Questions tagged [reference-frames]

A reference frame is a particular coordinate system chosen to represent physical entities. The notion is most often used in special and general relativity to denote particular coordinates chosen on the spacetime manifold.

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Special conformal transformations and image charges

Let us consider a grounded conducting sphere with radius $r$ and a point charge $e$ at a distance $R>r$ from the center of the sphere. For simplicity, we can choose the sphere to be centered at the ...
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Inelastic collisions in different frames of reference: regarding thermal energy loss

I am currently reading Introduction to Special Relativity by James H. Smith, and I am attempting to complete the exercise problems for chapter 1 before moving on. The 4th problem asks Show ...
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What is the resolution of this Lewis-Tolman-like paradox?

Though my question stands on its own, here is a brief overview of a well-explored question, the Lewis-Tolman Lever Paradox, which I think might be helpful in finding the resolution to my question. The ...
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Fixed coordinate frame as limit of rotating coordinate frame

I have a question about a fixed coordinate system as limit of rotating system. Consider for example a pendulum. The Lagrangian in the rotating frame is given by \begin{equation} L(\mathbf{r}, \mathbf{\...
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Role of the observer in Gödel's universe

I am here to clarify myself about the role of the observer in Gödel's solution (1949) of Einstein's field equations. The Universe we are dealing with is anisotropic, since the axis of rotation ...
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Lorentz transform in Unruh effect

I'm re-reading about the Unruh effect and while I broadly understand the concept of plugging through the coordinate transform and the Bogoliubov transformation, I'm curious as to whether there is a ...
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555 views

What happens to objects sucked into a black hole after the black hole evaporates away?

Suppose an object falls into a black hole that's so massive that it wouldn't get torn apart at the event horizon. What happens to it after the black hole evaporates away? According to the theory ...
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80 views

General Relativity - Confusion between choosing basis (orthonormal & coordinate) and coordinate transformations

I am reading the book 'Gravity' by Hartle and presently I am at the section discussing orthonormal and coordinate bases. I am confused about a few points I had read previously and can't exactly ...
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Significance of energy in a time dependent quantum box

The Hamiltonian for a particle in a finite box is $$H = \frac{p^2}{2m} + V(x)$$ which will give time evolution as $$ i\hbar d/dt|{\psi(t)}\rangle = H|{\psi(t)}\rangle \, .$$ However, if I do a ...
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276 views

Lagrangian equations of motion for ball rolling on turntable

The equations governing the motion of a ball of mass $m$, radius $R$ rolling on a table rotating at constant angular velocity $ \Omega $ which are derived using Newton's laws are: (I present these for ...
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Angle between velocities: Elastic collision question in 3D

I have been given a scenario of a proton (particle 1) travelling with u1 = 3î+ 4j–6k and a Helium-3 nucleus (particle 2) travelling with u2= 3î+ 4j–2k. The two particles collide and the proton (...
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What does a basis rotation correspond to physically for linear position-momemtum?

For polarization and angular momentum, rotating the basis corresponds to a very straightforward physical transformation, namely, the physical rotation of an experimental apparatus about an axis in ...
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These components of the angular velocity are given in what reference frame?

When we have a rigid body, the rigidity constraint allows us to write the trajectory $\mathbf{r}_i$ of the $i$-th particle as $$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),$$ where we are ...
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385 views

Rotating reference frame in quantum mechanics

I have this problem from an exam but I don't know how to start any section, could you help me? We have a laboratory system rotating around $Z$-axis relative to an inertial referencial frame with ...
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Shape and even connectedness of accelerating components in SR is frame dependent?

In some inertial frame consider a disk of radius 1 lightyear at rest. Then along the edge of the disk there are some people in spacesuits at rest hovering right above the disk (which has negligible ...
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Location of event horizon in moving black hole

Say a black hole is travelling at $c/2$, does the shape of the event horizon change? What about the location of the event horizon? If it is travelling at a hypothetical $c$, does the event horizon ...
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Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
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176 views

From Lorentz Invariance Violation to the preferred frame of reference

I've read here and there that Lorentz Invariance Violation (LIV) would imply the existence of a preferred frame, a frame where some physical laws are valid, while invalid in other frames. The fact ...
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Rotating Observers in Special Relativity: Coriolis-like effect?

Do any non-inertial "forces" [terms in the metric] (like Coriolis in Newtonian mechanics) appear to a rotating observer (reference frame) in special relativity? Is the resulting spacetime after ...
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Does the equivalence principle imply that light must move slower when moving away from a massive object?

