Local Definition and 491 Threads

When I was taking a look at this page, I noticed that she is "known for proving the local existence and uniqueness of solutions to the vacuum Einstein Equations". But this doesn't make sense to me(the uniqueness part). Just consider the Minkowski and Schwarzschild solutions. They're both vacuum...

Homework Statement Hi everybody! I'm preparing a maths exam and I unsure how to answer this question: What is a local extremum of a function ##f: \mathbb{R}^2 \to \mathbb{R}##? Explain why ##\nabla f(x) = 0## when ##x## is a local minimum of ##f## and ##f## is continuous and differentiable...

I'm fairly new to differential geometry (learning with a view to understanding general relativity at a deeper level) and hoping I can clear up some questions I have about coordinate charts on manifolds. Is the reason why one can't construct global coordinate charts on manifolds in general...

Homework Statement Is it possible to introduce local charge on a conductor? Homework Equations - The Attempt at a Solution I know that electrons can move freely from atom to atom in the conductor, so if you introduce excess electrons to the conductor, they'll spread out and there won't be a...

Can someone concretize the difference between a "hypothetical reality" where hidden variables are local and hidden variables are nonlocal in the following context: Some physical event occurs involving particles A and B (which are/become entangled and will exhibit correlations) at time T and...

Homework Statement A person stands in an open space listening to the sound from two speakers. The speakers generate sound with a frequency of 489.5 Hz, the speed of sound in air is 343 m/s. The speakers are 2.00 m apart and the person walks away from one of the speakers along a line that is...

If I took a charged particle and accelerated it, that acceleration would have an effect on charges potentials, allowing for the radiation of electromagnetic waves. This acceleration would be local to a point in spacetime and the observed potentials would depend on the frame of reference of the...

Hello all, I could really use some advice. Here's my backstory: I used to work as an actuarial analyst; however, I wanted to get into a job that actually does more in the way of value creation in the economy. I want to do this as I want to eventually be in a position that allows me to sort of...

"A 2.4% Determination of the Local Value of the Hubble Constant" by Riess et al has led to some excited news stories recently. I don't see it discussed anywhere here. Looking for the essence of the paper, I note three things: The two measurements considered are "the Hubble constant ... measured...

Hey! :o Let $p$ be a prime. We define $$R=\{m/n\in \mathbb{Q}\mid m,n\in \mathbb{Z} \text{ and } p\not\mid n\}$$ I want to show that $R$ is a local subring of $\mathbb{Q}$. To show that, do we have to show that there is a $I\subseteq R$ which satisfies the following conditions? $I$ is the...

... except one weak exception of the entanglement? Assuming that unitary QM (aka MWI) is a-local (c) Demystifier, and the ultimate reality is the Hamiltonian, somehow mapped into our 3D space, it is more surprising that the nature we observe is local. If would be more logical to expect multiple...

Have always drooled over these awesome and mega priced babies until they started dissspearing. Cop says they are being replaced by sat phones which I thought were a nightmare to get a connection and crazy expensive. He would not discuss the performance. So awesome HF antenna versus sat phone...

Hello! Good morning to all forum members! I am studying general relativity through the wonderful book: "General Relativity: An Introduction for Physicists" by M.P. Hobson (Cambridge University Press) (2006). My question is about Riemannian manifolds and local cartesian coordinates (Chapter 02 -...

Hi all, I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's conversation on computations with tangent vectors and pushforwards ... in particular I need help with an aspect of Lee's exposition...

When I was taking my introduction to C class, our professor heavily stressed that we were supposed to use local variables except when indicated otherwise. When we used C for microcontrollers with the same professor, he had the same requirement. Does this reflect a standard among computer...

Homework Statement *A star on the celestial equator has right ascension of 16h00m00s. At what time of day will this star be at it's highest point, on Febuary 29th 2016. * Homework Equations HA = LST - RA The Attempt at a Solution When LST=RA, it'll be at it's highest point. How do I...

