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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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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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Concerning the increase in mass as velocity increases [duplicate]

This increase in mass is relativistic. Let an object approach the velocity of light, as it does we as observers notice that its moving very slowly, and it's mass is increasing significantly. What ...
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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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3answers
432 views

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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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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Velocity of particle in non-inertial frame [closed]

Can velocity of the free particle remain constant in non-inertial frame as contrast to free particle in an inertial frame? I know the answer is straightforward yes but taking a different perspective ...
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Lagrangian in non-inertial frame

Does Lagrangian in non-inertial frame may/may not depend on coordinate but always has to dependent on velocity and time for free particle in contrast to inertial frame where lagrangian is always ...
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1answer
60 views

Lorentz Factor from Minkowski's Original Paper 'Space and Time'

Consider the following figure: Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure. He ...
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Questions about an inertial frame

Can someone explain to me what I put in bold? Inertial frame definition: When the coordinate axes are stationary with respect to the mean position of the "fixed" stars or if they move with uniform ...
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1answer
60 views

Mach's principle and centrifugal force

How does Mach's principle explain the centrifugal force as a result of the relative circular motion of the distant stars? Why does this, in the light of Mach's principle, make a net force although the ...
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1answer
26 views

Choosing the sign for speed in Lorentz transformations

I am studying the Lorentz transformations and while I [believe] I understand the principle of it (you’re sorta “translating” from one frame of reference to the other), I am having a lot of trouble ...
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2answers
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Steady velocity forces

When an object is moving at constant "steady" velocity, the resultant force is equal zero. But I can not understand how the object moves and at the same time, backwards and forwards forces are the ...
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3answers
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Sign conventions for relative velocity problems

I am having trouble solving relative velocity problems because I can't seem to understand the sign that goes along with the velocity of different objects. $$ v_{ac} =v_{ab} + v_{bc}. $$ How do the ...
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1answer
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Illusion that $v > c$?

I am currently studying length contraction in special relativity (and having the hardest time getting the harder exercises in my book right) and there is the following exercise in my book is driving ...
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4answers
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What is the correct formula for relative velocity?

I have consulted byjus.com, HC Verma and Khan academy, all are saying different. byjus and HC Verma book is saying that formula for relative velocity is $V_a +V_b$ but in Khan academy they are telling ...
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2answers
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A beginner's question on time dilation [closed]

I have just started understanding relativity so the question might look absurd. I know that the faster we move through space , the slower we move through time. But I haven't understood it fully. I ...
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97 views

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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Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
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2answers
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Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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1answer
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Frame uniformly moving to an inertial frame in Landau & Lifshitz mechanics

How to prove frame moving uniformly in straight line to an inertial frame is an inertial frame? (Assuming I do not know Galileo's relativity principle and Galileo's transformations and also taking an ...
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1answer
236 views

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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How do u get Eq3 from Eq2&Eq1 [closed]

I keep getting the wrong results by subbing eq1 into eq2 It’s from Kleppner’s an introduction to mechanics 2nd edition
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45 views

Minkowski diagram

I have not well understood the picture of geogebra regarding the angle of time (t') that is inclined compared to (t) of 26.57°angle . In the picture we see that the velocity is setted at 0.5c, for ...
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2answers
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Lorentz-transformation

I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S': $$x' = \Lambda x$$ these transformations do not leave the differences $\Delta x^\mu$ ...
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Is the gravitational waves velocity also $c$, regardless the adopted inertial frame, and the source movement conditions? [duplicate]

The second postulate of STR was made exclusively for light (electromagnetic waves)? If gravitational waves also travel at velocity $c$, then are they obliged to fulfill this second postulate? Any ...
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2answers
152 views

The Earth revolves around the Sun or the Sun revolves around the Earth

Well, in today's world we know that the earth resolves around the sun. But that is seen from frame of reference of sun or an observer stationary wrt sun. From frame of reference of the earth, sun ...
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441 views

Combining two Lorentz boosts

Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$? To answer this, I start by defining $\theta \equiv ...
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2answers
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Do objects move in 2 directions at once?

