A set of numbers used to quantify location in space.

learn more… | top users | synonyms

1
vote
4answers
4k views

When an object moves downward, is its height negative?

The question is: A ball is thrown directly downward with an initial speed of 8.00m/s from a height of 30.0m. After what time interval does it strike the ground. So I went through the problem ...
20
votes
6answers
1k views

Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
0
votes
1answer
158 views

Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
9
votes
4answers
148 views

How do we know the Schwarzschild solution contains an object of mass $M$?

The Schwarzschild metric is $$ds^2 = - \left( 1 - \frac{2GM}{r} \right) dt^2 + \left(1-\frac{2GM}{r}\right)^{-1} dr^2 + r^2 d\Omega^2.$$ In Carroll's GR book, it is claimed that $M$ is the mass of the ...
7
votes
1answer
170 views

What coordinate system is used to describe planets positions in the universe?

How are planets positions described in the space and in respect to what? For example is Sun the origo and right now at this moment Earth has [coord_X, coord_Y, coord_Z]? or maybe [lng, lat]? ...
3
votes
1answer
67 views

Homogeneity and isotropy and derivation of the Lorentz transformations

In deriving the Lorentz transformations I have found (from reading a few different sets lecture notes) that it is argued that they must be linear and thus there general form must be $$x'=Ax+Bt,\quad ...
0
votes
0answers
24 views

What are the components of r-hat in spherical coordinates?

so I've found a lot of identities that relate the spherical unit vectors to cartesian unit vectors. What is the expression for the spherical unit vectors IN spherical coordinates? I'm tying my brain ...
0
votes
0answers
26 views

Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
4
votes
1answer
270 views
3
votes
1answer
116 views

Diffeomorphism invariance and geodesic action

I'm trying to understand the role of diffeomorphism and isometry invariance in the geodesic action in GR: $$ S = \int_{\tau_1}^{\tau_2} \! d\tau~ g_{ab}(x(\tau)) \frac{dx^a}{d\tau} \frac{dx^a}{d\tau} ...
2
votes
2answers
47 views

How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
1
vote
2answers
226 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
4
votes
3answers
156 views

Velocity in a turning reference frame

I often see the relation that $\vec v=\vec v_0+ \vec \omega \times \vec r$ in a turning reference frame, but where does it actually come from and how do I arrive at the acceleration being $$\vec ...
1
vote
1answer
30 views

Fluid Mechanics: Stream Function for Axisymmetric flow

I have problem in understanding the result of stream function in Axisymmetric 3D flow: I know that the result is (for spherical coordinates): ...
0
votes
1answer
36 views

Coordinate Transformation in Classical Mechanics

The coordinates in one inertial frame are represented by $(x,t)$. Under coordinate transformation, the coordinates in another inertial frame can be represented by $f(x(t),t)$. It can be shown that the ...
1
vote
0answers
35 views

Interpreting meaning of coordinates given a metric

I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. $ds^2=-(1+2 \Phi(r))dt^2 + ...
1
vote
1answer
62 views

On the proof of the existence of geodesics coordinates

From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is $$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} ...
1
vote
1answer
33 views

Eddington-Finkelstein coordinate

The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as \begin{align} u&=t-r^*\\ v&=t+r^* \end{align} where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$ The ...
0
votes
1answer
60 views

Different forms of centripetal acceleration

For a circular motion centripetal acceleration can be expressed as $$a_{c}=\frac{v^2}{R} \hat{u_N}\tag{1}$$ Where $\hat{u_n}$ is the normal unit vector. Nevertheless in the expression for ...
2
votes
2answers
432 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
0
votes
2answers
52 views

How to convert electric field from spherical coordinates to cartesian?

I have 3 components, $r$, $\theta$ and $\phi$, for an electric field in spherical coordinates (and the $\phi$ component happens to be zero), let's say I just want to convert the $r$ component into ...
2
votes
1answer
163 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
0
votes
0answers
35 views

Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
0
votes
1answer
368 views

What is the procedure (matrix) for change of basis to go from Cartesian to polar coordinates and vice versa?

I'm following along with these notes, and at a certain point it talks about change of basis to go from polar to Cartesian coordinates and vice versa. It gives the following relations: ...
3
votes
1answer
451 views

Stokes' theorem in complex coordinates (CFT)

I am studying CFT, where I encounter Stokes' theorem in complex coordinates: $$ \int_R (\partial_zv^z + \partial_{\bar{z}}v^{\bar{z}})dzd\bar{z} = i \int_{\partial R}(v^{z}d\bar{z} - v^{\bar{z}}dz). ...
5
votes
3answers
1k views

Centrifugal Force and Polar Coordinates

In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
0
votes
0answers
31 views

Centripetal acceleration in polar coordinates

$ \left( \ddot r - r\dot\varphi^2 \right) \hat{\mathbf r} + \left( r\ddot\varphi + 2\dot r \dot\varphi \right) \hat{\boldsymbol{\varphi}} \ $ I'm not convinced about the term $- r\dot\varphi^2 ...
1
vote
0answers
45 views

Gauge invariance in gravitational field

I have read that the linearized equation for the metric fluctuations $h_{\mu\nu}$, namely: $$ \partial^2h^{\mu\nu}-\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha}) ...
0
votes
0answers
35 views

