Questions tagged [special-relativity]

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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About the derivation of the time dilation

I'm referring to the common example of deriving time dilation from the light clock. Let O be standing still with his light clock and O' move at a speed of u. We consider the O measures his time as $...
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Extending Maxwell's Equations from Flat Spacetime To Curved Spacetime

Assume we are working on a Minkowski (i.e. flat) spacetime. Let $A^{\mu} = ( \phi/c, \textbf{A})$ be the contravariant potential four-vector. Then, assuming a covariant Minkowski metric of $\eta_{\...
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Time Ordering and Causality in General Relativity

The time-ordering of two space-like separated events is undefined in special relativity. Is there an analogous concept in GR?
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How is the speed of light constant in this situation?

Let's take an example, where A is a photon moving with the speed of light, and B is a car, that moves with half of the speed of light At t=0, a kid in B(thinking that the car is not moving) observes ...
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Restoration of the speed of light [duplicate]

If you can slow down the speed of a photon, how does it speed back up to the speed of light once the slowing down is disabled?
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This step in the derivation of the velocity transformations in special relativity [closed]

I have seen in two places now, on wikipedia and in the book I'm reading, this step in the derivation of the velocity transformations, taking the quotient of the following. $$dx'=\gamma (dx-Vdt)$$ $$...
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Length contraction and Time dilation in traveling [closed]

Can a person, in principle, travel from the center to the edge of our galaxy in a normal lifetime? Explain, using either time-dilation or length-contraction arguments.
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How fast does a particle need to go to have a significant probability to quantum tunnel through a star?

According to this answer tunneling probability depends, among other things I don't know, on the length of the barrier. Due to length contraction when going at relativistic speeds, it seems it should ...
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How does a photon decide what to hit along it's path? [duplicate]

In general, let us have a light emitting point A and two light absorbing points B and C, such that the three points fall on a straight line and B is somewhere between A and C. For simplicity, let us ...
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Four vectors and the Lorentz Transformation

From Lifshitz and Landau Vol.2. The Lorentz transform of Cartesian coordinates: $$x=\frac{x^{\prime}+V t^{\prime}}{\sqrt{1-\frac{V^{2}}{c^{2}}},} \quad y=y^{\prime}, \quad z=z^{\prime}, \quad t=\...
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Simultaneous events [closed]

A cart moves on a track with constant velocity v as shown in the figure below. The points A and B are on the ends of the cart and points C and D are stationed along the track. We define event AC as ...
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Why can I not recover the original spacetime coordinates of this event with this method? [closed]

I am trying to perform two Lorentz transformations consecutively and recover the original spacetime coordinates. I am using the following method. Two observers synchronise their clocks as their ...
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Can the image of an object travel faster than the speed of light? [duplicate]

supposing an object moves from f to 2f of a convex lens at the speed of light, then will the image which moves from infinity to 2f of the lens be moving faster than the speed of light?
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Smaller elapsed time with higher velocity, but free fall maximize elapsed time, who clearly have a velocity compare to a stationary object

I am a little confused because an object with velocity would experience smaller elapsed time compared to an object that is not. But in GR elapsed (proper) time is maximized by free fall who have ...
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Is the magnitude of the four-velocity vector in spacetime arbitrary?

I know that the squared magnitude of the four-velocity vector is plus or minus $c^2$, but I’m a little confused on whether or not this vector has been normalised arbitrarily, since it is often claimed ...
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Is reference frame-dependence continuous? [closed]

Envision a 3D space (x,y,z). On the y-axis, there are infinite particles, so that for every y value there is a particle on the axis. For example, there is a particle located on y=o.5, another on y=2....
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Representing a four-vector by a rank 2 tensor

When representing a 3-vector $(x,y,z)$ as a skew-symmetric matrix like this: $X=\begin{pmatrix} 0 & -z & y\\ z & 0 & -x\\ -y & x & 0 \end{pmatrix}$ $X$ transforms a a rank 2 ...
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Spin dependence of particle decay

I was wondering How does the spin of a decaying particle influence the kinematics of the decay? For example: I know that for a spin-0 particle decay such as $$ \pi^0 \rightarrow \gamma\gamma $$ ...
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In which article the concept of four-vectors was first introduced? [closed]

I'm trying to find the first paper in which the concept of four-vectors was introduced. I read "Principle of Relativity" by H. Minkowski but he only presents the notion of metric and invariant space-...
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Reconciling different reference frames in Einstein's train-lightening thought experiment

In all accounts of Einstein’s train-lightening thought experiment the ground observer sees the two flashes simultaneously because he remains “at rest” with respect to the landscape, while the train ...
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What will happen to speed of light in an accelerating frame? [duplicate]

I was just wondering about the line that nothing can surpass the speed of light but if we try to observe it from an accelerating frame. Does reference frame have any effect on light?
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Transformation of space at almost the speed of light from different observers

I hear this a lot in documentary movies, where they claim that if you would be able to travel through space near the speed of light, then things would seem squished, the Earth would seem like a 70 ...
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Four vector of a proton as seen from the rest frame of another

I have a question regarding the four-vector of two protons. My task is to determine the four-vector of one proton as seen from the rest frame of the other. I'm having a hard time understanding ...
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Consecutive position measurement yield arbitrary fast movement?

Suppose we got a particle inside a long tube, and two observers Alice and Bob situated at two very distant points of the tube. Alice performs a measurement on the position (checks whether it is in ...
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How is the zeroth term of the Minkowski force derived?

I'm working through T.M. Helliwell's Special Relativity on my own, and one of the questions asks to show that the Minkowski force $K_\mu=dp_\mu/d\tau$ can be written $$K_\mu=\left(\gamma\frac{\mathbf{...
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Are there any effects time dilation, kinetic or gravitational, has on modern physics and the modern world?