Thought experiment: Elevator going up at an extreme acceleration, pulse of light bouncing up, and down between mirrors on the floor, and the ceiling. Won't it take light longer to travel from the ...
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Parallel Axis Theorem and Kinetic Energy of the Earth

I'm looking for a little clarification on the parallel axis theorem and computing the total kinetic energy of the Earth in it's orbit round the Sun. So the Parallel Axis Theorem states that $I = I_{...
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Force exerted by rails on a high speed train

I need to find the ratio between horizontal and vertical accelerations exerted on a train by the rails it is running on , given that the train is traveling East at a speed of $v_r=250$ km/h, along the ...
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Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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Calculating acceleration of end point of rod

Suppose I have a rod hinged at its end, of length $\ell$ free to rotate about an horizontal axis; initially in the horizontal position and I have to calculate the acceleration of its other end point. ...
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Time derivative in rotating frame

In Goldstein (2ed) sec 4.9 - Rate of change of a vector, why does he say that the instantaneous angular velocity $\omega$ is not a derivative of any vector? $$ (d\textbf{G})_{space} = (d\textbf{G}...
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Acceleration interpretation in accelerated frames in general relativity

I would like to know whether my physical interpretation of some dynamics in accelerated frames is correct. In a frame with acceleration $a$ we have the metric $$ds^2 = (1+ax)^2 dt^2 - dx^2$$ The ...
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120 views

How to deal with no-slip non-holonomic constraints in Lagrangian?

I'm solving a dynamical system of a ball of mass $m$ and radius $R$ rolling on a rotating platform ("turntable") for which I found the Lagrangian to be: $$L=\frac{1}{2} m (\dot{x} - \Omega y)^2 + \...
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1answer
109 views

Centrifugal force in effective potential

$$E = \frac { 1 } { 2 } m v _ { r } ^ { 2 } + \frac { L ^ { 2 } } { 2 m r ^ { 2 } } + U ( r )$$ This is the formula of total energy of an object with mass $m$ orbiting an assumed stationary body of ...
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What are the fundamentals of motion in a non-inertial reference frame?

First of all, note that I understand what is considered off and on topic here. I'm posting this because I likely lack some sort of conceptual understanding of motion in non-inertial reference frames, ...
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Does angular momentum depend on coordinate frame?

I am working through a problem and getting what seems to be different answers in different reference frames. The angular momentum of a point mass with respect to an axis that doesn't go through the ...
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1answer
1k views

Relative acceleration of bodies on opposite sides of a pulley

This is a problem that I encountered while solving problems related to constrained motion: With all the data given in the above question, I believe that the monkey just holds on to the rope and does ...
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How to impose this constraint on two particles on General Relativity?

Let $(M,g)$ be spacetime and consider a system composed of two particles of masses $m_1$ and $m_2$ connected by a massless rod whose lenght varies in time. This constraint is quite easy to implement ...
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Centre of mass in General Relativity

In the paper from Costa 2014, Figure 1, it discusses how the velocity of an observer influences where the center of mass of a spinning object is measured. If an observer is moving with velocity $v$ ...
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Gravitational time dilation and the pace of time

If we are in empty space far from a black hole, at rest relative to the hole, we would look at a clock and a light source inside the gravitational field of the hole, then we would, according to the ...
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About General Relativity and Reference Frames

So, I came up with this question which is intriguing me since a bit. Maybe it's stupid, but it's always better to ask. The question is about inertial reference frames (I'll name them IRF) We know ...
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How to make sense of this definition of a reference frame?

Reference frames in General Relativity seem simple to understand and hard to come out with one agreed definition. In the intuition it represents a certain "point of view" of several observers. In ...
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Does an object travelling at speeds approaching $c$ observe an increase in the expansion rate of the universe?

According to the theory of special relativity as an object approaches light speed it experiences length contraction. This means that the distance it observes between it and it's destination reduces as ...
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Quantum mechanical origin of pseudo forces

I am thinking about this from quite some time but could not come up with any satisfactory explanation. In a nutshell, how would one explain the pseudo forces felt by non-inertial observers given that ...
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247 views

Foucault pendulum, where did I go wrong?

I wanted to approximate the number $N$ of periodes needed, such that the foucault pendelum turns one time. Though my result is off by the factor 2 of the results I found. What I did: I assume the ...
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What happens when one uses a blender in zero gravity?

I was recently told by a friend that using a blender type apparatus in a zero gravity environment will act like a centrifuge instead mixing properly. Is this the case? Furthermore, can anyone provide ...
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Is there an absolute accelerated frame of reference?

I know from special relativity and from a little common sense that there is no absolute inertial frame of reference; that is, physics acts the same no matter what velocity you go at. However, that ...
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How does work function transform in Einstein's special theory of relativity?

A photon with energy greater than the work function hits the metal, and an electron is knocked off. Now, suppose we were in an inertial frame moving with a velocity $v$ with respect to the metal such ...
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Geodetic effect and Frame dragging

Two gyroscopes pointing perpendicular to each other were housed inside Gravity Probe B which performed polar orbit around Earth to test Einstein's theory of relativity. As the probe is orbiting ...
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Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”?

I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words, ...
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Subluminal speed when going in a circle around someone

Some time ago I thought about such situation: There are two people in the room. Both have synchronized watches on their wirsts. Then the person A starts running around person B with the speed of 0....
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How strong is the force of space expansion?

There are many questions about space expansion, its cause, or its effects. But I have the feeling we never get straight and simple answers. I do not expect answers to be simple in general, but I ...
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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 $x'=x-vt$, $y'=...
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About the speed of light

If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. ...
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Car parking special-relavity puzzle

Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution? Let's suppose a car is going to park to a garage and the garage is ...
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Clarification of proper time and inertial frame of reference

“Standing beside railroad tracks, we are suddenly startled by a relativistic boxcar traveling past us as shown in the figure. Inside, a well-equipped hobo fires a laser pulse from the front of the ...