# 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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### 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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### 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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### 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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### 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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### 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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### 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. ...