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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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 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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Why do Galilean transformations change both states and operators?

When a Galilean transformation on a quantum system is performed, the states and the operators change: $$|\phi\rangle \rightarrow |\phi\rangle'$$ $$\hat A \rightarrow \hat A'$$ I don't understand the ...
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Arbitrary frames in special relativity

Consider this quote by James J. Callahan in his book The Geometry of Spacetime where he summarizes the conclusions of his chapter on arbitrary frames in SR (page 165): Once again we find that the ...
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Axiomatization of SR: can we replace light rays with timelike world-lines?

If I eliminate a lot of details and just sketch the general ideas, then a common way of presenting SR is this: Axiom 1: Clocks exist. Axiom 2: Light rays exist. This is the approach followed in, e.g....
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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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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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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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Would other parts of the universe have a different rest frame for their own Cosmic Background Radiation?

The CMB, once the Doppler shift from the Earth's motion is subtracted, is fairly uniform, which seems to imply that all the matter that emitted it moved at more or less the same velocity when it did. ...
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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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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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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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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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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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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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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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Time dilation in 2+ dimensions. Relativity problem

I am a student and due to school closures, I am reading ahead in physics. I have been learning about special relativity and I made up a problem for myself. I've drawn a diagram below: The diagram ...
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Active and passive transformation

Some active transformations on the system can be seen also as passive transformations for example the rotation of the system can be seen as the rotation of the observer in the opposite direction. ...
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Does non-uniform acceleration imply non-synchronizability?

In his paper "Synchronization in Uniformly Accelerated Frames", Tzvi Scarr claims that "We show that a system is uniformly accelerated if and only if all of the clocks in the system can be ...
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Black hole: Infalling matter vs. increase of event horizon

Suppose we have a non-rotating, non-charged black hole and a stationary observer that is not moving relative to the black hole, and some object is falling radially into the black hole. As far as I ...
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Trouble finding the (inverse) transformations between covariant and contravariant components

Consider a point in cartesian and polar coordinates, $P = \{x,y\} = \{r,\theta\}$, such that $x = r \cos\theta$ and $y = r\sin\theta$. I have an arbitrary vector (e.g. a velocity vector) at point $P$,...
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Spin-orbit interaction

When I derived the spin orbit interaction, I switched to the electron's reference frame, so it feels a magnetic field $B$. after calculations I get the spin orbit interaction in the electron's frame ...
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Does spin angular momentum change with reference frame?

I am guessing that the angular momentum of a particle measured by different inertial observers (no gravity) is different. At the same time, since quantum spin is an intrinsic property, Is it true ...
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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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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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Why does the parallel axis theorem apply in this case?

Next, the wheel is flipped over, so the angular momentum of the wheel is now negative. Obviously, the person must start rotating counterclockwise to conserve angular momentum. Since the person is ...
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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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Equivalence Principle and bending of light

Basically, the equivalence principle (EP) states that if someone is in a rocket in empty space with acceleration $g$ equal to that at the surface of the earth, any experiment he does cannot ...
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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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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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255 views

Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3 The rotation matrix associated with 1.2a and ...
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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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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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Einstein's Principle of Equivalence - Infinite Acceleration/Energy?

Hello and thank you for your time. I've been wondering about Einstein's Equivalence Principle core idea. That is, from experiment alone, one cannot differentiate between a gravitational field and a ...
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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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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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