A new way to visualize General Relativity

Some answers to the questions I have been asked: - Has this visualization not already been presented? No I don't think so : you may have already seen a visualization with a distorted 3D grid (like at 5:20), but the crucial point that distinguishes my new representation is its temporal dimension. It is the fact that the grid is perpetually contracting which allows us to better understand the way bodies fall (and which is more faithful to the equations). As far as I am aware this has never been represented in this way, surely because this is only possible with the video format. EDIT: I have since then discovered that this visualization does exist, at least a similar one called the "river model". It allows for an intuitive understanding of black holes for instance. - If space contracts, shouldn't there be an accumulation of space in the center? Beware no, it is not space which contracts : it is only the straight lines (geodesics) which get closer to each other due to the curvature of spacetime. In the same way that on the sphere the geometry does not change (see at 9:10) , the geometry of space-time is static, it does not vary. But this geometry gives a tendency for straight lines to come closer to the center - How to define a temporal speed? In relativity there are two different times: the time of the observer (the coordinate time / the time dimension), and the time of the object (proper time). Velocity in relativity is the derivative of the coordinates with respect to the proper time of the object. The "temporal speed" is therefore simply given by the rate at which the time of the observer passes compared to the proper time of the object. To find out more, check out my series about the Maths of General Relativity

Can we take a moment to appreciate that Einstein was able to picture this in his head without the 3D models. That's the part that blows my mind!

03:27 "It is not acceptable to describe gravity inside space time, using gravity outside spacetime." THANK YOU. YES. This has annoyed me to no end.

The feeling of it clicking when you mentioned that even if the apple is sitting still in space, it's still moving at a velocity through time was crazy. I've often wondered how gravity could pull something in, but I hadn't even considered time as a vector of motion. Literally made my jaw drop, thank you

This model deserves a lot more credit and needs to be spread more widely. A lot of people studying general relativity are often troubled with the obsolete and underrepresenting rubber sheet model while others might think there is no problem with the concept which is actually not accurate enough.

The best visualization of something that can't be visualized I ever seen.. Great job.

Message for those watching this video at the end of January 2021. I highly recommend you to watch the videos related to “The maths of general relativity”. Believe me, despite being totally ignorant in mathematics, I was able to “visualize” the effects of space-time curvature much more clearly !! This channel deserves an Oscar !!

That initial marbles on a fabric model is quite popular on the Internet for newbies like me who try to understand space-time curvature. Even though your final model differ a lot from that model, you didn't simply struck it down and put yours forward. Instead, you improvised it step by step and concluded with your model. This avoided unnecessary confusiom. Thanks for doing that. Really appreciate your work.

I've always found the elastic cloth visualisation problematic and was very happy to see that someone made a better explanation. Thanks for sharing ☺️

I've been trying to find an explanation like this for years. The usual demonstrations in school using 3D distortions of a 2D plane never sat right with me. Thank you for this!

Dude. Ditto everyone else. This is a masterpiece. I've been trying to understand gravity intuitively for as long as I was start enough to try. Many other videos got close. Yours sealed the deal. Keep doing what you are doing. You're a genius.

YOU ARE A STAR! I was taught the theory in college but never understood it, and therefore never sat right with me and knew there was a better way to explain it and that i was missing. and now 2 decades later, your explanation and visualization makes it all fit together. THANK YOU!!

The last 40 seconds of this video was such a huge insight. We aren't moving through space, more that we are on a trajectory through time. And the trajectory through time is dictated by the curvature of the space time grid. We're seemingly always moving in a straight path, just that the geometry is curved.

Don't stop making animation like this, youtube education is more than everything... Well done!

Finally someone has created a visual that describes ‘spacetime’ curvature and movement that makes sense. 🙏

What a fantastic explanation! I had given up on ever understanding how this spacetime curvature was supposed to work, and here it is! Many thanks!

i dont know if anyone beleives it or not.. but while in my school i imagined it exactly like this in my mind.. i thought it was normal anybody can imagine it this way.. i tried explaining it to my friend at school but i couldnt he didnt understand.. and after a few months here i am looking at this video.. im so proud of myself... considering the fact that i want to be a theoretical physicist.. this is giving me so much motivation to move forward in my aim that i can do it

High five to everybody who ended up here thinking the marble on a rubber sheet explanation just didn't quite cut it ✋ And great video. Glad to see it's how I imagined it to be :)

10:26 so a black hole is just collapsed matter that couldnt withstand the pressure of constantly accelerating upwards, and instead follows the natural movement of the grid

This was a fantastic visual representation and explanation. Excellent work!