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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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Coordinate Systems vs Reference Frames vs States of Motion [closed]

This is a broad conceptual question. I am really trying to understand symmetry as deeply as possible. Please let that guide your responses. In particular, I'm looking for help finding clarity on the ...
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photoelectric effect when the plate is moving

Consider a plate that is moving away from the light source with respect to the ground and the frequency of the light is equal to the threshold frequency. Now if we observe the same experiment from a ...
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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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Relative velocity greater than speed of light

Is it possible a relative velocity between 2 objects to be greater than the speed of light? I know that it is impossible to reach the speed of light considering us to be immobile but is this ...
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Lorentz transform of light cone vectors

I'm currently taking classes on Special Relativity and Minkowski space. I have one question: how would future-oriented, contravariant time-like, space-like and light-like vectors transform under a ...
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5answers
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Why does a sign difference between space and time lead to time that only flows forward?

Ever since special relativity we've had this equation that puts time and space on an equal footing: $ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$ But they're obviously not equivalent, because there's a sign ...
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Lorentz transformation of magnetic field

I am studying relativistic electrodynamics and I am stuck at a certain point regarding the transformation rules of the electric and magnetic fields. The stationary inertial frame will be called $S$ ...
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Should we need to consider time dilation effect when travel in a very fast rocket? [duplicate]

How long does it take for a rocket to reach a planet 10 light years away if the rocket's speed is just near the light speed? If the speed is 1 c, the folks will answer it will take 10 year to travel ...
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A fundamental question about charge and speed of a particle [duplicate]

Hi everybody and happy 2019. In my teaching sessions sometimes someone asks questions i cannot truly answer (although i have many arguments on it) and here's one that really puzzles me: A massless (...
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Magnetic field at the center of a rotating charged square loop

Consider a square loop of side length $2a$, with a total charge $Q$ uniformly distributed along its sides (so that the line charge density is $\lambda=\frac{Q}{8a}$), set spinning at angular velocity $...
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1answer
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Does light know the future? [duplicate]

As I understand it, if light is traveling at the speed of light, then from it's point of view space is fully compressed in its direction of travel. Does that mean that from it's point of view, light ...
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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 ...
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Reading “On the Electrodynamics of Moving Bodies”, why do I get $\beta^2$ instead of $\beta$?

Einstein writes $\xi=\phi(v)\frac{c^2}{c^2-v^2}x'$ and $x'=x-vt$ in his paper "On the Electrodynamics of Moving Bodies". Additionally, he defines $\beta=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. If I ...
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Can a free particle ever emit a particle?

I have found this question here Can a free particle absorb/emit photons?, along with other resources that show a free particle cannot emit a photon (in a vacuum). Now, I am 90% sure it does, but ...
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5answers
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What is physically different about a moving vs still object in space?

If I have two asteroids. One dead still in space and one whizzing by at 10,000mph. What is the difference between the two, physically? If I freeze time and look at the two of them - what differences ...
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1answer
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Gamma factor in special relativity

I try to derive the Lorentz transformation of a Lorenzt transformation frame an inertial frame $O$ to the frame $O'$ of a moving particle at constant speed v. We have four vectors $\textbf{x}'=\Lambda ...
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1answer
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General proof of $m^2 = E^2 - p^2$

All proofs I know of, starting from Einstein's famous 1905 article, only deal with special cases (actually, yes, I know that formula like $E=mc^2$ were known before Einstein in the context of ...
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1answer
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What information does the four vector of momentum dotted with itself give us?

