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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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Question about special relativity in Carroll lecture note

In the lecture of General relativity by Carroll, page 7 is written that: Notice the distinction between this situation and that in the Newtonian world; here, it is impossible to say (in a ...
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Is there a connection between the energy distribution and time dilation?

Can anyone please help me understand what is descibed bellow? Scenario 1. We have a pair of atomic clocks. Let's call them clock A and clock B. We switch both of them on at the same time. Clock A ...
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conventional matrix notation for distance interval

Why matrix notation for distance interval is represented by this? $$g_{\mu \nu}\Delta X^{\mu}\Delta X^{\nu}=(\Delta X)^Tg (\Delta X)=\Delta X^{\mu}\Delta X^{\nu}g_{\mu \nu}$$ Could you explain ...
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Paradox are all 4D distances zero?

The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero. Take a point A and a point B in the future at ...
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Dirac matrices in 1+1 dimensions

Given $\gamma^\mu$ in 1+3 dimensions with signature $(+,-,-,-)$, how can I obtain Dirac matrices in 1+1 dimensions expressed in terms of the $\gamma^\mu$?
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SuperString theory and mass-energy equivalence [on hold]

I have some doubts regarding Einstein’s mass-energy equivalence relation $E=mc^2$. This equation was also interpreted as release of c2 joule of energy if 1 gram mass of an element is completely ...
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3answers
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Explanation of Lenz's Law phenomena

If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe. Having the pipe otherwise accelerate the magnet would be in ...
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Retrieving the non-relativistic formulas for electric and magnetic fields from relativistic formulas

I was checking the formulas for the electric and magnetic fields components E and B given in this link from Wikipedia: https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#...
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If scientists prove that speed of light can move in a circle, does this contradict the theory of special relativity? [on hold]

if light moves in a circle it contradicts special relativity. Now, in the very strong gravitational field of a black hole light is moving in a circle, which indeed “contradicts” special relativity
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Poincare group and free theories

How exactly is the Poincare group related to the free relativistic theories in quantum field theory? I know Poincare group is the Lorentz group along with translations but don't see any connected why ...
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How to calculate mass from time dilation and radius?

I'm new to this site and I'm been searching the internet all over for this solution. I'm looking for an equation, that if given the time dilation at the surface of an object and its radius, it will ...
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How can I plan my physics learning? [on hold]

i would like to start learning physics on my own, but the problem is i dont know where to start, and what topics i should do after, Im a 16 year old learning at a high school with high level phycics, ...
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3answers
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Space (Lorentz-Fitzgerald) contraction

Lorentz transform can be written, according to wikipedia, as: $$ \begin{align} ct' &= \gamma \left( c t - \beta x \right) \\ x' &= \gamma \left( x - \beta ct \right) \\ y' &= y \...
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Could be possible to build a 4-vector in special relativity whose spatial component was the electric field E?

Hi everyone and sorry for my English. I would like to know if I can build a legitimate 4-vector as $E^\alpha=(E^0,\mathbf{E})$. I'd like you to check if my way is correct. 1- We already know that $\...
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1answer
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Why do two moving inertial frames of reference atribute the same velocity to each other?

In both relativity and Newtonian mechanics, it is a self-evident axiom according to which two inertial observers who move relative to each other measure the same velocity of, say, $v$. I want to know ...
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A Scalar Function Tranformation — Question on Notation in 't Hooft Document

I started reading a document by Gerard 't Hooft which can be found here. Right at the start I am puzzled by a simple expression. It is equation 2.2 showing how a scalar function transforms. I ...
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$\partial^{\nu} \partial_{\nu}$ vs. $\partial_{\nu} \partial^{\nu}$

I was doing a problem regarding field theory. I am given the following lagrangian density: $$\mathcal{L}=\frac{1}{2}\partial_\mu\phi_i\partial^\mu\phi_i-\frac{m^2}{2}\phi_i\phi_i$$ for three scalar ...
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Coordinate transformations

In Einstein's "The Meaning of Relativity" I don't understand the relation between $b_{\nu\alpha}$ in equation (3a) and $\lambda$ that pops up in equation (2b). I understand the fact that there's a ...
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3answers
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How does relativity affect the view of different observers

I understand how the Lorentz contraction works but was thinking about how that would manifest itself as perspective of a distant object by two different observers. One is traveling at high velocity ...
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2answers
68 views

Relativity thought experiment - spaceship travelling at speed of light [closed]

I have basis knowledge in special relativity, but I haven't studied it for too long and I'm stuck in a simple thought experiment. Assume that there is a spaceship departing from the earth at speed of ...
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1answer
64 views

Gear Theory — Entanglement — Spooky action at a distance explained? [duplicate]

