Definition Definition and 1000 Threads

Hi, this is my first message on thi forum :D I apologize in advance for my english. I'm doing my thesis work on the theory of relativity of Einstein-Cartan. I'm following the article of Hehl of 1976; it's title is "General relativity with spin and torsion: Foundations and prospects". I can't...

Homework Statement It is not really a homework question, but rather a translation problem. I searched everywhere, but I still cannot find a good translation into English of a term that is defined as: "In mechanics, the motion of a moving reference frame relative to another (primary) reference...

Hi all, I am looking for a precise definition of " Crow Flies Distance" on a rectangular grid. I have not found a precise definition yet, but from what I have read, I think it would be the standard Euclidean distance ## d((x_1,y_1),(x_2,y_2)) = \sqrt {( (x_1-x_2)^2+(y_1-y_2)^2}) ## Is this...

Hey guys, I need an explanation on the definition of the electric field. It was said in a post that " the definition of the electric field is defined in terms of how it is measured or tested". What do they mean by measured/tested?

Hey just to make sure, can we say apparent power S = V^2 / Z for a complex impedance Z? And do we have to worry about conjugates at all? Cheers

The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I am trying to fully understand Bland's definition of a direct product ... and to understand the motivation for the definition ... and the implications of...

In a river, water flows faster in the middle and slower near the banks of the river and hence, if I placed a twig, it would rotate and hence, the vector field has non-zero Curl. Curl{v}=∇×v But I am finding it difficult to interpret the above expression geometrically. In scalar fields, the...

"Definition: A map ƒ: A ⊂ ℂ→ ℂ is called conformal at z0, if there exists an angle θ ∈[0,2Pi) and an r > 0 such that for any curve γ(t) that is differentiable at t=0, for which γ(t)∈ A and γ(0)= z0, and that satisfies γ ' ≠0, the curve σ(t) = ƒ(γ(t)) is differentiable at t=0 and, setting u =...

Hey guys! After watching another awesome video of minutephysics: I couldn't help but wonder, what is a dimension? Thanks for your replies in advance,

What are the branches that we can say are categorized under [Quantum Theory](http://en.wikipedia.org/wiki/Quantum_theory)? I am thinking they are QFT, Standard Model and Quantum Mechanics. How about atomic physics and Solid state physics? Also how about Quantum Gravity and Quantum Information...

In my book definition of potential energy difference between two points as the work required to be done by an external force in moving without accelerating charge q from one point to another in electric field of any arbitrary charge configuration.I want to know why without accelerating ?

Question: If x | y, (is true), then x ≤ y and x ≠ 0. For instance, if x > y, then there are no integer solutions to equation kx = y and thus, x does not divide y. Is this a correct proposition?

A field is defined as a distribution throughout all space (or at least a portion of it). But all of (a portion of) space means all of space at a particular moment, no? But that sounds as if it assumes simultaneity. But I thought simultaneity was a meaningless concept, according to relativity...

Homework Statement http://imgur.com/goozE9f Homework Equations ##(dx_i)_p i= 1,2,3## 3. The Attempt at a Solution [/B] I'm reading Manfredo and Do Carmo's Differential Forms and Applications. This is the very first page Would you mind explaining me what is meant by dx, as highlighted in the...

I am having considerable difficulty in finding a precise definition of g-force. My understanding is that it is the acceleration an object would undergo due to just the non-gravitational and non-electromagnetic forces acting on the object. A corollary of this is that an object experiences zero...

I have been studying Fourier transforms lately. Specifically, I have been studying the form of the formula that uses the square root of 2π in the definition. Now here is the problem: In some sources, I see the forward and inverse transforms defined as such: F(k) = [1/(√2π)] ∫∞-∞ f(x)eikx dx...

Where does this definition come from: $$\ln n = \int_{0}^{\infty} \int_{1}^{n} e^{-xt} dx dt$$ Thank you very much.

If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.3 Polynomials ... [FONT=Times New Roman][FONT=Times New Roman]I need help with an aspect of the proof of Proposition 3.29 concerning elements of...

Hello, in this section of the wiki article on Rindler coordinates it is stated that the proper acceleration for an observer undergoing hyperbolic motion is just "the path curvature of the corresponding world line" and thus a nice analogy between the radii of a family of concentric circles and...

To keep the can immersed, an external downward force is needed to balance the net upward force(=F'b-W).

I was me asking why the complex numbers are defined how z = x + i y !? Is this definition the better definition or was chosen by chance? In mathematics, some things are defined by chance, for example: 0 is the multiplicative neutral element and your multiplicative inverse (0-) is the ∞. But, 1...

What is the intuitive logic behind setting up the definition of reparametrization as being a bijective map and all that(the inverse map being smooth) and not alone that the reparametrisation must give us the same image curve.e.g if we see (t,t^2) as being describing the same curve as (t^3,t^6)...

So the definition I have seen is: Given a topological space <S,F> it is compact if for any cover (union of open sets which is equal to S) there exists a finite subcover. By the definition of a topological space both S and the empty set must belong to the family of subsets F. Wouldn't <S, empty...

Let's start with an arbitrary solid body rotating around a fixed axis of rotation with angular velocity ##\vec \omega## in the ## \hat z## direction. For simplicity, let's say the origin O is on the axis of rotation. Take a look at the picture I sketched in the next post. Tried my best to be...

Hey, my name is Roy and I'm new to Physics Forums. I'm a retired medical and aerospace test engineer, now currently a freelance artist (kind of opposites right?) and I joined Physics Forums to hone my understanding of physics and ask the right questions in an ever expanding field of inquiry...

