How to accurately explain evaporative cooling?

I am trying to clearly express in one or two sentences how increased evapotranspiration could cool a region. The audience is educated but non- scientific. Is it accurate to say that the water vapor has removed latent heat? Is there a more clear explanation?


What is the pure energy in matter antimatter annihilation made of?

I used to read the term "pure energy" in the context of matter antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass ? Basically, what does "pure energy" in the context of matter-antimatter annihilation refer to?


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

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)


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

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?


Is there an equivalent to wetness for air?

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?


Recommendations for good Newtonian mechanics and kinematics books

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


Any recommendations for self-studying physics?

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!!


Reference request: Classical Mechanics as an Application to Smooth Manifolds

> **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?


Suggested reading for classical field theory

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.


Prerequisites for QFT?

> **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.


Book suggestion for Theoretical Physics with easy maths

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?


Good math books for physicists

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)?


Reference request for motion & related topics

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)


What kind of physics topics exist?

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.


Suggest me specific book for studying scattering theory and special functions

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.


A crash course in quantum mechanics

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)


General physics landau

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. ?


Studying QM without math and physics background

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.


Best physics olympiad resources

> **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.


Book recommendation

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)?


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

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%.


Classical Mechanics for Mathematician

> **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?


Math required for learning Lagrangian mechanics

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


Studying physics at undergraduate level: Prerequisites

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. )


Introduction to quantum mechanics

> **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.


Physics book for 15 year old boy

> **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?**


Good explanation of phase transitions, second law of thermodynamics

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.


Beginner Physics Resources?

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.


Link for resource on cosmology

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.


Can someone recommend good resources to self study physics please?

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.


Getting started general relativity

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


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

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?


Introduction to relativity books for an engineer

> **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!


Good First year physics lecture notes

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?


Physics textbooks reference request

> **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.


Exam on Physics for Graduate

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.


What is a good introductory book on quantum mechanics?

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?


Quantum Mechanics Text for Electrical Engineers

> **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?


Beginning Physics, Advise on Books

> **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??


Best books for high-school?

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.


Undergraduate Math Major Wanting to Learn Physics

> **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?


Physics books for mechanics

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?


Physics books covering classic mechanics

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 ?


Book recommendations

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?


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

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'.


Quantum harmonic oscilator - book that does it all right

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**.


Would love to learn quantum physics

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.


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

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?


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

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!


Learning about group velocity, phase velocity and particle velocity

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.


Book suggestion : geometric approach to electromagnetism

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.


Book for learning about constructing correct physical modeling

> **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.


Green theory and Laplace theory

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


Informal book on Classical Mechanics

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.


How can I answer the critical questions of mechanics?

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.


Books for a fresh physics undergraduate

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?


Reference books for classical mechanics with good number of solved examples

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


Material to read before taking College Physics 1?

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.


Where to read about Minkowski space

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.


Math and Theoretical Physics Topics & Textbook for Self-Study

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.


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

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.


Quantum Physics Books

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


Helping/explanatory notes for Landau&Lifschitz Physics Course

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.


A Mathematician Who Wants to Learn Particle Physics

> **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?


help me.. please

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


What is a good mechanics book without calculus

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.


Orbital motion (Mechanics)

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.


best fundamental physics book

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.


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

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?


Books to independently study physics

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.


Recommended book for beginners on advanced science topics

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!


Self-teaching physics recommendations?

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!


Books to study quantum thermodynamics and quantum decoherence

> **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?)


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

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.


Where to begin with Physics beyond high school?

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?


Electric potential energy in curved space-time

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?


Magnetic field inside a charged stream

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.


Are We Living in a Simulated Universe?

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?


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

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?


Applications of Algebraic Topology to physics

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.


Determination of auxiliary scale in dimensional regularization

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.


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

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.


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

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.


Mode-dependent Andreev reflection

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?


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

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?


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

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


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

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?


Optical Simulation Tool

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.


Free Optics Simulation Programs

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?


Are we crystals?

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.


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

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.


Thin Lens Methods and Object Perceived vs Literal Size

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.


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

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.


Special relativity and imaginary coefficient of the time coordinate

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?


Double slit experiment  and perforated walls' properties

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


Gravitational waves detection, any news?

