solution of a model we mean a solution of the relevant mathematical equation(s). That could imply the solution of an algebraic, transcendental, differential or linear algebraic (i.e. matrix) equation - there may be some others that I am missing but I think you get the idea. Approximate solutions generate varying types of feelings in me: Beauty and terror To me it is undoubtedly a part of the beauty of physics that by making suitable approximations one can quickly find useful solutions to many problems. Of course, not only beauty but terror is involved, because our solutions live and die by their approximations. So it is very important to be aware of the approximations one is making, and not taken them for granted and examine them carefully when our solution cannot explain the experimental data, or does not make physical sense. Fun A fun type in this category is the famous 'Fermi problem', e.g. i) How many piano tuners are there in Chicago? ii) How much would you charge to clean every window in Seattle? iii) How many times does the average person's hear beat in a lifetime? (Answer: About a billion times) Quite satisfactory answers can be found to these questions by making reasonable assumptions. (Wonder what ChatGPT makes of these questions?) Surprise In my own experience, the physical universe is surprisingly amenable to approximations. For example, I once had a postdoc start off on building a model, and he kept coming to me with these complicated expressions, so I kept telling him to make all kinds of approximations to simplify them. At the end of eight months, we had built a working model, which however had so many approximations that I thought not only would no one believe our predictions, we would not believe them ourselves! (I used to brag that our model had every approximation known to physics.) Amazingly, when the postdoc compared our predictions to experiment, the two showed rather close agreement. This was so unexpected - and in a way profound - that when he came to my office to tell me this, he was shaking. I have heard similar stories from other colleagues as well. Inevitability Of course, for sufficiently complicated models, there is no recourse except to feed the model to a computer. The computer typically solves the model numerically (but see below). This produces an approximate solution, limited by the numerical precision, etc. But very often the solutions are highly satisfactory as well as useful. The deep end of computational solution to physics problems includes forecasting weather, simulating stellar dynamics, computing the properties of materials, etc. Forms of computing like AI have even started suggesting which experiments should be done in physics. Exact Solutions of Approximate Models Simple models An exact solution to the model can be found if it possesses enough symmetry. This can happen if the model is simple (it involves few variables and constraints). Introductory physics is based on such 'simple' models: mass on a spring, mass on a slope, stone at the end of a string, person in an elevator, etc. Based on the valuable physical intuition and the protocol for mathematical solution provided by these example, we can tackle more complex problems. Complicated models For more complicated models, the challenge is to find enough symmetry in it, so it can be solved. This often necessitates the identification of constants of motion, operations that leave the system unchanged, etc. There is no guarantee that any model can be solved exactly, neither a general systematic method - creative thinking is the only prescription. Satisfaction But it is extremely satisfying - the word 'ecstasy' is not inappropriate here - when such a challenge can be met. The first cause of satisfaction is that a more general kind of knowledge about the model - not restricted to the parameter values used in any numerical solution - now becomes available. The second cause is aesthetic. This because symmetry - which is the source of the solvability - is associated with our sense of beauty. I have had the pleasure of making such a discovery three times (...in 25 years). In one of those cases, a symbolic calculation software (Mathematica) was responsible for the insight (so computers can provide exact analytic solutions too, in addition to approximate numerical ones). The need for exact solutions Exact solutions are not just vanity items, which can be made irrelevant by the power of numerical computation. They can sometimes be - in a sense - irreplaceable, able to account for important physical phenomena which approximate techniques miss. An example of this I like to keep 'in my pocket' is that of the BCS theory of superconductivity: Feynman had had spectacular success with the approximate technique of perturbation theory (his famous diagrams are basically terms in a perturbation series) when it came to quantum electrodynamics (the study of the interactions of light and matter). But when he used the same tool to try and solve the mystery of superconductivity, he failed. After Bardeen, Cooper and Schrieffer solved the problem exactly, it became clear why it could not be solved approximately using terms from a series à la Feynman. This was because the solution contained an essential singularity - which meant it could not be represented by a series!

