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Questions tagged [inertial-frames]

A specific reference frame that describes its coordinates in a manner that does not depend on time and is isotropic.

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Do these two refer to the same reference frame? [duplicate]

What exactly is the difference between a reference frame and a coordinate system (with respect to classical mechanics only)? Can we claim that these two coordinate systems is from same reference frame?...
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Can a non-inertial frame be viewed as an inertial frame?

Let's consider a non-inertial frame with an acceleration of $a$ relative to an inertial frame, if $a$ is really small and we don't need extreme accuracy, can we ignore this acceleration and treat this ...
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Galilean invariance of the wave equation

Given the wave equation for a material wave: $$\frac{\partial^2 \phi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2},$$ we can apply the Galilean transformation $x'=x-Vt$ and $t'= ...
Hubert van Luytelaar's user avatar
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Meaning of general Lorentz transformations

According to Wikipedia, the Lorentz transformations for two inertial frames are written:$$\begin{cases} t'=\gamma(t-\frac{\mathbf {r}_{\parallel }.\mathbf{v} }{c^{2}} )\;\;\;(*)\\\mathbf {r'...
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Cause of Coordinate Acceleration in Free Fall [duplicate]

So I understand that objects in free fall are in an inertial frame, at rest in terms of relativity. However, from a person on the surface of earth, a falling apple is accelerating constantly until it ...
Marco Chacon's user avatar
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Derive Minkowski metric from Lorentz transformation

I am trying to learn special relativity. My goal is to prove that given the fact that a 4-vector $\mathbf{x}$ is transformed as $\mathbf{Lx}$, between two inertial reference frames where $\mathbf{L}$ ...
morpheus's user avatar
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Motion of person in bus in inertial and non-inertial frame

A person is sitting in a bus that is moving with constant velocity, due to friction their is no relative velocity between bus and the person. Suddenly the bus starts to move with a constant ...
Hrishikesh Pandey's user avatar
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Einstein's notion of "covariant"

In his The Meaning of Relativity, pg. $11-12$, Einstein explains the notion of "covariant" along the following lines: Consider a point $\mathbf x$ on a straight line $\mathbf x -\mathbf A=\...
Awe Kumar Jha's user avatar
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Proper Time Along a Trajectory with Changing Velocity

I'm relatively new to SR and just encountered the Twin Paradox. I don't think I had trouble understanding the resolution to the paradox, but I was curious how an observer in an inertial reference ...
Lambda's user avatar
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What effect would relativity have for an objective with absolutely no momentum? [closed]

I know as you near the speed of light time slows down and mass increases to near infinite. What I'm curious about is what would happen if an object lost all momentum. No movement at all not even the ...
joshua landry's user avatar
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Clocks are not synchronized in moving system (book of David J. Griffiths) [closed]

In the electrodynamics book of David J. Griffiths, in section 12.1.2, there is a paragraph about the synchronization of the clocks on a moving train. I don't understand why " Clocks that are ...
Smith Jack's user avatar
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Length Contraction: is $t'$ or $t = 0$?

To demonstrate my confusion - let's say there is a rod traveling with velocity +v relative to S, and in S, the length of the rod is measured to be $L$. If I want to go from S to S', the frame where a ...
Emil Sriram's user avatar
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Non-inertial frames in quantum mechanics

In classical physics, non-inertial frames necessitate adjustments to Newton's laws due to acceleration and rotation, yet in general relativity, Einstein successfully incorporates such frames. Why does ...
Vishnu's user avatar
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Who will die first between two people on different spaceships, where both are in inertial frames? [duplicate]

Here's something that's really been confusing me. If two people on separate spaceships pass each other by, where both are in inertial frames, person A (on spaceship 1) could say that he is at rest and ...
Andrew Flynn's user avatar
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Energy of moving Sine-Gordon breather

A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation $$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$) $$ E = \int_{-\...
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Black hole production via light speed [duplicate]

As a test particle with rest mass approaches $c$ relativistic mass increases to infinity, does this mean that the energy required to continue the acceleration will create a black hole (as time also ...
John Pryme's user avatar
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Relative speed in unpolarized cross-section

In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
Rafael Grossi's user avatar
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How to prove $ g^{\mu\nu}\Lambda^{\rho}{}_{\mu}\Lambda^{\sigma}{}_{\nu}=g^{\rho\sigma} $ for the inverse metric?

