Lorentz Transformations | Special Relativity Ch. 3

What people said

Recommends Sean E. Lake · 2019-11 · Physics Stack Exchange · on “Checking the Lorentz Invariance”

@Constantin I recommend watching this playlist [LINK] , especially the Lorentz transform [this video] video and the length contraction/time dilation video [LINK] . Bottom line: the formula you want to depend on is a special case that only works sometimes.

Recommends Shirish · 2020-06 · Physics Stack Exchange · on “Angle-preserving linear transformations in 2D space for relativity”

I'm watching this minutephysics video on Lorentz transformations [this video] (part starting from 2:13 and ending at 4:10). In my spacetime diagram, my worldline will be along the $ct$ axis and the worldline of an observer moving relative to me will be at some angle w.r.t. the $y$ axis. When we switch to the other observer's spacetime diagram, the observer's worldline will be along the $y$ axis and my worldline would flip over to the other side, but the angle between the worldlines would be preserved. Then the video goes on to mention three possibilities: [LINK] The even at $(2,4)$ ends up getting mapped to $(0,T)$ , where $T<4$ , $T=4$ or $T>4$ . And it seems like the video is suggesting only on

Recommends viktaur · 2024-08 · Physics Stack Exchange · on “How does the eigenvector interpretation of Lorentz transformations generalise to higher dimensions?”

When I came across this YouTube video [this video] , I immediately realised how Lorentz transform corresponds to a linear transformation where the vectors representing the speed of light ( $\vec{c}$ and $-\vec{c}$ ) are in the only directions that do not change, thus being eigenvectors. After working out the math for a 2D spacetime $$ L\vec{v} = \beta \hat{t}$$ $$ L\hat{t} = \gamma (-\vec{v})$$ $$ L\vec{c} = \lambda_1 \vec{c}$$ $$ L(-\vec{c}) = \lambda_2 (-\vec{c})$$ I reached the Lorentz matrix $$ L = \gamma \begin{bmatrix}1&-v\\-v/c^2&1\end{bmatrix}$$ where $ \gamma $ is the Lorentz factor. I later realised the eigenvalues must be related to the relativistic doppler effect, as one of the values

Cites Ooker · 2018-06 · Physics Stack Exchange · on “How does projective geometry related with Fourier transform via Lorentz transformation?”

On one hand, the Lorentz transformation [this video] plays an important role [LINK] in classical electromagnetism. On the other hand, each Lorentz tranformation is also a Möbius transformation [LINK] of $\Bbb C$ (Needham, Visual Complex Analysis ): $$M(z)=\frac{az+b}{cz+d}$$ But what is the direct link between projective geometry and Fourier transform in physics? Can changing the perspective give rise to uncertainty principle [LINK] ? My knowledge is not very solid, but I guess we would start from the $U(1)$ group in QED then use the Peter - Weyl theorem [LINK] , but exactly where Möbius transformation plays a role in there? If possible, I'd like to have an intuitive answer. Related: • What proje

Cites Vespertilago11 · 2019-05 · Physics Stack Exchange · on “Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?”

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One of my friends recently showed me this video [this video] which is part of a larger series the presenter Mark Rober/minutephysics did on special relativity. In it he says that the Lorentz transformation he describes can be derived from two basic principles: 1) Velocity is relative and measured velocity depends on reference frame. 2) The speed of light $c$ is the same in all inertial frames. From principle 2 I gathered that in that case the world lines for particles moving at speed $c$ must be eigenvect

Cites SK Dash · 2020-03 · Physics Stack Exchange · on “Time measured by a person vs Time measured by the same person as observed from another frame”

Consider the definition of length. We may define it as the difference of the spatial coordinates between two points with respect to a reference frame, when it's temporal coordinates are the same. Basically length is the distance between two points when they are at the same time coordinate. Thus the relationship between length with respect to two different reference frame may be obtained using the Lorentz Transformation for the spacial coordinates. Consider, the following scenario, two reference frames A and B. A is stationary, while B is moving with a constant velocity v with respect to A. We assign x and t to the reference frame A, x' and t' to reference frame B. Note I will be taking $c=1$

Cites Solomon Slow · 2024-05 · Physics Stack Exchange · on “Misunderstanding of length contraction in special relativity”

Re, "...if so then the star should have moved close to me at faster than ." The star hasn't moved. Your acceleration has changed the way you look at spacetime (i.e., it has _transformed_ the coordinate system that describes your point of view.) [this video]

Cites Solomon Slow · 2024-08 · Physics Stack Exchange · on “Why does an accelerated clock record fewer events?”

This had me confused: The clock also continuously records its readings so that at the end of the experiment there is a single record upon which all observers will agree IMO, That's an unnecessary complication. ...the continuous record of indicated times recorded by the clock during the experiment indicates that subsequent to the acceleration less events were recorded by the clock. If all you're doing with the "record" is counting the number of recorded ticks between two events, then all you really are doing is asking how much time, according to the clock, elapsed between those two events. But if that's what you want to know, then you only need to record two things: What time was shown on the

Critical SK Dash · 2020-03 · Physics Stack Exchange · on “Length contraction and time dilation relationship”

Consider the definition of length. We may define it as the difference of the spatial coordinates between two points with respect to a reference frame, when it's temporal coordinates are the same. Basically length is the distance between two points when they are at the same time coordinate. Thus the relationship between length with respect to two different reference frame may be obtained using the Lorentz Transformation for the spacial coordinates. Consider, the following scenario, two reference frames A and B. A is stationary, while B is moving with a constant velocity v with respect to A. We assign x and t to the reference frame A, x' and t' to reference frame B. Note I will be taking $c=1$