Is the detection of gravitational waves a reality with nowadays technology? Are there recent news?


What cause scientists to study Black Body Radiation?

After spending hours understanding what exactly Black Body radiation and Ultraviolet catastrophe is, I cannot help myself asking what was the reason that make scientists such as Wilhelm Wien and Max Planck to study Black Body Radiation at the first place? What intrigue them to study a hypothetical situation? What they were looking for exactly that make them in studying this phenomenon.


MHD Flow in a channel with and external B field and circuitry determining E. Different circuits and Ohm's law

I was wondering if someone can explain why E is the way it is in cases 2,3,4 in page 9 of these notes ? In case 2 "Short Circuit", do I just have to assume that for a perfect conductor E = 0 for short circuit ? I don't really get why current density is negative in this case (or the 3rd case for that matter) and what it means physically, for current density to be negative... Any extra comments on what is going on in there would also be appreciated.


How do I calculate the work of a gas showed up on a graph?

I have this graph of a gas: ![gas graph](http://i.stack.imgur.com/DMQlN.jpg) Now, I need to calculate work of it, based on ABCD cycle of changes (that's a bit confusing to me, do I calculate AB, BC, CD separately?). How do I do it? Also, how can I calculate heat of this gas needed to exchange with enviroment, in order to maintain it's internal energy?


Can all theories of theoretical physics be generalized to any (arbitrary) number of dimensions?

Please explain from: mathematical point of view "laws of mathematics", and, physical point of view "laws of physics"? Or is there any bound on number of dimensions?


How to get the pressure?

A system of solar panels are fixed on top of a large water tank of height $40m$ and area $10m^2$. Atmospheric pressure is $100kPa$. What is the pressure at the bottom of the tank? The density of water is $\rho =1000kg/m^3$ and $g=10m/s^2$.               a 10kPa     b 1000kPa     c 2000kPa     d 200kPa     e 1kPa      My doubt: why is the answer not $100kPa+\rho gh$? explanation of concept will be appreciated. What I did was simply atmospheric pa +pressure due to water. The confusion lies in the fact that will we only consider the pressure due to water as the solar panel roof will balance the atmospheric pressure?


$a^3B_2$, $b^3A_2$ and $A^1A_2$ states in electron spectroscopy

I am new to electron spectroscopy. I have a basic question regarding the molecular transition. I have learned about the states $\Sigma_g^+$ $\Pi_g$.. etc electronic states. But I could never find in any books the states like $a^3B_2$, $b^3A_2$ and $A^1A_2$ states! For example, I am attaching a part from from the page 770 of the article (Analyst, 2003,128,765-772). Can anyone please explain me what are these states mean? Or any books/reference suggestions to learn will also be good. ![enter image description here](http://i.stack.imgur.com/s4u2M.jpg)


Could there be a star orbiting around a planet?

I wonder if there ever could be a star (really small) which may orbit around a planet (really big)?


Rocky Planet in the center of System

We all know that mostly stars are at the center of planetary systems, but is it possible that instead of star there was a rocky planet in the center with stars (and other planets and moons) orbiting it? To be more concrete: Is it possible for a star to have the same mass and radius as e.g. the Moon and orbit a planet like Earth at the same distance (at which Moon orbits Earth in actuality)? To further distinguish this from similar questions, I want to further ask whether the star will still be able to shine and fuse hydrogen if its mass and radius would be same as the mass and radius of the Moon. Or is there a lower limit to the size or a star that can shine and fuse hydrogen?


Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a certain period of time $[0,T]$. Then would someone please explain me how can we find a rotation matrix using Cayley-Klein parameter so that, for $t\in [0,T]$, we can express $\mathbf{m}(t)=R(t) \mathbf{m}_0$? Here $R(t)$ is a rotation matrix and $\mathbf{m}_0$ is the initial vector. I know that, in $[0,T]$, it can be solved analytically as $\mathbf{m}(t)=exp(At) \mathbf{m}_0$. Moreover would anyone please explain the relation between this two solution?


Is time travel possible? Is it possible to go back in time?

