Length Contraction is NOT an Illusion!
Special relativity is full of weirdness like length contraction and time dilation. It's the result of something called a Lorentz transform. It's almost exclusively done algebraically, but it makes way more sense if you do it geometrically. Brilliant for 20% off: brilliant.org/ScienceAsylum
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What the HECK is Time?!
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MinutePhysics on Length Contraction:
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Fermilab on Length Contraction:
• Length contraction: th...
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*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: kzhead.info/sun/iK2nnKaCa4ekook/bejne.html
but were photons not supposed to not experience time? if there is no time for a photon, how could it be traveling through time?
@@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?
@@sabrisevmezhicsevmez8135 I think so, yes. I'm not sure what you mean about the axis' getting distorted though.
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?
Geometry is underrated.
Agreed.
@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
And awesome!!!
Geometry is very important. Shape up or ship out as they say ;)
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.
This is probably the only channel which presents the material in a lucid way(no pun intended!) without dumbing it down too much. Absolute treat, Nick!
No pun intended? It was a great pun though!
@@Danilego Thanks 😁 but I was not going for it, I noticed it later.
Nick LUCID 😏
I find physics hard to understand when it's dumbed down. Much easier to understand when you do the math and look at the geometry
So you should meet the PBS Space Time.
I follow this channel from its very early days. And now as a physcis student, I can finally point to things and say: "Hey. I kinda know that!".
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?
@@grovermatic That's called the twin paradox, and if i remember correctly there is a video on this channel about that.
@@grovermatic 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.
@@grovermatic kzhead.info/sun/iK2nnKaCa4ekook/bejne.html
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.
Dude... I took an entire semester class in college on Relatively... And this explained it better. 👏👏 Welcome back!
Thanks! It's good to be back!
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 KZheadrs 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."
You should ask for your money back.
@@oflameo8927 I wish you could get your money back from colleges when the classes are poorly taught.
"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. ;)
Speed is a rate, which is just a ratio, which is just a slope (rise over run): hence speeds are measured as angles.
This video makes the universe look like a videogame. Everything can be explained down with geometry and vectors, just like in the games!
Or do the video games mimic reality of geometry? Just blew your mind lol
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.
@@russellpowell2656 or do the games mimic the game were in. Simulation theory. Now thats a wild ride
i want to like this comment but it has 42 likes....the meaning of life....
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"
I literally cracked up when you said MUONS FROM SPACE!!!!!!
BLACK BALLS IN SPACE!
@INERT LOL Sorry, I have a bad habit of saying it all the time :-P
@@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.
2:10 Your rocket's always longest when you measure it yourself 😉
"rocket"haha
🤦♂️ I'm surprised the dirty jokes took this long to show up in the comments.
@@ScienceAsylum I saw my chance and I took it
@@ScienceAsylum They happened sooner for me, but I'm moving kinda slow.
Don't forget to account for curvature.
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.
I'm not sure _anyone_ can get this at a first glance.
@@ScienceAsylum yeah, getting familiar with a concept that is pretty counter intuitiv should take you some time
@@chacubra 😀🙃 Time plays here also.
@@chacubra 😀🙃 Time plays here also.
@@ScienceAsylum my one singular synapse sure can't but it wants to so hard
This channel is so underrated obv.
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.
That was the BEST explanation on the subject that I saw. Simple, elegant, and clear. Thanks SO much!
Good to see you back. Hope you enjoyed your well deserved break.
I did. I feel rejuvenated!
Your definition of length as the separation of 2 events is an eye opener to me.
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. Explaining recording length as two events makes this much easier to understand.
You're welcome! Glad I could help 🤓
This is by far the best explanation of time and space dilation I’ve ever seen. Well done!!!
Nick, this was a great video and it really did help me understand both length and time contraction! Keep them coming up, man!
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!
Good to see you back! Sharing this video with family too.
Thanks! It's good to be back.
Again you just put the topic I was searching for, thanks you, sir. This is the first time I appreciated hyperbolic geometry, hyperbolic trigonometry and graphs for literally showing how things are/work/we see.
Brilliant. Really great explanation of space-time. Minkowski would be pleased. As always your graphics are a great visual aid.
Lucid, you have a lot of great videos, but this one's top five for me. Perfect depth! A giant leap in my understanding of space-time. Thank you!
Happy to help 🤓
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!
