title: Why is the charge on protons == to charge on electrons?

text: I am not a expert on physics, just another high schooler, so sorry if the question is obvious. This is something I've been wondering about for a while. Why is the charge on a proton equal but opposite to the charge on the electron? A proton is much larger than a electron, and apparently a lot more heavier too. Why, then, is it's charge equal to that on a electron? Just what is charge, and what defines it? What factors decide the charge on a particle? Also while we're at it, why does the atom in it's default configuration have the same number of protons and electrons? Edit: To expand on this a bit, from what I know the attraction weakens as distance increases. So if theoretically a huge amount of protons were to be somehow brought together despite the repulsions constantly increasing, would a atom with a extremely high atomic number defy the proton = electron rule? Note: This is not a duplicate. I read through the Phys.SE post Why do electron and proton have the same but opposite electric charge? but I did not find a satisfactory answer (Or even understand many of the professional terms :s)


title: Does the weight of a car frame has any effect on its horsepower?

text: I want to know whether decreasing the weight of the frame of a car will increase its horsepower. From what I understand horsepower is a measure of the car's ability to transport load, and decreasing the frame's weight will increase this ability. I tried to search this on internet and all I got was that it depends on the horsepower of the engine not the car itself. It is very confusing. If my assumption that the car's weight has an effect on horsepower is right, then what is the possible way for me to calculate it?


title: Is there an equivalent to wetness for air?

text: I was wondering if there was something equivalent to the property of being wet with water, but with air instead. For example, if I drop water on my shirt, I'll notice by its appearance and feel that it is wet, so in a sense its properties were changed by being exposed to water. So I'm wondering if similarly, by being exposed to ambient air, my shirt is somehow being changed, i.e. if it was in a vacuum would it feel or appear different than when it's exposed to air?


title: Shape of electric charges on sphere in equilibrium state

text: When electric charges of equal magnitude and sign are released on a regular sphere (and assume that they stick to the surface of the sphere, but they are free to move along its surface), what is the shape of the figure made by the charges as vertexes when they come to a state of equilibrium? Case 1 - Only one charge is there: Already in equilibrium as there are no other charges. Case 2 - Two charges: Two charges are on opposite points of one diameter of the sphere. Case 3 - Three charges: Three charges make a shape of an equilateral triangle. Case 4 - Four charges: A regular tetrahedron comes up when they reach the state of equilibrium. While extrapolating these cases to higher number of charges, one roadblock comes up: how to adapt a more-than-three-dimensional figure to the three- dimensional sphere? Any hint taking to the correct answer or better approach to the problem is welcome.


title: What does the phrase "limb of the earth" or "atmospheric limb" mean?

text: What does the term _limb of the earth_ (see this question, for example) or _atmospheric limb_ mean? The phrase strikes me as very odd, since earth is nearly spherical. Do other planets with atmospheres also have a limb?


title: Recommendations for good Newtonian mechanics and kinematics books

text: What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.?


title: Any recommendations for self-studying physics?

text: I'm new to this forum so I hope this post falls under the guidelines of what's acceptable. I'm currently finishing my grade 11 year of high school and I have hopes of attending one of the prestigious schools in the US such as MIT, Harvard, Stanford, Princeton, etc. I would love to be able to study physics in university and, since my school's physics courses are lacking any difficulty, I've been taking it upon myself to learn physics. I have a very strong ability to do the necessary math and have taken university calculus courses to prepare. However, the field is brimming with a wealth of resources and I'm just not sure what to choose and was hoping you would be able to help me out a little. I currently own Stephen Hawking's books: The Grand Design, The Universe in a Nutshell, and A Brief History of Time. Now I know these are written without the technical aspects, but I'm sure they'd make great reads when I find time. However, I'm more looking into resources which actually teach the math behind the ideas. I've found countless courses on MIT OpenCourseware and other online course resources including Leonard Susskind's The Theoretical Minimum courses. As far as books go, I've been interested in Leonard Susskind's two main books. I've also taken a great interest in Richard Feynman's work and so I'm interested in purchasing the Feynman Lecture on Physics boxed set with the accompanying exercise book being published this summer. I would like to listen to any recommendations any of you may have as to which resources I should use to gain a good understanding of physics. I would really like to learn using Feynman's lectures although I hope it isn't considered to be too old to be of much value. Any advice would be very much appreciated!!


title: Reference request: Classical Mechanics as an Application to Smooth Manifolds

text: > **Possible Duplicate:**   >  Classical Mechanics for Mathematician Last time I asked a question, but it does not sound specific. I am currently taking graduate topology class (using Lee's Introduction to Smooth Manifolds), but I am in math program (not in physics), so I might lack physical intuition. Is it better to learn Symplectic geometry first (such as da Silva's Lectures on Symplectic Geometry) then learn mechanics with symplectic geometry emphasis (such as Abraham & Marsden, etc), or is Spivak's Physics book self-contained in terms of both motivation and mechanics in manifold? How about Arnold? Is his physical explanation requires prerequisite in university level physics?


title: Suggested reading for classical field theory

text: I am reading a marvelous book _Classical Field Theory_ by E Soper, but it is mathematically too compact and sometimes I am unable to follow the equations. Can anyone suggest a side book for solution of my problem regarding reading the book? I also have _Classical Theory of Fields_ by Landau but its content and way of expression is not relevant with my book. The question which you people are saying is a possible duplicate of was asked by myself and in that question I tried to find a good book on Classical Field Theory.But here I need help to read a particular book on the same subject.So in this way I am trying to justify my attempt as to make it a new question.


title: Prerequisites for QFT?

text: > **Possible Duplicate:**   >  Book recommendations Is there a book that covers everything you need to know (and possibly more) before starting a course on QFT. Alternatively, I need a list of what you need to know. It would have to contain Lagrangians and Poisson brackets, and quantisation. I've had a course in QM, and one in EM. I know SR too. I have an IQ of 160 and have had to give up up on my third book of QFT.


title: Book suggestion for Theoretical Physics with easy maths

text: I am a Computer Scientist with literature interest in theoretical physics. I have already read books such as A Brief History of Time and Physics of the Impossible, and I am looking for suggestion for books with a slightly more scientific approach; where for example theorems are also explained in simplified equations. (like Eddington's Space Time and Gravitation) Can you suggest me some?


title: Good math books for physicists

text: In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese). I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)?


title: Reference request for motion & related topics

text: I'm starting a Robotics course at grad school and I could use some help to relearn and revise my concepts in the following topics :   1. Kinematics    2. Rigid Body Dynamics   3. Rotational Motion and Linear Momentum   4. Force Could you good people please let me know of 1) the best (subjectively speaking) intuitive sources that helped you learn the concepts? 2) some sources that showed examples instead of verbose explanations ? Any help/suggestions much appreciated! Thanks. (if there are any more specifics required, please let me know, I will edit the post)


title: What kind of physics topics exist?

text: The question says everything I want to know, but for more details: I enjoy studying physics but the problem is that I can't find any information with a summary of all physics topics, collected together. I also Googled this and took a look at other websites and searched this website but without success. So if someone knows most of the topics, then please let me know them. The topics I am looking for are the ones from basics, to the university, and beyond university limit. Any comprehensive information you can provide would be useful. ps: I did some research on math topics and I did find a book called _Princeton Companion to Mathematics._ It is a really good book and I was curious if there is a book for Physics too.


title: Suggest me specific book for studying scattering theory and special functions

text: I am doing msc physics. And we are studying major part of scattering theory. I used _Quantum Mechanics_ by Davydov, Griffiths, etc, to study scattering theory. But I am not understanding it properly, hence I want a specific book which will explain scattering theory very clearly.


title: A crash course in quantum mechanics

text: I am shortly due to begin a summer project lasting roughly 6 weeks with the aim of performing some relatively basic calculations in the theory of open quantum systems. However, at this stage in my undergraduate physics degree, I am yet to have studied _any_ quantum mechanics at all. As such, the first part of my project will consist of self-studying quantum mechanics to gain sufficient working knowledge to be able to perform the required calculations. Which books, or other resources, would be suitable to gain such a working knowledge, given that I have already taken courses in Linear Algebra and some basic Lagrangian and Hamiltonian dynamics? My supervisor mentioned that it might be better to learn quantum mechanics using the matrix mechanics formalism, rather than the wave function formalism. (Although, given my situation, I can't really yet explain exactly what calculations I will be performing, it might be helpful to see this page of my supervisor's publications to see what sort of field I will be working in: http://arxiv.org/find/all/1/all:+AND+nazir+quantum/0/1/0/all/0/1)


title: General physics landau

text: I've found Landau 's book for a first course in physics (not theoretical physics, its title is general physics),the book is freely and legally avaible on archive.org ,but it's from 1967,is that okey,or this material in it outdated? What's the most recommended first course in physics? Which such books/resources provide the best intuition, rigour, etc. ?


title: Studying QM without math and physics background

text: I rode all posted answers about this topic but i need to ask you another information. I have done a semester course called "Principle of Physics" (i am studying Biotechnology) and one called "Principle of Analysis" (integral and derivation basically). I would like to study QM so i want to ask you if it is better Griffiths or Dirac books considering my little background.


title: Best physics olympiad resources

text: > **Possible Duplicate:**   >  Book recommendations I am looking for good book recommendations at the level of high-school physics. I am having in mind to find out as to what are the typical books that say IPhO competitors (say from US) would be studying.


title: Book recommendation

text: I already learned the Physics' basics like Newton Laws, Electricity, and Optics. Can you recommend me a good book for advancing with my learning of physics(with some math)?


title: Trouble with classical mechanics self-learning (How to avoid going down the Physics rabbit hole?)

