Length Contraction and Time Dilation | Special Relativity Ch. 5
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Mark Rober's youtube channel: / markrober
This video is chapter 5 in my series on special relativity, and it covers how things that are moving (that is, moving relative to an inertial reference frame) at different speeds appear to be shorter in length... and longer in length. And shorter in time, and longer in time. It all makes sense, I promise, and is clear when you use the Lorentz transformation of coordinates of the events in question, enacted with a mechanical minkowski diagram, aka mechanical Lorentz transformation, aka spacetime globe.
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Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
Created by Henry Reich
My brain doesn't feel so good
A small price to pay for salvation.
My brain is fried
Mr. minutephysics, my brain doesn’t feel so good
Well he is explaining very fast. You should watch special relativity first
Me too
I just want to say thank you to TH-camrs like yourself 3B1B, mathlogger etc...I'm thinking of doing a physics degree and your beautiful explanations of complex concepts as well as beautiful visitations of maths principles is something to be admired. The amount of work that goes into these videos I can't even comprehend. I just think you should know that it's appreciated and that it is making a difference in my education (I am of course the only person whom I can speak for). Keep up the bloody amazing work because they're need to be more people like you in the world. The gift of explanation is something to envy Indeed.
This deserves waaaay more attention.
I feel the same about this channel, 3b1b, mathologger and veritasium and occasionally ted ed. (I hope I am not leaving out any other channel I love)
longcat taken to the extreme
finally! someone that understands and knows what longcat is.
XD
LMFAO
Longcat is loong
We cannot make the speed of light relative to the speed of light, but in this experiment, we make the speed of light relative to the speed?
That is one long cat
SomiTomi haha ya, it’s easier to learn this stuff with extremes because the effects can be seen easier. I remember in my physics C class that we had a question about Superman flying away from earth but towards a bad guy at .8c (perspective from earth) and I forgot the rest of the question. These questions were the easy one on the test...just need to keep trade of everything relative to each perspective
I ate a very long pig one time....
Its jormungandr from Nordic Mythology
Understatement
That’s what I thought 😂😂😂
these things should be a standard equipment of any high school teaching physics!
thelukass no one study this confusing shit at school
omar oyt your school suck then
Faishal Ridwan LOL there is no such school to teach this
Yeah they must but alas relativity was deleted from the lebanese curriculum for high school physics...won't take it until university
Housam Kak, sorry to hear that. At least you're in this channel watching the video though
OK, I teach this...have taught this...to thousands of people. Much of what you have said has been great as enrichment, and I love it. Your completion of this pattern with "duration contraction" is...unbelievably brilliant, and-I believe-a pedagogical imperative. Thanks sir.
Okay, I think I found a contradiction. In this video, Henry says "Your 3 is my 2." But in his other two videos, he says "my 5 is your 4," and "My 2 is your 1." I actually think this video is wrong and his other two videos are right. With 1100 comments, this may have been mentioned a few times already. Could that be? I'm asking you, Benjamin, because it's more likely you will reply than Henry. Please let me know if I screwed up. Thanks.
@@DavidSiegelVision can you explain further with time stamps? I didnt find any issues with this video
Yes, the table with all the options is what we need to approach Relativity problems in a less confused way, it clears up many apparent contradicctions and doubts.
@@DavidSiegelVision this is a shockingly silly question. I’m not sure how to begin answering except to say that you should re-examine the context in which each is said.
The use of that contraption is absolutely brilliant. I found it much easier to digest the ideas in that manner. Great work!
no its not
I usually watch all of your videos. HOW DID I MISS AN ENTIRE SERIES?!?! I just found out.
Great job! As I'm struggling just now to make one of my students understand relativity, you deconstructing the subject so well is going to help me help her.
Thank you!
Or just point her to the series. Or watch the vids in class.
I teach highschool physics and I approve this message. (Showing this to my students today) Thanks!
I love this series.Keep it up!
Error, cannot fine File name "series.Keep"
So sad that you can't charge that file name any money for violating some law
go away
m
Including the ‘duration contraction’ is what really makes this video intuitive. It validates one’s understanding of the previously explained phenomena. Creates quite a 3b1b vibe.
I understood time dilation with the use of atom-clocks but Lorentz contraction was totally bending my brain until I saw this apparatus you used. What a wonderful visualisation aid!
Ok, question: how did you get the title to do that?