I read somewhere that according to relativity, black holes and other space related stuff it is possible to jump into past.   Is it possible for anything to go back in time either continuously or by jumping? I doesn't fit my mind and seems totally illogical, unreasonable and even stupid thought because if it was possible, we must had someone who came from future. **UPDATE:** Time Travel Impossible, Say Scientists


Is time travel possible?

Time travel -- often featured in movies, books, or facetiously in conversation. There are also theories treating time as simply another dimension, which to the layperson might imply forward and backward movement is possible at will. But what do we know scientifically with respect to the _possibility_ or _impossibility_ of controlled time travel? **Are there any testable theories on the horizon that may support or eliminate controlled time travel as a possibility?** By "controlled time travel" I mean the ability to willingly transport a complex object or being through time (perhaps only to the past, or a copy of the past, which would be an answer too).


Can we develop in the future a technology that can send a message to the past?

> **Possible Duplicate:**   >  Is it possible to go back in time? I believe that everything is possible in this world. If that can be done then why aren't we receiving any message from the future.


Possibility of Time Travel?

Is time travel still considered as a possibility? What does the newer theories like string theory, M theory, etc. say about it.


Does Stephen Hawking not believe in Negative movement?

> **Possible Duplicate:**   >  Is it possible to go back in time?   >  Is time travel possible? According to Stephen Hawking, time travel to the future is not only possible but proven, however time travel to the past is impossible, however this doesn't make sense. It seems to me that an extension to Newtons laws of motion could be that there is something opposite of motion which exists in the universe. The concept is that the universe (or a universe) is ending, and sort of crunches itself up, this would result in negative motion, which in theory would result in backwards time as well. He believes it's not possible because of the crazy scientist theory, where a scientist uses his vortex to kill himself in the past, so who shot him? Well the answer to this is very simple, the scientist would require a dieing universe to perform the time travel, and he himself would have to be in it for him to travel through time, therefore, he wouldn't survive, as he would perish inside of the dieing universe, and never get the chance to shoot himself. Also, he had a party, where future scientists were invited. He wrote up a invitation which would be preserved through time for his future guests. However, his experiment isn't all that swift, because, a number of things can go wrong with his invitation over time, which would mean his "party people" would never arrive, because they never received the invitation. It's kind of like those that say the infinite universe is impossible, because someone in this infinite universe would have blown it up, it just simply does not preclude the existence of the infinite universe, but that's another topic.


Now, physicists are trying to send information backward in time. But, why are physicists almost sure that this would happen and why are they so confident about it? Did physicists solve the grandfather paradox? In that case it would mean that result would occur before the cause. That is very weird. Of course the universe is very weird(and hence very interesting) but is that the case? Can information be sent backward in time?


Time travel to future

> **Possible Duplicate:**   >  Is time travel possible? Is time travel possible? According to my friend, it is possible to go to the future but not the past. In Physics, particles move faster than the speed of light,$c$. However, consider a train moving close to the speed of light along the Earth's equator, and a particle moves in that train in the opposite direction of the train's motion. Thus, the speed of the particle with respect to Earth now becomes the products of the two velocities. Since the particle cannot travel faster than light, what happens? Is it theoretically possible to time travel into the future using this concept?


Time travel, is it possible?

I see there are many questions with this title, but this one is different, so please give it due thought: Is time travel possible? If so, Can we go both forwards and backwards in time? Paradox: I am studying for a very competitive exam, wherein I must put in a LOT of effort to hope for any success. Now, I am lazy. And assume that time travel is possible, and I have access to it. I decide to check my future, and (god-permitting) I see that I have passed with flying colors. Now, I "come back in time" and enjoy life, and don't study. So, it is just Impossible that I succeed. So, where is the flaw?? Does this prove that time travel must not exist, and will not exist?


Why do bigger tires = more friction?

> **Possible Duplicate:**   >  Why do people recommend wider tyres in car for better road grip? Static/kinetic friction says that the friction force is proportional to the normal force, via the coefficient of static/kinetic friction. Great. Imagine that you have a sports car. You'd like to improve your lap times at a nearby race track. So, you buy larger (width) tires. Bigger contact patch, so your car sticks to the road better. But wait, the normal force on the car didn't increase, and the coefficients of friction of the tires didn't change. Just the contact patch. What explains the increase in grip from larger tires?


How to calculate the horizontal acceleration?