Nothing can travel faster than the speed of light. Not even an electrical signal. Entanglement seems to violate this. But, does it? Imagine 100 gears lined up in sequence all the way across a ...
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How can it be physically proven that the higher velocities of light are one of the compounds of the speed of light? [closed]

The true roots of the theory of relativity that describe light and gravity need higher velocities than the speed of light to describe the full extra dimensions .
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Faster than light speed transfer of certain event

I am CS/Math person I am not quite sure what it means in physics information cannot be transferred faster than light (FTL). I tried to understand the proof of no transfer theorem but I lacked the ...
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2answers
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What is the reasoning behind 1 step in Einstein's derivation of the Lorentz Transformation

In Einstein's book "Relativity" there is a wonderful derivation of the Lorentz transformation, requiring no more than high school algebra (pp. 117 - 121). It is quite clear but I do not understand ...
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1answer
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About $(0,1/2)$ representations

While studying representations of Lorentz group, we get the generators to be $J_{i}$ - rotations and $K_{i}$ - boosts. We define $N_{i}^+$ and $N_{i}^-$ operators and these operators obey the same ...
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Confusion with covariance of the Dirac Equation

I'm studying the covariance of the Dirac equation: I start with the Dirac equation for observer A: $$(i\hbar\gamma^\mu\partial_\mu-mc)\psi(x)=0$$ and since $$\psi=S^{-1}(\Lambda)\psi'(x'),$$ I get: $$...
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2answers
51 views

Reflective photon rocket

A space-craft, also of rest-mass $M_0$ and initially at rest, is propelled by reflecting a plane-parallel beam of photons, generated at a rate $αM_0$ from a stationary source mounted on the launch pad,...
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2answers
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How can the universe be dodecahedron-shaped?

Physicsworld references "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background" by J.-P. Luminet et al., published in Nature (...
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1answer
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Another question about Four-velocity derivation

Consider,again (Question about derivation of four-velocity vector) the following: For a massive particle with position $x^{\mu}(t) = (x^{0},x^{1},x^{2},x^{3}) \equiv (x^{0},\vec{x})$ we define the ...
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2answers
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Naive question about the need to construct the 4-velocity

Special relativity was not born as a 4-covariant theory. Instead, Einstein derivated the kinematical quantities without spacetime,therefore without 4-vectors. Consider then the following: First ...
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1answer
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How can I go and also not go faster than light?

Suppose I am in a spaceship. In this spaceship there is also my friend. So my friend and my relative velocity is zero. So no matter how fast my ship goes my friend's velocity relative to me is zero($0$...
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1answer
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The delay of light in the air in the experience of Michelson

An experiment to test the special theory of relativity was carried out in the air. Therefore, the speed of light is equal to the phase velocity of light; it is different from the speed of light in a ...
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2answers
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Momentum in the rest frame

I am a little confused over the terminology of the rest frame. Say a photon collides with a massive particle then from the rest frame of the massive particle would it be the photon or the particle ...
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Is the speed of light greater if traveling at an initial velocity greater than zero? [duplicate]

I'm reading "a brief history of time" and he states "the speed of light should be the same whatever the speed of the source, and this has been confirmed," (24). Why is it not increased if it has an ...
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Variation of vector field under Lorentz transformation and gauge transformation

In a paper I am reading, it is stated that under a Lorentz transformation, the coordinates transform as $x^{\mu} \to \Lambda^{\mu}_{\nu}x^{\nu}$, and so the change in the (vector) field at the same ...
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Momentum in capacitor field; How can an EM field have zero momentum density but non-zero momentum flux?

Consider the case of a simple, stationary parallel plate capacitor oriented with its plates lying in the x-y plane. The E-field is simply given by: $$\vec{E} = \frac{Q}{\epsilon_0A}\hat{z} $$ with ...
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2answers
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Clock in a sealed box at half the speed of light. How would it know it is moving?

Consider a clock enclosed in a sealed box here on earth syncronized with my wrist watch. I send the boxed clock around the galaxy a couple of times at half the speed of light (or the full speed of ...
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Everyday magnetism as a consequence of perfect balance of electrical effects

Consider two charges moving in space, both at the same speed and parallel to each other. Because they are moving, they will behave like two currents and will have a magnetic field associated with ...
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1answer
64 views

Why would it take so great distance for an object to have the acceleration due to gravity?

Let's suppose that in a certain reference frame, a hyperbolic coordinate is used, i.e. $(x,t)=(r\cosh \omega, r \sinh \omega)$. On each hyperbola $r=R$, where $R>0$ is a constant, the proper ...
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1answer
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Distance contraction in special relativity

Say that a comet explodes over Jupiter. And we were watching this from earth. There should be a time lag in reality as the light takes finite time to reach us. Now if we supposed an inertial frame ...
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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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0answers
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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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5answers
139 views

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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7answers
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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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1answer
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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 $...