For example the dot product of the four vector, momentum, of a photon with itself is zero, is this simply telling us the particle is light-like or something else?
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1answer
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Proper time vs time

I'm reading about relativity and I thought I understood things clearly about proper time / coordinates until I read the analysis of the Doppler effect. A and B are 2 fixed points, there is a clock in ...
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1answer
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Invariance vs. Conservation of the Four-Vector Dot Product

This question refers to example 3.4 of Griffiths Introduction to Elementary Particles Second addition. In the example, a moving proton is collided into a proton at rest, producing 3 protons and 1 ...
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0answers
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Relative velocity before and after photon exchange

An atom has rest mass $m$ in the ground state and $M$ in an excited state. Two of these atoms are travelling towards each other, one in an excited state one in the ground state. The excited atom ...
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2answers
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$ct' = γ(ct − βx)$

I was reading a paper on S.R. saw this eq: $ct' = \gamma(ct − \beta x)$. However I am confused by the Minkowski's diagram: We know $\tan \theta = \frac{x}{ct}= \beta$. However, wouldn't it also mean $...
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2answers
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Why did Einstein pick his definition of synchronous clocks?

In his paper "On the Electrodynamics of Moving Bodies", Einstein defines synchronous clocks as clocks which satisfy $t_B-t_A=t'_A-t_B$. $A$ and $B$ are two points separated by empty space, and ...
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1answer
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Invariance of coincidence

I am reading the book "Space and Time in Special Relativity" by David Mermin. In chapter 13, at page 128 in my print, he says the following (screenshot): I'm referring specifically to the sentence "...
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1answer
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Relativity of Simultaneity and classic thought experiment

For the following thought experiment, How to do calculation in relativity of simultaneity Why is simultaneity considered as an act of seeing the bolts? Even for the passenger in the train, can we ...
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Time reversal in electromagnetism

In classical electrodynamics, we know that under time reversal the electric and magnetic potentials should transform as $$\phi'(x,t)=\phi(x,-t) \qquad A'(x,t)=-A(x,-t) $$ Now, using $(+,-,-,-)$ ...
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1answer
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Calculus of Variations help [closed]

I've been studying Chapter 6 in Taylor's Mechanics book. And am working through the odd-numbered problems. I am struggling with 6.13, which reads: In relativity theory, velocities can be ...
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What kind of average could give a Lorentz invariant energy-momentum tensor?

The electromagnetic (EM) radiation energy-momentum tensor is of the following shape, in the case of incoherent superposition of EM plane waves (I'm using $c = 1$ to simplify things, and metric ...
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1answer
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MTW Box 4.1 Contraction of EM 2-form with surface element bivector to give “magnetic flux”. What does that mean?

This is my attempt to make sense of Box 4.1-4.b of MTW's Gravitation. I'm not entirely sure I have the computation correct. But, even if it is correct, I don't really understand how the final result ...
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1answer
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When do Lorentz transformations take straight field lines to straight field lines?

If you look at elementary examples, it seems like a Lorentz transformation takes a field pattern with a lot of straight field lines to another field pattern with a lot of straight lines. Examples: an ...
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0answers
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Bernoulli principle and relativity [duplicate]

Bernoulli principle has many applications like airplanes take off etc. But when we apply Bernoulli's principle we dont refer the reference frame in which we measure the velocity of air for example. ...
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4answers
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$E=mc^2$: Why does the speed of light constant affect the Energy or Mass of an object? [closed]

So this is really just for fun. I often talk to my friend who studied some Physics degree (or similar) and he simply cannot accept the possibility it could be wrong in any way. To the point where he ...
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1answer
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Interpreting Time in Bells Spaceship Paradox

I’ve seen a lot of arguing about Bells Spaceship Paradox, so it appears to confuse even some physicists. In Bells Spaceship Paradox, two ships begin simultaneously accelerating at a constant rate ...
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1answer
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Transfer of heat in relativity and conservation of momentum

In relativity momentum is associated with flux of energy (not just mass), e.g. for a single particle $\textbf{p} = (E/c^2)\textbf{v}$ Imagine a rod which initially is hotter on one end. If the rod is ...
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2answers
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Why can't we insert gravity in the special relativistic lagrangian?

