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Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
truthful on my part and felt natural. What enabled you to have an edge in comparison to your other peers in that field? A high CGPA does wonders and becomes one less thing to worry about during the already taxing procedure of the internship season. Having previous internships and projects in the | medium | 1,105 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
relevant field helped to demonstrate my interest and suitability for the role. It also helps add merit to your claims. How to strengthen one’s resume? And how can we, as students, work on it now? As much as I hate to break it down to you, your interview will most probably start with technical | medium | 1,106 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
questions and end with technical questions. Most technical recruiters show little to no interest in your college PORS and would rarely go beyond the Internships/Projects section of your resume. My advice: focus on strengthening your skills and knowledge, not your resume. ENTREAT In case one’s | medium | 1,107 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
interest doesn’t match with his/her branch of study, how should one manage to pursue the same under the constant pressure of maintaining a good CGPA? How much do you agree/disagree with the fact that ‘CGPA matters despite not pursuing one’s branch as a Career’ & why? I have always thought about | medium | 1,108 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
CGPA as “the more, the merrier” Irrespective of whatever field you pursue, it’s hard to argue with the fact that a high CGPA “NEVER HURTS”. My CGPA has always provided me essential optionality, comfort and a vital edge in tricky and unforeseen situations. Over time, I have come to believe that your | medium | 1,109 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
CGPA has a negligible correlation with your intelligence and your interest in your branch, nevertheless, I still feel one should try to balance his/her academics accordingly. General tips for the readers IITR is known for its coding culture and the same can be seen from the number of firms visiting | medium | 1,110 |
Quantitative Analysis, Internships, Internship Experience, Career Advice, Motivation.
and offering SDE roles. In such a scenario and amidst the cut-throat competition of the intern season it’s absolutely normal to get a little nervous and hesitant at times, especially when you are pursuing such unorthodox roles. Stay in touch with your friends and family and don’t let the stress get | medium | 1,111 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
Become a top data engineer Photo by Clay Banks on Unsplash Data visualization is more than just presenting data. It is also about using data to tell a story. As a data engineer, understanding the art of data visualization may have a big impact on how your insights are interpreted and applied. | medium | 1,113 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
Here’s a practical guide to help you become good in data visualization: 1. Know Your Audience Understanding who will be viewing your visualizations is key to creating effective ones. Consider their level of expertise, interests, and what they need from the data. 2. Choose the Right Visualization | medium | 1,114 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
Techniques Different types of data call for different visualization methods. Here are some common techniques and when to use them: import matplpotlib.pyplot as plt # Example scatter plot x = [1, 2, 3, 4, 5] y = [2, 3, 5, 7, 11] plt.scatter(x, y) plt.xlabel('X-axis') plt.ylabel('Y-axis') | medium | 1,115 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
plt.title('Scatter Plot Example') plt.show() 3. Keep it Simple and Intuitive Simplicity is key to effective visualization. Avoid clutter and focus on conveying the most important information clearly. Example: Compare these two bar charts: Cluttered Bar Chart: In the cluttered bar chart, there are | medium | 1,116 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
multiple colors, excessive gridlines, and distracting background patterns. The title and axis labels are cluttered, making it difficult to read and understand the data at a glance. The legend is also overwhelming and adds unnecessary complexity. Clean Bar Chart: In contrast, the clean bar chart | medium | 1,117 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
simplifies the visualization by using a single color for the bars and removing unnecessary elements such as gridlines and background patterns. The title and axis labels are clear and concise, making it easy to interpret the data quickly. The legend is omitted since it’s not needed in this case, | medium | 1,118 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
further reducing clutter. Analysis: By comparing the two bar charts, it’s evident that the clean bar chart is more effective in conveying the sales data. The simplicity of the visualization allows the viewer to focus on the most important information — the sales performance for each month — without | medium | 1,119 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
being distracted by unnecessary elements. This makes it easier for stakeholders to understand the data and derive actionable insights from it. 4. Provide Context and Interpretation Help your audience understand the significance of the data by providing context and interpretation. Example: Annotate | medium | 1,120 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
a line chart with explanations of significant peaks or troughs. 5. Embrace Interactivity Interactive visualizations engage users and enable deeper exploration of the data. Example: Build a dashboard where users can filter and drill down into specific data points. 6. Test and Iterate Don’t settle | medium | 1,121 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
