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.
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!
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.
To get a better intuition for how spacetime diagrams work in Special Relativity, especially the way the axes shifted and sort of "pinched together" for the person in motion (the technical term for which is "Lorentz Transformation"), I highly recommend Minute Physics' series on it. He had a physical device made that recreates the hyperbolic geometry of those transformations in a very visually compelling way. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-1rLWVZVWfdY.html
This is at least my fourth attempt to understand spacetime. This is the second video I've watch and I've also read about it at least twice; once was in Carroll's book "From Eternity to Here". I still feel like I only kind of understand it, so maybe I just don't have much of an aptitude for complex physics.
@@alankoslowski9473 Think in this way: the trick here is that c is invariant i.e. c holds the same value regardless of the coordinate system from which c is measured. If you start to move, you will find yourself in a new time coordinate t' and in Newtonian mechanics the x' coordinate will be perpendicular to t' but in that case c will not be invariant. The only way for c to be the same in the two coordinate system is when the x' coordinate has the same angle to c as the t' coordinate. Therefore this skewed apperance of the primed coordinate system, which, in turn, creates time dilitation and length contraction. And yes, I'm more fond of the traditional way of teaching relatively ;-)
I tuned in during covid on almost all of your streaming lessons. Later I decided to copy these streaming versions of your biggest ideas to watch again so as to get better notions of the topic. The stream I think are much much better in terms of understanding these difficult physics subjects. (I think the books are for coffee table conversation pieces) The original streaming with the diagrams, the math, the explanations are what got me past the dark muddle and feel I have an even better grasp of these topics. This stream on the time cone when shown with the coordinate explanation really is the turning point for me understanding spacetime. The college level courses in calculus (differentials and integration) which I struggled with also was a huge help when following your streams. But it gets bumpy by the time we get to quantum physics.
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!
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 🙏
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 RU-vid. 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.
Dear Professor Sean M. Carroll, Firstly, I admire your series of RU-vid 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.
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
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! 👍🤘
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.
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....
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!
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
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!!! :-)
I'm not sure whether I feel smarter or dumber after watching these videos. I'd watch them more than once, but I'm afraid I'd figure out which one it was. :)
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 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 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.
Just finished reading “Something Deeply Hidden” and have started “From Eternity to Here”. The videos and podcasts definitely makes it easier to understand
Exactly the same for me, lol. I finished SDH and now I'm reading From Eternity to Here. These videos definitely help to put together the concepts and review everything! Have you read The Big Picture as well? It covers the way he sees the world, how his thinking method work, phisics, complexity, consciousness and a bit of ethics/""spirituality"". As he covers A LOT of stuff, it is not so much in depth as the other books, but it is still fantastic, and way easier to read. Definitely recommend it!
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 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!)
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.
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
abStruce... with an S. This is the best explanation of Space-Time I have heard as the owner of a physics Bachelor of Science. Definitely brought me a few new insights.
Thanks Prof. Carroll, this lecture was amazing. I am very grateful. While watching, I think I grasped why the doppler effect in radios occur (in ham radio, it happens when you communication with satellites in low orbits). And indeed in the wiki page en.wikipedia.org/wiki/Doppler_effect it says it's related to relativity! WOW! Before it was just a mysterious thing, now it (kinda) makes sense thinking in terms of the CONES in space time, and radio waves moving at the edge of the cone. I will have to think more about it. But if you happen to do a generic Q&A, perhaps you can mention/explain it? THANKS!!!!!!
LOL! There is a part of me saying,, "He's talking about the closest star to our solar system ya moron!", but there's another part of me saying, "Ha! He's got ya there, Sean!"
You mentioned that people like string theorists often think about extra dimensions of space but still just one dimension of time. I'm curious whether there are any theories with extra time dimensions? Mathematically it seems like it would be easy to add an additional dimension with a negative sign in the metric, but i'm having trouble thinking about what it would do to causality or anything.
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.
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!
Professor Sean Carroll, kindly suggest an updated book for "the biggest ideas of the universe".....theory + math both.....with required math.....Thank you Professor.
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")
Looks you are only one watching with attention. Twin paradox is not what Sean told us. Just see wikipedia for a start. I devised a solution in SR, just lazy to publish, plus I'm not sure my solution is original.
you are correct on the consideration more diemsional view for space and present we take only 3 + 1 dimesional calculations .hence space is confined to dimesnional difference on the move over mass
Awesome presentation Prof. Carroll. I'm very impressed with these casual videos you are doing. Question: Your last written statement, "General Relativity: Spacetime is dynamical, responding to matter / energy. => Gravity". Since we cannot measure space, time or space-time without physical tools made of matter / energy. Wouldn't it be equally true to say, "Matter is dynamical, responding to other matter /energy nearby => Gravity". The point being, we can't observe empty space-time, we can only observe its effects on the observable matter / energy it contains.
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.
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)
The durian fruit is also much like strings in string theory. A person gets a stick and bangs on it to hear the vibrating beauty inside like the universe holds. Different vibrating sounds mean different tastes in each durian. They can be hard or soft in different variations. So the decision is not just 2 choices of I hate it or I love it. The people that hate it only smell it. The people who love it feel deep down in their soul. Something AI can never have. I doubt a human made machine, even one reaching the singularity could ever develop a loving nurturing soul. The durian analogy is way more complicated than the people in the podcasts implied, much more. When I see AI can do that I’ll be amazed. Until then it is just a robot. An object forced into slave labor.
Question: are there any theories that include multiple dimensions of time? or; is there a useful reason that we might consider multiple dimensions of time? Thanks for the whole series!
not attempting an answer, but offering questions: What if we approach this by (re-)asking "What is measured?" What do we measure, when we measure "time"? Casual / informal / unpolished answer: "change" = the change of seasons, the change of the position of the sun in the sky, the change of growth in our children, the change in decay, etc.pp. What do we measure, when talking about "space"? again casually speaking: the position of any given object as well as the distance to a reference point. What I think "spacetime" beautifully does, is stating something painfully trivial: time and space viewed separately are basically cross section and longitudinal cut through the same cake, and it would be better understood if asking both when and where. In this sense, time and space already are dimensions both explaining the same phenomenon. How would adding more dimensions to "time" help us understand this phenomenon better? or in other words: what could we add to "before" / "now" / "after" that would explain the overall phenomenon better?
You could have a second time dimension in which the two together represent the world as experienced by you (your worldline) and all the other worldlines not experienced by you but which are also possible.
I keep coming back to my highschool physics classes when they talked about the difference between distance and displacement. I know they are different but how significant the difference is is not so intuative
Thanks prof Carrol, Finally I better understand some aspects of special relativity which was for me still rather vage and a bit confusing. Many thanks! Allow me to ask a question a bit out of context. If gravity is a pure consequence of the nature and curvation of spacetime and not, as often said “a real force”, why do physicists want to unify gravity with the 3 other forces? Is it correct that gravity just seems to act like a force since the path of an object in a gravitational field undergoes a linear acceleration as a consequence of the shape of spacetime? Thanks a lot.
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.