Hey, I think I know this guy.
Cody ♥️
Title to do what?
Notice how it has a supertext? [INTRO TO SPECIAL RELATIVITY S1 • E5]
He wants to know how to upload a video with that official looking "season" stamp attached to it.
Extra Credits has that on every video. Maybe you can ask them?
Fun fact: H.A. Lorentz thought time dilation and length contraction were real effects, i.e. that clocks literally run slower and objects literally get squished when they move. Einstein asked "relative to what?" and thought there couldn't be any answer to that question, i.e. "everything's relative". But that's never been proved. We might all be getting squished and living in slow motion without knowing it. 😶
1:40 - Or, to put it another way, imagine a person in New York City calls a person in Los Angeles.
New York Guy: "From my perspective, you are standing below me."
Los Angeles Guy: "Well from *my* perspective, *you* are standing below *me."*
That's a really good analogy.
From my "perspective", the Jedi are evil!
Then truly you are lost!
"I have the high ground!"
"From my point of view, I have the high ground!"
Assuming a roughly spherical Earth...
minutephysics: I will explain things in an easier way unlike others who uses tough methods.
Also minutephysics: *explains in a tough method*
Length contraction?
Nobody:
“When guys get into cold water”
You're not wrong
More known as shrinkage or the Costanza effect
@@mohamadalrashed9064 significant shrinkage !
Amazing video. I got confused on this exact point. I was trying to understand time dilation and length contraction using lorentz transformation and I was having trouble reconciling them. This conceptual understanding was what I need. FYI.. I asked chatgpt and it went off on a circular reasoning loop and gave up 😂
Me: Just sitting here pretending I understand everything being said.
Everytime I watch science videos I usually pause often to make sense of every single bit of information. Yours in particular make me do that a lot, which is actually impressive given how short they are.
Longcat is long
Ceiling cat's chosen hero come to save us all
SteelSkin667
Sooo long it evolves into a 'Cat-Snek'... or ferret.
Your meme relevance is time dialated!
The only thing that I got from this video.
I cast ComboBreaker
This feels like a dream. There's no way these videos exist. There's no way this is actually happening in this universe, it's hard to believe but it makes complete sense at the same time 😭. It's a whole new perspective to my brain which is used to quantum mechanics.. but I love this playlist too! I'll share it with my friends and etc who are interested to learn relativity from zero, since these videos broadened my perspective on reality, spacetime.
I honestly still haven't understood why the speed of light is constant. I'd love to investigate in that. Because there's gotta be an answer to the "why" right?
I really think that you and Mark Rober should start to sell your Larets (sorry if my spelling is off) transformation globe. I would be buy one immediately. Also, I think that for being TH-cam channels, you both have made massive contributions to both physics, and science education with this globe.
Lorentz transformation. Named after Dutch physicist Hendrik Lorentz.
Brilliant tool, Must be in all high schools and colleges
I suddenly found that physics is good YT topics. It requires many review.
man this is so good, I was trying to get my head around this since my bachelors. I would play with these graphs and never understand why time is dilated and length is contracted when they were so symetrical. This has cleared it up so well!!!!!!!!
Wow, I've been thinking about the time contraction thing for days, wondering why it isn't mentioned anywhere. Brilliant explanation!
Great work indeed! There's just a mistake at around 1:35 (your 3 is my 2).
The longest time is measured by the guy, who measures (so correctly: your 2 is my 3).
The misconception arises, because that picture is not correctly drawn. As you can see on the time globe, when transformed, time axes stretches and do not stay perpendicular to their space axes (in euclidean sense). So on that picture there can't be two time axes with perpendicular space axes, neither they can't have equally spaced seconds.
When Henry announced his time globe I was super excited that I would get an intuitive approach to relativity.
I don't know if it's just me, but I didn't get much. It still felt pretty abstract.
Worst thing is I already know these basic stuff :-/
I think it would be easier if there was a slow real time video of Henry just playing with the time globe explaining what's going on. You know like a practical demo class.
That might help me and others like me to understand these videos much better.
Never the less, these videos are one of a kind and extremely informative, but very cognitively loading.
Don't know if it helps but as he explained in another video you're only using one dimension of space and one dimension of time to get a two dimension plane. So the horizontal is the way you're moving and the vertical is time. So as you move you get farther away from the middle, but you will always go up. So Stading still wouldlook like this | but moving to the right will look like this /
Hope this helped
Yeah I felt the same, that (very nice) mechanical thing didn't really make things more clear. It's just another abstraction that doesn't really help understand what is really happening.