for your first visualization. Test different approaches, gather feedback, and iterate to improve. Example: A/B test different color schemes to see which one resonates best with your audience. 7. Leverage Visualization Libraries and Tools Use visualization libraries and tools to optimize your | medium | 1,122 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
process and quickly produce professional-looking visuals. 8. Pay Attention to Data Quality and Integrity Ensure that your visualizations accurately represent the underlying data by paying attention to data quality and integrity. Clean and preprocess your data before visualizing it to avoid | medium | 1,123 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
misleading interpretations. Example: Remove outliers or missing values from your dataset before creating visualizations to ensure accuracy. 9. Design for Accessibility Make your visualizations accessible to all users, including those with disabilities, by following accessibility best practices. | medium | 1,124 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
Example: Provide alternative text descriptions for images and use high-contrast color schemes for better readability. 10. Stay Updated on Latest Trends and Technologies The field of data visualization is constantly evolving, with new trends and technologies emerging regularly. Stay informed about | medium | 1,125 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
the latest developments and incorporate them into your visualizations to stay ahead of the curve. Example: Explore emerging technologies like augmented reality or virtual reality for innovative data visualization experiences. By implementing these additional best practices into your data | medium | 1,126 |
Data Analysis, Data Engineering, Data Science, Technology, Data Engineer.
visualization workflow, you will be able to produce visuals that not only inform, but also inspire action and promote meaningful change within your business. As a data engineer, continue to experiment, study, and upgrade your skills in order to become a data visualization expert. Please reach out | medium | 1,127 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
As a backend or distributed systems engineer, your ability to design, develop, and troubleshoot efficient, and secure systems lies not only in your coding skills but also in a robust understanding of operating systems, which is the foundation of all computing. In this introductory article, I’ll set | medium | 1,129 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
the stage for a series that delves deep into why OS knowledge is not just a nice-to-have, but a must-have as a backend / distributed systems engineer. Efficient Resource Management: Operating system manages hardware resources such as CPU, Memory and I/O devices. Backend and distributed systems | medium | 1,130 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
often require efficient use of these resources. Understanding how the OS allocates, schedules and manages these resources can help you to build efficient and effective systems. In my upcoming articles, I’ll delve into how the operating system allocates, schedules, and manages these resources. | medium | 1,131 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
Concurrency and Multithreading: Backend systems often handle multiple requests concurrently. Distributed systems, by nature, involve managing tasks across multiple machines. Knowledge of how the OS handles processes and threads is essential for writing programs that efficiently use multiple cores | medium | 1,132 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
and machines. In my upcoming articles, I’ll be discussing how OS handles processes and threads, showing how this knowledge can be leveraged for more efficient concurrent programming Networking: For distributed systems, network communication is fundamental. OS provides the basic building blocks for | medium | 1,133 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
networking such as sockets and protocols. Understanding how these components work at the OS level will definitely lead to better network programming and troubleshooting Security: Security is a major concern in backend and distributed systems. The OS provides various mechanisms for securing | medium | 1,134 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
resources, such as user authentication, file permissions, and process isolation. Knowledge of these mechanisms is crucial for developing secure applications. In my future articles, I’ll discuss how in-depth OS knowledge could help us to protect our applications against various threats. File | medium | 1,135 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
Systems: Understanding how the OS manages file systems is important for data storage and retrieval, which are core functions of many backend systems. This includes knowledge about how data is stored on disk, caching, and how to efficiently read and write data. Performance Optimization: To optimize | medium | 1,136 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
the performance of a system, you must understand how your code interacts with the underlying OS. This includes understanding aspects like how the OS schedules tasks, manages memory, and caches data Adaptability Across Platforms: Different operating systems have different APIs and behaviors. | medium | 1,137 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
Understanding these differences is important when developing applications designed to function seamlessly across multiple platforms or when integrating with other systems. Troubleshooting and Debugging: A deep understanding of the OS will help in diagnosing and fixing issues related to system | medium | 1,138 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
crashes, resource leaks, and performance bottlenecks. There you have it guys, let me know what you think. How has your understanding of Operating Systems influenced your approach to backend/distributed systems? What challenges have you faced where OS knowledge was key? Let’s start a conversation! | medium | 1,139 |
Distributed Systems, Backend Development, Operating Systems, Tech Trends, Software Development.