That was an amazing description. No matter how many times I see spacetime diagrams they always blow my mind. Just conceptualizing how differences in velocity induce a transformation that actually really occurs is insane to think about.
Congratulations on your amazing science videos. This one about the geometry of relativity is wonderful (and very enlightening). Keep up the nice job!!!
Am I the only person who watches Nick's videos 5 times in a row, pausing and rewinding between every other sentence? Great stuff, Lucid!
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.
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!
I feel like your videos are leading me back to school. My curiosity about the physical universe grows with every video you produce.
Great video! I love it when you go a bit deeper into the subject!
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"!
*"Events that occur at the same place from one reference frame may have occurred at 2 different places from another reference frame? "* Yes 😱🤯
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.
@@ItsEverythingElse Everyone will agree on the place and time if the two events happen at the same time _and_ place.
@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.
I'm so happy that you're back again with same enthusiasm after break...keep going sir!! :)
I feel rejuvenated!
The Science Asylum yay!!!! We all love your videos! Take a break whenever you need to; we appreciate the quality of a well done video!
we missed you here from Brazil, man! congrats!
Dont ever stop making videos please! I had a really, really good physics teacher but you are soo much better in explaining that its.. I have no words :D Love all your work
I'm pretty sure I remember my dad talking about seeing "Attack of the Killer Muons From Space!" back in the 50s. :-P
I bet it was directed by Roger Corman.
this movie never existed
Well , as you allready have 400 comments, I´m not going to annoy you with another. Keep the good work. Apreciations from Romania.
Wow, I’ve never had kinetic time dilation / length contraction explained SOOOO well. I love this channel keep it up Nick!
Nick, that was an excellent explanation and graphical description of length and time dilation
l see subjects lve seen many times before but somehow you twist it in a way that suddenly makes it click keep up the good work.
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?
Nick your videos are so good! Thanks by making these subjects more intuitive❣️
When you said spacetime diagrams are powerful...that was a hell of an understatement! It explains everything about relativity so well, both general AND special!
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.
That's great! It's nice to hear that the videos help. That's my goal 👍
All because the universe wants to keep the speed of light constant for every observer! Great Video as always!
Yup - same for Quantum physics. The universe keeps going nu-uh! every time we put a laser in front of a double slit! Will we ever find a way out!!!!
Or.. do we want to keep it constant for every observer?
@@ShadowManceri no we don't
@@ShadowManceriif it was an illusion on our end the sky would be blinding and time dilation wouldn’t effect our satellites
The best length contraction video ever made...it covers all the doubts and makes it feasible to get the idea without going into actual equation of transformation...the best video to start studying the topic
Wow! That is the best explanation for spacetime dimension I have encounter! Thank you so much. Keep up the great work teaching.
Oh my god, I’ve never understood length contraction and time dilation so well, the diagram really is powerful.
Makes perfect sense when you do the math! Love it! I always thought that it was ACTUALLY a different length.
They ARE different lengths! It's just that it depends on the observer
Matthew B. I meant LITERALLY different lengths; but he explained that.
These are SO well done, and I’m talking about all of your channel’s content, not just this one. If I commented on every video of yours I’ve watched in the last two weeks your inbox would explode. Thank you very much.
Thanks! There's so much hate on the internet, it's nice to get some positive reinforcement 🙂
I think this is the first time i actually fully understand an explanation for this topic no extra learning needed! Thank you!
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
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
You're very welcome 🤓
@@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?
Commenting to get answer
@@joshanonline I think what you want are space-time intervals. MinutePhysics did a video about them.
@@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.
I absolutely love these kind of videos that explain the concept deeply.
This video is awesome. So much thanks. All your videos are great but You really hit it out of the park here.
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.
Exactly, welcome to hyperbolic geometry. It might be obvious that the sides are different lengths... but it's _not_ obvious which is longer.
8:14 Wait why is the hypotenuse shorter that the perpendicular ? Or is it cause of Hyperbolic Trig?
Hyperbolic geometry is _super_ weird.
MaSK the reference angle is not 90 degrees like with regular cosine/sine. Hence the weirdness!
Well,i was about to ask this....got the same doubt...😅
@@ScienceAsylum your face in the thumbnail sums it up pretty good 😅😂
@@ScienceAsylum so much for intuitiveness.
Welcome back, Nick. Excellent as always.
Thanks! It's good to be back.
Production value of your videos has increased ten fold recently. Great work
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.