Oh good, it's not just me. It's a beautiful device but sometimes when he demonstrates something on it he goes a bit too quickly for me to feel like I've really gotten a grasp on what is happening.
Relativity isn't really very intuitive, and his explanations are good to get a basic grasp but I feel the mathematics behind it (and where these formulas he mentioned come from) are also necessary in understanding it. I know I need to look at the maths to understand it. Relativity involves pretty basic maths (I think to a high schoolers level) so you should be able to try learning like that.
The time globe giving a spatial dimension to time makes the explanation abstract. An intuitive explanation would be one grounded (and biased) in our perspective as a conscious observer. What occurs over there and how that information transforms as it travels across space to us (the observer) for us to perceive this dilation/contraction on this end? It's easy to imagine if you keep your dang spatial dimensions straight.
I cannot stress how insightful this series is. You really bring home some feeling I have for years a physics teacher, why "length contraction" feels off. And this in an amazingly clear way. Thanks so much!
Smart
I want the grid xD
Omg it's the guy who comments on every Johnnyboi_i video
quotevg Hey! 😅
quotevg every *Rocket* *League* vídeo to be exact 😉
pup RL I live on TH-cam
pup RL yes
This is the first video after millions I watched that ever say that time dilation and length contraction are not the two sides of the coin. Thanks a lot!
from my slow internet perspective: FIRST!!!
With Internet Explorer : FIRST!
An actually funny "FIRST" post. Well played
From my fast internet perspective - you are very small :)
Bob Lawblawblaw maby my clock was "slow" or I was "far away" from your internet speed of reference, but the one thing I learned from this series is that there is no preferred internet of reference.
yes there is. TH-cam's one.
R.I.P physics cat, your sacrifice has led to the production of a beautiful video to explain concepts to dumb-dumbs like me.
The Physics cat is always getting a raw deal. He's getting stretched out, contracted, doesn't know whether he's dead or alive.....it's gotta stop!
I learnt relativity in my 12th . It was not in syllabus but still was present in the book. Due to my curiosity in maths and the concept I began to read it by myself. Then the next encounters with relativity was from all the articles I read online. I had an moderate knowledge about relativity with many conceptual doubts. Now finally due to your videos many of my doubts are cleared. Thanks. 😊
Thank you for explaining complex concepts in a easier to understand way. You are educating the masses in a wonderful way.
Can i just say that your videos are simply AMAZING!!!! Like how are you so amazing!!? You explain better than any1 (despite your ever accelerating vocal speed 😂) Love your videos soo damn much and yeah, Would love if you uploaded more often...😃😃😃
these are some of the best videos on physics i've seen! i just have to say its a little fast and i've been watching every episode twice to get it right, so maybe slow it down? best of luck for you henry!
Always great videos!
That spacetime globe is putting in some work and it really helps a lot. Everything is 100 times easier to understand. It's brilliant, really.
I've made a mistake by clicking on that video
I can finally understand how time dilation actually makes sense. You are a savior of my sanity.
this series is literally covering the same thing as my physics class rn xD
This series is really good, and I really appreciate the effort you go to to SHOW everything going on. It's a bit fast though- even as someone who took ~2 semesters of relativity courses it's hard to follow some of the things you say. Speaking a little slower or pausing/repeating to allow people to process seems like it might help. Watching at 75% speed, the video is really really great.
4:00 shouldn't the colours of the lengths be the oposite?
To the left side of the equal the blue (or the length of the moving cat) and at the right side the orange (or length of the stationary one).
Yep
That is a very nice device you made as a tool to explain how time is "skipped." One suggestion I have would be to add the part from another video you made that explains how time is "skipped" in the twin paradox. This tool you made explains things very clearly.
"let's imagine I've placed a lightbulb at every point in space"
I would have never understood special relativity if I hadn't had this video, cause I don't have the time or the resources to study physics in college. So thank you MinutePhysics. Thank you VERY VERY much!