I am a math student and I have taken four-five lessons about special relativity in a course about Lagrangian and Hamiltonian mechanics, so be patient with me if my question is stupid. My teacher says ...
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1answer
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Problem on derivation of time dilation

In my lecture notes, there are two frames S and S'. The prime frame moves with uniform velocity with respect to the unprimed frame. In this frame, she derives the time dilation equation in the ...
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4answers
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How do we determine who is the “observer” when calculating time dilation? [duplicate]

I was reading about time dilation and I thought of a question. I really think that I am just misunderstanding something, so please bare with the question. But, I would appreciate if somebody could ...
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1answer
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Multiple objects with constant acceleration

There are a number of formulas involving acceleration at http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html. These formulas all assume that, at time 0, the origins of the rest ...
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Why doesn't the escape of electromagnetic waves from a microwave depend on the reference frame, because of the Doppler effect?

If an observer traveling towards a microwave oven at almost the speed of light blue shifts the microwaves enough to be visible light, how can the mesh on the oven door still stop to waves from ...
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0answers
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Is there some general theorem concerning the impossiblity of synchronizing an accelerated reference frame?

Discussions either around Born's rigid motion, or Dewan-Beran-Bell spaceships paradox, or Rindler hyperbolic motion, all seem to imply that a body which is accelerated with respect to an inertial ...
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1answer
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Trying to understand velocity addition and time dilation [duplicate]

I'm familiar with Einstein's formulae $V=\frac{u+v}{1+ \frac{uv}{c^2}}$ and $\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$, the former being velocity addition and the latter being time dilation....
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1answer
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Can we make a formula that describes the magnetic force as a function of electric field using length contraction equation ?

I know that the magnetism is just electricity and due to length contraction and the change in charge density moving charges experience what we call magnetic force. so my question is can we calculate ...
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4answers
127 views

Invariance of the relativistic interval

Imagine we have two events, $E_1, E_2$ in the coordinate systems $K, K'$ (with coordinates $(x,y,z,t),\ (x',y',z',t')$), whilst $K'$ ist moving with the speed $\vec v$ in regard to $K$. From the ...
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3answers
66 views

Rule of addition of velocities in water

Is the speed of light still the same for all inertial observers in water? If not, what are the rules of addition of velocities in water according to special relativity?
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0answers
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Demonstration of magnetic field lines “tension” and “pressure” using the Maxwell stress tensor

I would like to show that the magnetic fields lines are under "tension" along the lines and exert "pressure" perpendicularly to the lines, using the Maxwell tensor only. I have a sign ambiguity. In ...
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2answers
54 views

Questions on non-inertial reference frames

Suppose I am in an arbitrary reference frame and i want to know if it is inertial or not. So I decide to do a test, i take a particle of mass $ m $ and let go of it. I observe that the particle is ...
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1answer
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Derivation of Covariant Maxwell's Equations

I am trying to derive the covariant formulation of Maxwell's equations. I understand that all four of Maxwell's equations can be written compactly as $$\partial_{\mu}F^{\mu\nu} - j^{\mu} = 0 \;, \...
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4answers
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Exceeding the speed of light [closed]

I understand that the speed of light c is derived from the self-interaction between elections/photons, and is thus the maximum speed of anything composed of electrons/photons. Suppose that there is a ...
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2answers
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How is $\int \frac{d^{3}\mathbf{p}}{(2\pi)^3}\frac{1}{2\sqrt{|\mathbf{p}|^2+m^2}}$ manifestly Lorentz-Invariant?

When writing integrals that look like $$ \int \frac{d^{3}\mathbf{p}}{(2\pi)^3}\frac{1}{2\sqrt{|\mathbf{p}|^2+m^2}} \ = \int \frac{d^4p}{(2\pi)^4}\ 2\pi\ \delta(p^2+m^2)\Theta(p^0) $$ it is often said ...
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Problem in Special Relativity [closed]

"A space probe is sent to the vicinity of star Capella, which is $D = 42.2 \ light \ years $ from earth. The probe travels with a speed of 0.9930c. An astronaut recruit on board is 19 years old when ...