A set of numbers used to quantify location in space.

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371 views

Degrees of freedom in the infinite momentum frame

Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no ...
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2answers
513 views

Does the length of the sidereal day vary systematically?

I'm confused about some properties of the sidereal day, in particular whether its duration varies systematically over the course of the year.1 It seems to me that that must be the case, but the ...
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1answer
236 views

Mass Shell in Light Cone Coordinates

I'm reading Zweibach's introduction to string theory, and don't understand one of his claims. He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
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1answer
80 views

In the Heisenberg uncertainty principle

In Heisenberg uncertainty principle why do we only talk about uncertainty in position along $x$ axis, why not along other dimensions as well?
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4answers
105 views

Why is coordinate time frame dependent? [duplicate]

Here is what I understand by coordinate time. It is the time difference measured between two events, using two synchronized clocks, one present at each event, and the difference is measured in an ...
2
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1answer
151 views

Black holes and Time Dilation at the horizon

What is the difference between proper time and the observer time? Whilst thinking about Black holes, when we see the Schwarzschild metric $$c^2\tau ^2 = \left ( 1 - \frac{r_{s}}{r} \right )c^2t^2 - ...
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1answer
265 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
2
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1answer
871 views

Calculate the latitude / longitude coordinates of the location where the Sun is at the zenith

There are plenty of resources showing how to calculate zenith and azimuth of the Sun when the time and the location are given. However, I need to calculate the location where the sun is at the ...
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5answers
234 views

A reference frame is any coordinate system or just a set of Cartesian axes?

In Physics the idea of a reference frame is one important idea. In many texts I've seem, a reference frame is not defined explicitly, but rather there seems to be one implicit definition that a ...
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0answers
95 views

Kleppner derivation of Lorentz transformation

I am reading Kleppner.(Lorentz transformations) He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form $$x'=Ax +Bt, y'=y, z'=z, ...
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1answer
169 views

Langevin equations in translational and rotational direction

I want to describe the following system. A bead is connected with a tether. There is a force $\vec{F}_{up}=F_{up}\hat{y}$ that acts on the bead. The tether acts with a force on the bead, this force ...
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0answers
71 views

What's the meaning when Kerr-Newman metric's mass is zero?

Kerr-Newman metric represents the spacetime of a charged and rotating black hole. If the mass parameter is zero, this metric is still not the Minkowski spacetime. What's the meaning of a charged and ...
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1answer
226 views

question about ICRF/J2000 equinox orientation

The DE406 ephemeris data and the NASA Horizons website all report the Earth's current coordinates on 2014 Sep 27, a few days after the Fall equinox, as approximately [1,0,0] AU. However every ...
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0answers
73 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, ...
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0answers
67 views

Solutions of PDEs in different coordinate systems

Suppose we have a PDE, for example the Helmholtz paraxial equation: $$ \nabla_\perp^2A+2ik\frac{\partial A}{\partial z}=0 $$ Solutions depend on the coordinate system we are using, i.e. we obtain ...
2
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1answer
150 views

Space-Time Continuum [duplicate]

In special relativity it is said that " Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. " What is the ...
2
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1answer
178 views

Privileged coordinate system (or lack thereof) in general relativity

What does the following statement mean and why is it true? The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system. I have looked ...
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0answers
146 views

Falling into a black hole emitter vs observer

Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole. Suppose we define the quantity $$u=t- v$$ where $$dv/dr= ...
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0answers
2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
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1answer
3k views

In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?

I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a ...
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2answers
257 views

A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & ...
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1answer
38 views

$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
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3answers
141 views

How can we define a frame of reference in general relativity?

I have started reading general relativity. (A First Course in General Relativity, Bernard Schutz). I am finding very hard to understand a frame of reference. When I was reading special relativity ...
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2answers
182 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
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5answers
474 views

Is the polar coordinate system non-inertial or inertial?

Consider a car driving around in a circle lying in the plane and suppose we were interested in determining its acceleration as measured by an observer stationary on the "ground" or whatever. ...
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2answers
355 views

Coordinate and conformal transformations of the FRW metric

I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$ where $F(r,t)$ and $G(r,t)$ are arbitrary scalar ...
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1answer
118 views

From momentum to solid angle

Why $d^3\mathbf{p}=p^2\;dp \; d\Omega$ ? where $d\Omega$ is the solid angle that covers a particle with 3-momentum $\mathbf{p}$...
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1answer
478 views

Does change of coordinate system require acceleration?