I am trying to measure the acceleration and deceleration of a car by using an 3 axis accelerometer which is build in an iPhone 5s. Placing the iPhone flat inside the car with the y axis to the top of the car this works pretty ok. But now I want to be able to place the iPhone basically arbitrary inside the car. (like in the picture below) ![iPhone inside a car](http://forums.everythingicafe.com/data/MetaMirrorCache/farm3.static.flickr.com_2355_2206921565_5fd67cf1b6.jpg_a4f0a23c50a330cf1bf56cae6c33a893.jpg) Is there a way to calculate only the horizontal acceleration of the device in such a placement? (I am aware that you won't be able to differ a directional acceleration but that's sufficent for my project. If I am wrong, I would be glad to know if it would work) To do the calculations the following data is available   * User Acceleration (uX,uY,uZ) - only the acceleration the user imparts to the device   * the total acceleration of the device (tX,tY,tZ) - user acceleration plus gravity   * Gyro Data (gX,gY,gZ) - the device’s rate of rotation around it's axes   * the attitude of the device (quaternion, rotation matrix, (pitch,roll,yaw)) Many thanks in advance!


Macroscopic Bose condensate in Special Relativity

I remember from an experiment about the Josephson effect the state of each of the super conductors is fully described by a phase factor. From there I assume that is true for any Bose-Einstein condensate. So... Let there be a huge blob of Bose condensate in vacuum. In its reference frame, you can describe the wave function as a complex phase number, which is the same over the whole condensate. It will change over time, but at all times, it is the same everywhere. Enters Special Relativity: there is no simultaneousness. If someone in one reference frame "sees" the condensate in one phase constant over the whole condensate, but changing with time, another observer with relative velocity will "see" a phase gradient. Does that mean, that to the moving observer it does not seem like a Bose- Einstein condensate? Or does it just seem to be an excited version of it? I am confused.


What's the difference between photoelastic constant, photoelastic coefficient and the acousto-optic coefficient

I'm reading a few papers about how the optical properties of materials change when a under stress or a force acts upon them. I seem to be encountering the following three terms:   1. Photoelastic constant    2. Photoelastic coefficient    3. Acousto-optic coefficient Is there a difference between these three terms, as they seem to be used in context of describing very similar phenomena? Also, does Acousto-optic constant exist?


What causes a Phase-Transition

A phase transition occurs when for example, heat is applied continuously to a liquid and after a certain time it converts into a gas. How does this process work in detail? Is their a chain reaction that causes to liquid to reach a 'critical' point? Does the liquid syncronises in some specific vector, facilitating the phase transition? Finally could it be that the liquid theromodynamically self organisises into a state that causes the transition? To paraphrase, what exactly is a 'phase-transition' what occurs before, during and after one? Any additional comments you think would help explain this phenomenom to me would be great.


Does Newton's law and Quantum mechanics also apply for the matter which is not dead?

The following quote is extracted from the book "The Field-The quest for the secret force": > ...There was other, quite practical, unfinished business with quantum > theory. Bohr and his colleagues only got so far in their experiments and > understanding. The experiments they’d conducted demonstrating these quantum > effects had occurred in the laboratory, with non-living subatomic particles. > _From there, scientists in their wake naturally assumed that this strange > quantum world only existed in the world of dead matter. Anything alive still > operated according to the laws of Newton and Descartes, a view that has > informed all of modern medicine and biology._ Even biochemistry depends upon > Newtonian force and collision to work. Are the above statements correct? I always get stuck here, according to Newton's laws of motion, everybody continues in the state of motion or rest (w.r.t to an inertial frame), unless and until a force is applied on it. But, a rat, a dog, a girl!, always pass before me and fluctuate to rest and motion, rest and motion. Are they acted upon by any force to set them in motion or to get them into rest? If muscles help them move (Pratyay gosh has noticed this significant point), which force make the muscles move. According to Newton's law, they must be acted upon by a force, right? So, does Newton's laws of motion also apply for the matter which is not dead? Is Quantum mechanics applicable only for dead matter?


Light has a wave particle duality, how do we know?