text: I'm a retired police officer trying to learn classical mechanics on my own. I have gone through many links on the Internet including the classical mechanics quick reference textbooks from Physics Stack Exchange. But, I always have the same problem just as anyone trying to learn classical mechanics _on his/her own_ has had the experience of "going down the Classical Mechanics Rabbit Hole". > It turns out that only classical mechanics is the most difficult part of > physics to learn on ones own. I had a friend who confirmed this by comparing > how difficult it is to learn classical mechanics (including Lagrangian and > Hamiltonian formulation) on his own with electrodynamics and general > relativity. (Who are much much more difficult that all the field of CM) For example, suppose you come across the novel term vector space, and want to learn more about it. You look up various definitions, and they all refer to something called a field. So now you're off to learn what a field is, but it's the same story all over again: all the definitions you find refer to something called a group. Off to learn about what a group is. Ad infinitum. That's what I'm calling here "to go down the Math Rabbit Hole." For example, I had lot of difficulties with the book "An Introduction to Mechanics" by _Daniel Kleppner_ , _Robert J. Kolenkow,_ which seemed according to many views to be an easy approach toward Newtonian and relativistic mechanics. The authors in general only and quickly pushes equations in my front without giving any reason for why a certain procedure is correct, and give no explanation on most of the things. I had then one choice: search on the net. But when I do, to search for a term X, I get to wikipedia page X, who give a definition that contains another term Y, where I click to understand the full meaning of term X, but who then contain another term Z, who redirects to... which leaves me with no understanding. Another thing is that when I go here on Physics Stack Exchange, and when I see answers like:   * http://physics.stackexchange.com/a/14752/   * http://physics.stackexchange.com/a/67705/   * http://physics.stackexchange.com/a/71093/   * http://physics.stackexchange.com/a/64976/   * and many many others... (like an answer by David Z for a question that kinda looks like: 'Would a heavier object fall faster because they attract earth stronger', I have no idea where he found the equations he wrote down. Also in many applied physics questions and answers by Lubos Motl. And in some questions: like: 'Why Newton's third law apply to all inertial frame?' I have no idea about that even if I already learn a lot from Daniel's book.) I don't know where those guys got all that stuff. I feel like: Mechanics is not well organized. For example, in relativity we first learn about Galilean relativity, then special relativity then general relativity. Everything is in order and it makes of the understanding a lot smoother. (according to my friend) But in classical mechanics I don't know where to start or what to pick. In Lagrangian and Hamiltonian mechanics book, it is even worse. Result? I fail to correctly answer some basic questions like: what happens when a cup of water starts to melt? or even more easy physics questions. **So I'm searching for a clear textbook that explains Newtonian mechanics well, then goes to special relativity, then to Lagrangian and Hamiltonian mechanics.** My dream for the next years of my life is to understand mechanics: Newtonian, SR, Lagrangian and Hamiltonian. And to start writing a web page about explanations of different phenomena like John Baez this week on mathematical physics. And maybe to do research on problems in classical physics which would make of me the most happy man in the world. Regards. Thanks for your understanding and time. My situation is similar to this guy My background: I'm very old, so I forgot almost all the math/physics I've got in school, however, I've taken courses on Algebra, trigonometry and single variable calculus using KhanAcademy and some MIT videos. I've taken an MIT test on CalcI (just downloading the test online and verifying the solutions) and I scored 90%.


title: Classical Mechanics for Mathematician

text: > **Possible Duplicate:**   >  Which Mechanics book is the best for beginner in math major? I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through:   * multivariable calculus from Spivak,      * real analysis from Pugh,      * differential equations from Hirsh/Smale/Devaney (mostly focusing on linear system, existence & uniqueness, nonlinear dynamical system, bifurcation, and brief touch on chaos) (so no application covered)      * differential geometry from Pressley (but I hate pressley, so I am going to review through doCarmo)   * topology from Willard (but not all of them) The problem is I did not take freshman physics coures (because of annoying labs;;) My goal is to be able to read Abraham/Marsden's Foundations of Mechanics or something of that level. I was thinking of reading differential equations book's applications section first and... idk. What books do you think is suitable for me to start learning classical mechanics? P.S. Some people mentioned Arnold's Mathematical Methods of Classical Mechanics, but do you think it is self-contained in terms of physical intuition required?


title: Math required for learning Lagrangian mechanics

text: How much knowledge of maths is required for learning Lagrangian mechanics? Also from where can I learn this math?


title: Studying physics at undergraduate level: Prerequisites

text: I have been really interested in physics for some time and also take active interest in quantum mechanics. I would like to pursue physics as my undergrad major. What kind of prerequisites does one need to major in physics? (I am going to study physics in Japan and right now is not so good at maths cause I am learning Japanese only for the past 6 months and has been totally out of it. )


title: Introduction to quantum mechanics

text: > **Possible Duplicate:**   >  Book recommendations   >  What is a good introductory book on quantum mechanics? I intend to learn quantum mechanics . But I don't have any suggestions about good books to start up with quantum mechanics. I will remain grateful if I get to know about books which start up the subject with the original physical insight as well as with mathematical rigor. So, I hope the learned people here will recommend few books that form their experience are going to be the best to start up with.


title: Physics book for 15 year old boy

text: > **Possible Duplicate:**   >  List of good classical physics books my name is Bruno Alano. As stated in the title, **I'm 15 years old** (I'll do 16 on 7 of Feb) and much love **Computer Science** (C, C++), **Mathematics** and **Physics**. Some information may have been unnecessary, but my question is: **What is the suggestion of a good physics book for a teenager of my age?** I know basic things (speed, shoveller these issues and basic primary and secondary). A good reason for this is my Awe in mathematics and physics. Besides that maybe one day be useful in what I really want a career (science or computer engineering). **And another question: It is interesting physics in the area I want to go? I'm at an age that would be good to learn beyond what is taught in common schools?**


title: Good explanation of phase transitions, second law of thermodynamics

text: I am looking for a good explanation (website, book, video,...) of phase transitions. I am interested in atmospheric applications (so basically condensation, etc. of water in air). I would like an in depth explanation (so with derivations), which explains things from scratch (Second law of thermodynamics and so on). Maybe a video would be good, if anyone can point one out.


title: Beginner Physics Resources?

text: I'm interested in learning physics. I do realize that the subject is large and that it would be easier if I had a specific area of interest. However, I do not. I suppose I want to learn about the fundamentals of it all; the axioms that combine all physics fields. Or, in other words, a high school physics class. Specifically, a book or series of videos would be helpful. I looked over MIT and unfortunately the material wasn't for me. I don't mean to be "picky" so I am not completely ruling out any resource just yet. Thanks in advance.


title: Link for resource on cosmology

text: I have recently just begun studying cosmology. I have a background in physics. I would like a link to download video resources on Stephan Hawking's theories on physics and/or cosmology that have not been proved wrong.


title: Can someone recommend good resources to self study physics please?

text: I have a goal to educate myself up to the current level of knowledge we possess about the universe. I've tried textbooks, wikipedia, lectures, but i find each of them fundamentally flawed in different ways. Textbooks tend to be incredibly bloated, and I become unable to "see the forest for the trees" Wikipedia seems to be too technical/mathematically rigorous for my level of understanding Lectures feel very time consuming and i dont really feel as though i get a structured sense of how everything fits together. I feel as though all mathematical and physical concepts can be explained in simple terms, yet i cant find resources which present concepts like this. I don't want explanations that are completely dumbed down or necessarily lacking in math, but i would prefer explanations which give math intuition and take time to explain what the variables and symbols mean in laymen's terms. If anyone knows any resources similar to what i described, or has any advice it would be greatly appreciated! Edit: I should also mention that i had been referred to Hooft's outline of learning, as seen here: http://www.staff.science.uu.nl/~hooft101/theorist.html#ssphysics Which i find to be a trememndous help, but I'm still struggling as to the ideal places to find clear resources in regards to these subjects.


title: Getting started general relativity

text: What are some good books, videos, websites for getting started with general relativity? Mathematically rigorous preferred!


title: What is a good target to aim for when teaching myself quantum mechanics?

text: I'm interested in teaching myself quantum mechanics, and I'm looking for a good goal to aim for. I've got an undergrad maths degree and a graduate degree in probability theory and stochastic processes. I've worked fairly extensively with diffusion processes, so I understand how the Fokker-Planck equation works, for example. As far as I understand, the Fokker planck equation is related to the Schrodinger equation via something called a Wick rotation. I'm a bit hazy on the details, but I think this may have been Feynman's approach to QM. If anyone could recommend a text for someone with my background (linear algebra, group theory, ODE and PDE, probability), but with relatively little experience in physics, that would be very helpful. The maths shouldn't be a problem, but there's a chance I'll just get bored unless I have a specific goal. Maybe deriving the emission spectra of various atoms, or understanding quantum computing. Any other suggestions?


title: Introduction to relativity books for an engineer

text: > **Possible Duplicate:**   >  Getting started general relativity I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I lack the knowledge behind many of the relativity concepts in the novels. I've always felt curiosity in relativity so I decided that it was the time to buy an introductory book. I went to amazon and checked that there are dozens of "Introduction to genereal relativity" books in there. So here's my question: What book would you recommend to someone not matematician nor physicist but with (some) mathematical background as an introduction to relativity? Thank you so much!


title: Good First year physics lecture notes

text: My course textbook is Halliday fundamental of physics, this book is huge and since each week, they cover a lot of material in lectures (something about 6 chapters of the textbook), I find it hard to read this textbook because there are a lot of unnecessary details that reading them is not needed. I was wondering if you know of some good physics lecture notes that covers basically what is in Halliday fundamental of physics and it is short?


title: Physics textbooks reference request

text: > **Possible Duplicate:**   >  Book recommendations I am currently in the 11th grade (I am an Indian student) and I am looking forward to studying pure mathematics and theoretical physics in the future. I therefore request you to tell me books/textbooks to study physics. I know some integration and differentiation and I plan to study Richard Courant's book "Introduction To Calculus And Analysis: Volume 1" from Tuesday onwards.Besides, I am studying Halliday-Resnick Walker for the moment.


title: Exam on Physics for Graduate

text: Is there any book you recommend for graduation exam/higher studies? I have an exam on physics this week so I need some books to brush up my knowledge. Is there any book you recommend for that purpose? Other than Nelsons Parker Physics. What I ment here is a book which has all in one **_like_** **"Advanced Level Physics by Michael Nelkon (Author), Philip Parker (Author)"** http://www.amazon.com/Advanced-Level-Physics-Michael- Nelkon/dp/043592303X A book with all exercises alog with the lesson. For Advanced Level Examination.


