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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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How does exactly time dilate in a gravitational field, and how is it judged by different inertial observers?

When I tried to answer the SE question, Clock on a pendulum, I faced an ambiguity regarding time dilation in the gravitational field. To make the argument clearer, I designed the simpler thought ...
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Why don't all the bodies accelerate as all of them are brought into motion through a force?

Like in a Projectile, why isn't there an acceleration in the horizontal direction? I've seen things like there isn't any force acting (in the horizontal direction) but for the body to move there must ...
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Is the slowing of time with speed exactly proportional to the increase of mass with speed?

This article on time dilation explains how time slows and mass increases with speed. Are they proportional? And is time dilation with a specific speed-mass equal to the time dilation with a ...
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Is a force exerted in all reference frames (inertial and noninertial?)

Let's say we got a toy car equipped with an electric engine. The engine exerts a force on the toy car and accelerates it when the car is at rest. Let's say I'm sitting stationary on a bench and I ...
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35 views

Interval invariance under galilean transformation

If we have the classical distance between two points in euclidean space, we define: $ S=(x^1)^2+(x^2)^2+(x^3)^2=\eta_{\mu \nu}x^\mu x^\nu $ If we want to make a coordinate transformaction of the ...
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Michelson-Morley Experiment as evidence for Special Relativity

Context: Our state (NSW, Australia) recently got a new syllabus for the year 12 physics course, and as such we are the first year going through with the new course. One of the things we need to learn ...
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5answers
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Where is the momentum going?

When a ball of mass $m$ collides elastically having velocity $v$ with a wall, then it retraces itself with the same velocity. Impulse on the ball due to wall is $2mv$ and since there is no external ...
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Does Einstein velocity addition rule work only for speeds, or for velocity vectors as well?

Einstein's Velocity addition rule (https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity) was used to describe to replace galileo's in account for relativity. However, in many ...
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What does the first postulate of Special Relativity mean?

Physical laws are invariant regardless. It can be an inertial frame and also a non inertial frame. Now it is the case you cannot do any experiment in an inertial frame of reference to test if you are ...
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Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$ What would be the physical implications if different ...
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Particles approach each other with .8c [closed]

Two particles travelling with velocity .8c (observed from ground frame) each approach each other. What is their relative velocity wrt ground frame. According to me they should be added. I am very much ...
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1answer
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Understanding Mach Principle

I cannot get the essence of Mach's Principle. In my undestanding, it states that the cause of the so-called "fictitious forces" which arise in non-uniform motion has to be found in the relative ...
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2answers
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Does a magnet moving in a uniform electric field experience torque?

Assume a uniform electric field of $E_y$ along $y$ in the lab frame of reference $(x,y,z,t)$. A simple magnet bar is set in motion at $v$ along $x$ in this electric field so that the alignment of the ...
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7answers
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Paradox regarding phase transitions in relativistic systems

The main question I would like to ask is whether quantities such as density are dependent on the frame of reference. I have searched several forums and the answer is somewhat controversial. Some ...
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Adjusting Newton's laws with relativity concepts

I break my question into three parts, with increasing "guessing status". Please tell me which of them (is any) is correct. Suppose I am an observer in an inertial reference frame, away from all other ...
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The confusing Wikipedia article about Euler's equation of rotation

Here is an article from Wikipedia on Euler's equations. In the derivation of those equations, I find the torque $\mathbf M$ quite confusing. There are two torques there -- $\mathbf M$ and $\mathbf M_{...
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1answer
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Why doesn't accelerating reference frames in QFT lead to horrible paradoxes?

Background So I remember that in Special Relativity while one can define acceleration things can go horribly wrong has happened historically (I'm sure there many other paradoxes). The real reason of ...
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1answer
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Relativistic rockets paradox [closed]

The next problem is, as I understand, a spin on the ladder paradox which is extensively documented everywhere. There are two rockets ($A$ and $B$), of length $L_p=1$m which are traveling in opposite ...
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Why is relativistic velocity addition not symmetric?

The Galilean velocity addition formula is $$u' = v + u$$ This is symmetric if one swaps $v$ and $u$. What are the fundamental reasons why the (generalized) relativistic velocity addition formula is ...
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1answer
49 views

Linear momentum of a system remains conserved, but with respect to which frame of reference?

I have studied that linear momentum of a system remains conserved. But i can't figure out with which reference of frame it is conserved. Is it conserved with respect to system reference frame or in a ...
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3answers
102 views

Time difference as a result of Lorentz boost

So I am given two clocks A and B moving in $S'$ frame with a velocity $V$ relative to $S$ frame. The two clocks are separated by a distance $L$ and are synchronized in $S'$ frame. The objective is to ...
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1answer
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Do the balls keep moving forever?

In a hypothetical world where there is no friction, and all collisions are elastic would an object in lateral motion be perpetually moving and never come to a stop? Assumptions: Perfect vacuum: zero ...
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Establishing an inertial frame of reference by observing a closed mechanical system?

Suppose one has a closed system of $N$ material points with known masses, $m_1 ,..., m_N$ . Also given are their coordinates as functions of time, ${\bf r}_1(t), ..., {\bf r}_N(t)$, in some laboratory ...
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Find angle from two perpendicular relativistic Lorentz boosts

I have a frame $s'$ moving with velocity $v_1$ along the x-direction with respect to a frame $s$. A frame $s''$ is moving with velocity $v_2$ along the y-direction with respect to $s'$. I want to ...
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1answer
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Lorentz transformation boosts as matrices

I have seen Lorentz transformation boosts (say, along the x-direction) written as (in $c=1$ units): $$ \left[\begin{array}{cccc}{\gamma} & {-v \gamma} & {0} & {0} \\ {-v \gamma} & {\...
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Inertial frame and its transformation in anti-de Sitter spacetime

From the wikipedia, I learned and was able to follow mathematically the definition of anti-de Sitter space. As the maximally symmetric solution to field equations with negative cosmological constant, ...
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3answers
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Lorentz transformations for time co-ordinates (STR)

I am little bit confused with the implication of Lorentz transformations for time co-ordinates or atleast how to apply those! Consider 2 frames of reference $O$ and $O'$ in which $O'$ is moving with $...
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What is the difference between a translation and a Galilean transformation?