I’d love to hear your experiences and insights. Stay tuned to this series as we delve into critical topics like resource allocation, concurrency and synchronization, as well as the management of processes, memory, files, and storage systems. If this introduction has piqued your interest, please | medium | 1,140 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
It had nothing to do with “loving myself”. I used to hate looking at myself in photos. I always felt a deep sense of discomfort to look at any photo of myself. Camera shyness, my psoriasis, lack of confidence around style, what have you — I had it all. I hated photos, and would rapidly evade any | medium | 1,142 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
situation where there was even a remote chance of being in a camera. But, like a miracle, things changed. Yellow trail, Camp John Hay. Picture by Author. The click I was on a trip with friends a couple of weeks ago, and we were on a hiking trail. I loved the outdoors, and this place was perfect. | medium | 1,143 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
The trail was narrow but easy, and on both sides there was nature. Picturesque views of the forest on the left, and steep rock formations from the right. I was excited, so I took a lot of pictures. I took so many pictures of myself. So much, in fact, that when my little group approached another | medium | 1,144 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
“Instagrammable” spot in the trail, my friends turned to me and amusingly said, “go on, we know you want to.” And I did want to. And that was so mind-blowing to me. I paused in wonder, thinking back to the me just years ago. And then took a ton of pictures. At that moment, I knew I’d outgrown my | medium | 1,145 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
old self. Success! But … how? This was puzzling since I wasn’t really on a mission to change that aspect of my personality. Though I love how comfortable I am now, just recently I was already resigned to the fact that I’ll always be that one friend. The one who will forever wear a visible mask of | medium | 1,146 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
discomfort in pictures. But now I looked … Well, not great exactly. But comfortable, and easy. Confident. So how did it happen? It took some introspection, but I think I’ve figured it out. The secret is … Not self-love. Not becoming more fashionable, or knowing “my angles.” Not just spontaneously | medium | 1,147 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
being more confident. I just … took more photos. It was the simple and common fact of exposure. I wasn’t exactly fond of my face, I didn’t think I looked good. But there were school projects and role-play videos even before selfies became such a thing. Then there were random funny group chats, | medium | 1,148 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
funny filters, and girlfriends that demanded selfies like it was a precious resource. Little by little, my hang-ups around my appearance faded. I became more confident. But everything started with acceptance. Manufacturing self-confidence So, how do you actually become more confident? As far as my | medium | 1,149 |
Life Lessons, Self Improvement, Personal Growth, Self Confidence, Self Confidence Tips.
experiences went, it was through exposure. And this isn’t just something for something as small as selfies. I found that it’s also a general trend for anything that I felt initially uncomfortable with. Talking to strangers, job interviews — even writing. It all starts with acceptance: knowing | medium | 1,150 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
image generated by AI Climate change casts a long shadow, and the need for sustainability has never been more pressing. It can feel overwhelming, but there’s a powerful truth — every action, big or small, contributes to the solution. This article explores how individuals can make a difference, | medium | 1,152 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
dives into exciting green technologies on the horizon, and shares inspiring success stories that prove a sustainable future is achievable. Individual Action: Small Steps, Big Impact Even in our daily routines, we hold the power to reduce our environmental footprint. Here are some actionable steps | medium | 1,153 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
you can take: Embrace Renewable Energy: Explore options for switching to renewable energy sources like solar power for your home. If not possible yet, support companies committed to renewable energy production. Reduce, Reuse, Recycle: This timeless mantra remains crucial. Minimize waste by buying | medium | 1,154 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
less, repairing what you have, and properly recycling what can’t be reused. Consider composting food scraps to create nutrient-rich fertilizer for your garden. Conscious Consumption: Think twice before you buy. Choose durable, long-lasting products, and consider buying second-hand whenever | medium | 1,155 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
