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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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Why is the laboratory frame energy always greater than the center of mass frame energy?

I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'. A lot of resources provided mathematical explanations....
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4answers
3k views

What's the speed of light when viewed from the side? [on hold]

Suppose a pulse of light is sent from $A$ to $B$ in a rigid triangle $ABC$. While the pulse is moving from $A$ to $B$, what is it's velocity relative to $C$? The special character of the photon among ...
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1answer
35 views

Doppler effect in light (Observer moving away from source)

I understand this intuitively and can picture it in my head, but when I do it on paper, the result is a sign difference that I cannot understand According to this diagram the wavelength = ct-vt = t(c-...
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How to find inertial frame of reference? [duplicate]

How do you find an inertial frame of reference or what you can regard as it? How do you evaluate the difference between a given frame and an inertial frame?
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1answer
33 views

Should the rest frame of a lab positioned on a gravitating body be considered an inertial frame in special relativity or not?

In Newtonian Mechanics, the rest frame of a lab on the Earth is considered to be (approximately) an inertial frame. The fact that a thrown ball is not moving on a straight line corresponds to the ...
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1answer
32 views

Direction of motion and position [closed]

What does it mean to determine the direction of the motion of an object,is it arbitrary?If so,can there be a negative position?
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1answer
160 views

Can we decompose a general Lorentz boost in a rotation followed by three boosts along the coordinate axes?

$\newcommand{\betabold}{\boldsymbol{\beta}} \newcommand{\xbold}{\boldsymbol{x}} \newcommand{\ebold}{\boldsymbol{e}}$ For $\betabold\in \mathbb R^3$, with $0<|\betabold|<1$, let us denote the ...
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2answers
66 views

Equivalence principle and local inertial reference frames

Local inertial reference frames are defined as follows: Pick a set coordinates for the manifold (assuming the manifold can be described by global coordinates) $\{x^i\}$ such that $g(p) = \eta$ is the ...
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3answers
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How to distinguish force from accelerating frame of reference?

So in this question Is this the reason why acceleration is said absolute?, author asks is his reasoning about absolute acceleration right, and he concludes that we can measure absolute acceleration of ...
9
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5answers
720 views

Paradox in the definition of work [duplicate]

I'm trying to understand the Oberth effect and came across this paragraph that seems crazy to me: when the rocket moves, its thrust acts through the distance it moves. Force multiplied by distance ...
6
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1answer
119 views

How would General Relativity be different if we assumed Galilean instead of Lorentz transformations?

If we assume a universe where Galilean transformations are the correct transformations between inertial reference frames, would GR be any different ? Gravitational and inertial mass would still be ...
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2answers
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What direction would an engine spin in space?

I am working on a science project in school with a friend on artificial gravity in space. We are both wondering if we could use normal electric motors, to let the outer ring move. Since there's no ...
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1answer
25 views

Motion of bodies released form rest in a freely falling cabin

In a paper I was solving, there was a question stated as such: A narrow but tall cabin is falling freely near the Earth's surface. Inside the cabin, two small stones A and B are released from rest(...
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2answers
40 views

Clearing up a discrepancy when deriving the Lorentz transformation from length contraction

I've been working through the Feynman Lectures on Physics. I'm currently on lecture 15: The Special Theory of Relativity, specifically 15-5, the section on the deriving the Lorentz Transformation ...
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1answer
32 views

Relativistic equations are medium dependent?

Einstein proposed that light travels with a universal velocity from Maxwell's equations on electromagnetism. But light has different velocity in different mediums, so does this imply that the ...
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1answer
66 views

Shortening of distances in Relativity Theory

I am studying relativity theory and I have understood why distances become shorter from the perspective of someone who is travelling close to the speed of light. However, later on I read that the ...
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1answer
36 views

Can an energy-momentum four vector include the quantities of all objects in a closed system?