I've been told my whole life that light is either a wave or a particle. When it's traveling through space, it's a wave. When it hits a wall, or a photo- sensitive chemical strip or something similar, it's a particle. However, upon looking back all of the examples I've seen I can only recall instances in which we observe light as a particle. Are there in fact ways we can measure it as a wave?


The n-point Green functions and Heisenberg picture

Let's have the S-matrix: $$ S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle . $$ Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = \hat{T}e^{-i\int \hat{L}_{\int}d^{4}x}$, $\hat{L}_{\int}$ refers to the operator in the interaction picture. When we decide to get the matrix element of some process we will get $$ \int d^{4}x_{1}...d^{4}x_{n}\langle \beta |\hat{T}(\hat{\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{m_{int}}(x_{n})) | \alpha \rangle . $$ So it's convenient to introduce n-point Green function, $$ \tag 1 G_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}(\hat {\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{n_{int}}(x_{n}))| 0\rangle $$ and generation functionals for it. But recently I have read anywhere that as n-point Green function people use expression $$ \tag 2 G^{H}_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}(\hat {\varphi}_{1}(x_{1})...\hat{\varphi}_{n}(x_{n}))| 0\rangle , $$ where the operators of fields are in the Heisenberg picture. So they need to rewrite the operators into interaction picture: $$ \tag 3 G^{H}_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}\left( \hat {\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{n_{int}}(x_{n})\hat{S}\right)|0\rangle . $$ I don't understand why we need the Green function $(2)$ where the fields operators are in the Heisenberg picture if $S$-matrix "generates" rather Green functions with operators in interaction picture. Can you explain it why we don't use $(1)$ when talk about the Green functions?


How would I go about detecting monopoles?

A question needed for a "solid" sci-fi author: How to detect a strong magnetic monopole? (yes, I know no such thing is to be found on Earth). Think of basic construction details, principles of operation and necessary components of a device capable of detecting/recognizing a macroscopic object emitting magnetic field of equivalent of order ~0.1-10 Tesla near its surface, but with only one pole, reliably distinguishing it from normal (2-pole) magnets, preferably at a distance. Preferably a robust method, not involving extremely advanced technology. Detect the presence, possibly distance (or field strength) and direction. I know of SQUIDs, but these concentrate on extreme sensitivity. I'm thinking of something less sensitive but more robust (like, no need for the monopole to fall through the loop) and still able to recognize a monopole against a magnet. Also, how would such a macroscopic object behave practically? Such a "one-pole magnet" about the size and strength of a refrigerator magnets - how would it behave around ferromagnetics, normal magnets and so on?


Coset space and transitiviy

I have a question regarding coset space or homogeneous space $SO(n+1)/SO(n)$ which is simply $S^n$. I need some intuition regarding this result. As everyone knows that for a simple case of $SO(3)/SO(2)$, one can have $SO(3)$ as a group acting on $\mathbb{R}^3$ and $SO(2)$ as an isotropy group of $x\in\mathbb{R}^3$, then the group $SO(3)$ acts transitively on $S^2$ and we get $S^2$ as the coset. Since the result is just 2-sphere or $n$-sphere, is there an intuitive way of seeing it?


What is the electric field in a parallel plate capacitor?

When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two in the denominator comes from the fact that there is a surface charge density on both sides of the (very thin) plates. This result can be obtained easily for each plate. Therefore when we put them together the net field between the plates is $${\bf E}=\frac{\sigma}{\epsilon_0}\hat{n}$$ and zero everywhere else. Here, $\sigma$ is the surface charge density on a single side of the plate, or $Q/2A$, since half the charge will be on each side. But in a real capacitor the plates are conducting, and the surface charge density will change on each plate when the _other_ plate is brought closer to it. That is, in the limit that the two plates get brought closer together, _all_ of the charge of each plate must be on a single side. If we let $d$ denote the distance between the plates, then we must have $$\lim_{d \rightarrow 0}{\bf E}=\frac{2\sigma}{\epsilon_0}\hat{n}$$ which disagrees with the above equation. Where is the mistake in this reasoning? Or more likely, do our textbook authors commonly assume that we are in this limit, and that this is why the conductor behaves like a perfectly thin charged sheet?


Is it possible to control a treadmill's tread speed such that a plane on the treadmill will be prevented from moving?