possible. Support sustainable brands that prioritize ethical practices and environmental responsibility. Transportation Choices: Walk, bike, or use public transportation whenever possible. When driving is necessary, consider carpooling or opting for fuel-efficient vehicles. Electric vehicles are | medium | 1,156 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
becoming increasingly affordable and offer a cleaner transportation option. Green Your Diet: Reduce your meat consumption, especially red meat. Animal agriculture contributes significantly to greenhouse gas emissions. Explore plant-based alternatives and support local farmers who use sustainable | medium | 1,157 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
practices. These seemingly small steps, when multiplied by millions of individuals, have a significant collective impact. Green Tech: Powering a Sustainable Future Innovation is driving the development of exciting green technologies that offer promising solutions: Carbon Capture and Storage: This | medium | 1,158 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
technology captures carbon dioxide from emissions sources like power plants and stores it underground, preventing its release into the atmosphere. Vertical Farming: This method involves growing crops in vertically stacked layers indoors, using less land and water while maximizing yield. It’s | medium | 1,159 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
particularly promising in urban areas and can reduce reliance on traditional agriculture’s environmental impact. Biofuels: Fuels derived from renewable sources like plants or algae offer a cleaner alternative to fossil fuels for transportation and energy generation. Smart Grids: These intelligent | medium | 1,160 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
power grids optimize energy distribution, minimizing waste and allowing for better integration of renewable energy sources. Plant-Based Meat Alternatives: Advancements in plant-based meat substitutes offer realistic and delicious options for reducing reliance on meat production. Investing in and | medium | 1,161 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
promoting these technologies is crucial for accelerating the transition to a sustainable future. Success Stories: Inspiration for Change Looking for hope? Here are a few examples of successful environmental protection efforts: Costa Rica: This nation has become a leader in renewable energy, | medium | 1,162 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
generating over 90% of its electricity from clean sources. Bhutan: The small Himalayan kingdom has pledged to remain carbon negative, meaning they absorb more carbon dioxide than they emit. The Great Pacific Garbage Patch: Clean-up efforts are slowly making a dent in this massive plastic island | medium | 1,163 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
floating in the Pacific Ocean. Deforestation Reduction: Global initiatives like REDD+ (Reducing Emissions from Deforestation and Forest Degradation) are showing progress in protecting forests, vital for absorbing carbon dioxide. These success stories demonstrate the power of collective action and | medium | 1,164 |
Green Energy, Solar Energy, Renewable Energy, Emerging Technology, Fiverr Gig Promotion.
focused efforts. Conclusion Sustainability is not a destination but a continuous journey. By taking individual action, supporting green technologies, and drawing inspiration from success stories, we can collectively turn the tide on climate change and build a brighter, more sustainable future for | medium | 1,165 |
Physics, Physicist, Quantum Mechanics.
Construction of quantum mechanics in Einstein’s world by filling in the gaps in Dirac’s four papers on this subject Paul A. M. Dirac was one of the most celebrated physicists of the 20th century and made vital contributions to the proof that quantum mechanics and special relativity are compatible | medium | 1,167 |
Physics, Physicist, Quantum Mechanics.
with each other. His papers are now widely seen as a joy to read, yet they do not go all the way to providing the unification of these two theories. Professor Emeritus Young Suh Kim at the University of Maryland completes the line of reasoning of Dirac’s pivotal papers, published between 1927 and | medium | 1,168 |
Physics, Physicist, Quantum Mechanics.
1963 — offering new glimpses as to how such a unification could be achieved. In the early 20th century, the entire field of physics was at a turning point. Under the influence of Immanuel Kant, Albert Einstein thought things could appear differently to moving observers. He developed his special | medium | 1,169 |
Physics, Physicist, Quantum Mechanics.
theory of relativity which leads to his E = mc2. He then developed his general theory of relativity based on the same problem for accelerated observers. His special relativity is applicable to atomic and nuclear physics, while his general relativity is applicable to what happens in the universe or | medium | 1,170 |
Physics, Physicist, Quantum Mechanics.
