Can a Circle Be a Straight Line?

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General Relativity! Spacetime! And... Curved Lines? On this week's episode of Spacetime, Gabe talks about what it actually means for a line to be straight so we can better understand what we mean by the idea of "curved Spacetime". This is Part One of our series on General relativity, so be sure to check it out!

Links to Annotated Previous PBS Space Time Episodes:

Extra Credit:
Visualizing parallel transport and geodesics on a sphere:

More mathematical PDF about parallel transport and curvature:

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Comments:

Jordan Filipovski

MaybeFactor

scharfy

ourpensareourlips

JakeFace0

QuannanHade

Ali Muzaffar

Marko Nara

Indigo

Jose Catlett

Music:
u dont know im fadin

New SpaceTime episodes every Wednesday!

Hosted by Gabe Perez-Giz

[EugeneKhutoryansky]

Very good video.  Most discussions of this topic either lose their audience by going into tensor equations, or are completely oversimplified to the point of completely losing the essence of the topic.  This video strikes a good balance between the two extremes.

[nlp]

I am having flashbacks to the differential topology classes I took in grad school. It kind of hurts, but only locally.

[bangboom]

This is the first time a Youtube educational video has ever truly stumped me. Wow.

[ScienceAsylum]

6:52 "Connectedness and Topology are global. Curvature and Geometry are local." In one sentence, I suddenly understand topology. WHY DOESN'T ANYONE EVER SAY THAT?!?!  Thank you so much for simplifying (but not oversimplifying) difficult topics.

I try to do this on my channel a lot, but sometimes I fail because I only give myself about 4 minutes. Sometimes you just need more time and you do a good job with it in 10-12 minutes.

[Randompersonon-fu]

0:27 everyone knows that the coolest person in the party talk about physics

[Keithfert]

As a physics grad student, I can say that this is the best physics video I've ever seen here on youtube. I love the obviously very deep understanding of every subject and the hard-work that goes into learning and communicating about it. It's amazing! Thank you!

[hritxwik]

Watching "Why GRAVITY is not a Force" by Veritasium and then coming back to this helped me understand things a lot better than before.

[mitchellwilley]

This video is 10/10 excellent delivery. All information is clearly conveyed and easy to follow. It's compacted into a short video but the ammount of knowledge compacted into it is amazing. It is a little fast spoken but even if it was slow spoken you'd still have to probably pause it a few times to think about it so it makes sense to yourself. I think i found one of my new favorite channels.

[anushgudimetla]

Best youtube channel for learning General Relativity Properly, that too without math. Very great channel.

[onlyonewhyphy]

"Anyone could say those words at a party and sound cool..."
I wish! What party's this?

[llamaduck]

This channel impresses me so much with the well thought out and communicated information, the high quality editing, the fostering of intelligent conversation in the comments, and the number of ways that it impresses me.

[Lutranereis]

One the best ways to help get a visualization of a curved space, in my opinion, is performing rendezvous maneuvers in Kerbal Space Program. Since the orbits are curved, if you're a couple kilometers or more away from the target and thrust yourself towards it, the target will no longer be there when you arrive. 

You quickly learn through these maneuvers that thinking of travelling straight lines like we do on Earth doesn't actually produce the results we want in space. Instead, you have fire your engines or thrusters to a point ahead of an object's orbit.

[Epoch]

These are EXCELLENT videos! Often this stuff is "dumbed" so much that all the videos dealing with this topic are essentially the same and really teach nothing....or at least nothing new. I find your approach to be much more robust while taking into account that many people who come here probably have an interest in this subject to begin with.
I really understand nothing unless I can visualize it and those who claim to understand pure good for them, but I do not. I think these are things that will draw more and more interest over time. The internet culture is in its infancy and as time passes I am sure parents who have learned new things online will pass this along to their children. Clear, intelligent and concise descriptions in physics or any topic for that matter are very important to society as a whole. There is a reason people still enjoy lectures by Feynman and others. Too often is it the case that things are basically "dumbed" down because people who work in media fear their audiences are too stupid to understand these things. Everything is based upon selling to the widest swath possible. The problem more often is in the way things are presented rather than the material itself.

[turtlemasterroshi]

"Otherwise what I'm about to say will make no sense" funny.

[TheBlackDraka]

This is QUALITY content. Hands down, one of the best channels on Youtube.

[michaelkap]

I hvae two topics that I would love an explanation for:
1. 6:30 I would love a deeper explanation about the difference between conectedness and curvatue. Why conectedness is global and curvatue is local?
2. 5:45 I dont understand the transport of a parallel vector in the curved space, why it does the vector changes when it returns to point A?

[ryanbrown]

Great vid, keep it up! A lot of science youtubers shy away from heavier topics for fear of confusing their viewers, but I'm glad that you care more about educating people than just getting views

[amaraojiji]

Thank you.

Request: please, slow down at important parts to give viewers few second to digest idea. Thanks!

[lukefuller]

Spent the last 3 1/2 hours 100% comprehending the parallel transport tests. It's 4 am.

I love this channel.

[ryanm]

It's not often that an educational program manages to thoroughly challenge my brain without completely alienating me from its content. Programs like these are usually either so over-simplified as to be meaningless, or so esoteric as to be inaccessible to the uninitiated. This video, and this entire channel, hits the bullseye between the two every time. Keep it up!