I find easier to understand lenght contraction than time dilation. I think that i have understood both yet, but man, this is crazy. If someone has some problems i have some "ways" to explain this more or less clearly.
never seen anyone point out the duration contraction - super interesting
Hi minute physics! One cool thing that is never mentioned about special relativity is Terrell Rotation. It would be great too see this covered as I feel few people (even physicists) know about it. I have seen physics presentations showing objects travelling close to C being represented as appearing flat to the observer, however they would appear rotated to the observer. Hope to see this covered one day. =)
Ugh, why must reality be so (necessarily?) complex? Well, I guess its not so much THAT as it is to try and map your mind onto reality itself, to completely and consistently understand reality.There are no paradoxes in reality, only in the mind, which is a hint that somewhere, something subtle is going wrong with the way we are trying to map it out using our language and equations. But with a keen, logical eye, we can succeed! Thanks for trying to pinpoint the subtleties of physics, you rock!
Physics
Where cats are 600 million metres long
nice one 😂
If I was travelling away from a cat at 0.99C then a regular house can would possibly appear 600m meters long :)
And a cow is a sphere in vacuum
explains why our universe is so big
Yea. I definately think I would've been lost at length contraction with out your "space-time globe." It makes it a ton easier to understand and visualize. Awesome work.
Einstein must have time travelled to watch this video and discovered special theory of relativity
But this man here knows it when einstien has said it in past
Confusing 😵 eh
Extremely brilliant, as usual. The only tiny thing I didn't quite like was, at the very beginning: "when you change from a non moving perspective to a moving one", which sound a bit like "absolute movement/stillness exists". You always need to be extremely careful to all words when doing science popularization! ;) BTW, as I've said, probably the best physics channel around (at least, that's what I said on my own channel a couple of months ago :) ). Go on mate!
2:22 God, that's VERY long cat. I mean think about his nervous reaction system which will QUIET take some time to "respond".
I like that spacetime "globe"! I recently came to the realization of this double standard for time and space, after knowing SR for some 25 years or so. Glad to see that others already explained it way cooler than I could.
My brain isn't braining !!!
This instantly made thing so much clearer and explained why I was getting the inverse of the constant that a should be on a problem
For the past 2 years I've been trying so hard to wrap my mind around time dilation and all I can come up with in the end is....its not dilated, it's just perspective therefore subjective
Help me
I haven’t been looking into it much but that’s what I intuitively think as well. I have confusion rn
That's basically it from what I can tell.
In the beginning, the orange man's clock ticks every 2 seconds from his own perspective. Now the blue man is moving 1/3 the speed of light, so time slows down for him. This slow down in time is evident because the blue man concluded that the orange man's clock ticked every 2.12 seconds, not every 2 seconds. The astronomical speed of the blue man slowed down his subjective sense of time by .12 centiseconds. This means that the orange man's clock in ticking slower relative to the blue man in his trajectory.
Length contraction is a little more tricky, but it's the idea that the blue man travelling at 1/3 the speed of light sees the cat stretch, or in more theoretical terms, dilute. The problem is that you can't accurately measure the cat because the cat's head stretches further ahead in time and space than the tail end; the tail end is falling behind. Thus, taking a measurement at this point would not reflect accurate results because each part of the cat is at a different point in space and time. Therefore, you must measure the full length of the cat when both ends (head and tail), are aligned on the same plane of space and time. From there, you can get an accurate measurement. Einstein figured out through his intuition that the cat's length would appear shorter relative to the blue man moving at 1/3 the speed of light.
This is my understanding of what is happening. Please correct me if I am wrong! Honestly, I have even more respect for Einstein :)
The reverse effect in time and space is something that deserves more attention
Where can I get one if those spacetime globes? And great video, but kinda confusing still. Needed re-watch for getting it cleared.
He had it custom made. There is a mention of it in the first video of the series or maybe in the teaser, not sure anymore. I guess it could be a merchandise of minutephysics if that were to ever become a thing.
Hmm, Henry, what do you think? I would also like to buy one, unless they are absolutely a one of a kind.
Ill make a software version if I can crack the locus of those curved arcs.
@@diojoestar4766 what do you mean by that? The curves simply follow the function f(x)= t'* 1/sqrt(1-(v/c)^2) -> gamma factor
@@diojoestar4766 to clarify - the curves in the globe are unit hyperbolas following f(x) = sqrt(x^2+t'^2) where t' is the intersection of the t-axis
I love how at 2:23 minutephysics just casually explains the cat is longer than well over 1.5x the distance of the moon to earth
So if I get this right:
If I'm moving relatively to a cat, what I really see is parts of a cat from different moments in the past. The further a given part is from me, the more in the past it was. All of that from the cat's perspective.
