Visualization of Einstein's special relativity
Why Physics Stack Exchange recommends it
Physics Stack Exchange answerers point people to it as a quick visual of Lorentz transformations, showing simultaneity loss, length contraction and time dilation as a rotation in spacetime.
Recommended by 3 people across 3 different months, 2014 to 2017.
What it is
A short 2008 animation by udiprod that visualizes special relativity and the Lorentz transformation in a 3D view with two space dimensions and one time dimension. It contrasts classical physics with Einstein's relativity to show why the latter was needed.
Cited in 4 Wikipedia articles, including Special relativity, Lorentz transformation, Minkowski spacetime.
What people said
Recommends Stan Shunpike · 2015-05 · Physics Stack Exchange · on “Rotation in the x-t plane”
Bernhard Schutz discusses this reasonably well in his book A First Course in General Relativity . Consider sending a light beam horizontally along an $x$ axis and then receiving it back again. A space time plot of this would look like Here's an example of the rotation you are describing And this is how everything becomes distorted when you create such an $xt$ plane rotation: Note some major properties Simultaneity broken It shrinks moving objects (length contraction) Slows down moving clocks (ie time dilation) But it works and allows $$v_{light} = c$$ See this video for a visual (it's really cool!): [this video] And buy/rent/borrow Schutz's book. He nicely walks you through this part. The SR sect
Recommends Craig Gidney · 2016-03 · Physics Stack Exchange · on “3 points in space, relative motion, and the speed of light”
Special relativity doesn't forbid saving time by meeting in the middle. It also doesn't forbid you from time-dilating yourself by an arbitrarily large amount to get somewhere without personally waiting a long time. For example, see this web page [LINK] about relativistic flight times: Here are some of the times you will age when journeying [with constant 1g acceleration] to a few well known space marks, arriving at low speed: d Stopping at: T [your age on arrival] 4.3 ly Nearest star 3.6 years 27 ly Vega 6.6 years 30,000 ly Centre of our galaxy 20 years 2,000,000 ly Andromeda Galaxy 28 years When superman changes speeds, he switches inertial frames. In his new frame, where he's moving at 0.5
Recommends JM1 · 2017-12 · Physics Stack Exchange · on “Special relativity - loss of simultaneity - Is that real?”
This animation provides a decent visual depiction of not only the relativity of simultaneity but also of the physical consequences of time dilation and length contraction associated with it -- [this video]
Cites Uncle Al · 2014-02 · Physics Stack Exchange · on “Does the velocity of a light source influence the light”
[this video] [LINK] Light in vacuum travels at lightspeed for all observers. The paradox is taken up by relativistic Doppler shifting of the observed light's frequency. Light travels along null geodesic paths. Light defines a straight path through spacetime.
Cites snefs · 2016-01 · Physics Stack Exchange · on “Visual pictures of Lorentz transformations”
Let the Minkowski spacetime be the set $\mathbb{R}^4$ parametrized by coordinates $\underline x = (t,x_1,x_2,x_3)$. You can visualize this set with a $4$-dimensional cartesian diagram, with axes labeled $(t, x_1, x_2, x_3)$. You can help your intuition just by drawing the 3-dimensional one (suppressing one of the space dimensions). A Lorentz transformation is an isometry of the Minkowski spacetime, which means that it preserves the inner product given by the metric $g = -dt^2 + dx_1^2+dx_2^2+dx_3^2$. The associated matrix is $$ g = \left(\begin{array}[cccc] --1 & & & \\ & 1 & & \\ & & 1 & \\ & & & 1 \end{array}\right) $$ One has that all such isometries are of the form $\underline x' =\Lambd