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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How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the $\operatorname{SO}(3)$ rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As shown in f.ex. this paper, Euler ...
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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 centered at the ...
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Electromagnetic waves accelerating reference frame

A charge is at rest in an inertial reference frame. Consider this situation: From the point of view of an observer who is accelerating relative to the charge. Would the observer observe ...
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Physics of the dead man's (or jellyfish) float

This question arised during a discussion with a friend, when I discovered that he cannot do the dead man's (or jellyfish) float, i.e. float horizontally on the water, not even when he was a child. ...
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Electron in rotating frame

Suppose there is a stationary electron in an inertial frame $S$. Then there is only a static Coulomb field relative to $S$. However, according to a rotating frame $S'$, whose angular velocity relative ...
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How would this object manifest itself to the outside observer?

I tried asking this question on Worldbuilding.SE but did not get much response outside of, "you cant do that." I've also seen many similar questions without the type of answer I am looking ...
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Hamiltonian eigenvalues in a transformed reference frame

Under a time-dependent unitary transformation $V(t)$ of the state vectors $|{\psi}\rangle$ \begin{equation} |\psi'(t)\rangle = V(t) |\psi(t)\rangle \end{equation} The Hamiltonian $H(t)$ has to ...
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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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How to relate Riemannian and Lorentzian tetrad fields on the same manifold/spacetime?

Consider Gibbons and Hawkings paper wherein a Riemannian metric $\overset{\mathcal{R}}{g}_{\mu\nu}$ and everywhere well defined normalized line field $l_{\mu}$ on spacetime $M$ may be used to ...
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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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Spin-orbit interaction in the frame of the nucleus

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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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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Construction of comoving tetrad frame

Suppose I have some system, for example the Earth orbiting the Sun. In the Sun's rest frame we can define some basis $e_{\mu}$. If the Earth has 4-velocity $u^{\nu}$, how would one transform to the ...
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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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Newton's first law and Inertial systems

Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that ...
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Lorentz boost in curved spacetime

In Minkowski space, Lorentz boost is provided by the vector field $$b^{\mu} = a(x \partial_t - t \partial_x)$$ for some arbitrary constant $a$. The integral curves of this gives the trajectory of an ...
Brain Stroke Patient's user avatar
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What frame of refernce to select in statistical mechanics?

Suppose we have a solid particle suspended inside a fluid such as an ideal gas, as shown in the following picture: Our system is the solid particle and the environment is the gas (which acts as a ...
Antonios Sarikas's user avatar
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How to apply a screw motion for this case?

I'm completely new to the notion of a screw motion. As far as I know, it carries out the the rotation and translation simultaneously in comparison with the homogenous transformation matrix that ...
CroCo's user avatar
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Does a charge radiate EM waves in non-inertial frame?

A charge at rest would not emit EM waves but an accelerated charge would. But what is the observer is itself accelerated, will charge radiate EM waves as laws of physics should be same for all ...
Akshat Jangra's user avatar
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What are virtual and apparent forces?

Acceleration in a rotating frame can be written as: $$\underline{a}=\frac{\partial^2\underline{r}}{\partial t^2}+\frac{\partial\underline{\omega}}{\partial t}\times\underline{r}+2\underline{\omega}\...
Alex Hughes's user avatar
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Can a pendulum at resting equilibrium position still demonstrate the Earth's rotation?

I conducted an experiment in my youth, creating a 'sand pendulum' hanging from the bedroom ceiling to a bowl of flour. I did not set the pendulum into motion, but rather wanted to see if the force of ...
Conor Murray's user avatar
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Why isn't spacetime flat in Ehrenfest's Paradox?

