General Relativity: The Curvature of Spacetime

Relativity comes in different flavors, as it happens. We spent some time looking at Einstein's special relativity, so now it's time for the general variety. This is all about the geometry of spacetime, which curves around massive objects. This was a huge update on our understanding of gravity, so get on board!

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[bmilano]

The creativity, the heart and soul he put into creating the intro captured me in awe.

[Tomoose]

The fact that he was able to formulate these theories decades before space travel is staggering. I can't even comprehend the genius of his thought process.

This is coming from an engineer, I spent a good portion of my life studying mathematics. I am intelligent enough to truly understand his theory and how it works. However, when I take the the time to really think about where the study of math/physics was at that point in history I am always blown away by his genius.

I hope to live to see the day when someone matches his intellect.

This explained the difference between the special and the general relativity for me. So far I've been too lazy to check it myself. This video did it for me. The more you know...

[harikishore]

4:16 "space-time tells matter how to move
Matter tells space-time how to curve"

Should've added credits too.

[FlamableBeast]

Watched many videos before this that were too confusing, this one explains it well enough to be understood

[ElPurroco]

Professor Dave you are the best in teaching .... Thank you much for your fine, entertaining and fun teachings

[malayapaul]

I have liked all your videos not only because you very very very well but also because you help me in​ all the questions I have! great job

[jmcsquared]

Cool video. Minor error:

At 1:43 you make the comparison of bending paper around a third dimension to say that spacetime is bent around a fourth dimension. This is not correct in the following way. There are two types of curvature in differential geometry. One of them, extrinsic curvature, has to do with the way a surface is embedded in a higher dimensional space. However, intrinsic curvature has to do with the way the surface distorts distances locally on the surface itself, independent of how the surface is embedded into another space. A cylinder, for example, has extrinsic curvature (it is basically a rolled-up sheet of paper). But it doesn't have any intrinsic curvature, because its geodesics are actually straight lines (when you unroll the paper, circles on the cylinder unroll into straight lines). The reason this is an issue pedagogically is because it gives the listener the impression that, in addition to the four spacetime dimensions, there is a fifth dimension out there somewhere that we are curving around. There does not need to be such a thing for curvature to occur in a manifold.

[daverdz]

1:30 Finally someone who clarifies... there is a fourth dimension needed to represent the curvature of space!! Thanks man!

[mpali]

This theory finally “clicked” to me. Great simple explanation. Thanks!

[fadhilm.c.]

This is probably the most simplified explaination of GR I’ve ever seen.

[kabosumamadoge]

I love your explanation. You made everything easier to understand. Keep up the good work man!

[DOPICK]

Thanks for recommending this video. Made it really easy to understand and makes complete sense. Great stuff! 🚀

[lemayanelisha]

You are the first guy I have understood regarding general relativity

[michaelpisciarino]

1905: Special Relativity,

1916 General Relativity
- Describes The Geometry of Space Itself

0:59 Euclidean Geometry
1:29 Space Itself Is Distorted
2:08 Analogies
The Universe is Non Euclidean. 2:35 Parallel Lines can Cross moving through curved spacetime

3:16 An improvement on Newton’s Laws of Universal Gravitation
3:44
4:06 “Spcetime tells Matter how to move, And matter tells spacetime how to curve”
5:26 It is not complete

[adityadhardwivedi]

Wow! I have got a wonderful channel to study. Really very very Thank you Professor

[bobrussell]

Very good. Explained so that even dummies like me can understand it. I'm subscribing.

[sivsachin]

That 'bending of paper' explanation was excellent.

[paulpaul]

If gravity is caused by the curvature of space then where do gravitons come into this - hasn't gravity already been explained without the need for some theoretical particle?

[SalamMohammedZ]

WAW, you're awesome, I hope you were my teacher at school.