title: What is a good introductory book on quantum mechanics?

text: I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along. What are good introductory guides to QM along these lines?


title: Quantum Mechanics Text for Electrical Engineers

text: > **Possible Duplicate:**   >  What is a good introductory book on quantum mechanics? What is a good introductory text on quantum mechanics that could be used to train electrical engineers in device physics and band structure in a single semester?


title: Beginning Physics, Advise on Books

text: > **Possible Duplicate:**   >  Beginner Physics Resources?   >  Book recommendations I'm wanting to learn physics. In fact i'm a software engineer and i find physics very fascinating. But everything I read things concerning physics, I don't understand many things. What are the books that can be helpful for someone who don't know physics but have a good foundation of mathematics??


title: Best books for high-school?

text: Please don't close this thread, I now it might sound like a dozen others but I think that every case is different... I go to the first class of high school (that's how it's called in Greece, not sure how it's called in English standards) and I love physics. Recently I participated in a competition and I think I did well. Thing is, I can't find any really good textbooks. I want something inspiring with great problems and clear explanations. If I could find it as an ebook, it would be even greater. Also, it must also use simple maths or at least explain some of them, 'cause I'm still learning, naturally.


title: Undergraduate Math Major Wanting to Learn Physics

text: > **Possible Duplicate:**   >  Book recommendations So I'm a Junior level math major. I've seen some abstract algebra, some differential geometry, and some lie theory. I'm currently working through some standard topology. I don't at all claim to be an "expert" in any of the above, but I'll attest that I have some decent mathematical maturity. I've always had a soft spot for physics, and I wanted to develop my knowledge of it much more formally. Particularly things like general relativity and quantum mechanics seem very cool, but I'm lamentably pretty ignorant of them. Given my somewhat okay math background, is there a good starting point for someone like me?


title: Physics books for mechanics

text: What are the best physics books for learning mechanics? I am in grade 12 and would love to learn in depth about Newtonian mechanics and also maybe get started on Lagrangian mechanics?


title: Physics books covering classic mechanics

text: I am going to be a high school freshman next year and I have acquired a strong interest in physics. I have a mathematical background, upto, but not including, Calculus. I am looking for in depth resources covering classic mechanics enough to move onto more in depth texts on relativity as well as quantum theory. Again, I have a strong math background to all the work leading up to Calculus, and I will be taking Calculus next school year.


Could you recommend some good books on physics? I found out that some books on physics are not good, especially about Einstein's Relativity and quantum mechanics. Here is an example which makes me think so: While Space-man lives for 1 day, then how long does Earth-man live ? 1000 years or 1 second? A bad book makes my head spin for hours , it may be a good thing(I have some joy in it！）, but maybe it's a bad thing too sometimes. Someone says that "Michael Berry, Principles of Cosmology and Gravitation" is a good book. Any other good books ?


title: Book recommendations

text: Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start. All the questions linked below, as well as others which deal with more specialized books, can be found under the tag resource-recommendation (formerly books). If you find a question that should be added to the list, edit it into the existing list answer rather than creating your own answer for it. See our policy on resource recommendations for details. **Related Meta:** Do we need/want an overarching books question?


title: What resources may be helpful to learn physics from ground up (very basic level)?

text: I want to learn physics and the math required, but I never got the chance to learn properly in school due to mental illness. But, now, as a 22 year old, I wish I can start learning. Attending a college is not an option as I do not think I would find one that is willing to provide the psychological support a person suffering from psychotic depression/schizoaffective disorder needs in my city in India. Anyway, so I think I should start learning from resources online and by buying some (not too expensive) books. The problem is I'm not very good at math, as my knowledge of basics and foundation is very weak, probably worse than middle school level. Though I can probably do basic algebra, I'm not even sure I know what set theory is. My trigonometry and geometry is poor also and I doubt I would be able to do even simple problems. Physics is the same. So I really want something that will help me build my knowledge from ground up, as I now have an genuine interest in learning the subject. What got me interested was reading Stephen Hawking's Brief History of Time and some topics on quantum mechanics. So I want to learn now to be able to comprehend such stuff someday. So please recommend good resources/books I can use to start from VERY basic level, as most similar questions and discussions elsewhere that I found were asking for resources for the high school level and up. Also, it would be nice if the books were very interesting and not dry, maybe like Bill Bryson or how Cecil Adams would do it. Edit with regards to Qmechanic's setting the question as duplicate: The resources mentioned in the other question do not seem to me to be aimed at a very basic level of math and physics (starting from middle school level, so to speak.) and they appear to be aimed at those who possibly have some well-to-do knowledge of at least the basics or the foundation, unlike what I asked for. However, I could be wrong, but their question does mention 'high-school level'.


title: Quantum harmonic oscilator - book that does it all right

text: I am dealing with quantum harmonic oscillator. In every single book or video i have checked out i can read how the mathematical technique for solving this Schrödinger equation: $$ W\psi = - \frac{\hbar^2}{2m} \frac{d^2 \psi}{dx^2} + \frac{1}{2}m \omega^2 x^2 $$ is beyond the level of the book/video... I really want to learn this stuff and noone seems to be able to explain it. I have dealt with tunelling, particle in a box, potential steps... **so why do authors think i can't handle this?** **I need a good book recommendations**.


title: Would love to learn quantum physics

text: I would love to learn quantum physics and am extremely keen on it. Lets get to points. I was extremely weak at math and physics while I was in school, but I guess it's just the way things were taught. I have read some theoretical (the literal word) on quantum physics and am really keen to do the math involved. I love reading books and that's how I've spent most of my life. It would be the greatest thing ever if you geniuses could recommend a step by step guide (books only) to becoming a quantum physicist. I intend to learn everything involved and/or required. It would really help me and many other physics enthusiasts who currently see no other option than the conventional university education route. I am fully and completely prepared for this journey.


title: From Freshman Mechanics to String Theory: A Comprehensive Textbook Sequence in Physics

text: If a student with no background in physics and an understanding of only single variable calculus wanted to learn string theory, what sequence of textbooks would most succinctly, clearly, and comprehensively fill in the gaps, assuming a 100% retention rate of the textbooks' material?


title: An easy source to understand classical dynamics --- Rigid body Rotation

text: I've been having an extremely hard time at understanding rigid body rotation. The source that I'm currently studying from has been suggested by 't Hooft on his webpage. It's by Richard Fitzpatrick. Here's the link --- http://farside.ph.utexas.edu/teaching/336k/lectures/node61.html I have spent countless hours trying to understand rigid body rotation in the fixed frame and in the body frame, i.e. Euler's Equation and the Eulerian angles, but I just don't get it. Can someone please suggest an alternative source which could be easier to understand? It's really important for my work that I understand rigid body rotation properly!


title: Learning about group velocity, phase velocity and particle velocity

text: I am studying quantum physics and I would like to know a bit more in detail about group velocity, particle velocity and phase velocity. Can you guys suggest some books/online resources where I can learn the same.


title: Book suggestion : geometric approach to electromagnetism

text: I´m looking for a book on electromagnetism that is introducing the topic from a geometric point of view, focusing more on the theoretical structure than on the application.


title: Book for learning about constructing correct physical modeling

text: > **Possible Duplicate:**   >  List of good classical physics books I know physics. At least I thought so until I tried to make a model of the system of scales by myself. It was confusing. For example for a simple spring model everything is ok, but when you have 3 and more springs connected in some way, it is hard to determine how the forces and at which directions are applied. And even in simple one-spring model I do not understand how the direction is choosed (the direction of mx'') while drawing the system on the paper with forces applied on it. In general case, not only in case of springs I want to learn how to correctly determine the forces and direction in order to construct the correct differential equation (or system of diff.equations). Can you suggest me the books needed to learn for this purpose? I know some physics but no experience in constructing the models by myself. EDIT 1: For example I want to make a model of this system: ![enter image description here](http://i.stack.imgur.com/h6Xz2.jpg) There will be 5 variables. The problem is that I can't decide the directions of the forces considering the influence on each other.


title: Green theory and Laplace theory

text: I can not understand classical electrodynamics so well, maybe there is some book, video, lecture note can help me.


title: Informal book on Classical Mechanics

text: I just want a book on classical mechanics that covers the same ground as Goldstein's book but is more on the line of DJ Griffiths's Classical Electrodynamics. I mean less formal and more conversational.


title: How can I answer the critical questions of mechanics?

text: I have passed my 1st year of undergraduate study life somehow I could have managed. But recently I have decided to fill up the emptiness of knowledge over mechanics. Besides I have my studies of 2nd year. I am following "PHYSICS", volume 1 by Resnick, Halliday, Krane for mechanics. The questions of that book are so hard to answer. For example, a question - How would you criticize this statement : "Once you have picked a standard, by the very meaning of 'standard' it is invariable"? Being unable to answer so many questions does not making me happy. For classical mechanics I am following the book Herbert Goldstein. Actually what I want it is that I want to learn to answer those types of questions.


title: Books for a fresh physics undergraduate

text: I'm going to start a degree course in physics next year. So far in high school I covered some physics without calculus. I know that I will start everything from the beginning at university, but I would like to prepare in some ways. Then the question is: what should I do? Should I revise what I studied? Should I go head? Can you suggest (from your experience) what should I do before starting a physics degree course? PS In case you recommend to study some material, can you suggest a book?


title: Reference books for classical mechanics with good number of solved examples

text: I am looking for some classical mechanics reference book with a good number of solved problems.


title: Material to read before taking College Physics 1?

text: I'm transferring to a 4-year university from a 2-year college. I earned a Computer Science A.S., but must now combine Computer Science with Advanced Physics for my B.S. I'm actually **_very_** excited for Physics, but I am coming in from knowing nothing about the field. I did not take Physics in high school, and I will be taking Calc II while taking Physics I and Physics I Lab. This is a topic that I want to understand to my fullest extent, because I would like to work on Quantum Computers when I get out of college. Are there any "pre-review" or "course-summary" materials that I can read roughly within a month of starting classes? I would like to get a head start and ease in some topics that I will be learning in class, so the lectures are more of a review than a rush to take notes. Even something like Physics I For Dummies would be fine to purchase and read, I just want to see what Stack Exchange users would recommend. Thank you in advance! **EDIT:** I should be more specific - and say that I am taking Calculus based physics (which is what I was implying by mentioning Calc II), not algebra based.


title: Where to read about Minkowski space

text: When I learned Special Relativity, it was taught in terms of basic linear algebra, without any mention of the Minkowski space, proper time as integration on the metric, etc. However, when I am trying to learn General Relativity from several books (Wald, Carroll, Weinberg), it seems they all assume I am already familiar with SR and Minkowski space, and only briefly review it. So, I'm afraid I'll be missing some material here. What is a good source for SR from a Riemannian geometry point of view?


