Physics Forums Insights
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Science and Math Articles, Tutorials and GuidesThu, 24 May 2018 19:00:16 +0000en-UShourly1https://wordpress.org/?v=4.9.6PhysicsForumsInsightshttps://feedburner.google.comIntro to Algorithms for Programming
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https://www.physicsforums.com/insights/intro-to-algorithms-for-programming/#commentsSat, 19 May 2018 21:17:35 +0000https://www.physicsforums.com/insights/?p=19824Many threads here at PF include some question about how to learn programming. This is asked by Physics students who want to learn programming in order to help their study, work on some project or create some simulation among other things but also by students in other fields of science and by other members, including self...]]>https://www.physicsforums.com/insights/intro-to-algorithms-for-programming/feed/18Solving Einstein’s Field Equations in Maxima
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https://www.physicsforums.com/insights/solving-einsteins-field-equations-in-maxima/#commentsSun, 13 May 2018 18:02:08 +0000https://www.physicsforums.com/insights/?p=15073A few months ago, pervect pointed me to a post by Chris Hillman which is an introduction to the usage of Maxima for General Relativity. Maxima is a free (both as in beer and as in speech) symbolic algebra package, and it includes a library called ctensor that handles tensor components and looks to have...]]>https://www.physicsforums.com/insights/solving-einsteins-field-equations-in-maxima/feed/2Ask the Advisors: What’s Your Most Memorable Textbook?
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https://www.physicsforums.com/insights/ask-the-advisors-whats-your-most-memorable-textbook/#commentsFri, 20 Apr 2018 19:05:29 +0000https://www.physicsforums.com/insights/?p=19077We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses… Thanks to all the PF Advisors that shared their favorite textbook. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!]]>https://www.physicsforums.com/insights/ask-the-advisors-whats-your-most-memorable-textbook/feed/9Lessons From the Bizzaro Universe
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https://www.physicsforums.com/insights/lessons-from-the-bizzaro-universe/#commentsFri, 13 Apr 2018 13:07:54 +0000https://www.physicsforums.com/insights/?p=18630The terms Bizarro and Bizarro World originated in Superman comics, where strangely imperfect versions of Superman, other action characters, and even Earth itself were conceived of, and provided the basis of stories. And who can ever forget the Seinfeld episode entitled “Bizarro Jerry,” in which there are Bizarro versions of Jerry and all his friends....]]>https://www.physicsforums.com/insights/lessons-from-the-bizzaro-universe/feed/20Rindler Motion in Special Relativity, Part 2: Rindler Coordinates
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https://www.physicsforums.com/insights/rindler-motion-in-special-relativity-part-2-rindler-coordinates/#commentsWed, 11 Apr 2018 01:34:01 +0000https://www.physicsforums.com/insights/?p=18840Our destination In our last article, Hyperbolic Trajectories, we derived some facts about the trajectory of a rocket that is undergoing constant (proper) acceleration. In this article, we will explore what these facts mean for the passengers on board a rocket undergoing Rindler motion. The goal is to come up with a coordinate system that will...]]>https://www.physicsforums.com/insights/rindler-motion-in-special-relativity-part-2-rindler-coordinates/feed/27Either the Sun Is Getting Smaller or Gravity Is Getting Weaker
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https://www.physicsforums.com/insights/either-the-sun-is-getting-smaller-or-gravity-is-getting-weaker/#commentsSun, 08 Apr 2018 21:51:59 +0000https://www.physicsforums.com/insights/?p=18884Paper discussion: Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Antonio Genova, Erwan Mazarico, Sander Goossens, Frank G. Lemoine, Gregory A. Neumann, David E. Smith & Maria T. Zuber. Nature Communications volume 9, Article number: 289. Students of physics learn some interesting facts about the sun, spread over different lessons and...]]>https://www.physicsforums.com/insights/either-the-sun-is-getting-smaller-or-gravity-is-getting-weaker/feed/17Rindler Motion in Special Relativity, Part 1: Hyperbolic Trajectories
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https://www.physicsforums.com/insights/rindler-motion-in-special-relativity-hyperbolic-trajectories/#commentsSun, 25 Mar 2018 22:16:21 +0000https://www.physicsforums.com/insights/?p=18776Introduction: Why Rindler Motion? When students learn relativity, it’s usually taught using inertial (constant velocity) motion. There are lots of reasons for this, but mainly it’s because it’s the easiest kind of motion for deriving the results of relativity, and historically, thinking about inertial motion is what led to Einstein’s theory. An unfortunate side-effect of...]]>https://www.physicsforums.com/insights/rindler-motion-in-special-relativity-hyperbolic-trajectories/feed/5Interview with Astrophysicist Adam Becker
