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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Special relativity - what is the age of my twin after a one-way trip? [duplicate]
I have a twin who stays on Earth, and I will move to another planet 4 ly away. I will travel at a certain relativistic speed towards this planet.
What I just described here is the first half of the ...
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Are objects in an uniform field inertial?
It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't "feel" that it is accelerating and is thus ...
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According to inertial frame, how can a bead move in a groove made on a rotating table? [duplicate]
Context:
Consider a smooth circular table rotating uniformly. Along it's radius , a groove is made. While it's rotating , a bead is placed on the groove gently at some distance (say $x$) from centre. ...
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Why is the Lorentz transformation of fields linear?
I know that the coordinate, $x^\mu = (t,\vec x)$ is a 4-vector and it transforms as
$$x'^\mu={\Lambda^\mu}_\nu x^\nu.$$
The related (classical or quantized) field, $\phi_a(x)$, can be classified into ...
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Does the magnetic field, circulating the moving uniformly charged sphere, exert force/tension on it? If so, how is it interpreted in the charge frame?
I am aware of this SE question, however, it does not solve my problem. Assume that a bulk uniformly charged nonconductive sphere is set in motion along the $x$-axis in the lab frame of reference. ...
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Would an object moving close to the speed of light appear colder to a stationary observer? [duplicate]
If an object moves close to the speed of light time will slow down in its reference frame as seen by a stationary observer. If my understanding is correct, this means that all movement - such as the ...
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"Rear clock ahead" effect in special relativity
I've read (pretty much) all the questions in the site regarding the topic, however I wasn't able to comprehend the author's solution to the problem in its totality. The problem is from David Morin's ...
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Find the maximum height reached by an accelerated pendulum using energy conservation in an inertial frame of reference [closed]
Given a pendulum in an accelerated frame of reference (for the left) the goal is to find the maximum height H reached by the pendulum in its equilibrium. See the following image:
A simple approach is ...
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Landau/Lifshitz Particle Disintegration
In Landau/Lifshitz "Mechanics", 3e., there is a problem which asks the reader to find the relation between the angles $\theta_1,\theta_2$ in the lab frame when a particle disintegrates into ...
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Unable to understand the relation between the accelerations of a particle in rotational and inertial frame of reference
I was studying about the derivation of coriolis force and centrifugal force for a particle i.e. the relation between the accelerations of a particle with respect to inertial and uniformly rotating ...
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How is the law of conservation of energy valid in all frames? [duplicate]
I am aware there are similar questions already asked, however, I find none of the answers satisfactory, they either do not contain any mathematics at all, or mathematics of a level I am not capable of ...
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Lorentz Transformation of Wave Equation
Consider a 1D Wave equation: $$\frac{\partial^2 y}{\partial t^2}=v_1^2\frac{\partial^2 y}{\partial x^2}$$ So, we are given two frames, S and S' (moving along $x$-axis) with velocity $V$ relative to S. ...
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Homogeneity of space doubts [duplicate]
This question might have been asked so many times, but here we go again. I'm wondering what homogeneity of space means. All the descriptions say:
there's no special point in space, every point looks ...
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Mach's principle
The question is about Mach's principle.
Suppose ther̥e is a simple pendulum comprising a bob and string suspended inside an accelerating car in space with planets,stars around it(fixed).It will stay ...
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Speed of light postulate in special relativity in inertial vs. non-inertial frames
I'm trying to learn special relativity by myself. I've been following this series of videos, plus some other articles I've managed to find online. At this point I'm already quite far into the theory, ...
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Explanation for radial elongation in rotating bodies
Why does a rotating body, like a rod or a spring, exhibit elongation instead of compression even though every part of it experiences "centri-seeking" force? Is it plausible to understand ...
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Why doesn't Galilean relativity lead to a contradiction in SR?
Two identical spaceships commanded by Alice and Bob are at rest next to each other in outer space. The clocks of the spaceships are synchronised; and when they are close by Alice can see Bob's clock ...
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What is meant by angular property wrt body frame?
I keep seeing the phrase "angular velocity with respect to the body frame", or "angular momentum with respect to the body frame" in context of rotation of rigid bodies, especially ...
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Relativity of Simultaneity - Why doesn't the train/lightning example contradict the absolute speed of light?
I know similar questions have been asked here before, but none of them seem quite to address my particular confusion.
I'm not afraid of math (I did well in calc III last semester, for example) but my ...
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Time dilation query 2 [duplicate]
The examples for the theory show that The clock run faster or slower and show time interval, not that the time itself does not differ in two frames one is in motion relative to other. Then, what is ...
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Does a train that moves at relativistic speed and then decelerates to zero speed, seem to expand to an observer at rest near the tracks? [duplicate]
A train is moving with a relativistic speed, according to an observer at rest near the tracks. To this observer, the train seems contracted in the direction of motion.
Then, the train decelerates (...
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Details on analyzing relative motion
I have been viewing some videos and reading some articles about Relativity and relative motion. My search abilities seem to be rather lacking. I am looking for articles, questions, and/or forums ...
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Clocks of two stationary inertial frames
I am trying to prove Lorentz transformations using only the second postulate of Special Relativity. My proof makes use of the following fact:
"If two inertial frames (S and S') have no relative ...
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Why does acceleration in special relativity give rise to general relativity (and thus gravity)?
If we include accelerated motion in special relativity, the result is general relativity. But why should that give rise to gravity? Is that only because Einstein introduced the equivalence between ...
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Can we see the rest-energy of a mass as its kinetic energy in the $ct$-direction?
A mass $m$ at rest has an energy $E=mc^2$. Can we say this is its kinetic energy in the $ct$-direction?