I've posed the question in this particular way to avoid the ambiguity usually found in the posing of the "airplane on a treadmill" puzzle, e.g. I'm not specifying how the treadmill is controlled but asking _if_ it can be controlled in such a way that the thrust of the plane's engine is countered with an equal and opposite force. Assume the wheel bearings are frictionless and the wheels rotate freely. Please justify your answer. [EDIT] Idealize the problem such that we can ignore rolling resistance.


Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at closest approach, but an arbitrary distance away from the center of the moon?" The equation (eq.11) would be exactly the same! What does that mean? Since obviously the distance from the space junk to the moon changes continuously, yet the form of the equation remains the same. Using conservation of energy: $$\frac{1}{2}mv_i^2-\frac{GMm}{R}=\frac{1}{2}mv_f^2-\frac{GMm}{r}$$ And conservation of angular momentum: $$mRv_i=mrv_f$$ For any $v_f$ and $r$. Now look. We have two equations and two unknowns, $v_f$ and $r$. This suggests that there is a unique solution for both. If we solve for one and plug that into the other equation, we'll get a unique result (or perhaps end up with a quadratic equation, which doesn't fix the problem). How do we reconcile this?


Does quantum entanglement imply the existence of a non-causal structure connecting space-time together?

In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together as well. A more general question; is there even any relevance to the _discussion_ of the existence of a non-causal structure connecting space-time together? The reason I ask is because it initially seems too assuming to suggest that causal structure is the only meaningful structure just because it's intuitive; Consider the fact that two space-like separated events are even allowed to exist in a definable space (space-time diagram). Is there nothing physical _in principle_ between the two events which can be defined?


Why more than one Higgs?

Since by introducing _one_ Higgs Boson we can give a mass to the leptons and gauge bosons of the weak interaction: Why should we consider more than one Higgs (doublet) once we go beyond the standard model?


Why does the moon sometimes appear giant and a orange red color near the horizon?

I've read various ideas about why the moon looks larger on the horizon. The most reasonable one in my opinion is that it is due to how our brain calculates (perceives) distance, with objects high above the horizon being generally further away than objects closer to the horizon. But every once in a while, the moon looks absolutely huge and has a orange red color to it. Booth the size and color diminish as it moves further above the horizon. This does not seem to fit in with the regular perceived size changes that I already mentioned. So what is the name of this giant orange red effect and what causes it?


Why does the moon appear bigger  close to the horizon,  rising or setting?

> **Possible Duplicate:**   >  Why does the moon sometimes appear giant and a orange red color near the > horizon? I made a little research about this and found this article http://en.wikipedia.org/wiki/Moon_illusion that states the explanation of the moon being bigger at the horizon is still debated. I found this which looks pretty 'big' http://www.psychohistorian.org/img/astronomy/deep- sky/photos/ayiomamitis/20090804-moonrise.jpg but however this kind of repetitive shots http://apod.nasa.gov/apod/image/0706/UludagMoonrise_tezel.jpg show no decrease in the aparent moon radius. What I am trying to understand is if it is a real illusion, if the atmosphere makes the image bigger or what other explanation could be possible and of course plausible.


Does dark matter get drawn into black holes?

Would dark matter get drawn into a black hole? Also, could enough dark matter be concentrated to create a "dark black hole"?


I need help understanding a step in the derivation of the Schwarzschild solution

I am looking at Wikipedia's article on deriving the Schwarzschild solution. In the section "Simplifying the components", it says, > On the hypersurfaces of constant $t$ and constant $r$, it is required that > the metric be that of a 2-sphere: > > $$dl^2=r^2(d\theta^2+\sin^2\theta d\phi^2)$$ My question is why does the metric have to be this particular 2-sphere with a coefficient of $r^2$? We are not necessarily dealing with Euclidean space here.


strange modulation of radiactive decay rates with solar activity

Recently i found out this uber strange article about nuclear decay rates being somehow showing seasonal variations with a high correlation with sun activity. Two very precise questions: 1) **has this been experimentally confirmed/disproved?** an experiment using neutrinos from a fission reactor would be awesome, although probably a couple orders of magnitude below the required luminosity (at least to be comparable with solar sources) 2) **could the standard model possibly allow neutrinos to modulate decay rates in this way? or do we need new physics?** link to the public version of the paper **EDIT** brief explanation why i tag this question as `cavity-qed`; because _it is the only other known mechanism we are aware that you can use to shift decay rates of energy levels_ , it might be interesting to see if there are deeper relationships between both mechanisms involved **EDIT 27/01/2013** Another paper about this, but now the SuperKamiokande data is compared with data from Brookhaven: http://arxiv.org/abs/1301.3754 They also propose a model of the effect called neutrino "resonant spin-flavor precesion", and i'll be damned if i knew what that is.


