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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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Tensors and the Klein-Gordon Equation

Consider the Klein-Gordon equation: \begin{equation} \frac{\partial^2 \psi}{\partial t^2} = c^2 \Delta \psi - \frac{m^2 c^4}{\hbar^2} \psi, \end{equation} and define for each one of its solutions $\...
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Wave and relativity

From Wikipedia, "In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport." But Einstein said that energy equals mass so if a wave ...
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1answer
37 views

Deriving the geodesic equation using a Lagrange multiplier to fix affine parametrisation

The geodesic equation can be derived using the action $$S_0 ~=~ \int d\tau \sqrt{-\dot{x}_\mu\cdot \dot{x}^\mu}\tag{1}$$ (I am using the (-+++) convention and $\dot{x} = \frac{dx}{d\tau}$). To ...
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Difference between quadrivector and 4-vector

Why is the square of a 4-vector equal to $t^2+x^2+y^2+z^2$ while the square of a quadrivector is equal to $t^2-x^2-y^2-z^2$? Aren't they the same mathematical object?
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Physical meaning of the Casimir operators of Poincarè algebra

If one considers the algebra $su(2)$, it is well known that the Casimir Operator is $$ C=L_1^2+L_2^2+L_3^2. $$ It corresponds to the total angular momentum and correctly is a conserved quantity. ...
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Time dilation for circular movement [duplicate]

As a thought experiment, I was trying to find a way to constantly dilate time while keeping an object effectively in place. I quickly decided that moving forwards and backwards wouldn't work—the speed ...
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2answers
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Notation for the Representations of $SO(3,1)$

I was reading Zee's book "Quantum field theory in a nutshell" and came to the chapter regarding representations and algebra. He writes that the representations of $SO(3,1)$ are $(0,0),(0, 0),( \frac{...
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122 views

General Irreducible Representation of Lorentz Group

Background (just for context, you can skip it if you're familiar with Lorentz representations) A Lorentz transformation can be represented by the matrix $M(\Lambda)=exp(\frac{i}{2}\omega_{\mu\nu}J^{\...
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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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Special Relativity collision [on hold]

A certain elementary particles lives only a time $T_0\ \rm s$ (proper time) before disintegrating what velocity must the particle have if it is to reach a distance D before disintegrating? Note that ...
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Stars with different Speed of light [on hold]

Is the speed of light changes for each star depending upon the diameter or the speed is constant irrespective of the diameter in vacuum
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114 views

Definition of generalized 4-momentum

In nonrelativistic mechanics, given a lagrangian $L$, we define the action as $$S[q]=\int L(q(t),\dot q(t))dt\tag{1}$$ and we can prove (see, for example, this answer for eq. (2)) $$\begin{align} \...
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Question about Special Relativity similar to twin clock experiment

This question is related to twin clock experiment but also involves a third clock. Here it goes: Suppose the relative velocity between clock 2 and clock 3 is given by $v=0.8c$. This would mean that ...
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How can we measure relative velocity of fast objects when there is time dilation

First of all sorry about the question title. I find it very difficult to ask this in less than 150 characters. I am not a physicist and only have basic understanding of advanced physical concepts. So ...
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How to go from covariant form to vector form of Thomas precession equation

In Weinberg's Gravitation and Cosmology he derives the covariant equation for Thomas precession: $$\frac{d S^\alpha}{d\tau}= \left( S_\beta \frac{d U^\beta}{d\tau} \right) U^\alpha,$$ where $S^\...
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Stuck on Weinberg's quick derivation of Thomas precession

In Weinberg's Gravitation and Cosmology he has a pretty concise derivation of the Thomas precession formula (Eq. 5.1.13). But I don't get the first step... A particle with intrinsic spin is under the ...
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Confusion about 4-velocity

I know that 4-velocity is defined as $$u^\mu = \frac{dx^\mu }{d\tau}$$ $$u_\mu=g{_\mu}{_\nu}u^\nu$$ and $$u_\mu u^\mu=c^2$$ Is it true that $$\frac{d\tau}{dx^\mu} = \frac{u_\mu}{c^2} = \frac{1}{c^...
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Is the obeserver moving in Ehrenfest paradox?

On wikipedia https://en.wikipedia.org/wiki/Ehrenfest_paradox, it seems like it indicates there are two observers in Ehrenfest paradox. The first one is stationary in the center of the disk, this one ...
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Given an electromagnetic field in a frame of reference, find all other frames of reference where the electric and magnetic field are parallel

This is actually an exercise in Landau-Lifshitz's book. Their solution goes as follows. After we have found a frame of reference where $\mathbf E$ and $\mathbf B$ are parallel (let's call the common ...
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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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How to distinguish a spinor from a 4-vector?

Lets say we are given a four components object. To be explicit lets consider that these components are $ x^\mu = \mu $ with $\mu\in{0,1,2,3}$, i.e. $$ x^\mu \sim \left[ \begin{matrix} 0\\ 1\\ 2\\ 3 \...
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Covariant/contravariant manipulations for identity

On page 16 of Srednicki’s quantum field theory he says that we can get $$g^{\mu\nu}\Lambda^\rho_{~~\mu}\Lambda^\sigma_{~~\nu}=g^{\rho\sigma}$$ By starting with $$g_{\mu\nu}\Lambda^\mu_{~~\rho}\...
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4answers
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Reverse engineering a time dilation problem [closed]

Consider the following problem A rocket with a clock moves at $0.8c$ relative to the earth. An observer A on the rocket measures a time interval of 6 seconds. With respect to an observer B on the ...
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On contraction, aberration and redshift of light from a mirror for an observer who remains still

Last week I came across with a question from an old course I took in General Relativity which said this: Suppose you are traveling at speed v=0.9c respect to an observer who remains standing up still ...
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what is the behavior of an electronic oscillator at relativistic speeds?