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Does special relativity imply that there's such a thing as absolute time, or base time?
If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as "absolute time" or &...
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Problem with deriving the Lorentz Contraction [duplicate]
I am trying to prove the contraction. I know there are several ways one can do it. The way I am trying to solve is said to be complicated and that there is an easier way to do so. Because I don't have ...
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Is this formula, other than (2.38) in peskin's quantum field theory, also true?
This is soft interlude question. I am rereading the Peskin & Schroeder's Quantum field theory, p.23, (2.38) and some question arises.
First, let's refer to Lorentz transformations for scalar ...
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Lorentz-like transformations of 1+1 dimensional Minkowski space
Alice lives in 1+1 dimensional Minkowski spacetime. Bob travels at a constant
velocity $v$ with respect to Alice. When Alice assigns coordinates $(t,x)$
to an event, Bob assigns coordinates $F(t,x)$ ...
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Lorentz Transformations derivation
I was reading derivation of Lorentz transformation but I don't understand why the constant a here is equal to -c^2.
Full pdf: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
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What is the reason of different clock's measurements in different frames? [closed]
I tried to understand what is the reason of different clock's measurements in different frames.
For this I looked at easy example with distance S traveled by man with moving clock (velocity V1=2m/s) ...
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The train-and-platform VS Causality and Simultaneity
for long time I was ruminating on the train and platform experiment and “what if” extension of this experiment…
So, what if the light striking on either end triggers system (one on each end) with ...
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Alternative to Susskind's way to derive the equation of the $x'$ axis in relativistic spacetime diagram?
Note : sorry for the poor drawing above.
Note : in what follows, the speed of light is taken as unit : $c =1$ and the trajectory of a light signal sent from $(0,0)$ is $x = ct = t$.
In his ...
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The Lorentz factor $γ$, and Fermilabs derivation of it
Before diving into my question, we first must acknowledge Einsteins two assumptions:
The laws of physics are the same for every observer and reference frame.
The speed of light is constant for ...
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Please explain $E = γmc^2$ more intuitively [closed]
My name is Shaun and I am 14 years old.
Lately I have been trying to learn about $E = mc^2$, and I came across Fermilabs video about $E = γmc^2$, where $γ$ is the Lorentz factor.
My question is how ...
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How to write the force on a test particle as the negative gradient of potential energy in relativity?
In newtonian mechanics, the gravitational force on a test particle can be expressed as the gradient of the potential energy ($\phi$) as
$$\vec{F}=-\nabla\phi.$$
Now, if we consider a relativistic ...
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Relative black hole [duplicate]
Let's suppose a nutron star(because it directly collapses into black hole afterwards) , if we move with velocity near speed of light than in our frame neutron star will also move with velocity near ...
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How would I observe the trajectory of the planet Mercury from an inertial frame of reference?
If i were to make an observation of the orbital motion of the planet Mercury from an inertial frame of reference, would I observe the precession of Mercury's perihelion? or would I observe it moving ...
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Coordinate Transformation using a Matrix
Consider two inertial and resting frames $K$ and $G$. The only difference between the two frames is that the axes of $G$ has been rotated with $\theta$ with respect to $K$. $G$ is not constantly ...
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How to explain this simple phenomenon from a moving frame?
Let us suppose we have an electron moving with velocity $\vec v$ as shown in the fig. as seen from the ground frame. We know that when it enters the region with uniform magnetic field it will follow a ...
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Under what representation of the Lorentz group do scalar $\textit{fields}$ transform?
I know that if I am sitting in a spacetime $M$ at point $p$, vectors live in the tangent space $T_pM$, and tensors in the tensor product space etc. If I want to consider general tensor fields, I ...
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Galilean relativity in terms of homogenity for car example
I have a question related to Landau & Lifshitz's book. In that, he says:
If we were to choose an arbitrary frame of reference, space would be
inhomogeneous and anisotropic. This means that, even ...
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Ambiguous special relativity between two sources?
I am currently confused about things I read about special relativity (I'm a CS major and not as well-versed in physics as I would like to be).
I just watched a video on evaluating a Lorentz ...
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Doubt about Lorentz transformations derivation: $y$ and $z$ axis
Reading "Introduction to special relativity" by Resnick, I'm a bit confused about a detail in deriving Lorentz transformations.
Of course we consider the reference frames S and S' coinciding ...
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What's the correct interpretation for the relativity of simultaneity? [closed]
I'm currently reading "Introduction to special relativity" by Resnick, and I have a question about the relativity of simultaneity.
He uses this example:
So, from the point of view of $S$, $...
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Lorentz Transformation Time Dilation Equation
I occasionally see slightly different equations being used to calculate time measured by a moving observer.
Sometimes this equation is used:
$$t'=\frac {1}{\sqrt{1-\frac{v^2}{c^2}}}\left(t-\frac{vx}{c^...
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Mass as generator of two distinct sets of phenomena
We know that mass, which is a continous parameter, generates two classes of different phenomena: the ones where $m=0$ and the ones with $m \neq 0$.
When a particle has $m=0$ we have phenomena which ...
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Is there a *geometric* explanation for why photons have no rest frame?
I've read the various threads on this site that talk about it being impossible for photons (or massless particles in general, really) to have a rest frame, and the answers all seem to boil down to &...
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Lorentz Transformation - Intuitive way to determine when to use Inverse transformation
Any intuitive way to decide when to use Lorentz transformation and when to use its inverse relation?
For example: A particle is moving with respect to me with speed of 0.99C. If question is : What ...
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Relativity of bodies in motion in space
I have learnt that if we are travelling in space we have no way to tell if we are moving towards something or if it is the something that is moving towards us; to either object they judge that they ...
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