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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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Electromagnetic field conversion in non-inertial frame

I found these equations for electromagnetic field conversion in inertial frame for non relativistic case. If I have permanent static magnetic field with 3 components $B_x, B_y, B_z$ and permanent ...
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1answer
24 views

Question on force invariance under the Galilean Transformations (GT)

By the Galilean transformations, one can easily derive that two different inertial observers 1,2 always measure the same forces. That is: $$ \vec{F_1} \ \left(\vec{r_1}, \frac{d\vec{r_1}}{dt_1},t_1\...
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CONSERVATION OF MOMENTUM SPECIAL RELATIVITY PROOF [on hold]

Having a hard time figuring out what to do. I understand that we need to use the four vector and some kind of momentum transformation but I have no idea how to proceed with that.
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2answers
65 views

Twin paradox problem from a perverse perspective

Reformulation of the problem I want to study twin paradox but considering that the reference frame of the twin that travels to Alpha Centauri has no velocity. Instead of considering that the twin who ...
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2answers
56 views

What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
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2answers
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Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, ...
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1answer
43 views

How does the Equivalence Principle imply that derivatives of the metric vanish in a freely falling frame?

Why do the first derivatives of $g_{\mu\nu}$ vanish in a freely falling coordinate system? I would like to start from the Equivalence Principle that for any point in spacetime there exists a locally ...
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1answer
43 views

Relativistic effect in a current carrying wire

In many places I read that in the rest frame of a current carrying wire (electrons in motion), the spacing between the positive ions is length contracted and equal to the length contracted spacing ...
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0answers
53 views

Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
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1answer
79 views

Energy can be created

Consider a device which converts kinetic energy into electrical energy ( just like piezoelectric generator). Now I install this on two trains of very high mass approaching each other (moving in ...
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1answer
43 views

Why acceleration due to gravity is not reliably defined?

In Sean Carroll's Spacetime Geometry, there is the following line on Page No.50 in 2014th edition: "The acceleration of a charged particle in an electromagnetic field is uniquely defined with respect ...
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5answers
154 views

Is Relativity of simultaneity just a flaw in perception?

So I went through a couple of different books on special relativity ( including Einstein's own book) and I just can't seem to accept relativity of simultaneity as a real thing. I'll explain my ...
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2answers
66 views

Is force really defined by the second axiom of Newtonian mechanics? [duplicate]

Many people claim that force is defined by the second axiom of Newtonian Mechanics, which is: "In an inertial reference frame, the rate of change of momentum of a particle equals the sum of the ...
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1answer
432 views

Newton's theory of gravity is covariant under Galilean transformations

We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
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2answers
120 views

Can an object have constant speed and tangential acceleration without undergoing circular motion?

Is it possible for an object to be moving with constant speed and a constant magnitude of acceleration tangent to this velocity but NOT move in a circular path? If there are other situations could I ...
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1answer
85 views

How length is an invariant in Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time. But how can we prove (any postulates or theory) that the length is an ...
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Pole in the barn paradox [duplicate]

I was reading Schutz relativity when I came across the barn-pole paradox. I have seen many videos and explanations on the internet including Minkowski diagrams but I don't seem to understand it enough ...
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2answers
71 views

What does $U^{-1}(\Lambda)\phi(\Lambda y) U(\Lambda) = \phi(y)$ physically mean?

In QFT, let $U(\Lambda)$ denote a unitary representation of the Lorentz group. Let $\phi(x^{\mu})$ be scalar field operators in the Hilbert space; in other words: $$U^{-1}(\Lambda)\phi(x^{\mu}) U(\...
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1answer
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Reference frames and Newton’s second law

I have an understanding Issue. We were told that apparent weightlessness was due to the absence of Normal Reaction force.The example chosen was a man in a lift...the latter moving with different ...
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1answer
46 views

Do Events Conditional to Simultaneity Occur in Every Reference Frame?

Imagine a train with a table that contains a light on both ends (so that the line between the two sources of light is parallel with the line of motion of the train) and a light sensor in the perfect ...
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0answers
43 views

Violation of Einstein's speed of light postulate? [duplicate]

Consider the following scenario. You are moving towards the left with velocity c (Speed of light) and your friend is moving to the right with velocity c as well. Now the relative velocity of your ...
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1answer
69 views

Einstein's Simultaneous Lighning and the Lorentz Transformation

I am reading Einstein's book, "Relativity: the Special and General Theory" translated by Robert W. Lawson, and I have some questions concerning Special Relativity -- specifically, the thought ...
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2answers
66 views

Relativistic effects on charge

Does charge of the body gets affected by relativity or is constant in all frames of references?
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1answer
62 views

Is it correct to use Newton's third law on all these scenarios? [closed]

So I was thinking about Newton's third law for sometime lately, and my problem is more about the concept, I'm fine with solving problems. I thought of these scenarios and tried to apply Newton's three ...
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0answers
24 views

Lense-Thirring effect: Revolution, precession, rotation … inside rotating shell?

This is a very basic and vague question (I don't know general relativity, nor much physics, but am interested in this question for idiosyncratic reasons). Consider a rotating spherical shell of mass ...
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0answers
23 views

A confusion between geocentric and heliocentric model [duplicate]

As per Ptolemy, he proposed firstly geocentric model and that model if one see with aspects of relativity he would find true. Here is an example how Suppose you are in a train which is moving and you ...
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2answers
101 views

Deriving special relativity free particle Lagrangian using infinitesimal boost?