in far-away places. At the same time, Danish physicist Niels Bohr was studying the electron orbit around a proton in the hydrogen atom. Through his calculations, Bohr’s study led to the present form of quantum mechanics based on Heisenberg’s uncertainty principle, stating that the position and | medium | 1,171 |
Physics, Physicist, Quantum Mechanics.
momentum cannot be measured accurately at the same time. The position or momentum thus has a probability distribution. Albert Einstein. As Einstein and Bohr explored these two very different fields, they are known to have regularly discussed their findings with each other. It is possible that they | medium | 1,172 |
Physics, Physicist, Quantum Mechanics.
discussed how the hydrogen atom would appear if it were travelling with a speed close to that of light. However, there are no written records on this issue. Filling in the gaps In fact, this description would present an enormous challenge to the field of physics as a whole, which would only be | medium | 1,173 |
Physics, Physicist, Quantum Mechanics.
overcome by a brilliant mind from a new generation. Although Bohr’s quantum mechanics and Einstein’s relativity appeared to work well by themselves, the mathematical languages needed to describe them seemed initially to be completely incompatible with each other. Born in Bristol, England, in 1902, | medium | 1,174 |
Physics, Physicist, Quantum Mechanics.
Paul A. M. Dirac became the first to see that the two theories were not at odds with each other. Now widely seen as one of the greatest physicists who ever lived, Dirac presented his ideas in four crucially important papers, spanning five decades of his long career. Because of Dirac’s unique way of | medium | 1,175 |
Physics, Physicist, Quantum Mechanics.
seeing the world, physicists to this day find these papers incredibly enjoyable to read — Professor emeritus Young Suh Kim (University of Maryland) even compares them to poetry! Yet despite their brilliance, the lines of reasoning Dirac followed in his papers are not entirely complete. Paul Dirac. | medium | 1,176 |
Physics, Physicist, Quantum Mechanics.
In his research, Professor Kim explores these gaps in detail in order to show how Dirac’s plan could finally be completed. Here is the list of what Dirac did and what he could have done. 1927. The time-energy uncertainty relation In 1927, at 25 years old, Dirac had completed his PhD degree at the | medium | 1,177 |
Physics, Physicist, Quantum Mechanics.
University of Cambridge just the year before. At this early stage of his career, both theories of quantum mechanics and relativity were in their infancy and were undergoing rapid new developments through contributions from physicists like Einstein and Bohr. Among the most important new discoveries | medium | 1,178 |
Physics, Physicist, Quantum Mechanics.
was the ‘uncertainty principle.’ First formulated by German physicist Werner Heisenberg in 1927, the uncertainty principle states that the position and momentum of a given particle cannot be measured accurately at the same time. Thus, the particle position or momentum is spread over a localised | medium | 1,179 |
Physics, Physicist, Quantum Mechanics.
probability distribution. “Professor Kim has now built quantum mechanics of bound states by integrating Dirac’s three papers.” Dirac noted that there is also the same uncertainty between the time and energy variables. He then raised the question of whether his time-energy uncertainty relation can | medium | 1,180 |
Physics, Physicist, Quantum Mechanics.
be combined with Heisenberg’s position-momentum uncertainty to make the uncertainty principle compatible with Einstein’s special relativity, but he pointed out some of the difficulties. At the same time, Einstein’s special relativity had culminated in the development of the mathematical language | medium | 1,181 |
Physics, Physicist, Quantum Mechanics.
called the Lorentz group and Lorentz covariance. In 1939, Eugene Paul Wigner published his paper on the Lorentz group and discussed the internal space-time symmetries of particles. If the hydrogen atom is a particle, its electron orbit is the internal space-time structure with the internal | medium | 1,182 |
Physics, Physicist, Quantum Mechanics.
space-time symmetry. Professor Kim noted that Wigner’s description of the internal space-time symmetry eliminates the difficulties Dirac observed in his earlier paper of 1927 to combine his time-energy uncertainty relation with Heisenberg’s position-momentum relation for Einstein’s | medium | 1,183 |
Physics, Physicist, Quantum Mechanics.