> **Possible Duplicate:**   >  Book recommendations How to make strong base for fundamental physics? I want to learn the fundamentals of physics. But in a simple manners with very general examples. Please suggest me any URL or Books for it.


title: Math and Theoretical Physics Topics & Textbook for Self-Study

text: I am from Singapore, a civil engineering graduate and I've graduated from university in 2009. Throughout my school days I've been interested in Physics, unfortunately I was not accepted into the local university as my grades did not match up. And I couldn't afford to study abroad. Hence I took up whatever was offered to me at that point; civil engineering. Right now, I'm on a mission to self-study theoretical physics so that I can fully appreciate the beauty of it; I mean right down to the deep mathematical level of it. I am particularly interested in the subjects: General Relativity, Quantum Theory, M-theory. I acknowledge that first of all I'd have to master the math before I can delve deeper into the theoretical physics subjects. I would like to ask forumers the following questions: (1) - May I know what are the sequence of math & physics topics I have to master? I mean in a step-by-step way starting from high school level knowledge. (2) - Could you recommend texts both from the math & the theoretical physics side? Based on my research I have shortlisted a few and they are (a) Introduction to Mathematical Physics: Methods and Concepts by Chun Wa Wong. (b) A course in theoretical physics by P. john Shepherd (c) Introduction to Modern Physics: Theoretical Foundations by John Dirk Walecka & (d) A Unified Grand Tour of Theoretical Physics, Third Edition by Ian D. Lawrie. Are these books suitable and good for my cause? What other textbooks do you all recommend? I am willing to self-study patiently even if it takes me 10 years.


title: Good theoretical physics introduction for 6 year old very advanced in math?

text: I think now is a good time to introduce my son to theoretical physics. He asks so many questions about the universe, black holes, gravity, atoms, molecules, light, etc. He's borderline obsessed with the idea of more than 3 space dimensions. And he tries to apply math to everything. So I'd love to find a great introductory book, lecture, online class or something of that nature to feed his curiosity. The issue is he's only 6 years old (his birthday was only a few months ago). So his life experience is obviously very limited. His vocabulary and general knowledge is probably not a whole lot more than the average 1st grader. However, his math skills are extraordinary. He's working on calculus now, having mastered algebra and everything that's come before. Is there any introductory physics material that is heavy on the math and light on the vocabulary and assumed general knowledge? This would also be beneficial to non-native English speakers.


title: Quantum Physics Books

text: I`m very newbie in physics and want to study on amateur level. I`m interested in Quantum Physics, can anybody advice some books?


title: Helping/explanatory notes for Landau&Lifschitz Physics Course

text: I've recently restored my interest on theoretical physics (I have a master degree in Electrical Engineering) and began my study with first volume of the Physics Course by Landau and Lifshitz. This is a very good and interesting book, and it just blows my mind (both in a positive and negative ways) - you spend really a lot of time trying to understand everything out of this textbook. Maybe someone can suggest somewhat sort of helping sidenotes for this book? Thank you for your help.


title: A Mathematician Who Wants to Learn Particle Physics

text: > **Possible Duplicate:**   >  Book recommendations I'm a grad student in pure math, wrapping up a thesis in Lie theory. After years of talking to mathematicians and physicists, I've decided that it's time to get some formal training in physics, particularly in particle physics. I have no formal training in physics. We're talking only a childish understanding of basic mechanics and bits and pieces of relativity and CFT . . . I've seen Maxwell's equations once or twice . . . etc. But I know Riemannian/pseudo-Riemannian geometry, the representation theory of compact and semi-simple Lie groups, some PDE, and so forth. So hopefully the math shouldn't be an issue. With so little physics training (and hence little physical intuition!) what kind of books do you guys recommend?


title: help me.. please

text: I'm a total novice to physics so please forgive me but I'm looking for a starting point on sound, frequencies and everything to do with electricity. Preferably books because my internet usage is limited, would love to here back so please.. help me understand the world


title: What is a good mechanics book without calculus

text: I am very interested in physics and I want to improve my basics especially in mechanics. I have only started high school (junior) so I don't know much about calculus, which is used in most of the books. I am only looking for a conceptual books explained basic concepts nicely.


title: Orbital motion (Mechanics)

text: I am a student in Mechanical department and I took today a lesson with a title of _Orbital motion._ I need a good mechanics reference that discusses this topic.


title: best fundamental physics book

text: Good evening. I'd like to know, in your opinion, what would be the best fundamental physics book for a freshman? I want to start all over again. Thanks in advance.


title: Which Mechanics book is the best for beginner in math major?

text: I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through Goldstein's Classical Mechanics. What books would be good for a beginner?


title: Books to independently study physics

text: Can anyone give me a list of books to study so that I can "master" (whatever the precise definition of that may be) all the branches of physics? I want to start from the most elementary to the most advanced.


title: Recommended book for beginners on advanced science topics

text: I have a background in engineering so I have some familiarity with basic math and science. I've recently been reading about other topics such as Einstein's relativity and have become interested in learning more about this and other similar topics in science. Are there any books you can recommend that explains this and similar topics (also stuff like astrophysics, spacetime, etc), but aimed at a more amateur audience? Thanks!


title: Self-teaching physics recommendations?

text: I've been very interested in mathematics for a while now and, after being inspired by reading Feynman's biography, would also like to learn about physics. My mathematics background is fairly extensive. I've taken courses through calc BC, the basics of multivariable calculus and a fair amount of linear algebra, with plans to take statistics next year. My physics background is okay, in that I know what many of the individual symbols mean, but have never seen them put together in such a way that they yield all the wonderful results we see today. Could anyone recommend a good place to start that makes use of this math background without being incomprehensible to my fledgeling physics knowledge and a freely available online textbook to accompany the former? Thank you very much!


title: Books to study quantum thermodynamics and quantum decoherence

text: > **Possible Duplicate:**   >  Book recommendations My friend is having a hard time finding books to self-study quantum thermodynamics and quantum decoherence. (search on amaxon would bring almost no book... so what books should he choose?)


title: Need for a side book for E.Soper`s Classical Theory Of Fields.

text: I am reading now E Soper Classical Theory Of Fields now and sometimes it is very hard to follow the equations.So I need a side book to read it comfortably.Landau`s book is not helping as its content and topics are very much different.


title: Where to begin with Physics beyond high school?

text: So I'm in grade 10 but I finished all my physics classes, maths and further maths (Calculus). I would like to start with some harder stuff (university physics). What books do you recommend for both maths and physics? And if possible what steps should I take?


title: Electric potential energy in curved space-time

text: In flat space-time the electric potential energy between two charges is $\frac{k Q_1 Q_2}{r_{12}}$, where $Q$'s are charges and $r_{12}$ is the distance between them. What would happen if the two charges are placed in a strongly curved space-time, which makes "distance" and "duration" measures different from place to place? Will the two feel the same strength of electric force/potential energy?


title: Cannon on spacecraft: hitting yourself

text: Some Soviet space stations reportedly had anti-aircraft cannons installed. Could such a cannon hit the firing space station accidentally on a subsequent orbit? The muzzle velocity of the cannon is under 700 m/s, significantly slower than orbital velocity so the projectiles should have similar orbits to the station.


title: Magnetic field inside a charged stream

text: Outside a narrow charged stream (say, a beam of ions or electrons) is the same as observing a current through a conducting wire - there is a circular magnetic field around it. What would happen inside a charged stream (for example, inside a conducting wire or inside a solar flare)? I have a feeling that symmetry will rule that there is no magnetic field, but I am not sure.


title: is there any difference between these Differential $dx^2$ and $(dx)^2$?

text: * is there any difference between these Differential $dx^2$ and $(dx)^2$!?   * what is relation between them?


title: Are We Living in a Simulated Universe?

text: If the universe is just a Matrix- like simulation, how could we ever know? Physicist Silas Beane of the University of Bonn, Germany, thinks he has the answer!. His paper “Constraints on the Universe as a Numerical Simulation” has been submitted to the journal Physical Review D !. Are We Living in a Simulated Universe? **Remark:** This person claimed that the whole world is a great simulation, and the whole world started with a simulated big bang. and every things are results of spontaneous program self-organization and automorphisms. The big bang happened in a kind of supercomputer And now we're inside of it. the Big Bang occurred approximately 13.75 billion years to our eyes, But perhaps within less than a second for simulator.   * If the universe is just a Matrix- like simulation, how could we ever know?


title: When you apply the spin operator, what exactly is does it tell you?

text: The example I'm trying to understand is: $ \hat{S}_{x} \begin{pmatrix} \frac{1}{\sqrt{2}}\\\ \frac{1}{\sqrt{2}} \end{pmatrix} = 1/2 \begin{pmatrix} \frac{1}{\sqrt{2}}\\\ \frac{1}{\sqrt{2}} \end{pmatrix} $ My interpretation of this is that the vector shows you the probabilities of a particle being spin up or spin down if you square them. And I've been told that $ \hat{S}_{x} $ gives you the spin as an eigenvalue, but how? Since its 50:50 of getting -1/2 and 1/2. $ \hat{S}_{x} $ has only given you one of them. Is it that $ \hat{S}_{x} $ only measures the magnitude of spin in the x direction?


title: How to determine what an object is composed of?