Say I have a particle moving along the $x$-axis in the Earth's reference frame. It decays into an upsilon and a proton, each of which has an energy of 60 GeV. They are traveling in opposite ...
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2answers
94 views

The speed of light and the increase of relativistic mass [duplicate]

The speed of light theory predicts that as things travel faster their mass increases, so I think we if we look at a plane accelerating from mach one to mach two and measure the relativistic mass of ...
2
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3answers
91 views

Lorentz Velocity Transform With Tensor Notation [closed]

So I'm attempting to prove the Lorentz Velocity tranform: $${v_x}' =\frac{v_x-u}{1-v_xu/c^2} $$ using tensor notation. In this case obviously $\beta = u/c$ and $\gamma=(1-\beta^2)^{-1/2}$. The ...
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5answers
64 views

Distinction between various forms of relativistic energy

If I am told to find the total relativistic energy of a particle moving with some velocity v, do I use $E=\gamma mc^2$ or $E^2=p^2c^2+m^2c^4$ and take the square root. I am not sure the distinction ...
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1answer
45 views

Writing source four velocity for Lorentz boosted frame

I am trying to derive the source four velocity for Lorentz boosted frame. If the source four velocity for rest frame is denoted as $U^{\alpha} = (1, \bar 0)$, then how do I write this $U^{\alpha}$ for ...
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5answers
214 views

Why doesn't a charged particle moving with constant velocity produce electromagnetic waves?

A charged particle moving with an acceleration produces electromagnetic waves. Why doesn't a charged particle moving with a constant velocity produce electromagnetic waves? As far I understand, the ...
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2answers
70 views

If a massless observer is going at the speed of light, what speed will it measure of a light beam going parallel to it? [duplicate]

If a massless observer is going at the speed of light, what speed will it measure of a light beam going parallel to it?
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2answers
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Question on relative velocity [closed]

If a man is moving on a horizontal belt (with constant velocity w.r.t belt)which is also moving in the same direction with some velocity , then time w.r.t belt and w.r.t ground to travel some ...
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1answer
65 views

The absoluteness of time intervals in Newtonian mechanics: how is this input used?

One of the assumptions of Newtonian mechanics is that "time is absolute". Absolute, as I understand, implies that it is the same for all observers. But it's not quite true because if Tom's watch is ...
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1answer
52 views

Proving electromagnetic wave equation is Lorentz invariant

I am trying to prove that the electromagnetic wave equation is invariant under Lorentz transformation. I need to show that $$\frac{d^2U}{dx^2}-\frac{1}{c^2}\frac{d^2U}{dt^2}=\frac{d^2U}{dx'^2}-\frac{...
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2answers
103 views

In Minkowski spacetime diagrams, how is the formula $\tan(θ) = v/c$ for the angle between $ct$ and $ct'$ derived? [closed]

In Minkowski spacetime diagrams, how is the formula $\tan(θ) = v/c$ for the angle between $ct$ and $ct'$ derived?
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1answer
68 views

Derivation of coordinate transform for rotating frame of reference in relativity

I was wondering what is the relativistic coordinate transform between an rotating frame of reference and an inertial one. I have seen the following formula $$t=t'$$ $$x=x' \cos \omega t' - y' \sin \...
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1answer
48 views

Covariance of relativistic free particle Lagrangian under Lorentz transformation

How does the Lagrangian of a free particle: $$ L = - \sqrt{1- \Big(\frac{dx}{dt}\Big)^{2}} $$ transform under the co-ordinate transformation $(q,\tau)$? $$ q = \cosh(\psi)x + \sinh(\psi)t, $$ ...
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1answer
80 views

Lorentz covariance of Pauli-Lubanski pseudo-vector

The Pauli-Lubanski pseudo-vector is defined as: $$W_{\mu}=\frac{1}{2}\epsilon_{\mu \nu \lambda \rho}J^{\nu \lambda}P^{\rho}$$ Where the rotation and translation operators transform as: \begin{align}...
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1answer
43 views

Velocity in rotating frame projected onto axis in inertial frame

I want to look at the projection of the velocity of a particle in the rotating frame onto an axis in the inertial frame as a function of time. For example, I am calculating \begin{equation} \frac{d\...
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1answer
111 views