I love that we live in a world of such convenience where brain melting concepts can make sense to anyone who knows simple geometry. Thank you, minutephysics.
"the cat is six hundred million meters long"
This was really well explained!! I have been struggling with this concept since my freshman year in college and now three years later, it finally makes sense. Thank you!
The recording of your voice has a lot of high frequency clicks, whistling, mkrs krhsms, and prshks. With the bass plucking in the music they either disappear or become less distracting, but without the music they get uncomfortable.
accept the hipnoses. ;D
he could use a filter
I have to continually pause the vid to understand what you mean. Not that the content is super complicated, but you say things really fast. I still really enjoy learning from you
I wonder if he'll cover acceleration in SR. I'd love to see that.
As soon as you said "we only perceive a projection of the other world line as time and the rest as space" I think everything I learned in linear algebra suddenly made sense. But I'm also binge watching steins;gate so actually I don't know... but that's a really good way of describing this
I still can't wrap my head around this stuff.
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to (wrt) each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving wrt the second (Bob). The equations involving the time interval/the distance that is measured between a pair of events wrt one observer (Alice) and the velocity of that observer (Alice) wrt a second observer (Bob) is just another example of a transformation law that allows the time interval/the distance that is measured between the same pair of events wrt the second observer (Bob) to be computed. So in this case, it's a transformation law for the time interval/the distance that is measured between a pair of events.
There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
An event is something that can be ascribed a particular set of space and time coordinates wrt some coordinate system associated with an observer. The space and time coordinates of an event are determined by measuring the distance and time intervals between the event in question and some reference event which has been chosen as the origin for the spacetime coordinates. Events which have the same time coordinate are said to be simultaneous wrt that observer. Events which have the same space coordinates are said to occur at the same location wrt that observer. Transformation laws allow spacetime coordinates of events measured by one observer to be transformed into the coordinates that would be measured by another observer for the same events.
The time interval between a pair of events (A,B) that occur at the same location wrt one observer (Alice) will be measured to be longer by another observer (Bob) who is moving relative to the first observer (Alice). The two events (A,B) will also occur at different space coordinates wrt the second observer (Bob). The time interval between another pair of events (C,D) that occur at the same location wrt the second observer (Bob) will also be measured to be longer by the first observer (Alice) who is moving relative to the second observer (Bob). This is time dilation.
The distance between a pair of events (E,F) that occur at the same time wrt one observer (Alice) will be measured to be longer by another observer (Bob) who is moving relative to the first observer (Alice). The two events (E,F) will also occur at different time coordinates wrt the second observer (Bob). The distance between another pair of events (G,H) that occur at the same time wrt the second observer (Bob) will also be measured to be longer by the first observer (Alice). This is distance dilation.
We define the length of a moving object based on the positions of the end points of the object as they are measured to be at the same time coordinate. Simultaneous events (I,J) such as the end points of the object at a particular time coordinate, wrt an observer for whom the object is stationary, occur at different time coordinates for an observer for whom the object is moving. So by comparing the distance between the end points at the same time wrt one observer (I,J) with the distance between the end points at the same time wrt the other observer (I,K); we are no longer comparing distances between the same pair of events. This results in the length of moving objects being measured to be shorter along the direction in which it is moving. The same applies to the separation between bodies which are both moving at the same velocity. This is length contraction.
The density of an object and any other quantity that depends on the density will also be measured to be different depending on whether the object is moving or stationary wrt the observer. In a sense, this is all just an extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object wrt one observer to another depending on the ratio of their respective distances from the object. Measurements made by each observer is equally valid.
Al Rats Thanks for the explanation. I think I've got my head around it again now.
@@MrAlRats must both observers move at different directions? Because if they move at the same direction at the same speed, no transformation happens right? In other words, both observers must be relatively moving at different directions for the transformation to be observed? Because if both is relatively the same, they will be observing the same thing.
@@nazmiimtiyaz527 Whether a particular observer/object is moving or not, is itself a matter of perspective. From the perspective of a third observer, two other observers can be moving in the same direction at different speeds. In this case, the two observers will each perceive the other as moving. If the two observers are both moving in the same direction at the same speed (wrt a third observer) then they will perceive each other as stationary.
