*Are the lengths in the diagram at **8:14** backwards?* No, they're not backwards. They are correct. In a hyperbolic geometry, the hypotenuse can be shorter than one of the other sides. Pythagorean theorem (a^2 + b^2 = c^2) only applies to Euclidean space. The hyperbolic version is a^2 - b^2 = c^2. Instead of a plus, there's a minus. Get on board. *Wouldn't light travel along a 90-degree angle rather than a 45-degree angle?* No, light travels through time just as much as it does space. That's 45 degrees. An angle of 90 degrees would be traveling through space _without_ through time... also known as teleportation. Light does not teleport. Yes, it's true that light doesn't experience time or space, but a spacetime diagram is never drawn from light's reference frame. It's only ever drawn from a massive object's reference frame. For light, both of the axes would rotate up to the 45-degrees and be parallel to each other (and to the path of light)... which means there's no perspective to measure from anymore. *Twin's Paradox:* You can't really compare clocks the way we _want_ to compare clocks unless there are two events in common... which requires at least one of them to break the symmetry (either by accelerating or traveling around a curved universe or something similar). I discuss this in a video from a couple years ago: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-UInlBJ4UnoQ.html
@@sabrisevmezhicsevmez8135 He answered this question before: from the reference frame of a photon, time is frozen, but from our reference frame, it's not.
@@Lucky10279 so does it mean that if we tilt the spacetime diagram 45 degrees to the reference frame of a photon, it would be only traveling in space and not in time? Why do the axes get distorted when tilting the diagram and by which scale?
this helped immensely but one suggestion to help people understand, especially whats going on with this hyperbolic triganometry *weirdless* is to reiterate the differences in the spacetime graphs for the two observers. It kind of makes sense to me that the short side can measured as longer but only after I have visuallised the other graph. *(If I even understood that correctly)* Can I also suggest trying out swapping the two observers space time diagrams (rotating the axis in place for better visual aids and plotting that against something like a 3rd object or other measurments?
@The Science Asylum nope. This whole channel is underrated... how much years to learn.. how much hours to prepare a video... how much time to cut the vids... and i didn't talk about the motivation, the faith and the teaching skills. Only 232k subsricbers. Take a look at a trash rappers YT channel... makes me sad. Love you TSA, from Hungary
Agreed. _Especially_ trigonometry. It shows up all over the place in physics and linear algebra. Pretty anytime there's something involving rotation, contraction, or projection, it's likely that trigonometry is going to show up somewhere. Oddly, while I greatly enjoyed learning trigonometry itself (I used Khan academy and their trig course is quite well designed and made it really fun), it wasn't until I took linear algebra and then physics that I fully appreciated it.
In all seriousness, I love seeing things like this over and over, explained by different people. That, and playing around with it in my head are the only ways for me to really understand it. I'm not one who can usually just get it at first glance.
Wow..... I wish my physics teacher had explained it like that. I could never get my head around the 'atomic clock' and 'train' explanation, they never made sense to me.
I think helps that Nick can devote a couple weeks to each video and he consistently takes into account viewer feedback about what's helpful and what isn't. I'm going to guess that most Professor's are teaching several classes at a time and probably giving two lessons per class each week and so aren't able to devote that kind of time to planning each lesson and listening to student feedback, let alone making all the animations Nick does. In other words, don't be too hard on your professors. Their circumstances likely don't permit them to explain things the way RU-vidrs can.
@@Lucky10279 I dunno. I saw an old Winnie the Pooh cartoon where Winnie was bouncing down the stairs thinking "There must be a better way to go down the stairs... If only I had time to work out what it was."
"Speeds are measured as angles." That's so cool! Trigonometry is awesome. This is also the first time I've actually appreciated _hyperbolic_ trigonometry, so thank you for that. ;)
Dated a girl in my General Relativity class. One day she asked “Do you always last this long?” Looked her dead in the eyes and said: “It’s relative. Depends how fast we’re going.” Without skipping a beat she replied: “I guess that explains length contraction.” Yeah we didn’t date very long.
Edit: sorry, meant to tack this onto my own comment, not yours. Not that yours isn't a lovely comment. :-) I still don't understand the thought experiment of the astronaut who zips away at almost light speed for a while and because of time dilation returns back to Earth way younger than everyone else who used to be the same age. Fine, ok.... but doesn't that also mean that from the astronaut's point of view the Earth zipped away at near light speed and came back with its time having sped up instead of slowed down?
