It is ridiculous how perfect this entire series is. Thank you for giving the masses enough credit to teach us spacetime from the top down.

Even as someone who is educated on these subjects, I found this lecture very enjoyable and informative. You really have a gift for teaching.

Awesome intro to SR. I personally think 'the best way' (if there is a single best way, which as Sean says there probably isn't) to teach SR is to emphasize the analogy between Euclidean rotations along the unit circle and Lorentz 'rotations' along the unit hyperbola. People have a strong intuition for rotations along a circle, which they can use as a nice bridge to the much less intuitive Lorentz transformations, because really it's the same basic idea: make a transformation that preserves a distance. I also like this approach because it makes it easy to do a 'symmetry-forward' intro to the subject, which lets beginners see the power of symmetry in a simpler context that will then become useful as they advance.

Good god, this is amazing Sean. Thanks for teaching a Texan with a ged about the true structure of spacetime.

"You have a twin, two twins that's what makes them twins." - Sean Carrol 28 April 2020.

I love Sean Carroll - he's one of those people who were just born to teach / impart knowledge.

I love that this series exists. If only the other people I'm with in lockdown watched it too, I would be able to have conversations with people about topics more interesting than the weather and tiger king.

These and Brian Greene's Equation of the Day have been a great way to review all the physics I haven't seen since university many years ago. Thanks to all the scientists and mathematicians keeping us sharp with these lessons!

Can't get enough of these floating torso thumbnails.

Watching a legend’s lecture! This is the blessing of science & technology- you can watch the best of the bests from anywhere at anytime. 💟

You’ve improved my life immensely.

Thank you for doing these Professor Carroll, such an interesting series of lectures. I look forward to each and every one!

Sean Carroll I cannot thank you enough for doing this. Going through the motion of knowing more and understanding less which is exciting.

Love these videos -- the format is perfect -- the writing/drawing/grayboard sketches forces Sean to slow down, and pace the presentation -- love it!

This is the one I have been waiting for, space time, a dazzling feat of the human mind, I hope I understand it better, its a difficult topic for a layperson.

I enjoy all of your efforts and I have learned so much from you, quite painlessly too, I might add ! Thank you Professor.

Imagine Sean Carrol and Jim Al Khalili together in a scientific online school. The laymen applaud!

Best lesson I’ve ever had in special relativity! What an amazing job! Thanks for all your work!!

Thank you Sean! Honestly, I think your top-down approach is more intuitive.

Thank You. This is just such a gift to us during the covid-19 debacle we're navigating through. 👏✌🤯💓

As someone who grew up with more Buckminster Fuller geometry than Euclidian geometry, your "I'd rather do it this way" approaches are much more accessible to me; I like when you go there. I finally get relativity, since you are willing to move away from the x, y, z coordinates into a language that is more spacetime friendly. Thank you!

Sir, you are one of the best lecturers I have seen. Thank you.

These are so excellent! Thank you very much for doing this!!!! I wish everyone was as generous with their knowledge & expertise. Thanks again!

Sean you continue to create marvellously educational and inspirational content, thank you!

I don't understand how this doesn't have like millions views, this is the most interesting thing in the world and mr. Sean is such a great talker, thanks for sharing what goes on in your genius brain 🙏

This is absolutely great, the way you explain these physical concepts/idea's is just soooo good and understandable! Thanks for doing this!

Just found u did this whole series and digging in now. Thanks so much for doing this man. Youre a legend for putting this out there for free.

This is the first part I’m rewinding back over and over at certain moments to get the idea and I love it 😎

I went from having a rough idea to a profound insight into such an abstract concept in 1h? That's absolutely amazing. Thanks a lot good sir!

Sean is a wonder of our world, that expands our perspective, however complicated it may be...awesome work Sean. I've seen a good portion of your online videos, always captivated, as I crave the amazing guidance and understanding you bring to theoretical, and traditional physics.

thank you so much please continue with this that course was priceless the top down point of view that you exposed was extremely convenient for me because I needed a tidy framework to organize what I knew and understood about relativity and this is just on point

55:49 wow that blew my mind getting to see it that way

Excellent video, I liked your „top down“ approach very much! Thank you!

Quite literally, one of the best videos on youtube I've ever seen.

Thank you Sean for sharing your knowledge of physics with us.

Loving these videos. May our light cones continue to intersect.

The little sound effect the rocket made when the flames came out was quite adorable :P Thanks for this series Sean!

I love these videos! Love the candid vibe! Thank you so much!

You never fail to help me understand. Thanks Sean.

Sean is very pleasant and interesting to listen to. Thankful greetings to Sean for having these lectures!

The little mistakes and human errors are what makes this series man. There are too many “perfect” presentations that are a bit harder for regular folk to identify with. Love your stuff.

let me start by saying I dropped out of high school in 9th grade, at 36 i went back got my ged, and now at 40 im watching this brilliant teacher and actually able to understand some of this lol, good job Mr. Caroll big fan of your many worlds stuff too!

Thank you, Mr. Carroll.