I started this blog on Jan 17, 2023. The present post is a stocktaking of what this blog is and is not. What this blog is Not i) It is not a homework helpdesk for physics students. ii) It does not accommodate reader comments, as I do not have the time to filter or curate them. My belief that those who care enough or have something genuine to say will contact me indirectly through email/messaging has been verified. iii) It includes no visual information (except through links), and rarely equations. All discussions are language-based. That's my limitation and preference. I try to keep the post short. This has been appreciated. iv) It is not long-winded, and often falls short of being complete or providing comprehensive attribution. I have had to bear some grief for this. v) It does not stick to its author's nominal expertise. I like to explore and I'm not afraid to be embarrassed if I make mistakes, though I try hard to get everything right as far as possible. I have been - gratefully - corrected a couple times. This is the way to learn, I think. vi) It is not designed to be provocative or opinionated, though I am sure I fail in both aspects once in a while. vii) It has not yet been advertised widely on social media or the rest of the internet. What this blog Is i) It is designed to provide an exploratory and accommodating view of physics and related issues. I am sure it is colored, as I often explicitly mention, by my own views. I can only hope my views are of some interest, and that some people like me to share my enthusiasms. ii) It is aimed at helping me collect my thoughts and enforce some coherence on various topics that I am interested in, and often find myself discussing with others. Going the other way, on several occasions, I note that because I wrote a post I find myself better informed and more coherent in discussion with my colleagues. iii) It serves as a resource that I can refer others to - postdocs or students who are about to join my group, or other educators, to whom I wish to convey in brief my thoughts on a particular topic. iv) It helps me maintain a continuing dialogue with colleagues and students, who return with interesting comments, criticisms, recommendations and links to other resources. Thanks to all of you. Conclusion Thank you also for reading this blog. When I initially started it, in Jan 2023, I thought I would run it for a year and then decide whether to continue it. As of now I intend to. If you know of anyone who would be interested in reading these topics please share the website with them - there is always a link at the end of the post which can be used to subscribe to the site - for free - using their email. Here's to more stories!!

This post is about a choice people in physics often have to make: whether to pick theory or experiment for a career. Some comments based on my experience of 25 years (but none of it in any administrative positions): i) Natural Selection: If you have a gift/temperament for one but not the other, then the choice might be automatically made for you. I have heard it phrased as follows: "Theory is for you if you prefer spending an afternoon chasing down a minus sign in your calculations; experiment is for you if you would rather spend that time detecting a pressure leak in your apparatus." If you are equally gifted/interested in both, some areas of physics may be able to accommodate you. Certainly a number of people in Atomic, Molecular and Optical physics do both theory and experiment, and for me that was one of the initial attractions (before I found out I was better suited to theory). In Condensed Matter physics this might not be so easy. I know of physics departments where the CM theorists sit on the top floor while the experimentalists are all in the basement (they haven't been banished; the experiments are just more stable there). In High Energy physics and Astronomy, it seems quite difficult to practice both theory and experiment at the same time. The respective training and techniques are rather specialized and combining them in one career seems quite impracticable. ii) Collaborative/social aspects: Theorists have, and often exercise, the option of working by themselves. I have written some single-author papers. However, theorists also love to talk shop and nowadays many of them exploit fully the possibilities of establishing nonlocal collaborations, since computers and the internet make the exchange of information between virtually any two locations on the planet quite easy. I have found this useful not only in maintaining ongoing collaborations but using students and ex-postdocs as resources for onboarding/training new recruits to my group. I have found fewer experimentalists who work by themselves; in academia, the professor usually has a group of students; in the research institutes there are postdocs and other technical people; similar situations apply in industrial research. In the universities the experimental groups are typically larger than theoretical groups. Experimentalists are typically the engines of the department: they occupy more real estate, they bring in more money, they train more students and postdocs. Of course, exceptions are always there. Experimental