What I've tried so far: $$ \begin{align*} \left |\frac {e^{x+y^2}-1-\sin \left ( x + \frac{y^2}{2} \right )}{x^2+y^2} \right | &\leq \frac {\left |e^{x+y^2}-1-\sin \left ( x + \frac{y^2}{2} \right ) \right |}{\left \| (x,y) \right \|^2} \\ &\leq \frac {\left |e^{x+y^2}-1 \right |+ \left...

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows:In the above text, Kunz writes the following: " ... ... If $$K_0 \subset K$$ is a subring and $$\Gamma = \mathscr{V}...

I was talking to a friend recently and he said something to me that i just didn't understand. He is a physicist and i most certainly am not. I was telling him about similarities that i had observed between two things and was not sure if it was a coincidence or if there was a tangible link...

Hi! I just read in an inorganic chemistry book (by Whitten, et al.) that acids are defined as substances that produce H+ ions in dilute aqueous solutions, and bases are those that produce OH-. To me, this definition implies that a substance that has yet to produce an H+ or an OH- can already be...

In Sean Carroll's Lecture Notes on General Relativity (Chapter 3, Page 60), in the chapter on Curvature, he derives the definition of the Christoffels Symbols by assuming the connection is metric compatible and torsion free. He then takes the covariant derivative of the metric and cycles through...

I am trying to find the derivative of x^x using the limit definition and am unable to follow what I have read. Can someone help me understand why lim [(x+h)^h -1]/h as h ---> 0 = ln(x). This part of the derivatio

Mathematically, a state in QM is a ray on the Hilbert space. But: 1) How would you define "state" from a physical point of view? I know a lot of examples but not a general definition. 2) Given a specific quantum system, to find all the states and so the Hilbert space, all I have to do is to...

I just want to make sure I have this right because when I go to different sites, it seems to look different every time. This is the Weyl tensor: Cabcd = Rabcd + (1/2) [- Racgbd + Radgbc + Rbcgad - Rbdgac + (1/3) (gacgbd - gadgbc)R] Is this correct?

I am slightly unsure as to whether I have understood the notion of locality correctly. As far as I understand it locality is the statement that if two events occur simultaneously (i.e. at the same time) then no information can be shared between them (they are causally disconnected). Thus a...

Why is it that, in the definition of the path integral, we have the product of neighboring integrals of the form : ∫Φdx1...dxn when the whole idea is based on adding the contribution of neighboring paths. I need some help understanding why it is of the form ∫Φdx1...dxn and not the form...

I've been grappling with the idea in my head as to how I would explain to someone exactly what equality between two mathematical objects actually means. This maybe a very stupid question, so apologies in advance, but if I'm honest I struggle to come up with an answer that doesn't involve using...

What is current density

I am trying to learn differential geometry on my own, and I'm finally getting serious about learning the subject. I am using several books which I supplement with material I find on the internet. I have found some excellent lecture notes on differential geometry written by Dmitri Zaisev. I like...

In chapter 2.3 in Nakahara's book, Geometry, Topology and Physics, the following definition of a topological space is given. Let X be any set and T=\{U_i | i \in I\} denote a certain collection of subsets of X. The pair (X,T) is a topological space if T satisfies the following requirements 1.)...

Sorry, I am really struggling with the precise definition of the limit. I have a specific question I'm trying to work out lim(x->2) (4x2+2)=18 skipping the introduction part any advice? I am just not sure how to get rid of the 2 value to re-arrange |(4x2+2)-18| to look like |x-2| |x-2|<delta...

Hi I'm reading Elementary calculus - an infinitesimal approach and just wan't to make sure my understanding of what dy, f'(x) and dx means is correct. I do understand the basic idea: You make the secant between 2 points on a graph approach one of the points and at this point you get the...

I'm trying to practise, precise definition of a limit (epsilon & delta) Just to check I'm along the right lines here's a previous question to the one I'm stuck on If epsilon > 0 then there is delta >0 ... All that introduction stuff, then Lim x-> 2 (3x-1) =5 Hence |x-2| < delta then |3x - 6|...

I am well aware of an abstract definition of a general tensor as a map: \mathbf{T}:\overbrace{V\times\cdots\times V}^{n}\times\underbrace{V^{\star}\times \cdots\times V^{\star}}_{m}\longrightarrow\mathbb{R} I am happy with this definition, it makes a lot of sense to me. However, the physics...

When I learned the concept of specific heat capacity, I knew that 1J/(K*kg) means that it takes 1 Joule of energy to increase the temperature of a kilogram of matter by one Kelvin, but what does J/K, the unit of entropy, mean?

Does atomic fluorescence involve: 1. spontaneous emission (or only), 2. stimulated emission (or only) 3. change in magnetic quantum number $$\Delta m \neq 0$$ ? Thank you. Rarely can I find a definition on the internet. My guess is that atomic fluorescence involves spontaneous emission only...

Are temporary embryonic structures like gill clefts included under "Vestigeal organs"??

Homework Statement Use the ε-δ definition of limits to prove that limx→2 x2 = 4. The Attempt at a Solution |x2 - 4| < ε 0 < |x - 2| < δ |x - 2| |x + 2| < ε And that's where I get stuck, can I divide both sides by |x + 2| to yield |x - 2| < ε/|x + 2| = δ In which case, where do I go from...

Just wondering if there's a precise definition of what it means to be an elementary particle. I had assumed it was related to not being able to convert it into multiple "smaller" things, but then a photon is called elementary when it can be converted into smaller energy positrons and electrons.