@@andie_pants This is true for observers that are in inertial frames of reference, or in other words, not accelerating. But in your example, for the astronaut to zip away then come back, he would have to accelerate at some point, which makes all the difference. For more info, there is indeed a video on this subject on this channel.
Me too (though I'm actually an engineering student). It's a good feeling, especially when I can actually answer some of the questions people have in the comments.
@@zakopako82 I got you--whenever you feel tempted to say "I literally...", just say "Practically, I..." or "I virtually..." It has the same mouthfeel, is grammatically correct, and joyless dillweeds like INERT will leave you alone.
Everything we experience is our individual perception of the the information we receive. Everything we perceive is solely information including space and time. How far away something appears to be is in the information that we receive and our perception. I will tell you what is danced around by most scientists but is evidenced by the definitions of the words they use to explain the Universe. A point is a thing which has no parts and thus can only be conceived of let's say in imagination. Within a point can be defined an infinite number of points with a definite position relative to the boundary of the initial point. It's amazing how we can choose to imagine a beach just in general and the image of a beach will instantly appear in our minds eye and will actually replace what we see with our eyes if we focus on the image. If we continue to focus for a time events will naturally appear in our imagination like waves and wind without our needing to create them intentionally, the scene unfolds with our perception of the information attracted by our initial intention based on our previous experience. However, we can choose to imagine different things appearing in our minds eye in general ways like adding people or specific like particular people. Einstein said imagination is more important than knowledge. I think that's because knowledge is what has been conceived in imagination and doesn't exist anywhere else because there is no where else for it to exist.
That comment seems redundant. Vectors are just oriented line-segments, and line-segments are just a part of geometry. Add in areas and volumes and you can describe almost anything. Everything is geometry!
“The Universe doesn’t just look different to different observers , it is different “, Wow I never really thought of it that way , once again Nick you’ve educated me . Thanks .R.
It is a lie though. Unintentional but still a lie. Universe IS the same for every observe, and it just looks differently. The real explanation is: "Space and time aren't absolute realities, THEY ARE JUST MEASUREMENTS, dependent on the perspective"
This is mind altering. Events that occur at the same place from one reference frame may have occured at 2 different places from another reference frame? aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaah!!!!!!!!!! My respects sir. Here in Cameroon we'd say "you have sense"!
It is pretty mind-blowing when you put it like that. Unfortunately, (or fortunately, depending on how you look at it) the S.R. unit in my modern physics course did such a good job introducing this idea that it didn't blow my mind _at all._ It just seemed immediately intuitive to me. The again, I may be giving the curriculum too much credit. I'd also watched Nick's other SR videos multiple times over the years, so I was already familiar with the basic ideas of SR. If you want more details about this concept, look up "relativity of simultaneity."
@@ScienceAsylum "Events that occur at the same place from one reference frame may have occurred at 2 different places from another reference frame? " "May"? Under what circumstance(s) would they? I think that statement is really not worded correctly. Event time and position is always relative to the reference frame so of course they will always be different for different reference frames.
@Grabo Johnson, first we have to clear up some definitions. "Place" in this case is the "Event", which has two coordinates in Space-Time. Space and Time. There is only one Event. From a different Time Reference Frame, if the Event is seen at the same Space, it will be seen at a different Time. If the Event is seen at the same Time, it will be seen at a different Space. Hope that helps.
You definitely didn't go too deep. This was definitely helpful. I just wish this video was available a month ago when I was trying to figure this out. Your video makes WAY more sense that MinutePhysics video about length contraction and time dilation.
At some point, you should really do a video on spacetime intervals. So much of what people are asking about in these comments is answered by a proper understanding of Spacetime intervals. They're tricky to fully get though.
Thank you so much. I literally just thought the other day that thats a topic your take would be helpful for. I mean, I know how all of this works mathematically, but thats really not enough for me anymore. You spoiled me xD
@@ScienceAsylum Thanks. I needed this explanation. But I need to know more: Since distance is what we measure between two events happening at the same time and it's the same measurement elsewhere in 'normal space,' does Spacetime itself have a distance component to make sense of everything? Like a literal fabric at plank length. Otherwise there is no reason for the distance between same atoms to be the same or the speed of Light to be constant. Or is Time responsible for distance?