collaborations occupy a spectrum. If big science is involved (particle accelerators, telescopes, nuclear reactors, plasma confinement) then there are typically one or more locations (e.g. FermiLab, CERN, BICEP) at which collaborating groups converge to work. For groups doing table-top experiments, the collaborations often emerge out of the division of labor: one group does the fabrication, perhaps, another the experiment, the third the assay. In these cases, students and postdocs who have graduated out are not typically available to hands-on train new group recruits, but this can be handled by timing hiring appropriately. iii) Flexibility in research directions: In theory it is often relatively easy to switch research topics. Sometimes, of course, this requires a major investment in learning new theoretical techniques; still, the investment is not as expensive - in terms of time and money - as it would be if a similar change were to be made by an experimentalist. In my own career I have added on relatively new directions four or five times over a quarter of a century . On the other hand, acquiring new equipment and going through the learning curve for implementing a new platform is a nontrivial task for an experimentalist and few of them do this on a regular basis. iii) Reception in the community: As a practicing theorist I have found that my work is received much more credibility when it is supported by experimental data. If I say at the beginning of my talk that our theory is borne out by such-and-such experiment, then the degree of skepticism from the audience is typically very low, if not absent. On the other hand there are all kinds of objections about any standalone theory that I might present: how do I know this approximation is correct? How do I know that series converges? How do I know my starting assumptions are reasonable? Am I sure what I am proposing can be implemented experimentally? I am not complaining too much; all this makes for a lively discussion and I enjoy the attention our work gets as a result of it. Still, the difference experimental evidence makes is interesting and noticeable. In contrast, a well done experiment has the stamp of finality - see Kapitsa's well known quote on the topic - while a theory is 'just a theory'. So I think on average experimentalists enjoy a better reception from the community (of course there are exceptions), while the theorists enjoy an occasional high when their predictions are confirmed (or they present a tight theoretical achievement such as exactly solving a model for the first time). Conclusion Both theory and experiment have aspects that are enjoyable and aspects that are challenging. I personally enjoy doing theory very much; there are few things that get me going like a new idea. Since I have a PhD in experiment, I also find it natural to talk to experimentalists. I dare say they like talking to me as well -:).

This post is a review of My Tale of Four Cities, the autobiography of the astrophysicist Jayant Narlikar. Narlikar was known, among other things, for providing steady-state (Hoyle-Narlikar) alternatives to the Big Bang theory of the universe, and for combining Mach's principle with general relativity. The book was translated, by the author himself, from the original in Marathi and is divided into four parts corresponding to the times he spent in various cities over his life. He was born in Kolhapur, Maharashtra in 1938. Benares The first part of the book describes Narlikar's early life in Benares, where his father was a mathematics professor in the famous university. It gives a feeling for what the life of someone born into an elite academic family in India looked like. Apart from absorbing intellectual influences from his father, Narlikar was mentored by one of his uncles who wrote down mathematical problems on a blackboard at home challenging his young nephew. His mother was a scholar of Sanskrit, a language with which he was made quite familiar by his parents. A stream of academics, musicians, and other prominent people - friends and colleagues of his father - filed through the house. Cambridge Narlikar received a Tata scholarship to Cambridge (the interview process was dramatic and amusing; part of the loan had to be returned at a certain interest rate). He was advised by Fred Hoyle (who coined the phrase 'Big Bang') at Cambridge, where he passed the Mathematical Tripos, and where he was contemporaneous with physicists such as Stephen Hawking, Brandon Carter and George Ellis. This part of the book describes life in Cambridge in some detail, especially for students from India, in the post-independence era. This section also describes Narlikar's triumphal visit to India where he was feted by the press and recognized by the government with a high award, at the young age of twenty six. Mumbai Narlikar returned after several years in England to take up a faculty position at the TIFR (Tata Institute of Fundamental Research) in Mumbai (then Bombay). The description in this part of the book relates the issues facing Indian scientists choosing to return professionally to their country. However, it can be seen that due to his fame Narlikar's difficulties were often