General Definition and 1000 Threads

Homework Statement Let q ∈ C^m have 2-norm of q =1. Then P = qq∗ is a projection matrix. (a) The matrix P has a singular value decomposition with U = [q|Q⊥] for some appropriate matrix Q⊥. What are the singular values of P? (b) Find an SVD of the projection matrix I − P = I − qq∗ . In...

Homework Statement So they want me to obtain the general solution for this ODE. Homework Equations I have managed to turn it into d^2y/dx^2=(y/x)^2. The Attempt at a Solution My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the equation...

Is it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ? And I have another doubt. Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous...

Homework Statement Prove that, given a metric ##g_{ij}## such that ##ds^{2}=g_{ij}dx^{i}dx^{j}##, where ##x^{r} = x^{r}(\lambda)## , we have the following result for the arc length: $$ L(p,q) = \int_{p}^{q} ds = \sqrt{ g_{ij} \frac{dx^{i}}{d \lambda} \frac{ dx^{j}}{d \lambda} } d \lambda $$...

Hello! What book should I use as an introduction to General Relativity? Something that includes an introduction of the math behind GR (tensors for example) would be much appreciated. Thank you!

This may well be a textbook question, or even a duplicate in this forum, but I have no idea of how to compute the capacitance between two conductors in the general case: all the computations I saw in textbooks make heavy use of symmetries to compute the capacitance, e.g. capacitance between two...

I always hear that the two 'don't match' and disagree, but never in what... Someone mind explaining?

I've been doing a course on Quantum Computing and I haven't managed to figure out so far how entanglement would be a useful resource on a general purpose quantum computer. By general purpose quantum computer I mean some theoretical device that could possibly replace current classical computers...

In particular how does matter "clump" together to form stars and planets, and how do Galaxy/star systems form? For the latter question is the answer simply that near massive enough bodies, the spacetime curvature is significant enough that the geodesics within its vicinity are closed curves...

Hi, I'll try to keep this brief but this is a hard subject to keep brief. Thanks to all who take the time to read. I appreciate any advice even if it's just a repeat of what someone else has already said. I have a B.S. in physics from the University of Utah with a GPA of 3.4. I finished my...

I have read this paper http://www.sciencedirect.com/science/article/pii/S1355219813000695 that the author try to said that einstein not believe that gravity is not cause the space time curvature. I want to know that this is true or not. Because when I have read about general relativity I always...

haushofer submitted a new PF Insights post General Relativity as a Gauge Theory Continue reading the Original PF Insights Post.

Hi all, Just did a little bit of (layperson) reading about Anderson localization and disorder in crystal structures. Here's my question: shouldn't all matter contribute to 'restricting' the wave function of e.g., an electron, whether it's in a crystal structure or not? That is, what's specific...

...and what is the difference between true 4D and the minkowski space? To me, it would be much easier to see universe as a 4D and us humans just experiencing the dimension of time differently. In my mind i pictured the universe as a complete 4D structure which we humans experience in one...

For those who have read Schutz' book A First Course in General Relativity. Can this book be considered as a deep approach on the subject? Edit --- Do you think I will become a "expert" in general relativity just by reading books like this one I mentioned above? What time it take for learning...

If we look Einstein equation ##G_{\mu\nu}=0##, which nontrivial aspects it can gives? One phenomenon is gravitational wave. I suppose that we are also free at initial conditions for this equation, thus we can begin with curved space time? What else?

Hello, I wanted to know how Einstein's General Relativity and its equations simplify to Newton's Universal Law. Einstein's equation is obviously a much more generalized version of Newton's law and gives much more accurate predictions that Newton's laws even if we don't think of Newton's gravity...

How is this done in practice? I know that in GR the gravity is believed to curve not only space, but also time, and this prediction has been confirmed somehow in practice. How can we measure that? Because as far as i know, there is no device that actually measures time, but instead measures a...

In General Relativity, the subscripts of G and T are u-ish and v. How do we say them?

Hi all I'm looking for general information on "back pressure" specially in a syringe. So when you put your finger over the top of a syringe and depress the plunger then release the pressure on the plunger and the plunger moves back slightly. I'm struggling to find some specific information...

Homework Statement Let A:={x∈ℝ2 : 1<x2+y2<2}. Is A open, closed or neither? Prove.Homework Equations triangle inequality d(x,y)≤d(x,z)+d(z,y) The Attempt at a Solution First I draw a picture with Wolfram Alpha. My intuition is that the set is open. Let (a,b)∈A arbitrarily and...

Homework Statement A clock moving at v = (3/5)c reads 12:00 as it passes us in our frame of reference, how far away will it be (in light hours) when it reads 1:00. Homework Equations I denote a prime to mean the reference frame of the clock at rest. I use regular lettering to denote 'our'...

Homework Statement Find the general solution for the DE: t2y''-2y=0 Homework Equations These were given for other parts of the problem so I'm not sure if they're relevant. y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7 The Attempt at a Solution The t2 at the front was really stumping me and I'm not...

When does GR apply in gravitational fields as opposed to Newtonian gravitation? Another words, what would be the strength of the graviatational field before we abandon Newtonian gravity and start implementing GR? 10 g's, 20 g's?

Hello, If anyone could help me with the prerequitisetes for an undergraduate General Relativity and Cosmology course I will enroll into, It will be much appreciated. The syllabus is the following(sorry for the rough translation): -Review of Special Relativity -Spacetime in GR -Geodesics...