What is 656 Beagle?

What kind of object is 656 Beagle (1908BU)? I know it's a minor planet, but that includes a large array of different stuff. Specifically, I am looking at the general chemistry/geology of the object.


Some questions about chapter I.1 (by Minahan) of the "Review of AdS/CFT Integrability"

These questions are in reference to this beautiful review article by Minahan - http://arxiv.org/pdf/1012.3983v2 I gained a lot by reading some of its sections but not everything is clear to me. I would like to ask a few questions to clarify some of the things in it.   * On page 5 between equation 3.7 and 3.8 it says that the R-charge representation of the $S$ are "reversed" compared to that of the $Q$. What does it exactly mean ?    * There it does not explicitly specify the commutation relationship between $M_{\mu \nu}$ and $S^a_\alpha$ and $\bar{S}_{\dot{\alpha}a}$. Should I assume that its similar to that with $Q_{\alpha a}$ and $\bar{Q}^a_\dot{\alpha}$ ? Like if I may think -  $[M^{\mu \nu},S^a_\alpha] = i \gamma ^{\mu \nu}_{\alpha \beta} \epsilon ^{\beta \gamma} S^a_{\gamma }$ $[M^{\mu \nu},\bar{S}_{\dot{\alpha} a} ] = i \gamma ^{\mu \nu}_{\dot{\alpha} \dot{\beta}} \epsilon ^{\dot{\beta} \dot{\gamma}} \bar{S}_{\dot{\gamma} a}$ ?   * Comparing equation 3.12 to 3.9 I see some possible discrepancies. Is there a factor of $\frac{1}{2}$ missing with the term containing $D$ on the RHS of equation 3.12 ? In the same RHS of equation 3.12 in the $M_{\mu \nu}$ term why has the $\gamma ^{\mu \nu}$ of equation 3.9 become $\sigma ^{\mu \nu}$ ?    * In the statement just below equation 3.14 it says "Hence a primary operator with R-charges $(J_1,0,0)$ is annihilated by $Q_{\alpha 1}$ and $Q_{\alpha 2}$ if $\Delta = J_1$"...Is this a consistency statement?  From this how does it follow that thesame operator is also annihilated by $\bar{Q}^3_{\dot{\alpha}}$ and $\bar{Q}^4_{\dot{\alpha}}$ In the same strain can one also say that $\Delta = -J_1$ is consistent with the primary operator being annihilated by $Q^3_\alpha$ and $Q^4 _ \alpha$ ?   * I guess the above conclusions follow from taking different values of $a$ and $b$ in the equation 3.13. But one would get an extra factor of $\frac{1}{2}$ on the RHS of 3.13 if one puts in the factor of $\frac{1}{2}$ with the term containing $D$ on the RHS of equation 3.12 (..as I think it should be ..)   * On page 8 one creates bispinors $F_{+\alpha \beta}$ and $F_{-\dot{\alpha} \dot{\beta}}$ out of $F_{\mu \nu}$. I would like to know what is the intuition/motivation/reason for doing this ? Is the bispinor version of $F$ still have the meaning of a field strength ? If so then how does it relate to the bispinor version (?) $D_{\alpha \dot{\beta}}$ of the covariant derivative ? I think I have already put in too many questions for one question. May be I will ask some more about this review in a separate question.


how does human brain compare to a modern CPU in energy per bit?

Can someone compare the energy efficiency of human brain as a computer ? What is the energy in joules / flop ? may be some reasonable assumptions on the computational load of common tasks such as pattern recognition or speech synthesis can be used.


