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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1answer
30 views

Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
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Why aren't shape of galaxies depicted as a funnel?

Let's say if a galaxy is moving, shouldn't it be shaped like a funnel? I am saying this because it would take considerable time for the outermost star to know that the center of gravity has shifted. ...
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Lagrangian method for finding Lorentz transformation [closed]

Consider a very general case: one reference system (x', y', z') is moving away from another fixed system (x, y, z) with constant speed $v$ (like in the fig. a little bit below). Normally, using the ...
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Operators, gamma matrices and Lorentz invariance

In class, we have define the following operator: $$\Pi_{\pm} = \frac{1 \pm \gamma^0}{2} \tag1$$ Where, $\gamma^0$ is the usual first gamma matrix in Weyl representation. Applying it to a 4-...
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Minimum separation from the spacetime interval

I've been working through invariant spacetime interval questions recently, and I came across a question in my lecture notes where; $$\Delta s^2=\Delta x^2 -(c\Delta t)^2 > 0 $$ Now it is clear to ...
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9answers
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How does an isolated body in deep space 'know' it's rotating? [duplicate]

We can imagine an object floating in the known universe, maximally distant from any other large mass. Maybe it has been there since coalescing after the big bang. What physical phenomena tell it ...
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2answers
101 views

If the speed of light is a limit, is there a way to tell which direction we are moving through space and how fast?

Say two photons start at point A, and go in opposite directions. They will be traveling apart at 2x the speed of light correct? So if this limit is how fast you are able to travel through space (and ...
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1answer
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Why the speed of light is independent of the relative motion of observer? [duplicate]

As we use Lorentz transformation equation to relate velocity of particle measured by observer which is in frame s this frame is in relative motion having some velocity to that particle so Why the ...
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5answers
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Is relativity really relative?

Because of the relativity of linear motion, you can't tell the difference between whether your spaceship is moving and the stars are standing still or whether you're still and the stars are moving the ...
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2answers
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Can two electron moving in opposite direction move faster than light? [duplicate]

Suppose we are moving two electrons in opposite direction both having a speed of 1.6e8 meter per sec.When they will cross each other then their relative velocity will be 3.2e8 ms_1.Isn't it faster ...
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Particle in a gravitational field moving at constant speed in some inertial frame

While working on an unrelated problem I found an interesting result which I presume must already be known, but I cannot find any reference to it. It is the following: Consider a small particle P ...
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3answers
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Friction and Work in Inertial Reference Frames [duplicate]

Say a train is moving in the positive $x$-direction at 100 meters per second with respect to the ground frame. Now let's say someone is pushing a large box in one of the cars of that train in the ...
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Question about inertial frames and geodesics

Consider the following text: In Newtonian Mechanics the first law is given by: $$\Big[m \Big(\frac{d^{2}x^{a}}{dt^{2}} + \Gamma^{a}_{bc}\frac{dx^{b}}{dt}\frac{dx^{c}}{dt}\Big)\Big]\frac{\partial}{\...
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5answers
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Inertial and non-inertial frame

How to define an inertial frame of reference mathematically? I want a definition with proper chosen coordinate axis which will help me to differentiate it with the non inertial ones. I have been ...
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2answers
152 views

Doesn't the slowing of time when travelling at almost light speed create a paradox with an observer? [duplicate]

Disclaimer: I am extremely new to this and have no proper knowledge of this subject at all, this is just an idea that I had which I want to properly understand. I don't have any knowledge of necessary ...
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Transformation of opening angle in different frame of rerefence in special relativity

I have to find the minimum opening angle for the decay $\pi^0 \rightarrow \gamma \gamma$ given the energy and rest mass of the $\pi^0$. My question is that: since the center-of-mass frame's opening ...
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3answers
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Which observer measures proper time in the twins paradox?

I know that proper time is defined as the time which the clock moving relative to that observe shows. That is, a clock attached to observer A will always be As proper time. I also understand that this ...
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1answer
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Gravitational potential energy with both bodies moving [closed]

When deducing the formula for the gravitational potential energy of one body in relation to the gravitational force of another body, my teacher assumed that one body was standing still. I tried ...
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1answer
192 views

The derivation of the Lorentz transformation: addition of distances

In the derivation of the Lorentz transformation, one has a reference frame, $S$, at rest and another, $S'$, moving away at constant speed $v$. At time $t$ there is an event at a point $x$ in $S$. The ...
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6answers
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If photons don't experience time, does that mean time is a consequence of mass? [closed]

If photons don't experience the passage of time because they have no mass, does that mean time is a consequence of mass? To me that's a profound conclusion yet not one I see printed. Is it right?
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4answers
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Why does speed of light have to be constant?

My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light ...
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2answers
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Are these collisions equivalent?

Similar to the question if two cars with a velocity of 50 mph each colliding is the same as one car colliding with wall at 100 mph, I was wondering if the same amount of energy is produced when ...
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6answers
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Is the relative speed of light really invariant, irrespective of the motion of the observer? [closed]

If 3 observers are on a planet which 100 light years from a star, and the star goes supernova, if one observer moves towards the star and one moves in the opposite direction, each observer will see ...
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4answers
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When electron moves constantly, it's electric field moves with it instantly?

When electron accelerates, there occurs a propagated ripple on it's electric field. But when it moves constantly, does the field "follow it", i.e. changes instantly? How does it deals with the fact ...
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1answer
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Invariance of spacetime interval in special relativity: linearity

I'm trying to understand which assumption are necessary to prove the invariance of the spacetime interval $$\Delta s^2=c^2\Delta t^2-\Delta \mathbf{x}^2$$ in special relativity. The postulates of ...
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1answer
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Speed of light, can it be not constant? [duplicate]

What if we switch on a flashlight while travelling at the speed of light (we are travelling in vacuum, in a straight path)? What will happen and what will be the speed of light from the flashlight? ...
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1answer
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Why is the laboratory frame energy always greater than the center of mass frame energy for collisions? [duplicate]

I looked through lots of sources to answer the question, 'Why is lab frame energy (total energy) always greater than the center of mass frame energy?' Many of them provided lots of mathematical ...
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3answers
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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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What's the speed of light when viewed from the side?

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
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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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1answer
48 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
269 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
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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 ...
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5answers
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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 ...
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1answer
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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
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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
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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
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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
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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
44 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
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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 ...
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3answers
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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
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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
68 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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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
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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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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
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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 ...