Dear Professor Sean M. Carroll, Firstly, I admire your series of KZfaq podcasts, “The Biggest Ideas in the Universe.” Your capabilities to explain, fundamentally and precisely, phenomena in the preposterous universe that surround us are extraordinary. One of the podcasts that taught me a lot was chapter 6 - “Spacetime,” from this series. At last, I profoundly understood the principles of time dilation. It came to my mind that these principles solve a long-time existing riddle due to contradicting data about the duration of the universe according to the first chapter in Genesis of the Bible and according to empirical science. According to the first chapter in Genesis, the Universe, from the very beginning to our days, was created in six (seven) “days.” According to science, it lasted at least 13.813 +/- 0.038 milliard celestial years between the same events. From your podcast, I learned that measuring the duration of time in a four-dimensional space as “Spacetime” depends on the velocity of the surveyor. The 13.8 milliard celestial years were measured by satellites traveling at about 8 Km/second speeds. On the other hand, the Bible does not specify who measured or estimated the time reported in the first chapter of Genesis. It indeed was not done by an artificial vehicle. But if the surveyor traveled near the speed of light (~300,000 Km/second), he would measure approximately a duration of a celestial day. In such a case, both reported measurements, that of science and that of the Bible, are simultaneously correct. Regards. A. Lachish, Jerusalem, Israel.

Incredible series! Just discovered it and will not stop until I have watched the entire set.

Besides the normal course explanations...these discussions are very helpful in clearing many points which are confusing at a glance during the formal courses....Thanks a lot Prof. Carroll

The GREATEST PERSON in the world. Thank you Sean Carroll! Light bless you :D

It's always refreshing to see new approaches to the subject. Very nice and keep on the good job.

We really appreciate you taking time to do this.

Thank you. This was the best explanation of special mechanics I can recall. I really appreciate your effort.

Omg I didn't know you had a YT channel. I love watching your talks

10:26 Thank you for that information!! When you put it on a grid like that, it becomes clear (rather, it did to me) that if you have and x and y Axis, and two point, the line or path is the slop...but, if time isn't included, then we are just measuring distance (rise over run in units relating to linear space only). When we change our vertical axis to represent time, we know get more useful information. Our slope is still rise/run but now it's: _time(duration)/space(distance)_ instead of *space in one direction (distance)/space that is 90° off in angle of direction (distance)* Now, we can see the time it takes to travel a certain distance of space (using whatever units we choose to use, so long as it's constant: light-years, MPH, whatever). When that spacetime is curved, then using just space to find the shorter path from point A to point B is (as stated) "kind of like" walking up to a valley and deciding that the only way is to walk down, through and up the other side of the valley... when, if you had the ability.... flying across would take less time, even if that meant having to do more work (more events) than if you had just walked. You have to get the plane ready (fueled up, know where you're going to land, do a ton of preflight work), take off, fly that short distance, land and put the plane away. Intuitively, it seems like walking is less work and the easiest way to get from point A to point B..... but, if the time it takes to walk there is longer than it would be to go through the work of flying there, then the reality of the situation is: the shortest path from point A to point B, considering the time each choice (walking vs flying) takes, might be a longer path through space. In other words: walking would take less steps (events) and you would walk fewer miles, but you would take longer, making it the longer of the two routes time wise. If you flew, you would have to go through considerably more steps (events) and your path, including the flight, might be a longer distance of space covered. However, if you covered more space in less time by flying, then flying would be the shorter of the two routes, time wise. It's similar to space in that flying would be a straight line through space, making it the shortest path... but in space, most of the time... flying over a valley isn't an option for us 😂 so, it's kind of like space, like you said, but the shortest path through spacetime might be through more space than time. You get there sooner than just covering a straight line in space, but you end up covering more space...just in less time. Makes way more sense now! Thank you! 👍🤘

Good God I Love These Lectures Something Else!

Thank you so much for these! I just won your new book in a giveaway (thank you Matt Ingebretson!!) and I'm extra excited to have these lectures to keep me thoughtful while waiting for it to arrive.

Great video, as someone with only an amateur interest in physics I found this video to make more sense than the vast majority of videos about Spacetime and Relativity on KZfaq. In part because Sean shows what I consider a great way to think about the relationship between speed in 3D space and our movement through time. EVERYTHING travels through spacetime at the same 4D-speed, the 4-velocity it was called here. Once you wrap your head around that idea, differences in time experienced start to make more sense. Or at least to me they do.

Thanks, Professor. Well done and interesting. Enjoyed all 6

That was excellent, as were all the others talks I saw. Thank you.

There is also another way to see that it isn't about the acceleration: The Fermilab channel on youtube did a video about this topic some (space-)time ago where they introduced a second spaceship flying towards the observer on earth. The two spaceships exchange their times while passing each other (without stopping) and the second spaceship arrives on earth with a shorter time than the observer on earth measured, even though none of the three observers ever accelerated.

I enjoyed the time spent on this. Thank you!

Very very good quantitative discussion of big ideas in physics. Very impressed. Well it is Sean Carroll...

I like the blackboard solution that you have found for explaining the concepts related .

Thank you so much Sean ...I am learning so much from your excellent lectures; studying for a PhD in philosophy of physics and these videos are invaluable to me.