text: **Heads up** : This question has never been asked (here) before the way I will ask it here, so let's shed some light on it a bit. **Prelude and anecdote** (can be skipped): The other day I was walking home, and I passed a stop sign. I looked at it and asked myself, " **What kind of atoms make up this macro-sized metal-like object that visible light enables my eyes to see, which are also atoms I don't know?** " So I thought to myself ... _I really should go to physics.stackexchange.com to ask this._ They have so many great people there who volunteer their time and help without any immediate financial gain, and there is some very smart people there who are open-minded, and know that repetition is key to success. **The question:** So here I am ... my question is how do you know what materials are composed of? I ask this because: 1.There are no "grab and go" ways to quickly check out what atoms something is made of. How would I, as a curious person that I am who's into science in all respects, determine what the world is around me? 2.The tools needed to do this don't come cheap ... how could I, by using cheaper tools or techniques, determine what kind of atoms, molecules/chemical compounds, determine which exact atoms make up the things visible light enables me to see around me? I would like to look at something and go beyond just "It's plastic-like", but actually dig down to which monomer, polymer, or molecular structure it is, and how I can break it down to the individual atoms. Please ... I ask this with all respect, all seriousness, and all desire to want to further know the materials, compounds, and structures of the objects around me.


title: What are differences between Spin(3,1), SL(2,C), SO(3,1) and SU(2) representations? Which one is correct exact representation for spinor fields?

text: 1. I want to understand which group transformations exactly represent spinor fields. That is, do spinor fields transform under the Lorentz group $\mathrm{SO}(3,1)$ or under $\mathrm{Spin}(3,1)$? What are the differences? There are also $\mathrm{SL}(2,\mathbb{C})$ and $\mathrm{SU}(2)$ transformations. Do spinors transform under these transformations? We define spinors according to transformation rules. So, I want define spinors exactly considering transformation rules.   2. I read in some papers that spinors do not transform under general coordinate transformation, but that they transform under local Lorentz transformations. Are the local Lorentz transformations $\mathrm{Spin}(3,1)$?


title: What are all the lines on a double circuit tower?

text: I understand what three-phase power is. But when I look at some pictures of a double-circuit-three-phase-power-line I see two or three lines close together? What is the purpose of these lines close together? (the wires are attached by smaller wires or connectors) * * * Is there a separate alternator for the second group of three-phase? * * * ![Power line](http://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Electric_Sails.jpg/450px- Electric_Sails.jpg) It has 2 lines instead of 1 line for one of the phases. So instead of having two sets of A, B, C it has AA, BB, CC? Or is that second line just a neutral line? * * * This one has many wires! is it now AAAAA, BBBBB, CCCCC? ![power 2](http://tdworld.com/overhead_transmission/1200kV-Single-Circuit-line-1200kV- Double-Circuit-line-7.jpg) * * * This one is nice and simple! Just one line for each phase(x2)! ![third power line](http://www.power- technology.com/projects/beaulydenny/images/1-transmission-line.jpg)


title: Applications of Algebraic Topology to physics

text: I have always wondered about applications of Algebraic Topology to Physics, seeing as am I studying algebraic topology and physics is cool and pretty. My initial thoughts would be that since most invariants and constructions in algebraic topology can not tell the difference between a line and a point and $\mathbb{R}^4$ so how could we get anything physically useful? Of course we know this is wrong. Or at least I am told it is wrong since several people tell me that both are used. I would love to see some examples of applications of topology or algebraic topology to getting actual results or concepts clarified in physics. One example I always here is "K-theory is the proper receptacle for charge" and maybe someone could start by elaborating on that. I am sure there are other common examples I am missing.


title: Collision of Discs and Snooker Kicks

text: I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? **Problem 1** Suppose have two identical uniform discs constrained to move in a plane. Set disc $A$ spinning about its centre of mass, clockwise viewed from above. Now collide it with disc $B$. Assume that friction is the only force acting, and the collision is elastic. I believe that I should be able to work out qualitatively what happens from conservation of linear and angular momentum. The friction will provide a torque causing $B$ to spin anticlockwise about its centre of mass. Let $L$ be the line joining the centre of $A$ and $B$ at the moment of collision. But then by conservation of angular momentum $B$ must deviate to the right of $L$ after collision. And then by conservation of linear momentum disc $A$ will move to the left of $L$. The other option for conserving angular momentum would be for the disc A to start spinning faster, but this is ruled out by conservation of energy. Correct? _Note_ : this effect is observed in snooker when left hand side is imparted to the cue ball. **Problem 2** Now suppose that the discs are stood on end on a table and we do the same experiment, assuming no friction between table and disc. Then conservation of angular momentum must cause the first disc to jump in the air upon collision, by the same reasoning as before. Correct? _Note_ : I guess this is the origin of the "kick" in snooker. So really understanding how to prevent snooker kicks is the subtle problem of understanding precisely how much angular momentum is transferred between the balls. You ideally want to minimise this (i.e. have almost frictionless ball collisions, compared with the friction between cloth and ball).


title: Lowering and Raising Kronecker Delta

text: When an index of the Kronecker-delta tensor $\delta_a^b$ is lowered or raised with the metric tensor $g_{ab}$, i.e. $g_{ab}\delta^b_c$ or $g^{ab}\delta_b^c$, is the result another Kronecker-delta tensor?


Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A and ${x^\prime}^\mu$ for observer B .Both coordinates are connected by means of the Lorentz transformation. $${x^\prime}^\mu = \sum_{\mu=0}^{3}a^{\nu}_{\mu}x^\mu\equiv a^{\nu}_{\mu}x^\mu\ = (\hat{a}\overset{\Rightarrow}{x})$$ Where $\hat{a}$ denotes the abbreviated version of the transformation matrix and $\overset{\Rightarrow}{x}$ is a 4 dimensional world vector . I need to understand the Lorentz transformation equation that how it transformed . EDITED : How both coordinates are connected in that transformation .


title: Is it possible to take a QFT class knowing only basic quantum mechanics?

text: I'm in grad school and notice there are no prerequisites required for QFT in the physics department. In fact, the system allows me to sign up for the course just fine as a technical elective. But... my field is chemical engineering and I've only taken basic quantum mechanics. I would really love to learn more about QFT though since it's always been something I've really been interested and lightly study in my free time. From the perspective of someone who knows the physics required to take this course, is the material required to understand the subject outside the range of what I would have learned for an engineer (+QM)?


title: Determination of auxiliary scale in dimensional regularization

text: My questions are in italics. In the article [1] a dimensional regularization is presented on an electrostatic example of an infinite wire with constant linear charge density $\lambda$. It is shown that the direct computation of the scalar potential gives infinity: $$ \phi({\bf x}) = {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d l \over |{\bf x} - {\bf l}| } = {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d l \over (x^2 + y^2 + (z-l)^2)^{1\over 2} } = $$ $$ = {\lambda\over 4\pi\epsilon_0}\int_{-\infty}^\infty { d u \over \sqrt{x^2 + y^2 + u^2} } = \infty $$ But with dimensional regularization in the modified minimal subtraction scheme we get eventually: $$ \phi_{\overline{\rm MS}}({\bf x}) = {\lambda\over 4\pi\epsilon_0} \log{\Lambda^2\over x^2 + y^2} $$ where $\Lambda$ is the auxiliary scale parameter. One can then calculate the electric field (let's set $y=0$ from now on) as follows: $$ E_x = -{\partial \over \partial x} \phi_{\overline{\mathrm{MS}}}(x) = -{\partial \over \partial x} {\lambda\over 4\pi\epsilon_0} \log{\Lambda^2\over x^2}= $$ $$ = - {\lambda\over 4\pi\epsilon_0} {x^2\over\Lambda^2} \Lambda^2 \left(-{2\over x^3}\right) = {\lambda\over 2\pi\epsilon_0} {1\over x} $$ The article claims that the original scalar potential is scale invariant: $\phi(kx) = \phi(x)$. But since both $\phi(kx)$ and $\phi(x)$ are infinite, _I don't understand the argument._ The article claims that the dimensional regularization preservers translational symmetry. However, the only way to make $\phi_{\overline{\mathrm{MS}}}(kx)=\phi_{\overline{\mathrm{MS}}}(x)$ is to choose different $\Lambda$ for each side. _Are we allowed to do that?_ I thought that we have to set $\Lambda$ once and for all and then just keep calculating with it and it must cancel at the end. Update: based on Michael's comment below I realized that the article claims _translational_ invariance of the original problem, i.e. $\phi_{\overline{\rm MS}}(x, y, z+h)=\phi_{\overline{\rm MS}}(x, y, z)$ and that is obviously true, because $\phi_{\overline{\rm MS}}({\bf x})$ does not depend on $z$. So I think that answers this particular question. Still a clarification from an expert would be nice. [1] Olness, F., & Scalise, R. (2011). Regularization, renormalization, and dimensional analysis: Dimensional regularization meets freshman E&M. American Journal of Physics, 79(3), 306. doi:10.1119/1.3535586, available online here.


title: Background radiation: radon vs potassium 40

text: In doing a little research into natural background radiation, I came upon a table from the National Council on Radiation Protection and Measurement (NCRP). It shows that inhaled radon gas is by far the largest contributor to average annual dose equivalent from background radiation, for people living in the United States. [1] That table lists "other internally deposited radionuclides" as contributing only a small fraction of what inhaled radon gas contributes. Among those "other internally deposited radionuclides" is potassium-40. According to another source, the typical activity of potassium-40 in the human body is about 0.1uCi. [2] Typical activity of radon in outside air is said to be 0.4pCi/L, while for indoor air the average is 1.3pCi/L. [3] Given that the typical volume of air the average adult inhales is 0.5L, at any given time an adult has about 0.4pCi of radon in their lungs. [5] Note that the stated activity levels for radon are about a million times lower than those for potassium-40 (0.4 pCi versus 0.1 uCi). I also learned that radon typically decays via alpha decay. [4] Potassium-40, on the other hand, mostly decays via beta decay. [2] I understand that alpha radiation is given more weight than beta radiation, generally by a factor of 20 or so, when estimating the biological effects of radiation. [6] However, a factor of 20 falls far short of the 10 million or so times higher effect stated for radon versus all other internally deposited radionuclides in the NCRP table. The table implies that the one million times greater activity of potassium-40 results in only about a tenth (or less) the equivalent dose. That seems way beyond what could be accounted for with just a weighting factor. Why doesn't potassium-40 contribute much more to the equivalent dose? What am I missing?