@@joshanonline I think I can confidently answer your question if you evaluate it further. What do you exactly mean? In General Relativity itself there is no smallest Quantity of spacetime like a planck length if thats your question. "Normal space" doesn't really exist in relativity in the first place. Every point of view is "normal". They technically all disagree with each other. And all of them are correct. I don't understand why you need a "distance component" for spacetime to make sense of the measurements.
dude. lol...... I cannot explain how much time iv spent trying to learn concepts through traditional teaching. and i show people these vids and they start to get it after a few view and relative videos. i hope your videos will still be available when my kids start down the path.
I was very confused when in the time dilation diagram, one leg was longer than the hypotenuse. Then I remembered all those hyperbolic stuff from the beginning.
I really feel like this channel deserves to be at least 10x more popular. Perhaps even moreso, depending on how much an observer is moving relative to this channel!
If you know only what you need to know, then why learn new things? Then we're no difference than machines only programmed to do what we need to do. But then again, every time you go to a major news site it's always politic in the headline like I care.
Because your higher brain functions are seemingly still somewhat intact. Or do you really want to become one of those individuals who only care about beer, sex and money ?
You NEED to make sense of your everyday life, that's what physics is for (well, some people prefer religious services but that's not for everyone and it probably makes even less sense).
Because you enjoy learning about physics? Reading novels also doesn't give up any knowledge we need to know for work or everyday life, but we still do it because we enjoy it. ;)
The reason I like your relativity videos is you don't dance around the issues. You get straight to the point. I will say I don't quite understand it, but I understand it far better today vs my entire previous education and youtubers teaching me inaccurate material in hopes of making it more comprehensible
Thanks! I’ve studies this so many times, but seeing those animated space time diagrams really made me understand it more intuitively. I agree (now) - how could it be any other way?
measuring with hyperbolic cosines just *cosh* we can when you get paid for teaching people (including me) that hyperbolic cosines are a thing: cosh money
Imagine being inside a room. In the center we put a little square. Then, we walk around the room always looking at the square. We notice that the square is starting to change shape, of course we don't say that "the square has been length contracted", because we understand that it is us that are moving around the room, so naturally we are observing the square from diffrent angles - thus - the shape of the square is going to change from one perspective to the other as we rotate ourselves in the room... Length Contraction in Special Relativity is the same. By accelerating in space we decelerate in time, and thus we observe reality from a "diffrent angle", seeing objects taking diffrent shapes, not because they really did change shape, but simply because we observed them from a diffrent "vantage point"
Something that took me a long time to understand is why are those observers not measuring the same two events when calculating the interval, but the thing is, simultaneity is not fundamental, it's given by each observer and they may disagree.
One of my favorite thought experiments is to imagine a docking bay on the space station with two doors, fore and aft, so that the rocket can fly straight through. The docking bay is too short to hold the rocket at rest, but longer than the length-contracted fast rocket. Could you trap the fast rocket in the docking bay by shutting both doors while it's flying through?
Part of the difficulty in understanding is simply at the sort of relative speeds humans are used to, the changes are so so tiny. Edit: ‘relating to’ instead of ‘understanding’ is the better description.
Absolutely thanks to TSA for this video (and all the other ones I already watched )! If I don't understand something in physics, I eventually end up here at TSA. Afterwards I'm really healed from unaddressed questions. I love geometry!
thank you for this video!! please make more of them, I just love them. It really changes the way I see the world around me and when I have seen your videos they always have filled me with so much passion for physics. And I also laugh so much with your puns, they really make it so fun for me to learn with you Nick!
I don't know why there're only 234K subs, but I do far far more than love your videos. I just can't explain. My hands are vibrating while typing these words ... you're my soul mate 💛💛💛💛💛💛
Amazing, I remember studying this in modern physics, but it was just one of those things given with equations and no explanation for the why. Now, I actually understand the "why" of the length and time stuff. Thanks!
"It's all just geometry..." Why did nobody say it until now? Also, black is the new orange...does this have something to do with the fact that brown light is actually orange? Therefore black is orange? (because black is actually very dark brown?)
I love this show It reminds me of the great educational programs of my childhood, but advanced enough to give the great Cosmos with Carl Sagan a run for its money
There was a young lady named Bright, Whose speed was far faster than light; She started one day In a relative way, And returned on the previous night. To her friends said the Bright one in chatter, I have learnt something new about matter, My speed was so great, much increased was my weight:, Yet I failed to become any fatter
The space-time graph representation was great, but I Would have loved if you gave an explanation for The matrix transformation that causes the space-time space to transform.