According to Castigliano's theorem, the local compliance of an elastic structure, e.g. a cantilever, can be determined by integrating the products of stress intensity factor weight functions over the length of said structure. However, if I do that for a double cantilever beam using simple beam...

I'm used to Windows. I open notepad or wordpad and type <html> Hello world </html> and save it as a .txt file with an .html extension. How do I do this on a Mac? It seems the free included text editor is called textEdit. But it does not allow me to save as a simple txt file with an .html...

I'm trying to understand why the intersection multiplicity of two singular subvarieties is not equal to the complex dimension of the local ring but it is instead the Euler characteristic. Is it possible to find an intuitive explanation? I think that the following concepts need some...

I have this function: f(x) = √3x + 2Cos(x) I have to find the local maxima and minima,where -π ∠ or equal to x ∠ or equal to 2π. 1: Differentiate the function given. f'(x) = 3/(2√x) -2Sin(x) 2: Find where f'(x) is undefined or = 0 to get critical points. 3: Find f''(x) [The second...

Once i did the following : for (int i=0;i <100;i++) {...} Hence with the i defined only in the loop and the professor told me we shall never do that. Do you know any reason ? Thanks.

Hello, in general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let ξα the coordinates in the local inertial frame, so we get ds²=ηαβdξαdξβ. If we switch the frame of reference to coordinates xμ : ξα=ξα(x0,x1,x2,x3) and with...

First, I have to tell you that I don't have money and usually am not in need for shopping online or offline. But lately some local Citi bank's employees have been calling me repeatedly to advertise their platinum VISA credit cards. They say they will deposit into my account $2000 in advance and...

Homework Statement Determine the resultant force R that is equvalent to the forces exerted by the tugboats on the barge. Specify the coordinates of the point on the x-axis through which R passes. Pls check attached file! Homework Equations Moment=Force x perpendicular distance The Attempt at...

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry V: The Local Observables - Lie Theoretically Continue reading the Original PF Insights Post.

Where does the requirement come from that special relativity applies only locally? It is not immediately obvious from the two postulates. I'm asking because this is important for the validity of the Hubble Law.

Homework Statement y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2) find its local max Homework EquationsThe Attempt at a Solution i have differentiated it and found out dy/dx, in order to find the local max, i have to find out the value t when dy/dx=0 but i can't solve this equation

Hi. Bell's formulation of local realism is $$P(a,b)=\int\ d\lambda\cdot\rho(\lambda)p_A(a,\lambda)p_B(b,\lambda)\enspace.$$ Let's for simplicity assume there's only a finite number of states, so this becomes $$P(a,b)=\sum_{i} p_i\cdot\ p_A(a,i)p_B(b,i)\enspace.$$ I'm trying to translate this...

Hello guys . Through all the analysis of theory of general relativity we used what so called Manifolds Manifolds as we know are topological spaces that resemble ( look like) euclidean space locally at tiny portion of space And an euclidean space is the pair ( real coordinate space R^n , dot...

Hello. The ground plane is sometimes used as current return path. If current is low frequency and amplitude is small then voltage rising due to current flow can be ignorable. However, what is return current is actually very high in both frequency and amplitude? In our lab, gas discharge...

I have recently had a lengthy discussion on this forum about coordinate charts which has started to clear up some issues in my understanding of manifolds. I have since been reading a few sets of notes (in particular referring to John Lee's "Introduction to Smooth Manifolds") and several of them...

I hope someone with a deep conceptual understanding of terminologies would help me out here. I am having starting problems in understanding the approach of gauge theories. I have read suggested threads and I am still at a loss. I am an experimental physicist and know basics of electrodynamics...

I know the solution for R2. That is a for an infinite plane you can have one of 2 things (from the classification of 2D surfaces): 1) cross cap (cut a circle out of the plane and identify opposite points). 2) a oriented handle (cut two circles out and identify points on one with reflected...

Hello again, I have a small problem. I am looking for local minimum and maximum points of the function: \[f(x,y)=3x^{2}y+y^{3}-3x^{2}-3y^{2}+2\] The first question was how many stationary points are there. I have found the derivatives by x and y: \[f_{x}=6xy-6x\] \[f_{y}=3x^{2}+3y^{2}-6y\]...

