5
$\begingroup$

Recently started an introductory course of relativity, and started learning about space time diagrams.

I couldn’t figure out what are the uses of a spacetime diagram as an alternative to Lorentz transformations. When will one be better to use? Also, how can one use them instead of a Lorentz transformation, such as for deducing length contraction and time dilation?

$\endgroup$
  • $\begingroup$ Lorentz transformations are all you really need, but it can be confusing when dealing with the various non-intuitive features of special relativity, especially for beginners, so spacetime diagrams can be helpful to keep things straight in your mind. I quite like the diagrams that robphy draws on rotated graph paper, eg physics.stackexchange.com/a/452723/123208 $\endgroup$ – PM 2Ring Apr 8 at 9:00
  • 2
    $\begingroup$ "I couldn’t figure out what are the uses of a space time diagram as an alternative to Lorentz transformations"...one example: .try to analyze the behavior of a particle near a black hole, I bet you end up drawing a space time diagram $\endgroup$ – StudyStudy Apr 8 at 10:14
1
$\begingroup$

I couldn’t figure out what are the uses of a spacetime diagram as an alternative to Lorentz transformations.

They're not alternatives to each other. You can in fact represent a Lorentz transformation on a spacetime diagram. There is a nice modern pedagogy for teaching special relativity in which we do exactly this. The usual presentation is that you keep the events (points) fixed, while representing the change of coordinates as a distortion of the coordinate grid into a new coordinate grid shaped like a parallelogram. Some presentations in this style are:

$\endgroup$
2
$\begingroup$

Minkowski diagrams are related to the Lorentz transformations in the same way a graph is related to its funcion. You don't need the graph of $x^2$ to understand its behavior, but it can come in handy. It's useful, for example, to solve paradoxes like the ladder paradox or the twin paradox.

As for your other question, while it's easy to see length contraction on a Minkowski diagram, it's not that easy to measure it, because you can't just grab a ruler and measure lengths: the curves of constant length in facts aren't the good old straight lines of $R^2$, but are indeed hyperboles.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.