title: Where to place my second image charge? (Spherical ungrounded conductor)

text: I am trying to find the potential $V$ inside a sphere using the method of image charges. I have a conducting spherical shell. The charge $q$ is inside the sphere. The sphere is ungrounded and is an equipotential because it is a conductor. If I place an image charge $q'$ outside the sphere, I can make it equipotential if it is grounded i.e. potential$ V=0$ on the sphere. But since it is not grounded, there is some potential $V_0$ on the sphere. To make the equipotential $V_0$ on the sphere, I can put another image charge $q''$ at the centre except that that is not allowed because I can't put image charges inside the space that I'm investigating. Where else can I put the image charge? No matter where I put it outside the sphere it will not give me the $V_0$ equipotential on the sphere. How do I solve this?


title: Why is there no permittivity-type constant for gravitation?

text: When I look at electric or magnetic fields, each of them has a constant that defines how a field affects or is affected by a medium. For example, electric fields in vacuum have a permittivity constant $ϵ_0$ embedded in the electric field expression of a point charge: $E = q/4π ϵ_0r^2$. However, if I put this point charge in some dielectric that has a different permittivity constant $ϵ$, the value of the electric field changes. On a similar note, magnetic fields behave very similar but have the permeability constant $μ_0$ instead. From my understanding, I believe that this is not the case for gravitational fields since the universal gravitational constant $G$ is consider to be a fundamental constant. So I am assuming that even though gravitational fields do operate in different types of mediums, this somehow doesn’t affect the gravitational field value. My question is why is this the case, that is, why isn’t there a permittivity-type constant for gravitation?


title: Is mass proportional to the displacement from equilibrium in Hooke's law?

text: If I look at Hooke's law as it's defined in my textbook, it looks like: $F = -k\Delta s$ Therefore, the restoring force of an ideal spring will be proportional to the displacement from equilibrium, where $k$ will be the constant of proportionality. From this equation, I believe that it can't be said that mass is proportional to the displacement from equilibrium (even though it seems to be the case implicitly). However, if I substitute $ma$ for the restoring force: $ma = -k\Delta s$ Is it then valid to say that mass is proportional to the displacement from equilibrium, as well as mass is inversely proportional to acceleration? I've been thinking about proportionality a lot lately and this one sort of threw me for a loop.


title: Gravity doesn't seem to work the way it is supposed to

text: This has been a bit of an awkward question that's been plaguing me ever since I started watching space documentaries on discovery about 10 years ago. I was saving this for the day I would ever meet Professor Brian Cox where I can point and say "HA!" see you can't explain that one (he probably can and so could someone here). It's a simple question: when you get on a merry-go-round or something that rotates fast, then the force pushes you outward, but when they talk about things in space that rotate they refer to the force that pulls them inwards. So which is it. If I spun something like a big beach ball really really fast then I'd still be thrown off it. If I took that into space should that suddenly keep me glued to it? I apologise for my ignorance but I've never had this explained to me.


title: Light-like Interval

text: In SR, the interval $I$ between two spacetime events is called _light-like_ if $I=0$. Griffiths in his _Introduction to Electrodynamics_ book says that [page 503], > _If $I=0$ we call the interval light-like, for this is the relation that > holds when the two events are connected by a signal traveling at the speed > of light._ What does this statement mean?


title: How can they prove the superposition of particle states prior to measurement

text: If every time a particle's spin or momentum is measured, it gives a discrete answer (collapse of possibility states), how can they ever prove that prior to measurement it was in fact in a super-position of states? Is this solely a logical extrapolation from the wave-like interference patterns seen in the slit experiment? Clearly I don't understand something fundamental here.


title: Mode-dependent Andreev reflection

text: Consider the following Hamiltonian which describes massless Dirac fermion on the surface of a topological insulator nanowire, $$H = -i\hbar v_{F}\left[ \partial_{x}\sigma_{x} + \frac{\sigma_{y}}{R}\left( \partial_{\phi} + i\eta\right)\right]\ \text{.}$$ The nanowire has translational symmetry in $x$-direction and $\phi$ is the angle around perimeter. It has eigenenergies which can be written in the form, $$E_{k,n} = \pm \hbar v_{F} \sqrt{k^{2} + \frac{1}{R^2}\left(l_{n} + \eta \right)^2}\ \text{,}$$ where $l_{n} = n-1/2$ is quantized in integers $n$. The wavefunction can be written like this, $$\Psi^{\pm} = \frac{1}{\sqrt{2\pi L}}e^{\pm i k x}e^{i l_{n} \phi}\ \text{.}$$ Now, if You do the same thing but with the Bogoliubov-de Gennes equation You will get electron-like and hole-like solutions where the wavenumber $k$ woould depend on the total energy $\mathcal{E}$, transverse momentum $l_{n}$ and fraction of the magnetic flux quanta $\eta$. I am wondering if the Andreev refelction at the boundary between normal-region and superconductor can take place between different modes $l_{n}$. Is there something which prevents from electron-electron, electron-hole etc. scattering processes between different modes at the N-S boundary?


title: Joint-measure of POVM's

text: I feel disturbed by this question: Suppose $A$ and $B$ are POVM's with respective $\sigma$-algebras $\mathcal{F}_A$ and $\mathcal{F}_B$ and outcome spaces $\Omega_A$ and $\Omega_B$. Then why can't I take the following POVM $Z = A\cdot B$ defined on $\mathcal{F}_A \otimes \mathcal{F}_B$ as the joint measure? I mean it fullfills that $$ Z(U, \Omega_B) = A(U) \cdot B(\Omega_B) = A(U), \quad \forall U \in \mathcal{F}_A $$ and the same for $B$. And I guess you can define it to be $\sigma$-additive, at least in finite dimension of the outcome spaces?


title: How can I calculate the center of an object relative to a focal point and a moving observer?

text: I'm developing an app that contains a 3D scene which the user can navigate. As the user moves it gives the illusion that you are browsing a real landscape but for the illusion to work I need to know two things:   1. How to calculate the angular sizes of all the objects relative to their distances from the observer.   2. How to calculate the center of all the objects relative to the focal point as the user moves. The first one is easy but the second one still baffles me and I have no idea where to look for the answer. Let's examine the second one: As the user navigates towards the focal point, the center of the object moves across the line that is created between the focal point and it's center. Focal Point = $FP(x_0, y_0)$ Center 1 = $C_1(x_1, y_1)$ Center 2 = $C_2(x_2, y_2)$ The equation of the line is: $y-y_0 = m(x-x_0)$ where $m=(y_1-y_0)/(x_1-x_0)$ The center 1 $(x_1,y_1)$ is known because it is the starting center. Let's say the the object moved a distance $d$ from center1 to center 2. (1) $d^2=y^2+x^2$ (2) $y_2=m(x_2-x_0)+y_0$ (1) (2) = ... you can find $y_2$ and $x_2$ if you know $d$. Can you find $d$ from the illustration? Is there any other method? ![Illustration](http://i.stack.imgur.com/3eefl.jpg)


title: Is there any optical component that uniformizes the incoming light?

text: Is there any optical component in existence that uniformizes randomly pointing rays? ![The component \(greenish-yellow\) takes in random light and uniformizes it. Light is traveling from left to right](http://i.stack.imgur.com/IIXrV.jpg)


title: Pendulum water pump - apparent free energy

text: I've seen plans for a pendulum oscillator water pump that is claimed to pump a large volume of water (100 gallons) from a well of 100 feet deep. The pendulum consists of a 100 pound weight raised 6 feet. A second 20 pound weight is hoisted up a pole 20 feet high. This second weight powers a mechanism which gives the pendulum a very slight push on every swing so that it does not lose any momentum on any stroke. The only energy inputs into this system are the act of raising the 20 pound weight 20 feet and raising the 100 pound weight 6 feet. This is supposed to pump 100 gallons (833 pounds of water) up 100 feet. It seems to me that this is impossible, because we have applied a given amount of potential energy into this system: 20lbs x 20feet = 400 foot pounds 100lbs x 6 feet = 600 foot pounds So 1000 foot pounds total So this should be capable (at best) of raising 10 pounds of water (1.2 gallons) up 100 feet. I've been told that I don't understand the engineering principles of oscillation, and I've been assured that the math checks out. However, based on the very limited physics I know (and I admittedly don't know much) - you can't get more work out of a system than you put in. How is it possible to get more energy out of a system than you put into it?


title: Parity invariance of Einstein-Hilbert Lagrangian

text: How can we show that the Einstein-Hilbert action is Parity invariant? $$ S_{EH}=\int \sqrt{-g}R d^4x $$


title: Magnetic field due to electron in Hydrogen?

text: We can calculate the current density $\mathbf{j}$ of the electron in Hydrogen, and it is given by: $$ j_\phi=-e\frac{\hbar m}{\mu r\sin\theta}\left|\psi_{nlm}\left(r,\theta,\phi\right)\right|^2 $$ (derivation found here on page 6) How can I calculate the magnetic field produced by this current density? I could use the Biot-Savart law, $$d\textbf{B} = \frac{\mu_0}{4\pi} \frac{1}{r^2} \int Id\textbf{s}$$ where the integration should be (at least classicaly) the along the current loop, and $I$ = $\int \textbf{J} \cdot d\textbf{S}$. What should I use as $d\textbf{S}$ and $d\textbf{s}$ for an electron in Hydrogen?


title: How to compute drag coefficient given initial position, initial velocity and final resting position?

text: The equations I'm using are:               x = x + (DT * vx)     vx = vx * C      My DT is always 0.01 and the coefficient `C` (related to a linear drag coefficient, as mentioned in the comments) is greater than 0 and less than 1. The above will keep happening until x naturally reaches its limit. What I want is an equation to find C given the other three inputs: initial x, initial velocity x and final resting x(this is where the object has come to a stop and vx = 0). Right now it's tedious because I have to plug in ix, ivx and C and run my simulation to see where the object stops. Then I have to do further tweaking to get exactly what I'm looking for. Here are some samples:               initial x = 3.5     velocity x = -12.0     acceleration = 0.92     final resting x = 2.0          initial x = 3.5     velocity x = -14.0     acceleration = 0.92     final resting x = 1.75 For example(from the first dataset), we start at 3.5 we want to end at 2.0 and our velocity is -12.0 .. what do we need to use for C?