smoothed over (such as when he tried to get a telephone connection, a tedious and slow affair in those days - he was told at first that it would take 5 years). Since his profile was quite prominent, he was able to continue working with and visit protractedly, international collaborators. Pune The final part of the book deals with Narlikar's leadership of the IUCAA (Inter University Centre for Astronomy and Astrophysics) in the city of Pune. It contains many details about the logistics and bureaucracy involved in bringing up such an institution. Some inspiration for IUCAA might have come from a similar institute that Hoyle had set up at Cambridge, initially called IOTA (Institute of Theoretical Astronomy), later contracted to IOA as it expanded to include, for example, observational astronomy. Narlikar was also a successful science popularizer, writing nonfiction and fiction and scripting television shows. Conclusion The book is astonishingly detailed. The author either has a phenomenal memory or very detailed notes on his life - my suspicion is the former. The only error I could find in the more than five hundred pages is when Narlikar states that Yuval Ne'eman won the Nobel prize - he didn't. I was attracted to the book by Narlikar's scientific prominence and also by the fact that I overlapped in college with his two elder daughters - though they were ahead of me by a several years, and were not aware of me.

Over 13 years of professorial practice I have unfortunately received too many emails (including, but not limited to, from students and postdocs) which according to me are written unprofessionally. Below I will provide an example of an appropriate email (following only my precepts, others might have other opinions). Then I will provide some typical variations on this theme which I have seen over time, and explain why I think they are not appropriate. This post is supposed to be a resource for my group - but comments are welcome, of course. For the sake of specificity I will consider the case where the email comes from a student submitting an assignment. What it should read like "Dear Dr. Bhattacharya, Attached please find my assignment number 6. Sincerely, John Doe" What it should not read like i) No text in the body of the email I often receive only the assignment attached to the email. No salutation, no body, no signature. I usually reply saying that I am not an automated submission system and need to be addressed and told who is sending me an email. Sometimes I wonder if it would be acceptable if I send an acknowledgement just by hitting return on the email, and not type anything in the return message (probably). ii) No head or feet, only body: "Attached please find my assignment number 6." We don't know who the email is addressed to, nor who it came from. Did the sender type in my email address by mistake (it has happened -"Oops, wrong professor!" wrote the student after I pointed out her mistake - I had to look her name up in the RIT database), and do I have to open and read the attachment to figure out the answer to that question? No surprise if the attached pdf also does not list the author. iii) Incomplete salutation, with or without a signature "Hi, Attached please find my assignment number 6. John" This format is professionally disrespectful, as it shows that the sender does not even care enough about who the recipient is to make the effort to find out and type their name (this is bad enough in itself; on top of it the sender is asking for something from the receiver). The message conveyed by the sender is basically: "I don't care who you are or if you are a human being at all; just accept my assignment and grade it." I have actually received this type of salutation even from high-level professionals. This "Hi" salutation is probably something that the sender could send their friend, buddy or chat partner; but I fall into none of these categories. Besides, the email is a formal one, and should be businesslike. Has the sender ever received a letter from the bank or utility company starting with just "Hi"? Even the generic ones have a "Dear Customer" or some equivalent. iv) Misspelled name in address "Dear Dr. Bhachattarya, Attached please find my assignment number 6. Sincerely, John Doe" I am sympathetic to those who cannot handle my polysyllabic last name (students get around the problem by calling me "Dr. B"), but people mess up even my first name (which has only two syllables). I have regularly seen simpler and more 'standard' names being butchered, even on documents of critical importance. v) No signature "Dear Dr. Bhattacharya, Attached please find my assignment number 6." Almost there; the sender just ran out of energy in the end. To me a signature is required to indicate the willingness of the sender to take responsibility for the email. Caveat I am fully aware that over the course of several email exchanges it can get tiresome to repeat salutations and use formal signatures. The case described above does not refer to such a situation, in which the exchange can indeed become more informal. I have considered the case of the opening email in any exchange, which in my opinion has to satisfy some formal constraints.