In Srednicki's book, we have \begin{align*} g_{\mu\nu}\Lambda^\mu{}_\rho\Lambda^\nu{}_\sigma=g_{\rho\sigma} \end{align*} and let $ \Lambda \to \Lambda^{-1} $, use the relationship $ (\Lambda^{-1})^\...
liZ's user avatar
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In SR, why do we claim length contraction rather than faster than $c$ travel in the rocket frame? [closed]

In special relativity, a rocket traveling at .5c will take .86 years (in the astronauts frame) to travel 1 light year (in a stationary observer frame). There are two possible ways to look at this ...
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Meaning of of inertial frames in special relativity [duplicate]

One of the postulates of special relativity is The laws of physics are the same in all inertial frames There is a mention of inertial frames in the postulate. But the predictions of relativity are ...
Niladri Sarkar's user avatar
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Linearity of Amplitudes and Lorentz Frames

I know that this question may be a bit weird, but I decided to ask. Assume I have an amplitude, say in QED, which depends on a set of four-momenta $\{p_1,\ p_2,\ p_3,\ ...,\ p_n\}$. Further assume ...
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Do we need a notion of the center of mass in special relativity?

I don't see much mention of the center of mass in discussions of special relativity. I understand that there is a definition for it, but it is relatively obscure and seems to depend on mass-energy ...
Aidan Beecher's user avatar
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Differential form of Lorentz equations

A Lorentz transformation for a boost in the $x$ direction ($S'$ moves in $+x$, $v>0$) is given by: $$ t'=\gamma\left(t-v\frac{x}{c^2}\right),~x'=\gamma(x-vt)$$ In the derivation of the addition of ...
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Do magnetic force depend on frame of reference? [duplicate]

Consider two point charges If both charge are moving with velocity v in same direction with respect to a inertial frame of reference. Will the magnetic force would be zero between them? If one charge ...
Abhinav's user avatar
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${}$Doppler shift

If observer is moving and source is at rest then i can treat the scenario with approach in which observer is at rest and source is moving since this is what will be happening according to the observer ...
Muzzammil Ahmed's user avatar
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1 answer
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About Lorentz Invariant

I am reading Schwartz's book, Quantum Field Theory and Standard Model. I have some questions about invariance under Lorentz transformations. In the book, the scalar fields are functions of space-time ...
MichaelS's user avatar
2 votes
1 answer
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Lorentz Boosts and Hyperbolic Quaternions

How do you use the Hyperbolic Quaternion formula for a Lorentz Boost? I'm refering to https://en.wikipedia.org/wiki/Hyperbolic_quaternion : $$t' + x'r = (\cosh(a) t + x\sinh(a)) + (\sinh(a) t + x\cosh(...
entiges_Enton's user avatar
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Does relative velocity apply before or after the impulse?

I'm solving the following question from Kleppner and Kolenkow: My solution differs from the textbook solution not only in the magnitudes in parts (a) and (b) but also the conclusion in part (c). ...
Vulgar Mechanick's user avatar
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Invariance of Acceleration vs Invariance of Magnitude of Acceleration and help with proof

This question is a half-rant, half-question, as I am genuinely curious as to what the standard physics view is on this question. As someone who has studied math extensively (but not physics), please ...
atonaltensor's user avatar
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I am basically having doubt about where Lorentz transformation is being applied?

I was solving example 12.14 in Griffiths' Introduction to Electrodynamics) The question was: A point charge $q$ is at rest at the origin in system $S_{0}.$ What is the electric fieldof this same ...
nbkhdbkhbkndjdjbj's user avatar
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3 answers
130 views

Can you tell who is moving through time? [closed]

In relativity, there is no way to tell if you are moving through space. So, if you were inside of a box, there would be no way for you to tell if you were moving or not. However, can you know who is ...
John W's user avatar
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If velocity is relative, why does time dilate for some observers and not others? [duplicate]

I'm trying to get my head around relativity and time dilation. What I can't figure out is how time can dilate for fast-moving observers if all velocity is relative. Here's a scenario: Alice and Bob ...
Justin Morgan's user avatar
2 votes
3 answers
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If an observer was trapped in a closed box with no way to interact with the external surroundings how will he know if he is moving or at rest [duplicate]

I am a high-school student. Recently we learned the concepts of relative motion and velocity. The idea that anything in motion can subsequently be at rest depending on the frame of reference ...
AMAL's user avatar
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2 answers
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How is it that energy of matter yields gravity if the amount of energy in a system is frame dependent while the force caused by gravity is not?