Homework Statement [/B] (dy/dx)^2 = (1-y^2) / (1-x^2)Homework Equations Separating the variables I arrive with: dy/sqrt(1-y^2) = dx/sqrt(1-x^2) By integration on both sides by trigonometric substitution and putting it in a general solution: Arcsin y - Arcsin x = C The Attempt at a Solution If...

I am 29 with a wife and daughter, scheduled to graduate in 1 year with a B.S in physics. My GPA currently sits at a lowly 2.5, however I have been working full time(40 -52 hours a week) while being a full time student. I mostly have received B's in my core classes (2.79 GPA in major). Do...

Homework Statement show that the general solution of the differential equation d^2/dt^2 + 2 *alpha * dr/dt + omega^2 * r = 0, where alpha and w are constant and R is a function of time "t" is R = e^(-alpha * t) * [ C1*sin( sqrt(omega^2 - alpha^2) * t) + C2*cos( sqrt(omega^2 - alpha^2) * t)...

Hello! (Wave) I want to write the language of the automaton with the following transition function in regular form with $A$ as an initial state and $B,D$ as final states. $$\delta:\begin{matrix} & & 0 & 1\\ & A & B & C\\ & B & C & D\\ & C & D & B\\ & D & D & C \end{matrix}$$ I have...

please can someone very kindly verify this is correct? Thanks Andy

Homework Statement Find the power series in x for the general solution of (1+2x^2)y"+7xy'+2y=0. Homework Equations None. The Attempt at a Solution I'll post my whole work.

Bill_K submitted a new PF Insights post https://www.physicsforums.com/insights/precession-special-general-relativity/ https://www.physicsforums.com/insights/precession-special-general-relativity/

CPT symmetry and antimatter gravity in general relativity M. Villata Published 28 March 2011 • Europhysics Letters Association EPL (Europhysics Letters), Volume 94, Number 2 Abstract The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is...

Homework Statement Find the power series in x for the general solution of (1+x^2)y"+6xy'+6y=0. Homework Equations None. The Attempt at a Solution I got up to an+2=-an(n+3)/(n+1) for n=1, 2, 3, 4, 5, 6... a3=-2a1 a4=0 a5=3a1 a6=0 a7=-4a1 a8=0 The answer in the book says y=a0sigma from m=0 to...

Hello, Is the book General Relativity by Hobson, Lasenby and Efstathiou good in the sense that is intuitive on the mathematics AND physics that it presents? Please vote and if you could also comment your opinion it would be much appreciated. Thanks!

So, I have been trying to come up with a general solution for dI/dt in an RLC circuit. I have attached the work I have done so far. I don't know where but I am making a mistake and the waveform is not coming out right. Would really appreciate a look over my work to see if I made any obvious errors.

While deriving ideal gas equation - we take gas molecules to be contained in a cubical container (convinent shape) , but how do we derive it for a gas inside some arbitarily shaped container ? i think this has 2 answers 1) Using maths - but it will be mostly impossible 2) or it will be a...

So i don't have issues with most of his problems, but once in a while a question that requires a ridiculous math trick that i had no way of knowing comes up and i just wonder if this is something you pick up from various places, or can attain through a focused study of mathematics. the question...

The position vector of the center of mass of a triangle is ##\frac{1}{3}(\mathbf{a}+\mathbf{b}+\mathbf{c})##. Is the position vector of the center of mass of a planar four-sided figure ABCD ##\frac{1}{4}(\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d})##? Does this generalise to n-sided figure...

There are a few fundamental questions I wanted to ask about related to special relativity: 1) Firstly, is there an intuitive explanation for length contraction and why lengths are relative? For example, the fact motion is relative is intuitive. E.g. someone sitting inside a train moving 60...

Hello, I would like to know if anybody here has used the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray and how they found it. Thanks!

wrobel submitted a new PF Insights post General Brachistochrone Problem Continue reading the Original PF Insights Post.

Hi all, I was trying to get into safe mode in Windows Vista (2007 version) to disable some malware that had installed itself through the web. The standard instructions -- restart and press F8 just before the computer starts up seems to not work. I have heard that newer editions of Windows...

Hey everyone, I am a CS major, and part of my curriculum has me taking 2 sequences in various sciences. Initially I wanted to do physics & chemistry. I ended up taking Physics I, but am unable to take Physics II next semester due to scheduling conflicts; thus this summer I am taking the first...

What is the metric for the spacetime around an infinitely thin, infinitely long, uniform rod? Could it be written in the form ds2 = A(r)dt2 + B(r)dr2 + C(r)dh2 + r2dθ2 where h is the coordinate along the rod and r is the radial coordinate, or would it be something more complicated?

I found this item in Science daily, how will it help in general health https://www.sciencedaily.com/releases/2016/06/160623150109.htm

I have heard/read that Carroll's Spacetime and Geometry: An Introduction to General Relativity is one of the best books on General Relativity but its price is insanely high! Does anybody know any place which sells it at a lower price than, say, Amazon? If not, what are other books that cover...

Hi, I realized I didn't understand the physical model of something I know the theory of pretty well. I was considering the real power loss of an AC transmission line I2*R, then I realized that from source to load the electrons in an AC line don't actually move anywhere. (as far as I know) Yet if...

Question : General solution of dy/dt = -ay + b My solution : dy/dt = -a(y-b/a) (dy/dt)/(y-(b/a)) = -a Integrating both sides : ln | y-(b/a) | = -at + C e(-at+C) = y-(b/a) Ce(-at) = y-(b/a)

Hi, I would like say that in this link ( ) and starting from 56.28 Suskind tries to find the energy tensor equation using \phi, afterwards he finds a equation similar to wave equation in terms of \phi. My question is: For what does \phi stand ? I could not capture the meaning of \phi. Could...