Invariance of spacetime interval directly from postulate

In Special Relativity, the spacetime interval $$\mbox{d}s^2 = \mbox{d}t^2 - \mbox{d}x^2 - \mbox{d}y^2 - \mbox{d}z^2 \tag{$\star$}$$ between two events is well known to be invariant under Lorentz ...
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1answer
36 views

Inertia when pulling on a rope [duplicate]

Imagine a fragile cord attached to a ceiling with its other side attached to a sphere. On the lower part another cord is atrached to the sphere. Now visualize you pull STRAIGHT downward on this cord. ...
2
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2answers
43 views

What is the correct frame of reference for determining the magnetic force on a charge?

If two charges are both stationary in a given inertial frame, F1, then neither charge should experience a magnetic force due to the presence of the other charge (qv = 0). If we accelerate one charge, ...
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0answers
48 views

Inertial Frame Of Reference

An object is placed far away from all the objects that can exert a force on it. A frame of reference is constructed by taking the origin and axis fixed on this object. Will the frame be necessarily ...
2
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3answers
106 views

Which one is moving? [duplicate]

If there are two objects moving relative to each other at a constant velocity, is there any experiment the bodies themselves can do to determine which one is moving? EDIT: The comments say "NO". So ...
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0answers
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Why is the speed of light chosen to be invariant by all frames of reference? [duplicate]

General relativity is built upon 2 postulates, one of which says that the speed of light in vacuum is the same for all observers. But why did Einstein chose the speed of light, why not choose the ...
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1answer
81 views

Can we really not tell if we are moving?

It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is ...
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3answers
77 views

Relative velocity equation

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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2answers
42 views

Galilean transformations of velocity

If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because $$ \frac{dx'}{dt'} = \frac{dx}{dt} -...
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3answers
100 views

Problem in understanding energy-mass equivalence

From whatever approach (either from modern approach by Hamiltonian or from Einstein's original approach by considering momentum), we can derive that $p_{i} = \gamma mv_{i}$ and $$H = \gamma mc^2 = \...
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1answer
39 views

Large Lorentz Boost

I understand the general concept of a lorentz transformation and a lorentz boost. What does it mean for a lorentz boost to be large however? My current guess is that this is referring to a large ...
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3answers
106 views

Electric car in different inertial frames

Assume there are two inertial frames $A$ and $B$ where $B$ is moving with speed $v$ relative to $A$. Suppose an electric car is stationary in frame $A$. The car is accelerated to speed $v$ to be ...
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2answers
75 views

Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in ...
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1answer
62 views

Does the space and time wraping depends on the relative velocity of frame of reference? [closed]

why i am asking this question is that, i thought that photon takes no time to reach the earth or any other place in the universe due to length contraction. the reason for this is space wraps completly ...
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0answers
65 views

Discrete structure of moving light in space-time. Does the light actually moving or it is triggered by cells of space-time? [duplicate]

I have an idea that seems for me interesting and exotic. It is not about a traveling with speed of light or observing a frozen light. Rather it is about the nature of light/photons and discrete ...
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0answers
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Is the change in kinetic energy of a system the same in all frames of reference in Newtonian Physics?

I learned in Grade 11 Physics that energy is conserved. That fact depends on the truth of the following fact. For any system of objects, if its mass and momentum remain unchanged in one frame of ...
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4answers
157 views

Relative motion and time

When someone reaches to a speed which is close to the speed of light with respect to earth, will he see the things actually moving faster than when he is in low speeds?
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2answers
72 views

Postulates of Special Relativity

I have two questions about SR postulates. So first question, I heard two formulations of first postulate: "If a system of coordinates K is chosen so that, in relation to it, physical laws hold ...
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1answer
69 views

Lorentz Transformation Exercise confusion

So there is this very simple situation in one of my exercices: In the earth's frame of reference a tree is at the origin and a pole is at $x=20$km. Lightning strikes at both the tree and the pole ...