Spacetime rotations, understanding Lorentz transformations

What is a Lorentz transformation? How do we turn within space-time? Why is the speed of light invariant? All these answers in 15 minutes!

0:00 - Introduction
1:22 - Galilean Transformations
3:52 - Lorentz Transformations
6:56 - Hyperbolic Rotations
11:50 - Unifications
14:00 - Conclusion

This video is narrated by Octave Masson.
And if you liked this video, you can share it on social networks !

Alessandro Roussel,

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[newrever]

This channel is absolutely unparalleled! I've never encountered such clear explanations for these concepts.

[archiewerkie]

never tired of watching videos about spacetime.

[afotopoulos]

I am a physics major, and finished special relativity last semester. I had some ideas about the subject, and wanted to create some diagrams to explain it better. I was stuck in circular rotation, and i had completely forgotten about hyperbolic rotatios. THANK YOU VERY MUCH, AMAZING WORK!!

[yookalaylee]

Knowledge for free that previous generations couldn’t even have dreamed of. An amazing YouTube channel.

[cCiIcCo]

You are by far the best science and physics channel on YouTube imo! Greetings from Germany✌🏼

[mjames]

I love the way you explained this.
My dumb brain has always had trouble with spacetime diagrams and light cones, but this helped me to better comprehend the idea.
Thank you!

[kam]

This is a brilliant visualisation of Lorentz transformations and worldline diagrams! It gives a nice exposition of the relationship between energy and momentum, and why it's a valid approximation to add velocities together in classical physics. As someone doing a PhD in particle physics, this is a very helpful picture to have in my head when thinking about these concepts.

I would just like to clarify that the statement made at 11:24 does not literally mean that the speed of light is infinite (which would be in direct contradiction with statements made earlier in the video). Instead, from the perspective of a massive observer, reaching the speed of light becomes harder and harder the faster the observer is moving. The massive observer would require an infinite amount of energy to accelerate to the speed of light, so light can be thought of as infinitely fast, since no massive observer can reach its speed (even if they accelerated for a very long time).

[AntiCitizenX]

I think a really good follow-up to this video would be an exploration of the spacetime metric. Then you can introduce the flat metric tensor very intuitively. Finally, explore a uniformly accelerating frame of reference and show how the metric tensor suddenly isn’t flat, and you have a perfect foundation for GR.

[jinks]

This is THE BEST video on relativity and Lorentz transformations. You have a remarkable ability to explain the intuition behind concepts in physics without sacrificing precision. Many analogies abandon the rigor in order to demonstrate an idea, but you manage to distill such difficult material into a simple and intuitive understanding so that when one DOES learn the mathematics, they know where it goes. Top-notch content, bro.

[KillerRaccoon]

I've been binge-watching Andrzej Dragan's videos for the past few days, and during that time, I was also searching for a visualization of hyperbolic rotation of spacetime, but unfortunately, I couldn't find any. And boom... here it is :) Thanks!

[anrwlias]

This is the first time I've encountered the concept of the electric field being a rotation through time, but that makes such perfect sense! I've never had much of a problem with Relativity, but I've always found electromagnetism to be a bit puzzling. This clarifies so very, very much about it! Thank you.

[feynstein]

6:12 A very important distinction here is that only the order of events which aren't causally related can be changed by a Lorentz transformation. In a sense, the order of these events is irrelevant to the universe and thus subjective to the observer. However, if one event causes another, then it can't be done away by a Lorentz transformation. All observers must agree on what order the events take place in. They might not agree on the length or the duration between those events, but the order is fixed. In fact, that is how time is defined. If the order weren't preserved, time wouldn't exist.

[mekafinchi]

I think this is the best relativitity video on the channel by a mile. In all the stuff I've seen about relativity, I've never heard the Lorentz transformation described as a rotation, yet that simple notion makes its application and effects remarkably intuitive.

The greatest benefit comes from the two unifications described in the video. When the magnetic field is described as the reletavistic effects of the electric field, it makes sense but it seems to fold the magnetic field into the electric field rather than justify an electromagnetic field. However, the idea that the two are time- and space-domain versions of the same thing fully justifies the merged name - neither is the 'real' field.

[nice]

Excellent video. I loved how you mentioned the connection between electric and magnetic fields and energy and momentum

[quakeknight]

One thing this channel severely stands out compared to other educational channels is that it always answers the question "But how?" and in extra detail.

[MrShtrudL]

Finally I understand the Lorenz Transformations we learned in class! Thank you so much, always a pleasure to see one of your videos!!

[rwmcgwier]

I have watched every video you’ve made. This one was by far the most impactful. As a mathematician, doing the various transformations was trivial. But this is the first time I ever heard the word rapidity and it crystallizes everything in place in just a few seconds. Rapidity adds in spacetime. My goodness how grateful I am. Octave Masson’s voice is hypnotic.

[water]

This is already the most underrated channel. But it just keeps on surprising me...

[Mysoi]

Best explanation of a spacetime diagram! I am speechless with how amazing and visually appealing it is! Your channel is like a 3b1r of physics.

At 8:53, I was genuinely shocked when I had long believed that "cτ" represented the spacetime interval. It wasn't until recently that I came to realize the spacetime interval does not signify the worldline; rather, it denotes a 4-position vector in spacetime. The magnitude of this vector remains constant along the hyperbolic path of an accelerated observer, while proper time continues to elapse in Rindler's coordinates.

[GloryTacos]

Your channel is the best science channel hands down. Nobody comes close to making these concepts intuitive in the way that you do.