Physics Forums Insights
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Fascinating Science and Math ArticlesThu, 22 Mar 2018 03:48:39 +0000en-UShourly1https://wordpress.org/?v=4.9.3PhysicsForumsInsightshttps://feedburner.google.comStatistical Mechanics Part II: The Ideal Gas
https://www.physicsforums.com/insights/statistical-mechanics-part-ii-the-ideal-gas/
https://www.physicsforums.com/insights/statistical-mechanics-part-ii-the-ideal-gas/#respondTue, 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/0“Classical Physics Is Wrong” Fallacy
https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/
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 is wrong because it has been superseded by Special Relativity (SR) and General Relativity (GR), and/or Quantum Mechanics (QM).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/63Hilbert Spaces And Their Relatives – Part II
https://www.physicsforums.com/insights/hilbert-spaces-relatives-part-ii/
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
https://www.physicsforums.com/insights/interview-theoretical-physicist-clifford-johnson/
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
https://www.physicsforums.com/insights/hilbert-spaces-relatives/
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
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-renormalization/
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
https://www.physicsforums.com/insights/name-science-book-author/
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/17Mathematical Quantum Field Theory – Interacting Quantum Fields
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-interactingquantumfields/
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
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-freequantumfields/
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
https://www.physicsforums.com/insights/big-bang-infinities/
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/24Interview with a Mentor: Drakkith
https://www.physicsforums.com/insights/interview-mentor-drakkith/
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
https://www.physicsforums.com/insights/journey-cosmos-flrw-metric-friedmann-equation/
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
https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/
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
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-quantization/
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
https://www.physicsforums.com/insights/statistical-mechanics-part-equilibrium-systems/
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/18Coordinate Dependent Statements in an Expanding Universe
https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/
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
https://www.physicsforums.com/insights/demystifying-chain-rule-calculus/
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/4The Schwarzschild Metric: Part 3, A Newtonian Comparison
https://www.physicsforums.com/insights/schwarzschild-metric-part-3-newtonian-comparison/
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
https://www.physicsforums.com/insights/3-new-years-tips-cooling-off-debates/
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/19The Schwarzschild Metric: Part 2, The Photon Sphere
https://www.physicsforums.com/insights/schwarzschild-metric-part-2-photon-sphere/
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
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugefixing/
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
https://www.physicsforums.com/insights/schwarzschild-metric-part-1-gps-satellites/
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/4The Birth of a Textbook
https://www.physicsforums.com/insights/the-birth-of-a-textbook/
https://www.physicsforums.com/insights/the-birth-of-a-textbook/#commentsFri, 22 Dec 2017 16:29:35 +0000https://www.physicsforums.com/insights/?p=15286 It is said that you should accomplish three things in life: Plant a tree. Have a child. Write a book. Out of the three, I have completed at least one. At the time of writing this Insight, my textbook “Mathematical Methods for Physics and Engineering” just hit the virtual online shelves. This Insight will […]]]>https://www.physicsforums.com/insights/the-birth-of-a-textbook/feed/72A Journey Into the Cosmos – The Friedmann Equation
https://www.physicsforums.com/insights/journey-cosmos-friedmann-equation/
https://www.physicsforums.com/insights/journey-cosmos-friedmann-equation/#commentsFri, 22 Dec 2017 06:24:20 +0000https://www.physicsforums.com/insights/?p=16818 This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU This is an introduction to cosmology for someone who has some knowledge of calculus and basic physics. In this tutorial, we will take a journey into the cosmos to study cornerstone ideas in cosmology and their […]]]>https://www.physicsforums.com/insights/journey-cosmos-friedmann-equation/feed/6Mathematical Quantum Field Theory – Reduced Phase Space
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-reducedphasespace/
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-reducedphasespace/#commentsMon, 18 Dec 2017 01:34:39 +0000https://www.physicsforums.com/insights/newideaofquantumfieldtheory-reducedphasespace/The following is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 10. Gauge symmetries. The next chapter is 12. Gauge fixing. 11. Reduced phase space In this chapter we discuss these topics: Global gauge reduction for strictly invariant functions (action functionals): Derived critical loci inside Lie algebroids Schouten bracket […]]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-reducedphasespace/feed/4Work Ethic Is a Key to Success for Science Majors
https://www.physicsforums.com/insights/work-ethic-key-success-science-majors/
https://www.physicsforums.com/insights/work-ethic-key-success-science-majors/#commentsFri, 15 Dec 2017 20:34:45 +0000https://www.physicsforums.com/insights/?p=16752After earning a 4.0 GPA in his first semester as a Physics major at an esteemed state university, our son (and homeschool grad) attributes his success to: 45% work ethic, 30% homeschool subject mastery, 25% reasonable course load. I was surprised he gave such greater weight to the work ethic we imparted rather than actual […]]]>https://www.physicsforums.com/insights/work-ethic-key-success-science-majors/feed/13Interview with Mathematician and Physicist Arnold Neumaier
https://www.physicsforums.com/insights/interview-mathematician-physicist-arnold-neumaier/
https://www.physicsforums.com/insights/interview-mathematician-physicist-arnold-neumaier/#commentsMon, 11 Dec 2017 15:25:07 +0000https://www.physicsforums.com/insights/?p=16613Please give us a brief background on yourself Over 40 years ago, I studied mathematics, physics and computer science in Freiburg and Berlin (Germany). My Ph.D. thesis was in pure mathematics, but I was later drawn more and more into applied mathematics. Since 1994 I am a full professor of mathematics at the University of […]]]>https://www.physicsforums.com/insights/interview-mathematician-physicist-arnold-neumaier/feed/37Intransitive Dice with a Twist
https://www.physicsforums.com/insights/intransitive-dice-twist/
https://www.physicsforums.com/insights/intransitive-dice-twist/#commentsThu, 07 Dec 2017 15:44:45 +0000https://www.physicsforums.com/insights/?p=16627Intransitive dice are sets of dice that don’t follow the usual rules for “is better/larger than”. If A<B and B<C, then A<C. If Bob runs faster than Alice and Charlie runs faster than Bob, then Charlie runs faster than Alice. If die B wins against die A (larger number wins) and die C wins against […]]]>https://www.physicsforums.com/insights/intransitive-dice-twist/feed/6Mathematical Quantum Field Theory – Gauge Symmetries
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugesymmetries/
https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugesymmetries/#commentsWed, 06 Dec 2017 01:34:39 +0000https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugesymmetries/This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 9. Propagators. The next chapter is 11. Reduced phase space. 10. Gauge symmetries In this chapter we discuss these topics: compactly supported infinitesimal symmetries obstruct covariant phase space Infinitesimal gauge symmetries Lie algebra action and Lie algebroids BRST complex […]]]>https://www.physicsforums.com/insights/newideaofquantumfieldtheory-gaugesymmetries/feed/17Make Units Work for You
https://www.physicsforums.com/insights/make-units-work/
https://www.physicsforums.com/insights/make-units-work/#commentsFri, 01 Dec 2017 14:47:16 +0000https://www.physicsforums.com/insights/?p=15037How do we use units? You may see one of these speed limit signs, nearly every day. Even though neither of them display units, drivers know they are implied. In the United States, a Speed Limit 25 sign implies that 25 miles per hour is the maximum legal speed. The other type of speed limit […]]]>https://www.physicsforums.com/insights/make-units-work/feed/13