So, I am writing a paper on time dilation and I am basically done with everything, but in the last chapter, I should include which aspects of the modern world and physics are specifically influenced ...
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What is Rindler referring to when he writes ‘particles’?

I came across the following distinction between frames and coordinate systems from Rindler, “We should, strictly speaking, differentiate between an inertial frame and an inertial coordinate system, ...
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Refractive index of light upper bound?

Is there any upper bound for the refractive index of a theoretical material to occur? Would the relativistic effects be taken into consideration?
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Relativistic Rutherford Scattering

One can derive the cross section in a Rutherford-Scattering-like experiment, in which you treat your target as an infinitely heavy object. It is basically a non-relativistic scattering process in ...
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Is gravitational time dilation nothing more than kinematic time dilation in another form? [duplicate]

Once we get down to the quantum level, mass is derived directly from energy. From Wikipedia: Most of the mass of hadrons is actually QCD binding energy, through mass-energy equivalence. This ...
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Euler-Lagrange equations in QFT and metric signs

I'm having a probably dumb problem with the Euler-Lagrange equations and the dot-product in Minkowski spacetime. I know that some objects are defined naturally with lower-indexes, e.g. $\partial_{\mu}$...
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$s$-channel, $t$-channel and $u$-channel

I'm studying the $e^{+}e^{-}\rightarrow f^{+} f^{-}$ scattering, where $f$ is a generic fermion ($f^{\pm}\not=e^{\pm}$). I know the process is described by the $s$-channel, but why the $t$-channel or ...
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Index manipulation of Dirac matrices

In several places I see that Dirac matrix indexes are treated as usual 4-vector indexes that can be changed with the metric tensor, for example $$\gamma_\mu=g_{\mu\nu} \gamma^\nu. $$ Why is it true?
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Lorentz transformation of radiation density

Say in the lab frame $K$ we have a spherical shell radiating energy inwards radially, and the energy density in radiation is $u_{rad}$. A particle is moving radially outwards (say in the $\hat{x}$ ...
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Time needed to exchange momentum between two spheres [closed]

Two hypothetical relativistic spheres move to each other and the angle between their trajectories is let say 1° and they hit themselves not frontaly but lateraly so they touch themselves slightly.Does ...
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Length contraction of distances between two unconnected point particles moving at same velocities

The first part of my question is meant to confirm my understanding of length contraction in the context of the following simple thought experiment: Imagine three particles O(the observer), A and B in ...
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How does an EM wave modify the electric field in an observation point?

Part of the first answer to the question: Is there a travelling speed of for electric field? If yes, what is it? says: ...any change in an established field (say, due to shifting the position of ...
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Using the COM frame for momentum in Special Relativity

I'm having difficulty understanding 4-momentum in relativity. The problem I have is that two particles of equal mass are colliding, with one particle moving and one at rest. I know the three-momentum ...
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Special Special Relativity Question [duplicate]

According to what I've learned from physics professors, no object can go faster than the speed of light. So if you have object A moving .8c one way and object B moving .8c the opposite way...relative ...
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Relativistic difference of angle between two inertial frame

I was studying Prof. Padmanabhan's book on general relativity; "Gravitation: Foundations and Frontiers, which I found very well written. I just started the book and the exercises are also challenging. ...
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Effect of Length Contraction [duplicate]

As we know moving objects have a shorter length as seen from a rest frame. $$L=L_0\sqrt{1-v^2/c^2}$$ The first question that arises, is length contraction real or just imaginary for an observer in the ...
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Where am I doing mistake of concept in deriving the De Broglie equation?

When I am deriving de Broglie wavelength for a relativistic particle using $E^2=m^2c^4+p^2c^2$ and equating with $E=\frac{hc}{\lambda}$, and then putting $p=kmv$, $k$ being relativistic factor, I am ...
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Question regarding speed of causality and speed of light

Recently I came across a question regarding to why the speed of light and the speed of causality are the same. Link-Why is the speed of causality equal to the speed of light? I came up with an ...
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Is electrodynamics associated with $O(3)$?

Let $\mathbf{q}$ be a complex vector of three elements defined as: $$ \mathbf{q}:=\pmatrix{ E_x + iB_x\\ E_y + i B_y\\ E_z +i B_z } $$ I define the function $f(\mathbf{q})$: $$ \begin{align} f(\...
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Maximum proper time in Minkowski Spacetime for free particles

Consider two events $\mathcal{A}$ and $\mathcal{B}$ corresponding to the beggining and the ending of trajectories of two massive particles, respectively. The particle named $\mathcal{P1}$ is in free ...
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Normalization of the action in Special Relativity

The action for a massive point particle in Special Relativity is given as $$A =-mc^2\int d\tau,$$ Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could ...
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Holding the total velocity below speed of light

If a hydrogen atom accelerates to near the speed of light, the total velocity of the system must not exceed that limit. Even if the electron has no net angular momentum around the proton, as it could ...
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Differential Forms and Relativistic Electromagnetism

Let $\phi$ represent the electric potential and let $\textbf{A}$ represent the magnetic potential. Then, the electric field is given by \begin{equation} \textbf{E} = -\nabla \phi - \partial_t \...
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Physical intuition for the Geodesic equation derivation via Action Principle

The most commom derivation I've seen of the geodesic equation of a massive particle is by the use of the Variational Principle. My problem is that I can't realize what the meaning of find a spacetime ...
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To what extent is standard quantum mechanics actually non-relativistic?

I often hear that while QFT is a relativistic theory, standard quantum mechanics is not. But fields aren't inherently relativistic, you can easily construct non-relativistic QFTs, a relativistic QFT ...

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