Help needed to understand Kerr coordinate transformation

The (uncharged) Kerr metric for a black hole of mass $M$ and angular momentum $Ma$ takes the form $$ds^{2} = \Sigma\Big(\frac{dr^{2}}{\Delta} + d\theta^{2}\Big) + (r^{2} + a^{2})\text{sin}^{2}\theta ...
0
votes
1answer
56 views

Olympiad problem - struggling with polar coordinates [closed]

This is a physics olympiad problem; and I am still struggling with it. I will quote it here: " A particle moves along a horizontal track following the trajectory $r=r_{0}e^{-k\theta}$, where $\theta$ ...
1
vote
1answer
3k views

Deriving kinetic energy in cylindrical coordinate constraints

Consider a mass $m$ which is constrained to move on the frictionless surface of a vertical cone $\rho = cz$ (in cyclindrical polar coordinates $\rho, \theta, z$ with $z>0$) in a uniform ...
2
votes
2answers
191 views

What is the metric tensor for?

I am wondering how to use the metric tensor, in practice? I read the book and done the exercises in A student's guide to vectors and tensors by Dan Fleisch. The concept of a tensor and their ...
0
votes
1answer
64 views

Derivation of Squared Angular Momentum in Spherical Coordinates

While reading my textbook, I found the following: I tried to prove the above equation by doing the following. Knowing that : ...
-3
votes
1answer
58 views

If we live on the surface of Earth then why Earth images shows maps around it? [closed]

If you visits google map and go to earth we see the image as attached below. My question is if the earth is round like sphere ball and if we live on the surface of this ball (point me if i am ...
0
votes
2answers
201 views

Coordinate Singularity in Metric

Suppose I have some metric $$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$ which has a singularity at $r=0$. However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get: $$ds^2=g(t)dt^2+r^3 ...
0
votes
1answer
67 views

Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
0
votes
1answer
43 views

How does angular velocity transform on the surface of a sphere?

If we consider the earth as a sphere than it will have an angular velocity of $\boldsymbol{\omega}=\omega\mathbf{e}_z=\frac{2\pi}{T}\mathbf{e}_z$ where $T\approx24h$. Now we have given a location in ...
6
votes
3answers
219 views

How do we measure Schwarzschild coordinates?

In special relativity, we make a big fuss about setting up inertial frames of reference, and then constructing coordinate systems using networks of clocks and rulers. This gives an unambiguous ...
0
votes
2answers
45 views

Why is 90 degrees the standard for independence in vectors? [closed]

Why do so many laws and ideas in physics act separately if they are separated by 90 degrees? Say you have a force in one direction, x. You can't add a force within 0-90 degrees without changing the ...
1
vote
0answers
82 views

Absolute direction of time [closed]

As Universe is expanding into emptyness, we think that flow of time is forward. This means that expansion is directed forward in time. Even though we don't know for sure whether this expansion will be ...
2
votes
7answers
397 views

Why is force a vector? (The Feynman Lectures)

A vector is a quantity that transforms just the way the coordinates transform under rotation (while a scalar remains invariant under rotation). In FLP, he says suppose $F$ is a vector and probably ...
0
votes
1answer
49 views

Active transformation and passive transformation of a scalar field

For the Lorentz transformation $x \to x'=\Lambda x$, the active transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda^{-1}x)$ and the passive transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda x)$. ...
3
votes
5answers
159 views

Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
2
votes
1answer
207 views

Time dilation simple derivation

In a special theory of relativity we have a phenomenon known as time dilation. There is a simple explanation of this, with a thought experiment with a train and a flash light: We flash a light in a ...
1
vote
0answers
30 views

Relativity Coordinate transformation of Vector [closed]

I'm taking a first course in General Relativity but I've been struggling with coordinate system transformation. For example, if I have a Vector defined in Cartesian (x,y) coordinates as $V_x=x^2+3y$ ...
11
votes
4answers
933 views

Coordinates vs. Geometries: How can we know two coordinate systems describe the same geometry?

Specifically, I'm asking this because I'm taking a class on General Relativity, and in Hartle's book Gravity, in Ch. 12, after having spent some time using Schwarzschild coordinates, we are introduced ...
0
votes
3answers
98 views

Thinking about the properties of 'nothing' [closed]

If a certain identifiable part of space that has no type of measurable energy fields manifesting 'in it' for a given duration ; is such a totally empty space the same as 'nothing'? Anything with any ...
5
votes
2answers
123 views

Kerr Metric from rotated Schwarzschild?

Say we have got a system in GR that is described by the Schwazschild metric. Then we perform a coordinate transform that gives the metric in a rotating system. Why is the transformed metric not the ...
1
vote
1answer
63 views

Is it correct to think about a point in time as the set of positions of all “things”?

Is it correct to think about a point in time as the set of positions of all "things" (photons, electrons, etc) that exist in the universe at that moment, despite the fact that simultaneity is ...
1
vote
3answers
119 views

Is the local Lorentz transformation a general coordinate transformation?

There is a saying in Nakahara's Geometry, Topology and Physics P371 about principal bundles and associated vector bundles: In general relativity, the right action corresponds to the local Lorentz ...