Thank you for having done this series, im a engineer with a physics crush. This is pure gold.

I appreciate the time taken to explain in precise detail its awesome

Awesome stuff! Thank you.

I want just add up to all thanks below my own very thanks coming from underdeveloped Brazil where I am now blessed to get such an amazing content. Big hug (as latins used to say!)

For the excellent videos ,I enjoyed the time spent on this videos during Covid-19/ Lockdown .Thank you so much Prof.Sean !

Thank you Sean!

Very didactic explanation, Thanks Dr. Sean Carroll.

I remember during my intro PHYS class my prof mentioned stress-energy tensors during our solids and fluids chapter. Needless to say the entire class breathed a sigh of relief when he said tensors wouldn't be on the exam.

Thanks Sean, as a non-physicist I had never understood why the speed of light appears in so many equations - it just seemed weird that light was somehow so important in the fabric of the universe. Now that I understand that it is just a conversion factor and that it would be true even if light didn't exist it now makes so much more sense!

Fantastic! now I understand why the minus sign in Minkowski's formula for distance in spacetime. Thank you very much Sean. I read many books and blogs but never got this. Now I think I got it. Will watch this and other videos multiple times....

thank you for giving some of your time to this

Really great videos. Thanks. It would be nice if in your Q&A could talk about the special case of photons and how they "see" the Universe and (not) experience time (also maybe in the context of their interaction with other particles, e.g. in the photo-electric effect, when they "appear/disappear")

17:48 that's one bold statement right there, I would never have the courage to declare myself.

Sean Carroll, ladies and gentlemen! A legend!

Just finished reading “Something Deeply Hidden” and have started “From Eternity to Here”. The videos and podcasts definitely makes it easier to understand

These are fun, thanks for making them.

Loved it ! Thanks!

This is such a cool series. Thank you for the excellent brain massage.

Finished the lecture. This is the clearest and most bad ass space time explanation I've experienced. Thanks prof.carroll

Such a pleasure!

Brilliant series, thanks so much for creating. Wish I'd discovered this during lockdown!!

Photons and gravitons are not on all fours here in one very important sense. Photons are all around us while gravitons are hypothetical entities imagined to exist as a consequence of some attempts to shoehorn a successful statistical model of the microworld on to the very large-scale properties of extension and mass. It is far from clear the project of seeking a subatomical mediation particle for the force we infer from the nature of the motion through spacetime is well motivated, let alone that the particulate ontology of one of those efforts should be viewed as just another thing in the world, like light. The universe is under no obligation to conform to our theories, no matter how preposterous they may be. Otherwise, keep them coming - the videos, I mean. Thanks much.

Hey shortestest it's your birthday, we're gonna party like it's your birthday! Another great vid. Thankyou Sean, lockdown is sooo much better thanks to your output. 😁😷

I sometimes think, since I don't have the math background to even START to 'know' about relativity 'completely', (actually, I guess that means I ALWAYS think that), anyway, not having the math background, I think that by getting as many different versions of the explanations (for the layman) of relativity as I can, that I'll get more of a 'kick' out of the downright cool aspects of the subject. Well then that means I have to say that the two or three minute explanation of "length contraction" given in THIS video is by far the best one I've seen, in that it allowed me to integrate all the other explanations I've heard in a way I just can't adequately describe. It was truly so succinct and clear, in the context of this group of videos, that I feel my understanding has taken a 'quantum leap' after absorbing it. BRAVO! AUTHOR!! AUTHOR!!! :-)

great teacher you are! I am going to listen to this a few times more to comprehend as you want us to

Spectacular lecture. Many non-euclidian Xs and Os.

"Nearest star is 4 light years away" dear God, he's been inside so long he forgot about our 🌞.

Thank you for this! 14:05 to 18:13 and 37:05 to 46:12 are my favorite parts. "A feature of the Universe which is surprising to you, that's not what qualifies as a paradox.... Energy and momentum are tied together. ENERGY IS THE TIME COMPONENT OF MOMENTUM." :o)

Energy is the time equivalent of momentum... Absolutely mind blowing if true!

Simply excellent.

Very good. Thank you.

Thanks for taking the time professor. I'm absolutely loving these.

Impeccable!

Amazing. Thanks!

Nice sketches. Interesting info too. Like how you went BACK IN TIME to look at what you perviously wrote. It's clear to me that there's this "time stuff" back in the space of what you wrote. I mean, you could put a clock on the notes itself, and that would make more obvious as you scrolled back though your notes. I think we underestimate what travelling back in time really means. We seem to be able to do it with information.

Love all your explanations. I’m a big fan. I think it’s interesting Light cones look like hourglasses. Very fitting somehow.

The quantum realm needs more sean carrols to help us understand just how much we don't no and put us in our place , but thank you professor carrol for your work and contribution to science . From sean in Scotland

The defining of terms like spacetime help me to order these things in my mind. I still have a ways to go but I think I can grasp it better given the terminology. Thank you. It's been 4 1/2 decades since I studied physics and calculus. And for me it's not easy stuff. Now let's figure out the GUT.