Lorentz-covariant world. Werner Heisenberg and Eugene Wigner, photo by Friedrich Hund. Wigner was a Hungarian-born physicist and professor of physics at Princeton University. In 1939, Wigner’s younger sister named Margit came to see her brother. In the same year, Paul A. M. Dirac was visiting | medium | 1,184 |
Physics, Physicist, Quantum Mechanics.
Einstein’s Institute of Advanced Study in Princeton. Dirac met Margit met in Princeton, and Margit became Dirac’s wife. Thus, Dirac and Wigner became two famous brothers-in-law. However, these two physicists never discussed the compatibility of the uncertainty relations with Einstein’s special | medium | 1,185 |
Physics, Physicist, Quantum Mechanics.
relativity. Professor Kim spent four years at Princeton University as a graduate student and a postdoc from 1958 to 1962. While there, he studied Wigner’s 1939 paper on the Lorentz group, and had the privilege of asking questions directly to Wigner. In 1962, he became the youngest assistant | medium | 1,186 |
Physics, Physicist, Quantum Mechanics.
professor at the University of Maryland. In the same year, Dirac visited the University of Maryland for one week, and this youngest faculty member was assigned to serve as Dirac’s personal assistant. This gave Professor Kim an excellent opportunity to learn physics directly from Paul A. M. Dirac. | medium | 1,187 |
Physics, Physicist, Quantum Mechanics.
1945. Gaussian wave function for space-time distribution In 1945, Dirac formulated his time-energy uncertainty together with Heisenberg’s uncertainty using the Gaussian function. This Gaussian distribution is circular in the two-dimensional space of time and longitudinal coordinate. However, to the | medium | 1,188 |
Physics, Physicist, Quantum Mechanics.
observer moving along the longitudinal direction, this circle could appear differently, according to Einstein. How differently? Dirac did not say anything about this question, but left it as a homework problem for younger generations. Professor Kim became interested in this problem. Thus, Bohr’s | medium | 1,189 |
Physics, Physicist, Quantum Mechanics.
hydrogen atom can be described by a circular distribution as given in this paper. 1949. Introducing the light cone A few years later, Dirac published a paper entitled ‘Forms of Relativistic Dynamics’ (1949). Here, Dirac discovers that a square in the plane of longitudinal and time-like plane | medium | 1,190 |
Physics, Physicist, Quantum Mechanics.
appears like a rectangle with the same area. We could say that that the square becomes squeezed into a rectangle along the direction making 45° with the longitudinal axis and also with the time axis. This transformation is known as Dirac’s light-cone system. Dirac could have considered what happens | medium | 1,191 |
Physics, Physicist, Quantum Mechanics.
to the circular distribution he constructed in his 1945 paper, but he did not; presumably because there were no ways to see this effect in the real world. Indeed, this mathematical formalism enables us to address the Bohr-Einstein issue of the moving hydrogen atom. However, a neutral particle like | medium | 1,192 |
Physics, Physicist, Quantum Mechanics.
the hydrogen atom cannot be accelerated. On the other hand, modern particle accelerators routinely produce many protons with speeds close to that of light. Those protons are not the hydrogen atoms of Bohr and Einstein. However, Murray Gell-Mann’s quark model (1964) tells us that the proton, when at | medium | 1,193 |
Physics, Physicist, Quantum Mechanics.
rest, is a quantum bound state (just like the hydrogen atom) of more fundamental particles called the quarks. In 1969, Richard Feynman noted that the fast-moving proton appears like a collection of partons whose properties are quite different from those of the quarks. Thus, the Bohr-Einstein issue | medium | 1,194 |
Physics, Physicist, Quantum Mechanics.
of the moving hydrogen atom becomes translated into the quark-parton puzzle. Indeed, Professor Kim showed that the squeezed circle in Dirac’s light=cone system provides the answer to the quark-parton puzzle and thus to the Bohr-Einstein issue. “The progress of physics has been made through | medium | 1,195 |
Physics, Physicist, Quantum Mechanics.
synthesis, such as those of comets and planets, electricity and magnetism, wave and particle.” Through this integration of Dirac’s papers of 1926, 1945, and 1949, Professor Kim showed that quantum mechanics and special relativity can be combined to show observable effects in the real world. He then | medium | 1,196 |
Physics, Physicist, Quantum Mechanics.
became interested in whether Dirac’s papers could be used for synthesising quantum mechanics and special relativity. The question is whether quantum mechanics and special relativity can be derived from one basket of equations. Also on this topic, he noted Dirac’s 1963 paper on two coupled | medium | 1,197 |
Physics, Physicist, Quantum Mechanics.
oscillators. 1963. Coupled harmonic oscillators In 1963, Dirac published a paper on two harmonic oscillators. He considered the symmetry group for this system and this group is generated by ten generators. He then noted that these generators satisfy the closed set of commutation relations for the | medium | 1,198 |
Physics, Physicist, Quantum Mechanics.