1:03 Muons form space! I see some minutephysics (kind of) referances Nick
Yeah, he did a video on them. Also, _technically,_ they come from the upper atmosphere, not space... but that doesn't sound as cool.
@@ScienceAsylum 8:14 wait how isn't an hypotesnuse longer than the cathethus of the same triangle? (I'm a 15 italian dude so sorry for my ignorance)
@@eduardoGentile720 due to hyperbolic geometry . Hypotenuse can be less than base and perpendicular.
@@eduardoGentile720 Hyperbolic geometry is why. It's weird.
Absolutely love this channel. Can you make a video on Plasmons, Polaritons, and excitons? I have a very hard time understanding those concepts?
amazing video🙌🙌👍😍 I was not able to understand it earlier with equations. thanks nick
Very good 😊😊😊. My sincere compliments 😊.
1.7K views in 30 minutes. This restores my faith in humanity
0:35 The look on your face is so intense. I don't think I've ever seen someone get so excited about geometry before. That's the kind excitement that gets people invested.
You made LC much clearer by using the 'book-measure' example. Thank you.
Even vsauce and physics girl released a video at around the same time. That’s a recipe for party!
Neither for my profession nor for everyday life do I need to know this. Then why am I here? TBH.. I don't even know... but I appreciate it
You just answered the question of life my friend. It scales up all the way to the very purpose of existence. =)
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. ;)
Thanks for another amazing video, really appreciate your work
Best video on this topic. I just understood it all in one video. Thanks...!
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"
Yep. Different observers just see different 3D projections of the true 4D reality.
What you are talking about is the illusion/ projection. That is different from length contraction.
@@silverrahul please explain! :)
@@-_Nuke_- I mean, both of those effects are true. First of all, length contraction leads to change in length from the proper length. On top of that, what the observer sees through his eyes, is also different because of the effect which you described. Let us say, the square has a proper length with dimension of the side being d. The length contracted side becomes d2. And what the observer will "see" will not be a square of side d2. he will see, whatever shape depending on the angle of viewing , which was the part which you described. Length contraction is real, so also is the perspective. What an observer will see will be the combination of these 2 effects.
Why do I suddenly need to buy Advanced Theoretical Physics A Historical Perspective by Nick Lucid
🤷♂️ Who knows.... 😉
I got mine!
Thank you, the best video about length contraction I've seen so far.
This geometric interpretation is simply gorgeous!
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
😂
When you will make video on Schrödinger's wave equation
He already has and has not
I’ve seen it, so now he has.
@@maxpan9797 That's just, like, your frame of reference, man.
@@BlokenArrow 😆
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.
Thanks so much for this video! I love this channel...keep up the good work, Cheers!
Love the diagrams; they help immensely.
When he looks Gangsta in the video thumbnail you better pay attention otherwhise it will get supadoepa crazy in the science asylum.
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
this video was great. I know you've been frustrated by the GR videos, but your explanations are fantastic!
Thanks for helping me to understand these amazing concepts.
Absolutely fantastic! Explained in such an intuitive manner! Thank you!
you defiantly can play with a bit more details, but your videos help dude. Keep up the good work
I just bought your book and it's funny how I can hear your voice in my head while reading haha.
Just another great job, Nick!
Another terrific video Nick. YES, I do understand length contraction better after watching, and NO, you didn't go too deep - thank you!
Glad to see you're back!
Good to be back!
@@ScienceAsylum 😊
Very good explanation, thanks ! I also was hoping to hear about the invariant distance.
Perfect explanation, thank you!
Check your notifications KZhead changed some stuff so the bell may need to ring it again! Love this channel your enthusiasm is contagious
🤦♂️ I hadn't heard that. I'll look into it.
@@ScienceAsylum other channels I have been watching seem to be having the same issues... Other speculation is that KZhead is putting the video into the public different than what was the normal because after about a week or so their views seem to catch up to their average...I hope you get it figured out you are one of the best science channels I have watched and I hate to see you struggle....I'm a crazy for life!!keep on keeping on Nick Lucid!!!
8:50 "Or did i go too deep?" "No honey, you've fully mastered that length contraction thing."
As usual, awesome work!
Your channel is the best!!!!!! Thank you for making these videos!!!!!
That grid finally made this idea click solidly in my head. Graphs are magic, and so are you Mr Dr Scientist Man
Glad I could help 🤓
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 😊.
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 💛💛💛💛💛💛
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.