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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${}$Michelson-Morley experiment

In the Michelson-Morley experiment, the light from a source is passed through a semi-silvered mirror from where a part of it moves horizontally towards a mirror (from where we calculate $t_1$) and a ...
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Interaction between various forces, by which one is to calculate an angle?

I am new to Newtonian mechanics, and was wondering about the following question. I basically have the ingredients for the answer, but I cannot seem to find the way to put this together into one ...
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Different forces from different inertial frames?

I've been having trouble understanding this equation here derived in the picture given below. If I change reference frames to one which is moving at a velocity u with respect to the first frame, then ...
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Is there a flaw in Newton's first law? [on hold]

When there is no external force, the object can move in a straight line or rotate around its own center of mass in a uniform manner. When there is no external force, the object does not necessarily ...
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Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
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To Be Forever Young [duplicate]

It is clear from the Lorentz Parameters, applied to Einstein's Equations, that as velocity, v approaches speed-of-light, c, the denominator (1 - [v/c]) tends to zero; when v=c, time, t=0: time stops?! ...
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Why is the Earth not an inertial frame of reference?

From many sources I have found the explanation that the Earth is not an inertial frame of reference because it rotates around its axis. However, nobody mentions the rotation about the Sun. What I ...
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139 views

Intuitive explanation for the Lorentz transformation for time

I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
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Still confuse about tensor

In special relativity, a four-vector $\mathbf{x}$ in an inertial frame is related to $\mathbf{\overline{x}}$ through a Lorentz transformation $\mathbf{\Lambda}$: \begin{align} \overline{\mathbf{x}}...
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Is Landau&Lifshitz's argument for the classical Lagrangian's symmetries too strict?

I realize that this paragraph has raised more questions on stackexchange, but I wanted to ask this question nevertheless since I want to discuss it in terms of a counter-example. I’ve already ...
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A concise definition of a frame of reference in Newtonian mechanics?

I've read Wikipedia's entry on frame of reference and also followed all of the references cited in the text (Salençon, Brillouin, Norton, etc) but I'm struggling to find any concise definition in all ...
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Sound wave and Principle of relativity

Principle of Relativity: "An experimenter doing an experiment in an inertial frame of reference can never measure the velocity of its own frame of reference. OR a law of physics is never expressed ...
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Is temperature a Lorentz invariant in relativity?

If an observer starts moving at relativistic speeds will he observe the temperature of objects to change as compared to their rest temperatures? Suppose the rest temperature measured is $T$ and the ...
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Validity of Newton's second law in a non-inertial reference frame

Suppose two observers are mutually interact through gravitational force (assuming they are alone at space). If the reference frame is fixed in one of the observers could the observer in the reference ...
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745 views

What is the Galilean transformation of the EM field?

Consider a reference frame $S$ and which we observe some electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$. Let $S'$ be a reference frame moving at a constant velocity $\mathbf{u}$ with ...
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Motivation for the abandonment of inertial frames in general relativity [closed]

Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just ...
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Relative velocity equation [on hold]

In rectilinear motion, to find the relative velocity of a car with respect to a train, we subtract velocity of the train from that of the car. We use this method when the car is moving on the road. ...
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Why the velocity $v$ is taken as value and not as definition in special relativity equations?

Why the velocity $v$ is taken as a value and the definition of velocity not applied on a relativistic equations? The equations of time dilation and length contractions as we know are $$L = {L_0}{\...
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Transforming between two inertial frames

Suppose I have two inertial frames, $ S $ and $ S' $. In the first frame, let $ a = \frac{\text{d}^2 x }{\text{d} t^2} $ and in the second, suppose $$ a' = a \frac{\partial f}{\partial x} + v^2 \...
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Colliding elastically in lab and CM frame

Two spherical bodies of mass $m_1$ and $m_2$ are placed in gravity free space as shown. Initially, the body with mass $m_2$ is at rest and the body with mass $m_1$ approaches the other body with a ...
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Properties of inertial reference frames from different perspectives

I was thinking about the following, a block on an inclined plane no friction. However this inclined plane is in a truck accelerating forward. Note: the inclined plane doesn't slip. So I wondered what ...
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Example of anisotropy frame of reference

I have studied that an inertial frame of reference is the one that is homogeneous, isotropic and time-independent. For instance, a reference frame on a rotating wheel is not an inertial frame of ...
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Clarification of proper time and inertial frame of reference

“Standing beside railroad tracks, we are suddenly startled by a relativistic boxcar traveling past us as shown in the figure. Inside, a well-equipped hobo fires a laser pulse from the front of the ...
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Exact difference between '''Fermi normal coordinates''' and ''Riemann normal coordinates'''? [duplicate]

I want to know the exact difference between '''Fermi normal coordinates''' and ''Riemann normal coordinates'''? Here is a same question, but it's hard for me to understand. Difference between Fermi ...
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Heisenberg uncertainty and Lorentz contraction

Consider a particle in a frame moving with speed $v$ relative to the lab frame. By Lorentz contraction, the width of the wavefunction will be smaller in the lab frame, resulting in smaller $\Delta x$. ...
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The interference paradox

This is a thought experiment I created myself. Imagine two radio sources fixed at the ends of a rocket and they produce signal of same frequency such that they arrive at the center simultaneously and ...
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What do you mean by Newtonian space? [closed]

What do you mean by Newtonian space? When you see this question, most of you might be thinking that I am trying to crack a joke or something..but no. This was a genuine doubt which one of my friends ...
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Why can't we take space as universal frame of reference?

Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be ...
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Does the derivation of the Lorentz transformation depend on space having at least two spatial dimensions?

Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both ...
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What is the relativistic Hamiltonian for a charged particle in an EM field, using the magnetic scalar potential?

The Hamiltonian for a relativistic charged particle moving in a static electromagnetic field is the well known: $$H=c\sqrt{\left(\mathbf{P}-q\mathbf{A}\right)^{2}+m^{2}c^{2}}+q\phi$$ where,\begin{...
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Is it possible writing conservation of relativistic energy in this naive way?

Conservation of charge or rest mass can be written in this way and it is Lorentz invariant $$ \nabla \cdot (\rho \mathbf{u}) + \frac{\partial \rho}{\partial t} = 0 $$ So we could be tempted to naively ...
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On local inertial frame and acceleration in general relativity

[Q1] In the general relativity, a local inertial frame is mentioned. The local inertial frame is a notion, which is related to (or represents) the equivalent principle. Here, I understand that, in ...
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Difficulty in understanding why a car slips towards outside as seen from inertial frame

While turning on a road, why does a car slip towards outside, if we are observing the car from inertial frame of reference, i.e center?
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How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center)

A particle is revolving in horizontal a circle of radius $R$ with constant speed of $|\vec{v}|$ and constant angular velocity $\omega$. There is another observer standing inside the circle, at a ...
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Special Relativity pothole paradox [duplicate]

Consider a man who is 1 metre in width and is running (at relativistic speeds) towards a pothole in the ground which is also 1 meter in width. In the reference frame of the man it appears as though ...
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In Special Relativity, is it allowed to ask 'How much time has elapsed in a second inertial frame at a particular moment in the first inertial frame'?

Or is it a meaningless question? For example, A and his friend B are the same age initially. B travels relative to A at a very high speed. A keeps observing B from his frame. At one moment, A ...
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To prove: the integration measure is Lorentz invariant (Schwartz's problem 2.6b)

I am stuck on Schwartz's ("Quantum Field Theory and the Standard Model") problem 2.6b, and would be grateful for clarification. (I'm aware that this question has been asked and answered elsewhere (...
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What's incorrect about this reasoning regarding special relativity?

Say two spaceships start at the same point and from the vantage point of your inertial reference frame $S$, Spaceship A travels at $.75c$ and Spaceship B travels at $.25c$, travelling in the same ...
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Isn't inertia experience by person in moving bus same as torque

When a bus moves suddenly, the person standing in it tilts backwards. This concept is explained using inertia(tendency of body to resist change in its state of motion) but when the bus moves suddenly, ...
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How to prove a 4D vector is a 4-Vector?

This is a fairly open ended question. Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
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Special Relativity - Reference Frames $S$ and $S'$

Consider the standard arrangement in special relativity. Let S' move in the +ve x-axis with a velocity V with respect to S Question: S then moves with a velocity -V with respect to S'. Is this an ...
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How to prove the constant speed of light using Lorentz transform?

I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way ...
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Special Relativity- Lorentz transformation

We know that in lorentz transformation , x'= lorentz factor*(x-vt) Suppose, that in unprimed frame , x=0 ; and the primed frame moves with velocity c wrt unprimed one. Then accor to the transformation,...
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Accelerated frame vs gravity frame

Can accelerated frame change curvature of space as gravity does? Can there accelerated frame be pure inertial frame?
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Lagrangian of free particle in non-inertial frame

As in Landau & Lifshitz 1st chapter "If an inertial frame К is moving with an infinitesimal velocity e relative to another inertial frame K', then v' = v+e. Since the equations of motion must ...
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What is the relativistic energy of a bounded static particle?

Premise: The speed of light is set $c = 1$. Let's consider an electron in an external electromagnetic field. Its four-momentum will be $$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$ ...
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Does Sagnac effect imply anisotropy of speed of light in this inertial frame of reference?

There seems to be a consensus that the one - way speed of light is anisotropic in a rotating frame of reference (Sagnac Effect). According to this article Einstein synchronization "looks this ...
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Prove no contraction in the orthogonal directions

When talking about relativity, we always mention Lorentz contraction. If a body is moving with velocituy $V$ in the $x$ direction, its length will be contracted in that direction. The length remains ...
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Quantum mechanical origin of pseudo forces

I am thinking about this from quite some time but could not come up with any satisfactory explanation. In a nutshell, how would one explain the pseudo forces felt by non-inertial observers given that ...
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5answers
696 views

Explanation for a much simpler version of the twin paradox?

I have seen the classical twin paradox before. It uses a twin stationary on Earth and the other traveling away and back. I have seen many contradictory solutions for it, some use general relativity, ...