The Surprisingly Subtle Limits of General Relativity

Einstein's theory of gravity---general relativity---was the last great pillar of pre-quantum physics. Gravity, he says, results from the curvature of spacetime in the presence of massive objects like stars. Then lighter particles moving nearby just travel along the straightest possible routes that they can through this curved geometry, called geodesics. And yet over 200 years earlier Newton wrote down a vastly simpler force law for gravity and used it to derive the orbits of the planets in our solar system to remarkable accuracy. So how is it that these two radically different descriptions of gravity fit together? And how does Einstein's theory go beyond Newton's, to predict the existence of black holes? (Like the Sagittarius A* supermassive black hole at the center of our galaxy that the Event Horizon Telescope collaboration released the first ever picture of just last week!) We'll explore it all in this video. We'll learn about geodesics, gravitational time dilation, the Schwarzschild solution of Einstein's equations, and the black hole geometries that emerge when you squish a star into a ball smaller than its Schwarzschild radius. You'll come away with an appreciation for how Einstein's theory can capture the same physics as Newton's inverse square law in the limit when gravity is weak, and at the same time describe black holes in the opposite limit when gravity is strong.

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About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.

About me:

[lardmaster]

One thing I really love about this channel is the fact that it’s unafraid to get involved with the Math whilst explaining the deep concepts underlying the Universe.

It’s so easy for an educational channel on Physics to go purely for the concepts, without explaining how or why they came to be, so that the viewer walks away thinking they learned something, when in actuality the content went in one ear and out the other.

On the other hand, it’s also a pitfall for someone knowledgeable in the subject to delve right into Maths without explaining any of the underlying intuition or concepts. Useful for students trying to solve university problems, but not for an educated public seeking to further their understanding.

This channel has the balance just right! Great job, Elliot!

[ritemolawbks]

You've produced a very high-quality video. This is one of the best explanations of gravity I've seen! I've watched it several times now.

[zedcodes]

I'm a 2nd year Physics student. Ive just discovered your channel and I'm watching every video you posted, one by one. It's pure gold! Thank you so much and please keep up the amazing work!!! 💚

[MaxxTosh]

Love the video so much!! Would you be interested in going through the math that shows how GR explains Mercury’s precession? I’ve been wondering about it forever!

[passerby]

This is such a well made video, having an extremely precise scope and amazing narration. I don't know how deep you can go into GR with this format, but I sure hope you do.

[Arseniy_Afanasyev]

! Thank you very much for the open access to the notes! Finally, I don’t have to take notes on everything myself, so as not to get confused later, and it didn’t seem that I could forget something)

[aadhiimrana]

Nice one, Elliot! I think that's quite a good explanation! Keep up the good work man.

[sphakamisozondi]

The way you have broken down the components of GR makes it easy for a person like me who is not a physics major to understand. Thank you Elliot, Shoutout from South Africa

[gahanchattopadhyay]

Amazing man amazing😭😭😭😭I can't believe that these things are actually getting into my head, please keep making such free contents 🙏🙏

[sayanpal]

This is one of the best videos on the basics of General Relativity. Such wonderfully crafted and framed with so much clarity and care at different junctures!
Very useful video. Thanks from the heart for putting this up.

[rockland]

Excellent video, very easily explained such a complex subject.

[urnext]

I appreciate your hard work sir.... These videos are great and highly informative....

[nerdsgalore]

Finally some GR! Hope you go more into the details in the future!

[ikarienator]

Such an excellent video! BTW The Schwartzchild radius is computed with the assumption that all the mass is concentrated at a single point in the center. So the real reason the equation doesn't work inside the star is because of mass, not radiation. In fact, inside a (uniform and spherical) massive object, the inverse square law also doesn't directly work and the force is proportional to the radius (like in harmonic oscillators). That's because the mass from outside of the radius is pulling from the opposite direction and cancelling the gravitational force.

[jaechoi]

I saw the thumbnail, thought it was some BS popular science BS handwaving explanation, clicked, and was in awe. Thank you for satisfying the minority who loves seeing the hairy math. Subscribing isn't enough after seeing the rest of your content.

[steffenleo]

Great explanation especially in geodesic equation 👍👍... I saw similiar video years ago but not so Details explained... Thanks a lot Dr Schneider for your huge effort to make such great Videos and upload in Youtube so everyone could understand Physics.... 👍👍🙏

[jensphiliphohmann]

About 04:20: _The result is an ellipse with the Sun in one of the focus points._
To sufficient accuracy, yes. Actually it's the common center of mass but since Sun outweighs Earth by a factor of over 3×10⁵ and all other masses of the solar system still by about 500, it's fine.
Also, the statement about 05:15 is true if m<<M which is not entirely the case if we take M to be Earth's and m to be Moon's mass, or M and m to be the masses of two components of a double star.
The same caveat holds for General Relativity since large masses m take their own influence on the geometry around the central mass M.

[dav]

Touchy topic, thank for clear explanations. I guess many people wish they had you as a teacher.

[biagi]

Really nice video! I'm so happy I just started learning about special relativity...and I can't wait to delve more into its details!!! Have a nice day :)

[roxashikari]

Oh, I've been waiting for a GR video!