How does the voltage between two charged sheets change if change their distance

Suppose I have two charged capacitor plates that both are isolated and carry a charge density $D = \frac QA$. According to textbook physics the electric field between them is given by $E=\frac D {\epsilon\epsilon_0}$ and the voltage by $U = Ed = \frac {Dd}{\epsilon\epsilon_0}$ with $d$ the distance between the plates. According to the formula for the voltage from above I could set any voltage between the plates if I just separate them far enough from each other and also the electric field would be constant no matter how far the plates are apart which is also quite counter-intuitive. As far as I remember this is true as long as $d$ is small compared to the size of the charged plates. But what if this condition no longer holds? What is happening then? Is there another formula for this case that is comparably simple? I would suppose that for very large $d$ the whole thing can be seen as two point charges which would give a $\frac1r$ dependency of the voltage. But what is happening in between?


What is the time correlation function in the Green-Kubo formulation of ionic current?

I am reading a paper, and I came across the Green-Kubo formulation, where the conductivity $\sigma$ of charged particles is related to the time correlation function of the $z$-component of the collective ionic current $J_z(t)$: $$\sigma_{GK} = \frac{1}{V k_B T} \int_0^{\infty} dt \; C_{JJ}(t)$$ where $C_{JJ}(t) = \langle J_z(0) J_z(t) \rangle$ and the collective current along the $z$ direction is $J_z(t) = \sum_{i=1}^N q_i v_{z, i}(t)$. $V$ is the volume of the system and $q_i$ and $v_{z, i}$ are the charge and $z$-component of the velocity of the $i$th charged particle. $\langle ... \rangle$ is an equilibrium ensemble average. My question is, what is the time correlation function? Is the time correlation function $C_{JJ}(t) = \langle J_z(0) J_z(t) \rangle$? Or is the time correlation function the integral: $\int_0^{\infty} dt \; C_{JJ}(t)$?


In the Niagara Falls, which factors prevent rise of T H2O falling a certain height?

I need some ideas on a problem. The first part says: Whats the posible rise in the temperature of the water falling 49.4 m in the Niagara Falls? That one was easy, with answer 0.112 Kelvin. ($\Delta T = \frac{g*h}{c_{H_2 O}}$) The second part asks what factors tend to prevent that rise in temperature? Im thinking kinetic energy, preassure, air conductivity but im not sure. Thanks in advance


naive question on Boltzmann equation and conservation laws

The Boltzmann equation in absence of external force reads: $\frac{\partial f}{\partial t} + \vec{v} \cdot \frac{\partial f}{\partial \vec{r}} = \left( \frac{\partial f}{\partial t}\right)_{coll}$ Where the r.h.s. stands for the change in the distribution function of the velocities owing to collisions. I won't specify here a particular collision kernel as it is not necessary for my question...I think. It is common to introduce   * The particle density $n(\vec{r},t) \equiv \int d^3v \:f(\vec{r}, \vec{v},t)$   * The mean velocity field $\vec{u}(\vec{r},t) \equiv \frac{1}{n(\vec{r},t)}\int d^3 v \:\vec{v} f(\vec{r}, \vec{v},t)$ It is then easy to integrate over the velocities the force-free Boltzmann equation above and find the famous conservation law: $\frac{\partial n(\vec{r},t)}{\partial t} + \nabla_{\vec{r}}\cdot(n(\vec{r},t)\vec{u}(\vec{r},t)) = 0$ That is because, if the collisions conserve the number of particles, then there should not be any 'source' or 'sink' on the r.h.s. My naive question is the following: The above conservation law for matter can be recast as $\frac{\partial n(\vec{r},t)}{\partial t}+ \nabla_{\vec{r}}\cdot \vec{J}(\vec{r},t) = 0$ with the particle flux $\vec{J}(\vec{r},t) = n(\vec{r},t)\vec{u}(\vec{r},t)$. This is fine but it does not seem very general. For instance, it does not seem to encompass a diffusive flux does it? Hence, although this equation is very general, it does not seem to lead to Fick's laws of diffusion and yet I kind of remember that one can get the latter from some kind of expansion of at least a linearized Boltzmann equation... Could somene unlighten me on this apparent paradox?


Pictures of nuclear explosions some milli/nano seconds after detonation

Where I can find photos of nuclear explosions just after detonation (before 5-10 ms, the shorter the better)?