Wow, thanks for the video. My English is not so good, but with subtitles I think I get the point of your videos 😊 And this video was really mind blowing for me. Thanks for all your work, love your channel 😊.
Probably, I only do that once or twice, five times is a bit too much... there's a point when one has to acknowledge the finitude of his/her own capacity of understanding.
Please go deeper.... Deep Deep inside physics... generally we are taught only literature of physics...not the real physics..i found real physics here.. thank you Nick.
Up and Atom did a video on it, and so did Eugene Khutoryansky if you want to check either of those out. I have to warn you that they're both kinda of hand-wavvy though. I get the impression that they're scared to get too detailed because that requires really digging into the math. To be fair, fully understanding it requires an understanding of linear partial differential equations, which are kind of complicated. Still, considering just how well Nick explained Maxwell's equations, which are also differential equations, without getting into the technical details of the math but also _not_ hand-waving it away, I'm sure he could do a really job explaining Schrodinger's equation. I was seriously impressed with his explanation of Maxwell's equations -- absolute best explanation of them I've come across, including those explanations that _do_ dig into the details of the math, even though I do have the background to understand the math. Nick's just got a way of finding the perfect balance between being too abstract, getting lost in the details of the math (that's what textbook explanations tend to do) and being too hand-wavvy. I'd love to see him explain Schrödinger's equation that way. We'll just have to be patient; I'm sure he'll get to it eventually.
You have no equal on the internet. A lot of people try, but none of them match your Explanatory Powers. Because of the understanding I’ve obtained from your videos, I’ve caught a couple of really high volume channels actually screwing up explanations and drawing incorrect conclusions.
Hyperbolic geometry, while visual, is extremely counterintuitive to our Euclidean-accustomed brains. Isn't there some way to "map" this geometry onto a more familiar Euclidean one? Kinda like how we project a sphere onto a plane? And yes, I know this doesn't lead to true equivalence and there will always be some distortion but the distorted projections are still quite useful. We do still use geographical maps after all. Can't we do the same for spacetime?
After watching probably 10s of videos about this concept during the past 6 years this is the first time I am actually understanding it enough to be completely mind blown. Also, it's weird how your clock on the vid matched my clock here at 01am. I should go to bed.
If spacetime adapts in a way that nothing massive can travel at speedlight, but massless things like light and gravity do travels at speedlight without trully experiencing space or time... isn' it breaking locallity??? This because, thinking in the electromagnetic or gravitational effects between two massive objects distancing away from each other, the fields' effects of the first object always will reach the second object at some time, even if they have been separated by all the time and space of our universe!!!.... and even if both are traveling each one at 99.99% the speed of light....speedlight effects always are going to be faster than the distancing speed between the two objects under relativity theory...meaning that everything is affecting everything in the universe (i believe this imply non-locality).... this is kind of nonsense or isn't it??
This book looks interesting. I have the weird feeling the maker of this video would approve of this book BTW, it's probably rocket clown not rocket clone
As we go away from object length contracts and if object is moving time dilates Am I right? I watched it three times If we used a spherical space ship the length contraction would happen or radius?why only length contracts not width?
I find that geometry explanations are unintuitive. I find it better to think of relativity like this. First: consider a time machine that travels an hour into the future taking 1 minute for the rider. If the time machine sets off at 12:00 and is watched, an observer will see, over the course of the next hour until 13:00, the clock in the time machine slowly tick to 12:01. The time machine is acting exactly like time dilation behaves - well, instead of parking it in the corner of the laboratory for an hour it turns out we just need to move it really fast. Once you can establish that time dilation is time travel into the future (of the observed object, into the observers future), you can show that kinetic time dilation is actually time travel in terms of a time boost per distance covered in the observers frame. Or to correct for the observers in that frame that are not travelling, a negative time offset for every point in the direction of motion in the moving objects (rockets) frame. I.e we can imagine every frame is covered in synchronized clocks. But, because objects in moving frames are time traveling, observers see the clocks in moving frames with non synchronized times: they grow larger to the rear and more negative forwards. This means the rear of any object is being viewed at a slightly more recent time - in the objects frame - to the front. And because velocity is a function of time, this means the rear has moved further than the front.
For some wierd reason i got emotional after this video😂😂😂😂😥 i was dying to know how length contracts with time since 8th grade and i am in 11th grade now thanks for enlightening me Lord
Thank you very much for uploading this videos, they are awesome and so are you, I have learned a lot thanks to you only, this should be part of a school program