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https://www.physicsforums.com/insights/interview-with-astrophysicist-adam-becker/#commentsSat, 24 Mar 2018 19:04:58 +0000https://www.physicsforums.com/insights/?p=18759Adam Becker is an astrophysicist and science writer whose first book “What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics” just hit the bookshelves! Give us some background on how you got interested in physics and some experiences in youth/school that were formative. I don’t remember a time when I wasn’t interested...]]>https://www.physicsforums.com/insights/interview-with-astrophysicist-adam-becker/feed/129Statistical Mechanics Part II: The Ideal Gas
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https://www.physicsforums.com/insights/statistical-mechanics-part-ii-the-ideal-gas/#commentsTue, 20 Mar 2018 23:42:46 +0000https://www.physicsforums.com/insights/?p=17820Read Part 1: Equilibrium Systems The Ideal Gas: Boltzmann’s Approach (The Microcanonical Ensemble) Consider a monatomic gas of ##N## non-interacting particles with mass ##m## occupying the volume ##V##. Since the particles of the gas do not interact with each other, it is not difficult to explicitly calculate ##\Omega_{E}##. The position of each particle is constrained to...]]>https://www.physicsforums.com/insights/statistical-mechanics-part-ii-the-ideal-gas/feed/9“Classical Physics Is Wrong” Fallacy
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https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/#commentsThu, 15 Mar 2018 15:17:10 +0000https://www.physicsforums.com/insights/?p=18644One of the common questions or comments we get on PF is the claim that classical physics or classical mechanics (i.e. Newton’s laws, etc.) is wrong because it has been superseded by Special Relativity (SR) and General Relativity (GR), and/or Quantum Mechanics (QM). Such claims are typically made by either a student who barely learned...]]>https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/feed/142Hilbert Spaces And Their Relatives – Part II
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https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/#commentsTue, 06 Mar 2018 18:25:08 +0000https://www.physicsforums.com/insights/?p=18465 Operators. The Maze Of Definitions. We will use the conventions of part I (Basics), which are ##\mathbb{F}\in \{\mathbb{R},\mathbb{C}\}##, ##z \mapsto \overline{z}## for the complex conjugate, ##\tau## for transposing matrices or vectors, which we interpret as written in a column if given a basis, and ##\dagger## for the combination of conjugation and transposition, the adjoint...]]>https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/feed/3Interview with Theoretical Physicist Clifford V. Johnson
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https://www.physicsforums.com/insights/interview-theoretical-physicist-clifford-johnson/#commentsMon, 26 Feb 2018 16:42:17 +0000https://www.physicsforums.com/insights/?p=18432Clifford V. Johnson is a professor in the Physics and Astronomy Department at the USC. “I mainly work on (super)string theory, gravity, gauge theory and M-theory right now, which lead me to think about things like space-time, quantum mechanics, black holes, the big bang, extra dimensions, quarks, gluons, and so forth.” Clifford V. Johnson runs a...]]>https://www.physicsforums.com/insights/interview-theoretical-physicist-clifford-johnson/feed/7Hilbert Spaces and Their Relatives Part I
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https://www.physicsforums.com/insights/hilbert-spaces-relatives/#commentsFri, 16 Feb 2018 15:25:53 +0000https://www.physicsforums.com/insights/?p=18356 Basics Language first: There is no such thing as the Hilbert space. Hilbert spaces can look rather different, and which one is used in certain cases is by no means self-evident. To refer to Hilbert spaces by a definite article is like saying the moon when talking about Jupiter, or the car on an automotive...]]>https://www.physicsforums.com/insights/hilbert-spaces-relatives/feed/1Mathematical Quantum Field Theory – Renormalization
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https://www.physicsforums.com/insights/newideaofquantumfieldtheory-renormalization/#commentsThu, 08 Feb 2018 01:34:39 +0000https://www.physicsforums.com/insights/newideaofquantumfieldtheory-renormalization/This is one chapter in a series on Mathematical Quantum Field Theory The previous chapter is: 15. Interacting quantum fields. 16. Renormalization In this chapter we discuss the following topics: Epstein-Glaser normalization Stückelberg-Petermann re-normalization UV-Regularization via Counterterms Wilson-Polchinski effective QFT flow Renormalization group flow Gell-Mann & Low RG Flow In the previous chapter we have...]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-renormalization/feed/9Name the Science Book Author Quiz
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https://www.physicsforums.com/insights/name-science-book-author/#commentsSun, 04 Feb 2018 20:16:37 +0000https://www.physicsforums.com/insights/?p=18240Let’s see how well you know your science book authors. Some are classic, some modern! Don’t forget to post your score in the comment thread linked at the bottom. ]]>https://www.physicsforums.com/insights/name-science-book-author/feed/23Mathematical Quantum Field Theory – Interacting Quantum Fields