O(3,2) de Sitter group applicable to the five-dimensional space consisting of three (x, y, z) space coordinates and two time variables. Among the ten generators, three of them are used for rotations in the (x, y, z) space. There are three boost generators with respect to the first time variable, | medium | 1,199 |
Physics, Physicist, Quantum Mechanics.
and three for the second time variable. There is one rotation generator for two time variables. This symmetry is derivable purely from quantum mechanics. The rotations and boosts with respect to first time variable is useful, and essential transformations in special relativity. The remaining four | medium | 1,200 |
Physics, Physicist, Quantum Mechanics.
generators involving the second time variable are strange, but can be flattened to become three translation generators along the three (x, y, z) coordinates and one along the first time coordinate. This flattening process is called the group contraction process. The best illustration of this | medium | 1,201 |
Physics, Physicist, Quantum Mechanics.
contraction process is the transformation of Einstein’s Lorentzian world into the Galilean world by making the velocity of light infinite. local_doctor/Shutterstock.com The algebra of Heisenberg’s commutators can be derived from that of the harmonic oscillators. In fact, this is the way in which | medium | 1,202 |
Physics, Physicist, Quantum Mechanics.
Heisenberg formulated his uncertainty brackets. The system of Lorentz transformations and translations along the space-time directions can also be derived from the same set of equations. Indeed, quantum mechanics and special relativity can be generated from the one basket of equations. Physics as | medium | 1,203 |
Physics, Physicist, Quantum Mechanics.
art of synthesis Let’s look at the history of physics. Humans looked at the sky. They noted that stars move, some with closed orbits (like planets) and others with open paths (like comets). Isaac Newton synthesised them with his law of gravity and his second law of motion. Electricity and magnetism | medium | 1,204 |
Physics, Physicist, Quantum Mechanics.
were developed separately, but James Clerk Maxwell combined them into one set of equations, leading today’s wireless world. Einstein’s special relativity synthesised the energy=momentum relations for massive and massless particles. Quantum mechanics synthesised the particle nature and wave nature | medium | 1,205 |
Physics, Physicist, Quantum Mechanics.
of matter. The covariant oscillator formalism is a product of Paul A. M. Dirac’s life-long efforts to synthesise quantum mechanics and special relativity. The remaining task is to synthesise quantum mechanics and special relativity into one scientific discipline. Dirac’s 1963 paper serves as a | medium | 1,206 |
Physics, Physicist, Quantum Mechanics.
prelude to this ambitious plan. How close do you think we are to a fully unified description of quantum mechanics and general relativity? In 1963, Dirac produced the symmetry of the O(3,2) de Sitter group from quantum mechanics of two harmonic oscillators. The O(3,2) de Sitter group is called the | medium | 1,207 |
Physics, Physicist, Quantum Mechanics.
anti-de-Sitter group in general relativity applicable to a curved space-time. The question is whether we can observe this anti-de-Sitter symmetry in the real world and explain it in terms of the oscillators and their Heisenberg brackets. It is a challenging problem. References 1927. Dirac, P. A. | medium | 1,208 |
Physics, Physicist, Quantum Mechanics.
M., The Quantum Theory of the Emission and Absorption of Radiation, Proc. Roy. Soc. (London) [A114] 243–265. 1945. Dirac, P. A. M., Unitary Representations of the Lorentz Group, Proc. Roy. Soc. (London) [A183] 284–295. 1949. Dirac, P. A. M., Forms of Relativistic Dynamics, Rev. Mod. Phys. [21] | medium | 1,209 |
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