I've been told that the gravitational field arises due to the energy density terms in the stress-energy tensor of matter and therefore that all energy of matter exerts a gravitational field effect, ...
Hadi Khan's user avatar
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Seemingly equivalent linear form of the Sagnac effect

This is a derivative of the question regarding the Sagnac effect. Judging from the metric $ds^2=-dt^2+(rd\phi)^2$ for a constant $r$ for this question, it should be no different from that on a line ...
Hans's user avatar
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Special relativity and accelerating twins

Imagine two twins synchronise their clocks and then twin A quickly accelerates to velocity v. After a time T twin B quickly accelerates to 2v and catches up with twin A. Which one will be younger? How ...
Moji Ghadimi's user avatar
2 votes
1 answer
141 views

Transformation of wavefunction

While learning QM, I was wondering how would the wavefunction of a particle, suppose charged particle, look for different observers moving with respect to each other. To begin with, let the electric ...
Users's user avatar
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The principle of relativity and why Inertial frames attribute the same velocity to one another

In introductory texts introducing relativity, it is always assumed that frames measure the same velocity for each other. For example if frame S' moves at velocity v with respect to respect, then S ...
Talha Ashraf's user avatar
1 vote
2 answers
131 views

On Landaus&Lifshitz's derivation of the lagrangian of a free particle [duplicate]

I'm reading the first pages of Landaus&Lifshitz's Mechanics tome. I'm looking for some clarification on the derivation of the Lagrange function for the mechanical system composed of a single free ...
GeometriaDifferenziale's user avatar
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1 answer
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Length contraction doesn't affect the perpendicular direction...but it seems as if it can

A is a stationary observer watching B who is moving relative to A. Both of them hold two identical light clocks and each shoots light rays to estimate the lengths of their clocks. A's light ray will ...
I am Einstein's user avatar
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Unsubstantiated assumption in a problem about two particles rotating around each other

In solving the following problem from Kleppner and Kolenkow the solution assumes there is a point $C$ along the line joining $m$ and $M$ such that Both $m$ and $M$ execute uniform circular motion ...
Vulgar Mechanick's user avatar
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2 answers
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How Fast Must a Man Run to See Rain Falling horizontally?

The fact that tan 90° is undefined indicates a key issue in the problem. Does this mean it is impossible to observe rain falling at 90 degree? When rain is observed to be falling at 90° with the y-...
Dron Bhattacharya's user avatar
2 votes
3 answers
195 views

Sagnac effect viewed in the rotating frame

Consider the Sagnac effect. It is quite simple viewed from the rest inertial frame what the time difference should be. However, if viewed from the frame fixed to and rotating together with the emitter/...
Hans's user avatar
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Time Dilation when they meet

I am starting over because what I was asking was unclear. I have read many articles, such as How can time dilation be symmetric? and others suggested by people here and understand the overall concepts ...
DMacks's user avatar
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Why $\sigma$ wouldn't change under standard Lorentz transformation in Weinberg QFT V1 Ch2

Weinberg defines one particle via state vector $\Psi_{p,\sigma}$ that is eigenvector of four-momentum and a label $\sigma$ to denote all other degrees of freedom. This is physically understandable, ...
Ting-Kai Hsu's user avatar
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1 answer
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Centre of mass and reduced mass in classical mechanic

Can we derive reduced mass from Cetre of mass equation if CM is not taken as origin? And Under what conditions can reduced mass concept be used or not?
Phyoe Kent's user avatar
1 vote
1 answer
52 views

Suppose there is no friction force to balance Coriolis force? [closed]

Question 1: Why in rotating frames, is it necessary that an object's acceleration is always directed radially outwards in the $\hat{r}$ direction and why is there no component in the tangential ...
Kampann's user avatar
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Special Theory of Relativity Contradiction [duplicate]

I’m struggling with an apparent contradiction of special theory of relativity (STR) that I cannot resolve. Imagine two twins flying by each other in space along the same straight line but in the ...
Becarev's user avatar
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2 votes
3 answers
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Is a Lorentz transformation allowing an infinite value $c$ still a proper Lorentz transformation?

Is it correct to say that inertial systems are related by Lorentz transformations even if we do not know if the "invariant speed" is finite or infinite? To me, this is incorrect because $c$ ...
Real Pattern's user avatar
1 vote
3 answers
161 views

Whether nonlinear coordinate transformations are symmetries of flat spacetime

I am editing this question after the answers are posted just to present my question a little clearly (without changing the main theme of the question). Moreover, this question is solely about flat ...
Solidification's user avatar

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