title: Potential energy & entropy of three particles

text: Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question. ![enter image description here](http://i.stack.imgur.com/24umY.jpg) Let's consider that we have three free charges that somehow can change their charge in time. $$ Q_1(t) = \sin(\omega t) \\\ Q_2(t) = \begin{cases}1 & \mod(t,2)=1 \\\ -1 & \mod(t,2)=0\end{cases} \\\ Q_3(t) = 2\cos(2\omega t) $$ where $t$ is the time measured in seconds. We say that all particles have same mass $m$. We also consider gravitational potential energy to be negligible. I am trying to find   1. potential energy in time   2. entropy variation in time I understand that this might not be solvable analytically, but as I said, I am trying to simulate this on a computer. I have the forces over time, but I really _don't_ want to integrate them spatially to find the potential energy, as in my simulations, the particles can count thousands. Could you point me out an easier way, or a simplification that I could try? About the entropy, do you think this has no sense as the system if far away from equilibrium, or for any other reason? If you think this is a valid thing to measure, could you tell me any ideas on how to do it?


title: How do I show the fractional change in Kinetic Energy in a completely inelastic collision?

text: Given the formula $$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$ Now I know these that the conservation of momentum is always applicable. Also I understand that $$KE=\frac{1}{2}mv^2$$ and $$p=mv$$ When trying to solve it I get $$\frac{m_2(v_2)^2}{m_1(v_1)^2}-1$$ Is their anything I am doing wrong? If so, what do I need to do to go about this equation? Also, what is the significance of this the negative value in M? **Disclaimer: I am not looking for the complete answer, I am looking to find out how to solve it so I can be sure to know how to do this in future situations. Please edit this post as you see fit for the sake of the quality of the content in this site to help others understand the same problem as well. I thank you all in advance for your contribution.**


title: Forces involved in strapping something down

text: Say I have a hollow cylinder and I wanted to strap it down to the bed of a truck. I would tension the strap on one end, and it would exert a force on the cylinder. My intuition tells me that the strap would crush the hollow cylinder down toward the truck bed, but when I think about it, there are inward forces perpendicular to the truck bed caused by the straps on the cylinder as well. Is this correct thinking, or are all of the forces only vertical?


title: Why does welding produce UV light?

text: Looking directly at a welder is dangerous because large amounts of UV light is produced. What makes this light? Is it electrons from the current that excites metal atoms, and these atoms sends out UV light? Or does the extreme heat have anything to do with this? Is it dangerous to look directly at a nail being melted (glowing brightly) by hundreds of amperes? Is it dangerous looking at an oxyhydrogen explosion in itself, or could it be dangerous if the explosion touches other substances exerting UV light because of the extreme heat of the explosion?


title: Vertical Circular Motion

text: I know that I can use conservation of energy to find the velocity of a particle at a point when it's travelling in a vertical circle by saying $$mgr(1-\cos{\theta})=\frac{1}{2}mv^2$$ then rearranging to get $v=\sqrt{2gr(1-\cos{\theta})}$ But I want to see this done 'the long way' using newtons second law directly and then probably solving a differential equation, but I'm not sure how to do it and nothing I've tried is getting very far.


title: Relative acceleration with pullys

text: I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks, The Question: > A string with negligible mass passes over a smooth pulley V with a particle > A of mass $18kg$ on one end of the string and a pulley ($J$) of negligible > mass on the the other end > > Another string with negligible mass passes over pulley $J$ and has a > particle $K$ of mass $12kg$ on one end and a particle $L$ of mass $9kg$ on > the other end. > > Show the common acceleration of $A$ and $J$ then show the relative > acceleration of $K$ and $L$ to $J$. So far I have worked out that the tension in the top string is equal to twice the tension in the bottom string. $T-2S=0a$ $$T=2S$$ I then plug this into $18g-T=18a$ to get $18g-2S=18a$ From that equation I get $S=9g-9a$ After that I plug the value of $S$ into the equations for $K$ and $L$ then in the equation for $L$ $g$ is canceled out and I am stuck.


title: Why does the electric field perpendicular to every point on the surface of a conductor?

text: I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism by Edward M. Purcell). I am in chapter $3$ pg $92$, and the book discusses conductors. The following is from the book: Because the surface of a conductor [in Fig $3.2$] is necessarily a surface of constant potential, the electric field, which is $-\nabla \varphi$ , must be perpendicular to the surface at every point on the surface I have omitted the picture because it is not relevant. Can someone please explain this reasoning ? I understand that the potential $\varphi$ is a continuous function, and since $E=0$ inside the conductor and since $E=-\nabla\varphi$ I get that $\varphi=0$ inside and on the surface (from continuity) of the conductor. However, I don't understand the reason the book gives for explaining why the field is perpendicular to every point on the surface


title: Second quantization with qubits

text: Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 qubits? Does this mean that quantum field state cannot be described with quantum computer with fixed number of qubits? Or may be this is wrong and the "power" of qubit is sufficient?


title: Transformations of gamma-matrices through Pauli matrices transformations

text: I have the transformation law of the Lorentz group for Pauli matrices: $$ \tag 0 (\sigma^{\mu})_{a \dot {a}}{'} = \Lambda^{\mu}_{\quad \nu} N_{a}^{\quad c}(\sigma^{\nu})_{c \dot {c}}(N^{-1})^{\dot {c}}_{\quad \dot {a}}, $$ where $$ N_{a}^{\quad c} = 1 + \frac{1}{2}\omega_{\mu \nu}\sigma^{\mu \nu}, \quad N^{\quad \dot {c}}_{\dot {a}} = 1 + \frac{1}{2}\omega_{\mu \nu}\tilde {\sigma}^{\mu \nu}. $$ Also I have the relation $$ \tag 1 \gamma_{\mu} = \begin{pmatrix} 0 & \sigma_{\mu} \\\ \tilde {\sigma}_{\mu} & 0 \end{pmatrix}, \quad (\tilde {\sigma}_{\mu})^{\dot {a} a} = \varepsilon^{ab}\varepsilon^{\dot {a} \dot {b}}(\sigma_{\mu})_{d \dot {b}}. $$ How exactly can I get the transformation law $$ (\gamma_{\mu}){'} = \Lambda_{\mu}^{\quad \nu}\hat {S}\gamma_{\nu}\hat {S}^{-1}, \quad \hat {S} = 1 + \frac{1}{2}\omega_{\mu \nu}H^{\mu \nu}, $$ $$ H_{\mu \nu} = \frac{1}{4}\gamma_{[\mu} \gamma_{\nu ]} $$ from $(0)$? I failed when I tried to write explicitly transformations of Pauli matrices in $(1)$: I can't pick out $\hat {S}^{-1}$, because I entangled in the indices.


title: What exactly do we see on the famous neutrino image of the sun?

text: An answer to the question If we could build a neutrino telescope, what would we see? contains a link to a neutrino image of the sun  by the Super- Kamiokande neutrino detector. ![neutrino image of the sun](http://i.stack.imgur.com/dSed3.jpg) There it says that the image actually covers a large part of the sky of about 90x90 degrees. As the diameter of the sun from earth is around one half of a degree, it must be that many of the neutrinos didn't come straight at us. This seems surprising (to me), as neutrinos should hardly interact with the atmosphere. Maybe the central few pixels of the image are extremely much brighter than the others, but this image doesn't show the difference between those and the surrounding pixels? Or is something else going on?


title: In real laser applications, how big is the complex parameter (i.e. <n>) of the corresponding coherent state of the field?

text: In quantum optics, the output from a laser is modelled using a coherent state; what are some orders-of-magnitude for the complex parameter (usually denoted $\alpha$) of the coherent state corresponding to real laser fields used in experiments?


title: Magnetism, spin and time reversal

text: I am somewhat confused about this topic. It is usually explained how magnetic fields avoid breaking time reversal symmetry by the example of a field produced by a circulating charge current - run time backwards, the current direction is reversed and so is the field. But what about the moment associated with the electron spin? Is the spin of an electron not an intrinsic property? So why (if indeed it does) would running time backwards change the sign of the spin?


title: Why does my car parking proximity sensor alarm go off when a motor cycle goes past?

text: My car has proximity sensors to help me park. I've noticed that when motorcycles whiz past me the proximity alarm goes off. I originally though that the motorcycles were just too close, but now I have observed that that isn't the case; cars or other road uses at a similar distance and speed do not set off the sensors. What's special about the movement of a motorcycle that sets off the alarm?


title: Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

text: Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases only and I could not extend them to infinite dimensional cases. Please give some reference or some outline of approach.


title: Transmission of porous membrane with vertical cylindrical pores

text: There is some porous dielectric membrane with strictly vertical cylindrical pores. I would like to find theoreticaly optical transmission spectra of this membrane, depending on the bulk material optical dispersion, radius and height of cylindrical pores and the distance between their centers. In result I want to find a formula for optical transmission spectra depends on wavelength (to compare with experiments). The material is dielectric, so it's only about complex diffraction and Beer–Lambert–Bouguer law, but I don't know how to start with porous system.


title: Time difference in clocks of an accelerated frame

text: If we have two inertial frames $S$ and $S'$ and $S'$ is moving to the right w.r.t. $S$ with a velocity $v$. Suddenly $S$ undergoes negative acceleration (no longer being inertial) and after some time the acceleration stops when the frame has reversed its velocity. How much will be the time difference between two, previously synchronized, clocks in $S'$ separated by a distance $x$ (as measured by $S$) after the acceleration has been ceased and will it depend on the history of acceleration or just on the initial and final velocity?