In a previous question, the metric in the frame of reference of a rotating disc takes the following form: \begin{align} ds^2 &= - dt^2 + dx^2 + dy^2 + dz^2\\ &= -\left(1 - \omega^2 ({x'}^2 + {...
Chang Hexiang's user avatar
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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 ...
emacs drives me nuts's user avatar
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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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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. ...
Phineas Nicolson's user avatar
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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 ...
Electric to be's user avatar
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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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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 (...
ThymeTravel's user avatar
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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 ...
rongarret's user avatar
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Scalar versus invariant in Newtonian mechanics

I looking up coriolis transport theorem for rotating refrence frames and while reading through this derivation he wrote: In Newtonian mechanics, scalar quantities must be invariant for any given ...
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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 ...
trampster's user avatar
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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 ...
Gold's user avatar
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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 ...
god of llamas's user avatar
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3 answers
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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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How do steam work in micro gravity?

Imagine an astronaut spills boiling hot coffee inside the orbiting space station, where do the steam go? I mean the coffee will likely form into many many balls but they at still very hot!
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What would an inertial observer see watching a particle as the local temperature drops below the electroweak unification temperature?

Above about $10^{15} K$ (the electroweak unification temperature), the Higgs field doesn't interact with elementary particles to grant them masses. Above this temperature, they are all massless. This ...
Logan J. Fisher's user avatar
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Can you experience length contraction in an accelerating reference frame?

Imagine I am floating in space some large distance X above a neutron star or high mass object and I am using rocket boosters to stay stationary relative to the object. Assume no other forces acting on ...
murram20's user avatar
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164 views

Decomposing velocities in the tetrad frame

Background At each point in a manifold we can find an orthonormal set of basis vectors $\hat{\mathbf{e}}_\alpha$ such that $$ g(\mathbf{e}_\hat{\alpha}, \mathbf{e}_\hat{\beta}) = \eta_{\alpha \beta} $...
user246795's user avatar
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840 views

Proof of principle of transmissibility of force

The principle of transmissibility states The point of application of a force to a rigid body can be moved anywhere along its line of action without changing the external reaction forces. My question ...
user716190's user avatar
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Frame of reference of a freely falling observer in General Relativity

Suppose I have an Einstein manifold (a manifold with a metric that solves the Einstein field equations. We can take $\Lambda = 0$ for simplicity in this example). The worldline of a freely falling ...
OutrageousKangaroo's user avatar
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Confusion about changing frames of reference in loop integral

I have what seems to be a pretty stupid problem I've been stuck on for days. Consider a three-point, one-loop interaction like the image below. For example, it could be a higher-order contribution to ...
Sotiris's user avatar
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Frame of Reference chosen in Hafele-Keating experiment

I do not understand why we chose the frame of reference which is at rest with respect to Earth's center. I get that it does not experience the acceleration due to centripetal force of Earth's rotation ...
Dipanshu Jain's user avatar
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Is there a way to know if you accelerate in empty space or in a uniform gravitational field?

If I'm in a room that accelerates through empty space uniformly I won't measure tidal forces. The situation is the same as standing on an infinite massive plane. So I could think, while looking ...
MatterGauge's user avatar
2 votes
1 answer
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Principle of Equivalence for non-uniformly accelerated system

Consider a frame being accelerated according to the law of gravity, $a=-K/r^2$ where $K$ is some constant and $r$ is measured from some point. Since here the acceleration is exactly the form of ...
GedankenExperimentalist's user avatar
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If someone in freefall towards earth used a telescope to look at someone in a spaceship accelerating at 10m/s/s, would they see their clock run fast?

Basically I'm quite confused about relativity haha. I've been told that the only two things that affect whether you'll observe someone else's clock ticking at a different rate than yours are Your ...
André Popovitch's user avatar
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$\left(\frac{d}{d t} \mathbf{L} \right)$ in a rotating coordinate system

We've a vector $\mathbf{A}$ lying in space and changing according to some rule. We introduce an inertial frame and find $\left(\frac{d}{d t} \mathbf{A} \right)_{i n}$ in it. We also introduce a ...
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What is the definition of a tetrad/vielbein?

This is hopefully a simple question about definitions. In mathematics, we have the tangent frame bundle, which is often just called the frame bundle. Local smooth sections are then called smooth ...
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