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https://www.physicsforums.com/insights/newideaofquantumfieldtheory-interactingquantumfields/#commentsMon, 29 Jan 2018 01:34:39 +0000https://www.physicsforums.com/insights/newideaofquantumfieldtheory-quantumobservables/This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 14. Free quantum fields. The next chapter is 16. Renormalization. 15. Interacting quantum fields In this chapter we discuss the following topics: Free field vacua Perturbative S-matrices Conceptual remarks Interacting field observables Time-ordered products (“Re”-)Normalization Feynman perturbation series Effective...]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-interactingquantumfields/feed/3Mathematical Quantum Field Theory – Free Quantum Fields
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https://www.physicsforums.com/insights/newideaofquantumfieldtheory-freequantumfields/#commentsMon, 29 Jan 2018 01:03:22 +0000https://www.physicsforums.com/insights/?p=17834This is one chapter in a series on Mathematical Quantum Field Theory The previous chapter is 13. Quantization. The next chapter is 15. Interacting quantum fields. 14. Free quantum fields In this chapter we discuss the following topics: Wick algebra Time-ordered product Operator product notation Hadamard vacuum state Free quantum BV-differential Schwinger-Dyson equation In the...]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-freequantumfields/feed/1Intro to Big Bang and Infinity Concepts
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https://www.physicsforums.com/insights/big-bang-infinities/#commentsSat, 27 Jan 2018 15:05:27 +0000https://www.physicsforums.com/insights/?p=18000This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU In the cosmology section of the Physics Forums, I encounter many big bang and related infinity problems. Hence, in this article I want to explain the Big Bang, the topology of the Universe, and the concepts of...]]>https://www.physicsforums.com/insights/big-bang-infinities/feed/30Interview with a Mentor: Drakkith
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https://www.physicsforums.com/insights/interview-mentor-drakkith/#commentsWed, 17 Jan 2018 13:44:06 +0000https://www.physicsforums.com/insights/?p=17931 Give us an early bio on yourself Well, I was born and raised near Dallas, Texas as the only boy of 4 children. I grew up with 3 sisters, though I had another sister, 3 stepsisters, and a stepbrother that I did not live with. I’m only 10 minutes younger than my twin sister...]]>https://www.physicsforums.com/insights/interview-mentor-drakkith/feed/7A Journey Into the Cosmos – FLRW Metric and The Friedmann Equation
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https://www.physicsforums.com/insights/journey-cosmos-flrw-metric-friedmann-equation/#commentsTue, 09 Jan 2018 20:58:20 +0000https://www.physicsforums.com/insights/?p=17612This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU Previous Chapter: A Journey Into the Cosmos – The Friedmann Equation Chapter 2- FLRW Metric and The Friedmann Equation In this chapter we will further investigate the Friedmann equation and we will...]]>https://www.physicsforums.com/insights/journey-cosmos-flrw-metric-friedmann-equation/feed/1The Fundamental Difference in Interpretations of Quantum Mechanics
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https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/#commentsTue, 09 Jan 2018 19:16:37 +0000https://www.physicsforums.com/insights/?p=12126A topic that continually comes up in discussions of quantum mechanics is the existence of many different interpretations. Not only are there different interpretations, but people often get quite emphatic about the one they favor, so that discussions of QM can easily turn into long arguments. Sometimes this even reaches the point where proponents of...]]>https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/feed/190Mathematical Quantum Field Theory – Quantization
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https://www.physicsforums.com/insights/newideaofquantumfieldtheory-quantization/#commentsMon, 08 Jan 2018 15:29:51 +0000https://www.physicsforums.com/insights/?p=17527The following is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 12. Gauge fixing. The next chapter is 14. Free quantum fields. 13. Quantization In this chapter we discuss the following topics: Motivation from Lie theory Geometric quantization Moyal star products Moyal star product as deformation quantization Moyal star...]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-quantization/feed/15Statistical Mechanics Part I: Equilibrium Systems
