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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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Invariance of spacetime interval in special relativity: linearity

I'm trying to understand which assumption are necessary to prove the invariance of the spacetime interval $\Delta s^2=c^2\Delta t^2-\Delta \mathbf{x}^2$ in special relativity. The postulates of ...
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Visual effect in Special Relativity [on hold]

I have an exercise: A distant camera snaps a photograph of a speeding bullet (speed v) with length b in its rest frame. Behind the bullet and parallel to its path is a meter stick, at rest with ...
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Why the length of the the rod contracts as the time passes more and more?

My question may be too obvious but please consider me as an apprentice into the special theory of relativity. Suppose i take a stick moving at relativistic speed v in the positive x axis . I want to ...
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Can the space-time be a discrete lattice? [duplicate]

I would like to know how much conjectures about the space-time's being discrete are valid. There is a short article here: https://www.meta-religion.com/Physics/Quantum_physics/is_space.htm One ...
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Speed of light, can it be not constant? [duplicate]

What if we switch on a flashlight while travelling at the speed of light (we are travelling in vacuum, in a straight path)? What will happen and what will be the speed of light from the flashlight? ...
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How is the complexification of the Lorentz Lie algebra related to the need for Dirac's 4-component spinor in QFT?

There have been several questions with good answers in physics.stackexchange about the motivation of the complexification of the Lorentz Lie algebra, basically as a mathematically nice way to deal ...
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Relativity of Simultaneity thought experiment

I am trying to come to grips with the thought experiment. My understanding is that: (1) from the view of the observer on the railway embankment, since the train is moving with speed v from A (A') to B ...
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What part of special relativity is factored in in relativistic redshift velocity equations?

While doing research into redshift equations (doppler redshift and cosmological redshift), both types of redshift had two equations for finding recession velocity: a 'non-relativistic' equation and a '...
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What if we shine a laser to east and another to west, will they arrive at the same time?

If we have two lasers based at the equator and we direct one of them east and the other west on to two screens each 10 km away, will light emitted synchronously at the lasers arrive at the same time ...
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Different weights for time and spatial derivative in Lagrangian Density

I'm new to QFT and trying to understand the form of the Lagrangian densitys used. As a simple model you often see a Lagrangian density of the form $${\mathcal L} = \frac{1}{2} \partial_j \phi_n \...
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Mathematical proof that the centre of mass energy is the smallest energy in a collision

I recently answered this question about how the energy of a system of colliding particles is minimised in the centre of mass frame. I'm happy with the qualitative answer that treating the collection ...
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2answers
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What is possible intuitive explanation of inelastic relativistic collsion?

In classical mechanics, we say an inelastic collision happens when some energy is transferred to heat and noise without changing the total sum of momentum. However, in special relativity, every ...
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Does a circle become bigger or smaller when rotating? [duplicate]

Say a circle is rotating about its centre at a relativistic speed. If it were not rotating in your reference frame, its circumference divided by its diameter would be $\pi$. Now, because it is ...
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1answer
76 views

Additive speed of light for three bodies

I know this question, or similar ones have likely been asked before, but I have tried reading several, and they just don't properly explain what I'm trying to understand. The quick version of the ...
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1answer
46 views

An accelerating rod in special relativity [on hold]

If A solid rod is at rest on the x’-axis of an inertial frame $S’$. Then, at $t'_ 0 = 0$ the rod starts moving with constant acceleration a parallel to the $y’$-axis, while the frame $S’$starts moving ...
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71 views

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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3answers
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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
59 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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1answer
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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
50 views

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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1answer
135 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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1answer
35 views

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 [closed]

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 [closed]

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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115 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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3answers
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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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2answers
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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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0answers
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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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1answer
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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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1answer
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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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1answer
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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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2answers
107 views

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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3answers
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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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1answer
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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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1answer
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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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1answer
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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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2answers
55 views

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
44 views

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 ...