Linked Questions

11
votes
1answer
712 views

Combining two Lorentz boosts

Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$? To answer this, I start by defining $\theta \equiv ...
2
votes
3answers
3k views

Derivation of the general Lorentz transformation

The standard Lorentz transformation or boost with velocity $u$ is given by $$\left(\begin{matrix} ct \\ x \\ y \\ z \end{matrix}\right) = \left(\begin{matrix} \gamma & \gamma u/c & 0 & 0 \...
4
votes
1answer
409 views

Composition of Lorentz transformations using generators and the Wigner rotation

I solved this problem by painful calculations of Lorentz matrices. However, I heard that there is a much easier solution using the generators of boosts and rotations and their commutation relations, ...
1
vote
1answer
773 views

Appearance of an angle of inclination on a horizontal rod moving upwards after a Lorentz Transformation [closed]

If i have in one inertial reference frame called $S':(x',y',z',t')$ a rod with lenght $l$ in the plane $z'=0$ and parallel with the $x'$ axis, moving with a velocity $u$ in the direction of the $y'$ ...
4
votes
1answer
281 views

Special *set* of inertial frames in an EM field?

Just looking for confirmation of my understanding of the Wikipedia article on classification of electromagnetic fields: The article states that in the case where $E\cdot B = 0$ and $E^2-B^2 \not= 0$...
3
votes
1answer
432 views

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 ...
2
votes
2answers
480 views

Two sets of coordinates each in frames $O$ and $ O' $ (Lorentz transformation)

Suppose inertia frame $O'$ is moving at velocity $v$ relative to inertia frame $O$. Let the coordinate systems of $O$ be denoted by $(x,y,z)$ and the corresponding one on $O'$ be denoted by $(x',y',z')...
2
votes
5answers
145 views

Lorentz transformation: qualitative explanation

Long story short, how can I qualitatively explain what is the Lorentz transformation and why it does so? I am looking for a description of its general behavior instead of "it works due to an XYZ ...
3
votes
1answer
550 views

Wigner Rotation

I'm trying to show that the composition of two Lorentz boosts produces a boost and a rotation using the generators from the Lorentz Group. If $\vec{K}$ denotes the Lorentz Boost generators and $\vec{S}...
1
vote
1answer
163 views

Special Relativity - Perpendicular Boosts Equaling to a Rotation after a Boost

[Question] I recently read that two perpendicular Lorentz boosts equal to a rotation after a boost. Can anyone here show me an example of this happening? Thank you for your time and assistance! ...
3
votes
2answers
114 views

Thomas-Wigner rotation of a stick directly from the Lorentz Transformation

I'm trying to better understand Thomas-Wigner rotation. I understand how to calculate it for the case of a perpendicular pair of boosts. But I also want to see the rotation more directly. The effect ...
3
votes
2answers
113 views

What are the Lorentz Transformation equations when the relative velocity of an entity is in an arbitrary direction?

The Lorentz Transformation equations are generally presented as a transformation of spacetime between two observers, when they each move at a velocity $v$ along the $x$ axis relative to each other. My ...