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https://www.physicsforums.com/insights/statistical-mechanics-part-equilibrium-systems/#commentsSun, 07 Jan 2018 21:12:49 +0000https://www.physicsforums.com/insights/?p=17258This is the first of a multi-part series of articles intended to give a concise overview of statistical mechanics and some of its applications. These articles are by no means comprehensive of the entire field, but aim to give a clear line of reasoning from Boltzmann’s equation to non-equilibrium statistical mechanics. It is hoped that...]]>https://www.physicsforums.com/insights/statistical-mechanics-part-equilibrium-systems/feed/19Coordinate Dependent Statements in an Expanding Universe
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https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/#commentsSat, 06 Jan 2018 18:34:10 +0000https://www.physicsforums.com/insights/?p=17405In this Insight we will discuss the general Friedmann–Lemaitre–Robertson–Walker (FLRW) universe, in which a set of comoving observers with proper time ##t## observe the universe to be homogeneous and isotropic. In such a universe, the line element takes the form $$\newcommand{\dd}[2]{\frac{\partial #1}{\partial #2}}ds^2 = dt^2 – a(t)^2 [dr^2 + f(r)^2 d\Omega^2] \equiv dt^2 – a(t)^2...]]>https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/feed/2Demystifying the Chain Rule in Calculus
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https://www.physicsforums.com/insights/demystifying-chain-rule-calculus/#commentsTue, 02 Jan 2018 21:33:35 +0000https://www.physicsforums.com/insights/?p=12816Introduction There are a number of posts on PF involving a general confusion over the multi-vairiable chain rule. The problem is often caused by a lack of clarity about the roles of functions and variables and what precisely each derivative means. This insight is an attempt to clarify things. Part A: The Single-Variable Chain Rule...]]>https://www.physicsforums.com/insights/demystifying-chain-rule-calculus/feed/7The Schwarzschild Metric: Part 3, A Newtonian Comparison
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https://www.physicsforums.com/insights/schwarzschild-metric-part-3-newtonian-comparison/#commentsMon, 01 Jan 2018 16:44:08 +0000https://www.physicsforums.com/insights/?p=17078A Short Proof of Birkoff’s Theorem derived the Schwarzschild metric in units of ##G = c = 1##: \begin{equation} ds^2 = -\left(1 – \frac{2M}{r}\right)dt^2 + \left(1 – \frac{2M}{r}\right)^{-1}dr^2 + r^2d\theta^2 + r^2 \sin^2\theta d\phi^2 \label{metric} \end{equation} and I used that metric in The Schwarzschild Metric: Part 1, GPS Satellites to show that Global Positioning System (GPS) clocks...]]>https://www.physicsforums.com/insights/schwarzschild-metric-part-3-newtonian-comparison/feed/23 New Years Tips For Cooling Off Debates
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https://www.physicsforums.com/insights/3-new-years-tips-cooling-off-debates/#commentsSat, 30 Dec 2017 15:29:18 +0000https://www.physicsforums.com/insights/?p=17202 Civil discussion and debate is critical to Physics Forums. But it is also important in everyday life. When arguments get overheated, people may avoid engaging with friends and family and the relationships could wither and die. If the only safe topic you can discuss with your friend is weather, your relationship is in danger....]]>https://www.physicsforums.com/insights/3-new-years-tips-cooling-off-debates/feed/20The Schwarzschild Metric: Part 2, The Photon Sphere
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https://www.physicsforums.com/insights/schwarzschild-metric-part-2-photon-sphere/#commentsFri, 29 Dec 2017 15:59:17 +0000https://www.physicsforums.com/insights/?p=17047 A Short Proof of Birkoff’s Theorem derived the Schwarzschild metric in units of ##G = c = 1##: \begin{equation} ds^2 = -\left(1 – \frac{2M}{r}\right)dt^2 + \left(1 – \frac{2M}{r}\right)^{-1}dr^2 + r^2d\theta^2 + r^2 \sin^2\theta d\phi^2 \label{metric} \end{equation} and I used that metric in The Schwarzschild Metric: Part 1, GPS Satellites to show that Global Positioning System (GPS)...]]>https://www.physicsforums.com/insights/schwarzschild-metric-part-2-photon-sphere/feed/2Mathematical Quantum Field Theory – Gauge Fixing
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https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugefixing/#commentsThu, 28 Dec 2017 01:34:39 +0000https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugefixing/The following is one chapter in a series of Mathematical Quantum Field Theory. The previous chapter is 11. Reduced phase space. The next chapter is 13. Quantization. 12. Gauge fixing While in the previous chapter we had constructed the reduced phase space of a Lagrangian field theory, embodied by the local BV-BRST complex (example 11.21),...]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugefixing/feed/1The Schwarzschild Metric: Part 1, GPS Satellites
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https://www.physicsforums.com/insights/schwarzschild-metric-part-1-gps-satellites/#commentsWed, 27 Dec 2017 21:16:08 +0000https://www.physicsforums.com/insights/?p=16980 A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then triangulating your location based on that information [1]. Since light travels at 300 million meters per second, your location will be off by about 1 meter if the clock times are off by only...]]>https://www.physicsforums.com/insights/schwarzschild-metric-part-1-gps-satellites/feed/4