Imagine an LC circuit in which the capacitor consists of two metal discs of area $A$ and spacing $D_0$ which is connected to a solenoid coil which for convenience has length $D_0$, cross-sectional ...
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If an observer were to move toward the moon at a significant fraction of the speed of light, will its cross section appear a different size? [duplicate]

I've read that length contraction occurs only in the direction of motion, but I'm confused on how to interpret this question. If I travel toward the moon at a significant fraction of $c$ then distance ...
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Does a shadow truly have a speed? Is it an illusion? [duplicate]

If a shadow is no information, does that mean when you say a shadow is faster than the speed of light it is the equivalent of saying no information is faster than the speed of light? If a shadow is ...
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Expressing the conversion from units of time to units of space in special relativity rigorously

In their book Spacetime Physics, Taylor and Wheeler stress the analogy of the speed of light $c$ to a conversion factor $k$ which converts between miles and meters and subsequently convert freely ...
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Does a person moving at almost the speed of light observe their own mass increasing? [duplicate]

Firstly I'm not a physicist/not formally studying the subject, but I do have an increasing interest in the subject. I understand from the Lorentz formulas that mass increases relativistically, but if ...
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COM frame in Relativistic particle physics

I have a home work: Consider a head-on collision of a 'bullet' of rest mass $M$ with a stationary 'target' of rest mass $m$. Prove that the post-collision γ-factor of the bullet cannot exceed:$$(m^...
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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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Landau's 4-Accelaration Problem

I was going through Lev and Landau's 2nd volume on classical field theory. I came across a doubt. It's stated in the solution that we go to the frame having particle's velocity zero, which basically ...
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Does infinite mass exist? [closed]

So when I search up if infinite mass exists, google provides me with a source that states infinite relativistic mass does exist at the speed of light which is why it is impossible to ever reach to ...
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Two objects moving relativistically towards each other [duplicate]

Let's say I have two objects moving relativistically toward each other, so the object on the left is moving to the right, say, at .3c and the object on the right is moving to the left at .7c, and they ...
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1answer
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Switching between Lorentz frames

I know that for a Lorentz trasformation: $$x' = \gamma (x-ut)$$ and $$t'=\gamma (t-\frac{u}{c^2}x)$$ and $$v'=\frac{v-u}{1-\frac{uv}{c^2}}$$ If I want to switch Lorentz frames, and find x, t, and v ...
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Contradiction? Electron mass, speed $c$ vs electrons being all the same [closed]

I understand that all matter increases in size when approaching speed c I also understand that all electrons are exactly the same. Assuming the mass of the electron is also effected by approaching ...
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Useful Momentum Relation for Relativistic Particles [closed]

I've seen that $$p = \sqrt{(\frac{E}{c})^2-(mc)^2} = \frac{1}{c} \sqrt{{E_k}^2 + 2 E_0 E_k}$$ for a relativistic particle on hyperphysics and in my modern physics class. I understand that the first ...
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Can a spot from a spinning flashlight go faster than the speed of light, and what does a frame of reference sitting on that spot experience? [duplicate]

The first part of my question has already been asked and answered. They say the spot can break the light speed barrier. Now for the second part, what would a frame of reference sitting on top of the ...
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3answers
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How to measure angles in Minkowsky space, and how do they transform?

I want to know how an ordinary angle $\theta$ transforms under a Lorentz boost. For that purpose I consider a 4-vector given by $$ a ^ \mu = ( t , \cos \theta , \sin \theta , 0 ) .$$ The angle I ...
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117 views

Non-Relativistic theories of light [closed]

Why can light be easily described using non-relativistic theories, since it moves at maximum speed (ie it can not be more relativistic than it already is)?
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Length contraction and Spacetime diagram

I don't understand why $x_c=l/\sqrt{1-v^2}$ if interval between A and C is equal, then: $$ l^2=-t^2+(x_c)^2$$ thus : $$ x_c=\sqrt{l^2-t^2} $$ why is: $$ x_c=\frac{l}{\sqrt{1-v^2}} $$ Please ...
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Twin paradox in ideal gas: does higher temperature imply slower decay

In the twin paradox (which is actually not a paradox), one twin brother stays on earth (inertial reference frame), while the other travels to another planet and comes back. On his return the stay-at-...
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How fast would a falling object impact a massive star when released from $10*10^{24}$m away? [closed]

Take the most massive known star, R136a1, with a mass of $5.3 * 10^{32}$kg and a raidus of $2.5*10^{10}$m. Now place a $1$kg metal ball $10*10^{24}$m away (about a billion ly, while still being SI ...
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Tensors in a two-dimensional Euclidean plane

Consider a two-dimensional Euclidean plane with coordinates $(x^1,x^2)$ If we define a set of new coordinate $z^1$ and $z^2$ $$z^1=x^1+ix^2$$ $$z^2=x^1-ix^2$$ A question is if a symmetric tensor $T^...
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2answers
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What is the exact relation between anti-matter and relativity?

I have seen in relativistic QM that, when trying to create the Dirac Equation, it only make sense to be acting on -- at minimum -- a 4-component vector (actually a bi-spinor). I guess this is because ...
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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
32 views

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
66 views

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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Does time dilation really exist? [duplicate]

I'm very curious to know what is the concept behind time dilation and length contraction. What's the theory that relates them? How does it work
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3answers
84 views

A question regarding the speed of light in a vacuum, specifically putting a 'color' in

I know that red and blue etc. lights are produced when 'white' light is put through mediums. I have learned that all light in a vacuum, all electromagnetic waves, travel at the same speed in a ...