title: Mixed conductive and convective heat transfer

text: I want to make a finite element analysis of a cold airflow through warmer pipes. In particular I want to see how the pipes cool down and the air heats up, as it travels through the pipes. Wich are the equations and boundary conditions that I have to consider? I assume that the velocity field is already given, call it $v$. Currently I solve the following equation $$ \rho c_p(\frac{\partial T}{\partial t} + v\cdot \nabla T) - k \Delta T = 0 $$ ($T\ $ temperature, $\rho\ $ density, $c_p\ $ heat capacity at constant pressure, $k\ $ heat conductivity) over the whole domain, where inside the pipes I use the given velocity field and in the pipe material I assume $v = 0$. The constants like $\rho\ $ jump on the boundary. I have an initial condition of the same temperature everywhere and then apply a Dirichlet BC at the pipe inlet of a colder temperature. I know that this describes convective heat transfer and for $v=0$ the equation reduces to conduction heat transfer. But does it describe my problem correctly? I do not have a boundary condition on the pipe/air boundary. Do I need one? Which one? The heatflow inside the metal pipe seems to be very slow, I expected it to be somewhat faster. The thermal diffusivity, i.e. the term $\frac{k}{\rho c_p}$ is of the magnitude $10^{-5}$, I took this value from the literature. However this makes the diffusion part of the equation very slow. Is this correct? Thank you!


title: Optical Simulation Tool

text: I am a student and trying to design an aperture from which a light will pass will project on a sensor. I tried to find some software simulation tool for this purpose where i can draw the aperture (entrance side) and put diffuser or lens and then see the response of the light for some specific wavelength. I found one tool "Synopsys Code V" but it is very paid solution. So can anyone tell me some substitute for this. I am looking for Free simulation tools.


title: Free Optics Simulation Programs

text: I'm having an extremely difficult time finding an optics program that is easy to use and offers accurate physics simulations. I'm not asking for much, I just want to be able to simulate a laser going through a beam splitter and then be able to drag and drop mirrors and angle them to be able to see where the laser beams end up. I want to intersect two laser beams that underwent beam splitting and redirect the beams... Does anyone know of any free software that can do this?


title: Are we crystals?

text: Can we say that we are crystals because just like crystals we are made up of very small unit (cell) making up almost the same shape (our body) everywhere.


title: How to transfer propane from a SMALL cylinder to a SMALL metal cylinder

text: I made a metal cylinder that is the **SAME** size as my 400g propane cylinder (picture: here). I want to transfer **ALL** (or almost all) of the propane from the propane cylinder to my metal cylinder, preferably without using an air compressor or something like that. The reason why I'm doing this is because I'm building a rocket and I can't get the propane to flow out of the propane cylinder fast enough.


title: What makes us think we can actually detect gravitational waves?

text: This refers to the discussion about gravitational waves for the YouTube video _LIGO Gravitational Wave Observatory_. I have two questions:   1. When the gravitational wave passes through the space where the light is traveling, the light beam will itself be distorted as per the distortion of space (because the gravitational wave distorts _everything_ in its path) and the slight change they expect to detect should be nullified. For instance, suppose the wave shrinks one of the pipes by half and increases the other by double, the waves inside would be distorted similarly, resulting in no overall change in the interference. Am I missing something here?   2. It takes a huge amount of energy to distort something (for example, a block of iron). If the gravitational wave distorts _everything_ it passes through (such as the Earth, the Sun and space itself), it will lose its energy at a very high rate in trying to do this distortion (much more than what the inverse square law implies) when it passes through solid objects. The current understanding is that gravitational waves do not get effected by anything and pass through a solid as if was vacuum. How is this possible?


title: Thin Lens Methods and Object Perceived vs Literal Size

text: When using the ray trace methodology to solve a given thin lens question, does the arrow (commonly used as the example object when tracing) represent the literal height of the object or the perceived height of the object relative to the lens? Refresher image below: ![a generic ray trace](http://boson.physics.sc.edu/~rjones/phys153/raytracelens.GIF) Same for the equation methods. When using below equation for magnification, derived from the thin lens equation, does $h_0$ represent the the literal height of the object or the perceived height of the object relative to the lens? $$ \frac{i}{o}=\frac{h_i}{h_o} $$ Note: in the event that these aren't the standard notations, $i$ is the image's distance away from the lens, $o$ is the object's distance away from the lens, $h_i$ is the height of the image, and $h_o$ is the perceived or literal height of the object.


title: Prerequisites for Halliday Resnick Walker

text: I am in grade 10. I have developed an interest in physics but unfortunately I do not know/ have not studied calculus yet as my school board does not recommend it in grade 10. I have a copy of fundamentals of physics, Halliday Resnick Walker, I read chapter's one and two briefly and I understood the conceptual part. But when it came to derivation's of the equation's I couldnt understand it. Please, can you recommend any book/video lecture to solve this problem. Thanks


title: Which direction does a galaxy move in respect to its axis of rotation (Black Hole)

text: As Galaxies travel through the universe, how do they orient? And, does this orientation apply to stars and their satellites? that is to ask if the movement of a galaxy or star is perpendicular to its satellites and its rotation.. One might even compare this proposed action to that of a tornado in that the planets or stars would 'follow' in the 'wake' of the star or blackhole like debris.


title: Special relativity and imaginary coefficient of the time coordinate

text: I read somewhere that part of Minkowski's inspiration for his formulation of Minkowski space was Poincare's observation that time could be understood as a fourth spatial dimension with an imaginary coefficient. Clearly, taking the Euclidean norm of the vector $$(i \Delta t, \Delta x, \Delta y, \Delta z)$$ gives the correct spacetime interval (assuming appropriate units), but I don't really know where it goes from there (possibly something to do with Moebius transforms?) I think this is mentioned in Taylor and Wheeler's book, but I may have read it elsewhere. After the historical note, the author (whoever it was) said it was "preferable" to use Minkowski geometry straight off, rather than mucking about with time as an imaginary space coordinate. Could anyone elaborate on Poincare's formulation? Why is Minkowski's methodology better?


title: What makes nuclear binding energy so much stronger than chemical energy

text: The strong force acting between quarks and responsible for holding protons together is 100 times stronger than the electromagnetic force. How come the nuclear binding energy derived from the strong force is millions time stronger than chemical energy. (rather than 100 times)


title: geometric quantization of the moduli space of abelian Chern-Simons theory

text: I wish to understand the statement in this paper more precisely: > (1). Any 3d Topological quantum ﬁeld theories(TQFT) associates an inner- > product vector space $H_{\Sigma}$ to a Riemann surface $\Sigma$. - > (2) In the case of abelian Chern-Simons theory $H_{\Sigma}$ is obtained by > geometric quantization of the moduli space of ﬂat $T_{\Lambda}$-connections > on ${\Sigma}$. The latter space is a torus with a symplectic form $$ ω =\frac{1}{4π} \int_{\Sigma} K_{IJ} \delta A_I \wedge d \delta A_J.$$ > (3) Its quantization is the space of holomorphic sections of a line bundle > $L$ whose curvature is $\omega$. For a genus g Riemann surface $\Sigma_g$, > it has dimension $|\det(K)|^g$. - > (4) The mapping class group of $\Sigma$ (i.e. the quotient of the group of > diffeomorphisms of $\Sigma$ by its identity component) acts projectively on > $H_{\Sigma}$. The action of the mapping class group of $\Sigma_g$ on > $H_\Sigma$ factors through the group $Sp(2g, \mathbb{Z})$. We are talking about this abelian Chern-Simons theory: $$S_{CS}=\frac{1}{4π} \int_{\Sigma} K_{IJ} A_I \wedge d A_J.$$ > Can some experts walk through this (1) (2) (3) (4) step-by-step for focusing > on this abelian Chern-Simons theory? partial answer of (1)~(4) is fine. I can understand the statements, but I cannot feel comfortable to **derive them myself**.


title: Why doesn't time change in the non-relativistic limit of Lorentz transformations?

text: A simple boost in the $x$ direction is given by: $$ \Lambda = \begin{pmatrix} \cosh(\rho) & \sinh(\rho) & 0 & 0 \\\ \sinh(\rho) & \cosh(\rho) & 0 & 0 \\\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1 \\\ \end{pmatrix} $$ Which get linearized to the following transformation: $$ x^0 \mapsto x^0 , \quad x^1 \mapsto x^1 + \frac vc x^0 $$ How come the zeroth component is not linearized to $x^0 \mapsto x^0 + \frac vc x^1$? Is that because there is another factor $c$ in the time components? Since $x^0 = ct$, that would mean the time is transformed like $$ t \mapsto t + \frac v{c^2} x,$$ and $c^{-2}$ is just so small that is ignored? Or is it just to fit the Galilei transformation?


title: Double slit experiment  and perforated walls' properties

text: I have a doubt about how double slit experiment is made. Let's think about the perforated wall, what are the requirement for it? Can a photographic plate could be used as a wall ? I see a problem here, as a photographic plate serve also as a detector, then the single photon experiment could end up with a single point in _the wall that contains the slits_ and not in the plate located _behind the slit's wall._ Of course the "one photon count", is knowing the emition before the slits (if this count were made after, it will be a detector making a measurement and would simply reflect the particle effect) The wall with the slits could absorb the photon(removing electrons from the material) before something happen on the other side, if that happened, there would be no experiment, the photon won't pass through the slits, just because its energy was already used (supposing all energy is used and the photon doesn't split). There must be some kind of specification about the material of the wall, need to be special, in the sense of needing a higher energy (than the test photon) to pickup electrons, then the light won't stop there, for that, I think the wall can't be made of a photosensible material, but I don't know, and here I am asking.. thanks for any answer


title: Estimating age of the universe by Hubble's law?

text: Hubble's law states that $v=Hx$ Age of the universe is calculated by $T= \frac{x}{v} = \frac{1}{H}$ but the velocity is not constant; it changes with distance, so I think that this equation cannot be applied because simply the velocity is NOT uniform $v$ should have been replaced with $\frac{\mathrm{d}x}{\mathrm{d}t}$, so it gives this differential equation $\frac{\mathrm{d}x}{\mathrm{d}t}=Hx$. Nevertheless, when this differential equation is solved, and we substitute for initial condition ($x=0$ when $t=0$), it appears that there are no solutions, because it will be an exponential function, which can't take the value $0$ ever. What is wrong with my understanding?