This question came about from a side discussion that arose on this: Does GR provide a maximum electric field limit? Can we change our choice of coordinate system completely independent of physical ...
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1answer
51 views

A particular coordinate transformation of a metric tensor

So, this was a problem set question for my GR class due yesterday, and I can't for the life of me solve it, it seems I am missing something very trivial. Either the given answer is wrong, or I am. ...
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1answer
241 views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
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1answer
405 views

How can I find the motion equations of the 2-dim harmonic oscillator?

First of all: I am no physicist, so I am rather helpless. I need to find the moving equations of the 2-dim. harmonic oscillator. If it is possible it should be rather elementary, because, as I said, ...
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1answer
86 views

Which symmetry for which distance function

For evaluating the electric field of some charge distribution one can use $$\phi(r):= \frac{1}{4 \pi \varepsilon_0}\int_{\mathbb{R}^3} \frac{\rho(r')}{||r-r'||_2} dr'.$$ My question is: What symmetry ...
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1answer
497 views

Can false origin be anywhere in a graph?

Can I start labeling my $x$ and $y$ axes from non-zero values when drawing a graph? Or is there any convention to only label $x$-axis from non-zero value when using a false origin and not $y$-axis? ...
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1answer
753 views

Trajectories using Polar Coordinates

Once I asked my teacher how to find the trajectory of any particle that is acted upon any force.(Generally) He Told me that I couldn't do it as I did not know polar coordinate geometry as of then but ...
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1answer
253 views

Inverting Generalized Coordinates

In Corben's classical mechanics on pg. 9, it says that given generalized coordinates $q_m = q_m(x_1, ..., x_n,t)$, then if the Jacobian is non-zero everywhere, you may express $x_i = ...
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1answer
393 views

Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity

I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
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1answer
827 views

converting force from spherical to Cartesian coords

So I am working on my assignment, and have a question about converting coordinates. I dont know whether I should ask here or the math SE, so lets give it a try here. The force in question is ...
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1answer
77 views

What is the function type of the generalized momentum?

Let $$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$ denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action ...
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2answers
145 views

Do rotation matrices rotate about inertial or body angles? [closed]

I have Yaw, pitch, and roll angles in that order (Euler 321) to apply to a body reference frame in cartesian coordinate system. I want to know what the body reference frame vector coordinates are ...
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1answer
63 views

Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality

In Roger's book, the following is stated: (I'm paraphrasing because my book is in spanish) "We consider time as part of a space, namely $\mathbb{E}^1$, instead of it just being a copy of the line ...
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1answer
101 views

Is metric tensor invariant under rotation?

It is said that metric tensor depend on the local coordinate system and therefore are not intrinsic to the surface of an 3d-object? How is it possible, kindly provide any proof or discussion. Also is ...
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2answers
307 views

Is a double integral required to find the moment of Inertia of a non-uniform sphere?

Consider some ball of given radius $R$, with a mass density function that depends on the radial variable, $\rho=\rho(r)$ where $r$ is the distance from the center of the sphere. What is the moment ...
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2answers
242 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
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1answer
98 views

How big or small is a reference frame in Relativity?

What exactly is a frame of reference? Does it have an objective existence and if so what is it? What's the size of a reference frame? Is a reference frame the same size for a stationary frame of ...
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1answer
1k views

Radians to Rotate Earth to Match ECI Lat/Lon with ECEF Lat/Lon

I am attempting to model GPS Satellite positions on the globe for a set of ephemerides. I have a verified set of ECI ( http://en.wikipedia.org/wiki/Earth-centered_inertial ) XYZ Coordinates and a ...
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2answers
192 views

What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
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2answers
482 views

What is the physical meaning of the Eddington - Finkelstein coordinates?

I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this mathematical procedure. (really two transformations, but i think that is a ...
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1answer
2k views

Christoffel symbol for Schwarzschild metric

I know that the christoffel (second kind) can be defined like this: $$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
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1answer
106 views

Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?

In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime. If I ...
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2answers
145 views

How big is an inertial frame?

How big is an inertial frame? Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year. Thus light from its end closer to the fixed point to the end farther ...