What is the difference between a translation and a Galilean transformation?
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4answers
183 views

Why can't we define absolute rest?

If, according to the theory of relativity, as objects gain velocity and approach the speed of light then time for them slows down, why can't we define absolute rest as the inertial frame in which time ...
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2answers
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Finding properties of Poincare Transformation

I have started studying the Poincare group for the first time, in preparation for my first QFT course, and I wish to be able to solve the following problem: A Poincare transformation ($\Lambda,a)$ ...
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1answer
103 views

Reference frames symmetry in Special Relativity

I have a couple of questions related to reference frames in STR. Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c. I'd like to look at this example ...
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196 views

If an atom can have only discrete energy values, why it can move on any speed?

Atom, as a quantum system can have only certain energies. Also, energy, specifically kinetic energy depends on velocity, which should mean, that an atom should move only on some strict velocities, and ...
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Thought experiment and possible contradiction between electromagnetism and special relativity (Part I)

I have designed a simple and qualitative thought experiment through which I believe that I have encountered an inconsistency in the relativistic electromagnetism. A point charge $+q$, with respect to ...
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1answer
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Special Relativity Frame Ambiguity [duplicate]

If I have some predefined coordinate system — “my rest frame,” then I pick an “inertial frame” moving at some velocity with respect to my “rest frame.” Special relativity states that in the rest frame,...
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2answers
105 views

Why physics should be the same in all inertial frame? [closed]

One of the postulates of special relativity is that physics should be the same in all inertial frame. Suppose we have two observers $A$ and $B$ suppose that $A$ is accelerated. Now suppose that we ...
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0answers
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Why is force invariant under a Galilean transformation? [duplicate]

I've had a look around online, but I haven't been able to find something which answers this in a way I understand. Essentially, I'm trying to figure out why force is invariant under a Galilean ...
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2answers
92 views

Can Newton's laws be reformulated with reference to “relative” frames

I was reading: https://arxiv.org/abs/1205.2326 page 2 which gives thorough discussion of the three laws. In particular there is a refutation of the (paraphrased) 2nd law implies the first because ...
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4answers
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Einstein's train, considering the thunder

From Einstein's "easy" explanation https://www.bartleby.com/173/9.html (Yes, I have reviewed 8 other answers to similar questions. Please bear with me.) M is on the platform, T (aka M') is on the ...
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Which frame to consider for time dilation? [duplicate]

Clearly for constant motion we cannot define absolute rest or motion. So ,when dealing with time dilation problems for example twin paradox , how do we define which frame is in motion? If we ...
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2answers
96 views

Basic Special Relativity Question [closed]

I am trying to understand the implications of c being relative to the frame of reference. Is the following analysis correct? N is on a slow train moving 3 m/s and M on the platform next to N both ...
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5answers
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Sum of gravitational force $W$ and contact force $N$ on a book at rest on table is not 0

There is a book on the table fixed rigidly to the earth. The book is at rest with respect to the earth. The acceleration of this book with respect to the earth is 0. The forces on this book are a) ...
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1answer
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Using Lorentz transformations with variable velocity

A particle is moving in a system of reference $S$. In its proper system of reference, say $S'$, the particle is still and it is described by the event $(c\tau,0,0,0)$. In the inertial frame $S$, the ...
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Are laws of Physics same in frames having zero relative acceleration?

If two frames have the same acceleration, then they'll be moving with a uniform speed with respect to each other. Are laws of Physics the same in these two frames?
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Grasping (Inertial) Frames of Reference [duplicate]

I am new to studying Special Relativity and have some trouble truly understanding what the phrase (Frame of Reference) tries to imply. So I understand that an inertial frame of reference, for example,...
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3answers
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Is kinetic energy relative? [duplicate]

Assume there is a rocket with 10 kg of fuel in a large empty space without any external forces such as gravity. Rocket burns 1 kg of fuel and gets a $v_1$ velocity gain. Now it is moving in $v_1$ ...
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How can we tell if the Earth is spinning without any external references? [duplicate]

The rotation of the Earth about its axis makes it bulge at the equator and contract at the poles due to the centrifugal forces. How do we know, without any external references, that the Earth is ...
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Lorentz Transformation Perpendicular Photons

I'm trying to derive the Lorentz Transformation on my own but I'm stuck. This is probably something stupid, but I cannot figure out why I am not getting this right. enter image description here Here'...
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1answer
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The Proof of $\cos\phi=\gamma$ Equation in Special Relativity [closed]

In the Introductory Special Relativity book, by W. G. V. Rosser, page 182, Section 7.3, the author is defining the 4-vector methods using complex numbers. In his derivation, he writes the following ...
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With respect to what does a Gyroscope maintain its orientation?

Assume ideal conditions, no friction, no energy loss in any form. Just an ideal gyro, in ideal conditions, spun into rotation and left alone. And placed somewhere on earth. From what I've read so ...
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1answer
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Which Frame of Reference is Correct?

I am reading a lot about the theory of special relativity, but I have a very basic question about this theory I still don't understand. Consider a particle in two inertial reference frames $\Sigma$ ...