At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics. I want to see how to do the analogous derivation in special ...
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1answer
45 views

Biological aging interval equals Proper Time interval?

In special relativity does proper time interval equal biological aging interval in every inertial reference frame?
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3answers
63 views

Method to observe clocks on spaceships moving near $c$?

I have read the explanation for clocks slowing down on a spaceship moving relative to a stationary observer -- something like a beam of light between two mirrors taking longer for the observer to ...
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2answers
64 views

Relativity from a basic assumption

Is it possible to derive Lorentz transformations just by assuming that if two spaceships are moving away from each other with a constant speed, it is impossible for them to tell who is moving, even if ...
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0answers
36 views

Equivalence in all inertial frames

Suppose there is a train moving to the right. and inside the train there is an observer, A. Outside the track, there is another observer B. When the train passes in front of B, right at the instant ...
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0answers
40 views

Proving two space-time intervals are equivalent with matrix algebra

η=$ \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} $ v=$ \begin{bmatrix} ct\\ x\\ y\\ z \end{...
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3answers
50 views

Inertial frames and Rotation: shooting up a ball from a rotating platform

A short cylindrical tube is fixated in a horizontal platform and shoots a ball vertically in such a way that it falls back into the tube. Now imagine that the platform is spinning with a certain ...
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5answers
102 views

Varying constants in special relativity [closed]

The first thing you learn in special relativity is: All "inertial" frames of reference are equivalent. There is a frame - invariant speed limit, usually called speed of "light." So, geometry is a ...
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2answers
65 views

Spacelike and timelike intervals confusion

I'm confused about this, specifically the spacetime interval. A timelike interval is one in which 2 events can be related to each other in a given reference frame within its light cone, that is, it ...
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2answers
44 views

Collision between two objects where the center of mass never moves

I had the following problem: Image two cars approaching one another in opposite directions. The first car is twice as massive as the second car. They move so that the center of mass of the two-...
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0answers
20 views

With respect to which system are accelerations written in a non-inertial frame?

If $\vec{a}=\vec{a_0}+\vec{a_r}+\vec{\omega}\land(\vec{\omega}\land\vec{r})+\frac{d\vec{\omega}}{dt}\land\vec{r}+2\vec{\omega}\land\vec{v_r}$ being $\vec{a}\to$ absolute acceleration of the ...
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2answers
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Paradox are all 4D distances zero?

The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero. Take a point A and a point B in the future at ...
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2answers
39 views

Is an inertial force needed to be added to second Newton's law when transforming from cartesian to cylindrical coordinates?

Let's consider I have a particle moving on the $x,y$ plane. On this particle acts the Lorentz force, however it does not necessary perform a rotation by the axes origin $(x,y)=(0,0)$. I would like to ...
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1answer
38 views

Doppler effect and frame of reference

We know that in an inertial frame we can never tell if the frame is really at rest or moving with constant velocity but can’t we check if there is a change in frequency by a sound emitted by the frame ...
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1answer
21 views

Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?

I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question). Following Landau and Lifshitz's Mechanics, on page 110 ...
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2answers
87 views

What is the reasoning behind 1 step in Einstein's derivation of the Lorentz Transformation

In Einstein's book "Relativity" there is a wonderful derivation of the Lorentz transformation, requiring no more than high school algebra (pp. 117 - 121). It is quite clear but I do not understand ...
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1answer
50 views

Another question about Four-velocity derivation

Consider,again (Question about derivation of four-velocity vector) the following: For a massive particle with position $x^{\mu}(t) = (x^{0},x^{1},x^{2},x^{3}) \equiv (x^{0},\vec{x})$ we define the ...
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2answers
66 views

Naive question about the need to construct the 4-velocity

Special relativity was not born as a 4-covariant theory. Instead, Einstein derivated the kinematical quantities without spacetime,therefore without 4-vectors. Consider then the following: First ...
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1answer
72 views

How can I go and also not go faster than light?

Suppose I am in a spaceship. In this spaceship there is also my friend. So my friend and my relative velocity is zero. So no matter how fast my ship goes my friend's velocity relative to me is zero($0$...
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2answers
41 views

Momentum in the rest frame

I am a little confused over the terminology of the rest frame. Say a photon collides with a massive particle then from the rest frame of the massive particle would it be the photon or the particle ...
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0answers
32 views

Is the speed of light greater if traveling at an initial velocity greater than zero? [duplicate]

I'm reading "a brief history of time" and he states "the speed of light should be the same whatever the speed of the source, and this has been confirmed," (24). Why is it not increased if it has an ...
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2answers
84 views

Clock in a sealed box at half the speed of light. How would it know it is moving?

Consider a clock enclosed in a sealed box here on earth syncronized with my wrist watch. I send the boxed clock around the galaxy a couple of times at half the speed of light (or the full speed of ...
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5answers
160 views

Lorentz transformation of electric and magnetic field vs. 4-vector

I have a very general question about Lorentz transformations of electric and magnetic fields vs. 4-vectors . It arised from my previous post. I will describe the difficulty I encountered. ...
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4answers
83 views

Why do we differentiate a 4 vector with respect to proper time to obtain 4-velocity?

The coordinates of an event in spacetime are given by the 4-vector $(ct, \mathbf{r})$, where $\mathbf{r}$ is the spacial coordinates of the event. This 4-vector can be seen as 4-displacement of a ...