Happy New Year to all readers! This post takes the new year opportunity to celebrate the birth anniversary of the physicist S. N. Bose. Preliminary remarks i) Fundamental particles in physics are basically of two types. If their intrinsic spin (a quantum label) is an integer (as for photons), they are called bosons, after Bose. If their spin is half-integer (as for electrons or protons), they are called fermions, after Fermi. Note: This holds for naturally occurring particles in a three-dimensional world. In engineered, two-dimensional materials, particles which are neither bosons or fermions, can exist. They are called anyons, and they are relevant to the quantum Hall effect (an effect in fundamental physics) and quantum computers (an application - Microsoft is especially interested!). ii) There is a printed English biography of Bose, which I have not read, but plan to buy [1] (Addendum: I bought and read it - compact but very good). There seems to be a Kindle-only book as well; again, I have not read it. There are several biographies/monographs on him in Bengali, some of which I have read. Bose's selected works with commentary have also been published, of course there is a Wikipedia entry on him; there are several independent websites and blogs which talk about him as well. Non-academic biography Bose was born on January 1, 1894 in Kolkata, the first of 7 children. He married Ushabati Ghosh, the daughter of a physician, in 1914. They had 9 children, 7 of whom survived infancy. Bose passed away on 4 February, 1974. Academic biography i) Bose first attended the New Indian School, then the Hindu School (1907), then Presidency College (1909; where he received a bachelor of science in 'mixed' i.e. applied math), all in Kolkata. Subsequently, he obtained a Master's degree from Science College. He then joined this college as a lecturer. ii) 1921: Bose moved to the University of Dhaka, in Bangladesh as a reader in physics. It was during this time that he wrote the seminal paper on what later came to be called Bose-Einstein statistics. The paper was originally rejected by a British journal. Bose then sent it to Einstein who got it published in Germany. Einstein then wrote follow-up papers extending Bose's treatment of photons to material particles. This was Bose's major contribution to physics; its details (and Bose's travels in Europe, see below) are described well in Jagdish Mehra's article, available online. Bose had also translated Einstein's work on relativity from German to English. iii) 1924-1926: Bose toured Europe, meeting Einstein, Marie Curie, Langevin and others. When he returned, he was made the Head of the Department at Dhaka University - although he did not have a PhD - on the basis of a recommendation letter from Einstein. Apparently he had received a visa from the German consulate without having to pay the fee, also by showing Einstein's letter. (Don't try these at home). iv) 1945-1956: Around the time of partition Bose returned to Kolkata University, taught until his retirement and was then made emeritus professor, and subsequently vice-chancellor of Visva-Bharati University in Santiniketan. This position he left in 1959. In 1958 he had been elected a Fellow of the Royal Society. The polymath and polyglot Bose did not really pursue physics like a career physicist; his contributions to the subject are therefore not numerous or sustained (though perhaps any of us would give their right arm to have credit for Bose's work). One reason behind this was that he had many interests outside of physics. He studied chemistry, archaeology, and the fine arts. He was interested in literature, which he read in Bengali, English, Sanskrit, French, German and Italian. He was interested in music and played the esraj. He was interested in science popularization and wrote extensively in popular magazines. He was interested in animals and had many cats. Conclusion Bose's work on particle statistics has been deemed Nobel-worthy by many scientists. He himself was apparently satisfied by the recognition he had received for his contribution. The standard model of particle physics admits 17 distinct fundamental particles: 5 of them are bosons. Having a third (5/17~0.29 ) of the world named after you is no mean feat, I would say. [1] https://www.nbtindia.gov.in/books_detail__9__national-biography__2207__satyendra-nath-bose.nbt