If a velocity vector of an object can be divided into an x and y component relative to a second object's position, and both objects have gravity that attracts both objects to each other. We then know ...
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Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One ...
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1answer
104 views

Are there 2 laws of motion or only 1?

It seems clear that Newton's first law is a special case of his second. Although perhaps people might argue that it emphasizes the centrality of inertial frames. But is the third law also just a ...
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Special Relativity; 3 Momentum Conservation

In SR, I understand you can use 4 momentum conservation, but what are the special cases where you can use 3 momentum/energy conservation? An example I have seen is with $$P_1=(M_1, 0) \\ P_2=(M_2,0) \...
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Factorising a 4D Dirac delta function in a rest frame

I'm working through a QFT problem and at one stage in the solutions we have this step: $$\delta^{(4)}(p - q_1 - q_2) = \delta(E_1 +E_2 - M)\delta^{(3)}(\bf{q_1} - \bf{q_2}).$$ We are working in the ...
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3answers
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Definition of Newton's first law [duplicate]

I have always had a doubt in the definition of the Newton's first law. In general, it is stated in a form like: An object at rest remains at rest, or if in motion, remains in motion at a constant ...
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1answer
50 views

Necessity to consider the square of Four Momentum

Why do we often need to consider the square of four momentum transfer $Q$ in scattering experiment or particle physics/cosmology instead of just the $Q$ itself?
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1answer
113 views

In what sense do photons exist?

In a photon's frame of reference travel is instantaneous, so presumably a photon cannot exist in its own frame of reference. I am not aware that a "beam" of photons interacts via gravity despite ...
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Lorentz invariance of Maxwell's equations in matter

I know that Maxwell's equations of electromagnetism are Lorentz invariant in a vacuum. But what about in a generalized medium, e.g. a metal, a rubber, a dielectric, a magnet? I have read it comes down ...
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2answers
148 views

Newton's First Law and things that are very old [closed]

Recently I've been revisiting physics text books, and books by Feynman, and others. A curious thought has arisen, while I was reading about Mach's principle, and it seems to gnaw on my mind. I hope ...
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6answers
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Twin paradox - is acceleration relative? [duplicate]

The usual answer to the twin paradox is that the twin who undergoes acceleration is the one who finds the other has aged more, because the trajectory of the 'travelling twin' does not amount to a ...
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2answers
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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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Invariance of forces

In Newtonian mechanics, the inertial forces depend on the reference frame and the other forces are invariant. Are they still invariant when special or general relativistic effect are involved?
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1answer
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What is proper name for non-inertial forces in GR?

General relativity works in all reference frames, so inertial forces are real in it. And due to the equivalence principle, gravity should be also considered inertial. So what is a good term for the ...
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1answer
136 views

Why does time slow down ONLY for objects travelling at high speeds?

Today in physics class, we learned about the theory of relativity and how it relates to time dilation. We were given the example of two photon clocks- one stationary relative to the Earth, and the ...
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1answer
59 views

Speed of light as the maximum speed and movement course

Assuming we have 3 objects d,e,f moving on the same line while e is stationary, d is moving to the left at 'almost speed of light' and f is moving to the right at 'almost speed of light'. What is the ...
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1answer
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Fundamental Principle of Dynamics and equations of geodesics with proper time

I just wanted to have a little precision. In the expression below translating the PFD (Fundamental Principle of Dynamics) in tensor calculus (or more precisely the inertial principle) : $$a^{\nu}=\...
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1answer
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How do we know who is moving? [duplicate]

If I am in a free float environment and there is another object at rest relative to me, and then I start to accelerate towards this object, do I know I am the one who is moving, since I am the one who ...
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1answer
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Questions about special relativity, index in the Lorentz matrix

I'm studying special relativity I have read this: We have $ x^u = (ct, x^1,x^2,x^3) $. If we apply Lorentz transformation we can write: $x'^u = \Lambda^{u}_{\hspace{0,2 cm}\nu} x^{\nu} $ $x'_u =...
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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 ...