Homework Statement (c) Show that ##tan(x) + cot(x) \equiv 2csc(2x)## (d) Hence or otherwise, find the coordinates of the local maximum and local minimum points of the graph of ##y = tan(2x) + cot(2x), 0≤x≤\frac{π}{2}## Homework Equations Most likely a lot of different trigonometric formulas to...

In page of 15 of 'An Introduction to Quantum Field Theory,' Peskin and Schroeder writes In a local field theory the Lagrangian can be written as the spatial integral of a Lagrangian density, ... , which is a function of one of more fields and their derivatives. Can you explain what the term...

I am a high school senior graduating in a couple of weeks. This summer, I'll be starting college on track to complete a degree in Aerospace Engineering. I'm fairly certain engineering is what I want to pursue, but it's still unclear to me what the engineering work space and day-to-day would be...

calculate the sunset local time for a location : latitude = 36 N , longitude = 6 E if the apparent solar time at this moment was 17h,45 , and ? i started with hour angle h = 86.25 , after that i tried to determine the declination angle d but i don't have the day number and the month , also that...

Hello! (Wave) A $m \times m$ grid is a graph of which the vertices are ordered pairs of natural numbers $(n_1, n_2)$ with $1 \leq n_1 \leq m$ and $1 \leq n_2 \leq m$. Two vertices $(k_1,k_2)$ and $(k_3,k_4)$ are neighbors iff $|k_1-k_2|+|k_3-k_4|=1$. We suppose that a unique number $y_w$ is...

Is it possible to measure the vacuum energy locally? I wonder if it might change with gravity? I'm told that we can measure the vacuum energy globally by measuring the acceleration of the universe's expansion. But can we measure it locally? Or are all local measurements independent of the vacuum...

I have great trouble with the concept of 'local' as it seems very generic in ways. Local can be a plank distance away, or a meter away.. or even a Hubble radius away (if your scale is in Hubble radii (sp) or so). If distance in the direction of travel approaches zero as velocity approaches the...

I considered posting this in the Food thread, but I think it might be better for it to be in its own separate thread. First of all, let me clarify that I love, LOVE ethnic cuisine and foods that are local to a particular region. I find that I learn a lot about groups of people or the local...

Homework Statement Find the local maximum and minimum values and saddle points of the function f(x,y) = x^2 + xy + y^2 + y Homework Equations Local max/min critical points saddle The Attempt at a Solution 1) partial derivative: fx = 2x+y fy = x+2y+1 from here, I'm a little confuse on...

Homework Statement Let f\colon\mathbb{R}^m\to\mathbb{R}. All partial derivatives of f are defined at point P_0\colon = (x_1, x_2, ... , x_m). If f has local extremum at P_0 prove that \frac{\partial f}{\partial x_j} (P_0) = 0, j\in \{1, 2, ..., m\} Homework Equations Fermat's theorem: Let...

I've ran into a problem where my local University, that I would be able to attend for no cost due to my close proximity (staying at home) and scholarships, does not offer physics as a major, only a minor. If I were to attend a different University, my scholarships wouldn't cover my costs due to...

Are many-particles systems theories like the Standard model of particle physics examples of local hidden variable theories?

Homework Statement I am trying to find a local inertial frame for the following metric: ds^2 = -(1+\Phi(x))dt^2 + (1-\Phi(x))dx^2 I can get the transformed metric to equate to η at any point, but I can't get the first derivates wrt the transformed coordinates to vanish. Homework Equations...

Is it okay to define a local operator as an operator whose matrix elements in position space is a finite sum of delta functions and derivatives of delta functions with constant coefficients? Suppose your operator is M, and the matrix element between two position states is <x|M|y>=M(x,y). It...

Hello everyone, I'd like to know if my understanding of local and integral quantities is clear. An integral quantity refers to the entire physical system, it is not defined point by point. A local one is defined point by point, for example ρ(x,y,z). Can I consider the charge dq as a local...