This blog is dedicated to a question a lot of undergraduates applying to graduate school in physics ask me before they have obtained any offers (typically during the application process): what should I choose to study in graduate school? They appear to be confused by the question, and agonize over it quite a bit. For some thoughts on this issue, read on: i) It may be too early to decide. Some students might not have had exposure to research in any field. Some might have had some exposure. Even those with substantial exposure - say a first author paper - may be advised, in my opinion, against becoming too set on pursuing that same field in graduate school. I think it is fine to say that's what you are interested in, in your application, and relate it to your experiences to build your case for being admitted, but you should keep an open mind when you reach the PhD program. In my own case I spent a summer as a senior undergraduate working in an experimental group handling a medium energy particle accelerator (at TIFR). I applied to graduate school with the stated intention of becoming an experimental high energy physicist. A week after my arrival (at the University of Rochester), late in August 1995, I met a new-ish professor walking along the hallway with Science magazine in his hand. On the cover were images of a Bose-Einstein condensate; this new state of matter had just been made, was generating buzz, and soon would be recognized with a Nobel prize (in 2001 - that's very soon, for a Nobel). The professor was working on similar things and took me downstairs to his basement lab where lasers were being used to cool atoms. This changed my mind, and I chose to do my thesis on optics instead of high energy physics. In this fashion (sic) you may change your mind as related/new fields come into being while you are getting in to grad school or taking courses there: laser cooling was an example from my grad school days; a more recent example is the explosion in gravitational wave astronomy. ii) Sometimes, it may not matter. I obtained a PhD in experimental cold atom physics and now work in theoretical quantum optics. I have many colleagues who have made similar or more dramatic switches (string theory to theoretical solid state physics; condensed matter theory to experimental atomic physics; astrophysics to solid state physics, etc). There is plenty of distinguished company here: for example, Max Delbruck and Venki Ramakrishnan won Nobel prizes in Medicine and Chemistry, respectively, although they had PhDs in physics. Pierre Gilles de Gennes worked on neutron scattering and magnetism for his PhD, then switched to the study of liquid crystals, for which he received the Nobel prize. Depending on the problem you become interested in, with some effort, you can change your field even after your PhD. Thus there is - perhaps - no wrong choice (of subject in graduate school). iii) Switching fields might even be beneficial for your career. In a previous post I described how Paul Corkum was able to make pioneering contributions to attosecond physics by applying his PhD training in plasma physics to the problems he faced in optics. Indeed if we go back a bit and look at the great theoretical physicists, for example, many of them have contributed in diverse fields: Landau (solid state physics, quantum electrodynamics); Onsager (electrolytic solutions, magnetism, superfluidity, thermodynamics); Feynman (quantum electrodynamics, superfluidity, particle physics), C. N. Yang (particle physics, condensed matter physics, statistical mechanics - he's still going strong at 101!). More recently, Anton Zeilinger (from neutron scattering to optics - I'm not saying anything about neutron scattering here!). I think the physics PhD not only trains us in a specific discipline, it trains us how to learn, and therefore become able to switch fields. iv) The decision might be made for extra-scientific reasons. You may find a well-funded, charismatic mentor in one of the two fields you are interested in, and not in the other. You may get along better with the students in one group than the other. And so on. Conclusion Many graduate schools now have students rotate between various groups so they can get a taste of everything available before they make a choice. This should help remove much of the selection anxiety that entering-level students experience, and lead to better-informed decisions both in the part of the student as well as the advisor. This is also the reason I advise students to apply to schools where they will have plenty of choices for research disciplines, rather than that one university which has a world class research program in the single discipline that they are currently interested in. What are you going to do, I ask them, in case you change your mind? Of course there are many more challenges waiting along the way until students finish their PhD, but once they are in graduate school there may not be as many wrong choices as they fear (as far as subject choice is concerned).