This was the most lucid explanation of length contraction and time dilation as ever got!!!! Thanks for putting in so much efforts.
Man, I love the spacetime globe. I wannit!
Touch a specific spot on your rectangle item with lights turning on simultaneously to make these words appear on it or press the left button when your ????? thing is at a specific location so that this jamble of words, which is, again, being projected by a rectangle, has a 1 or a 2 by it if you watch these informational dialects and don't know what the narrator is really saying, but you think it's satisfying, so you still watch it.
My brain has a 1gbs input rate without buffering and I just received confirmation that this video is too much info too fast and thus there is no information capture or retention. Fail.
Click the little settings spinner - you can change the speed.
Ian Haggerty My spinner is out for repairs.
you are revolutionizing teaching science. complex concept, logical, clean and elegant explanation (only throwing equations to connect the science to the math at the end). That reminds me of Stephen hawking's "Brief history of time" book
Holy God this was confusing I watched it 4 times lmao
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to (wrt) each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving wrt the second (Bob). The equations involving the time interval/the distance that is measured between a pair of events wrt one observer (Alice) and the velocity of that observer (Alice) wrt a second observer (Bob) is just another example of a transformation law that allows the time interval/the distance that is measured between the same pair of events wrt the second observer (Bob) to be computed. So in this case, it's a transformation law for the time interval/the distance that is measured between a pair of events.
There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
An event is something that can be ascribed a particular set of space and time coordinates wrt some coordinate system associated with an observer. The space and time coordinates of an event are determined by measuring the distance and time intervals between the event in question and some reference event which has been chosen as the origin for the spacetime coordinates. Events which have the same time coordinate are said to be simultaneous wrt that observer. Events which have the same space coordinates are said to occur at the same location wrt that observer. Transformation laws allow spacetime coordinates of events measured by one observer to be transformed into the coordinates that would be measured by another observer for the same events.
The time interval between a pair of events (A,B) that occur at the same location wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (A,B) will also occur at different space coordinates wrt the second observer. The time interval between another pair of events (C,D) that occur at the same location wrt the second observer will also be measured to be longer by the first observer who is moving relative to the second observer. This is time dilation.
The distance between a pair of events (E,F) that occur at the same time wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (E,F) will also occur at different time coordinates wrt the second observer. The distance between another pair of events (G,H) that occur at the same time wrt the second observer will also be measured to be longer by the first observer. This is distance dilation.
We define the length of a moving object based on the positions of the end points of the object as they are measured to be at the same time coordinate. Simultaneous events (I,J) such as the end points of the object at a particular time coordinate, wrt an observer for whom the object is stationary, occur at different time coordinates for an observer for whom the object is moving. So by comparing the distance between the end points at the same time wrt one observer (I,J) with the distance between the end points at the same time wrt the other observer (I,K); we are no longer comparing distances between the same pair of events. This results in the length of moving objects being measured to be shorter along the direction in which it is moving. The same applies to the separation between bodies which are both moving at the same velocity. This is length contraction.
The density of an object and any other quantity that depends on the density will also be measured to be different depending on whether the object is moving or stationary wrt the observer. In a sense, this is all just an extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object wrt one observer to another depending on the ratio of their respective distances from the object. Measurements made by each observer is equally valid.
@@MrAlRats cool
Great video mate, great to hear all this stuff again, and the way you present it all is way better than at uni, good work!!
Could one compare this to the shutter speed effect?
Excuse me, shutter? I don't mean to be rude but do you mean shuttle, like the space shuttle.
Mark Rober deserves a Nobel Prize for inventing the Lorentz Transformation Globe
Anyone else watch it 3 times and still didnt understand?
Only me? Thats fine
He made an effort but it was not good enough for the majority...Since his work is to translate to a simple languange the theory...
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to (wrt) each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving wrt the second (Bob). The equations involving the time interval/the distance that is measured between a pair of events wrt one observer (Alice) and the velocity of that observer (Alice) wrt a second observer (Bob) is just another example of a transformation law that allows the time interval/the distance that is measured between the same pair of events wrt the second observer (Bob) to be computed. So in this case, it's a transformation law for the time interval/the distance that is measured between a pair of events.
There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
An event is something that can be ascribed a particular set of space and time coordinates wrt some coordinate system associated with an observer. The space and time coordinates of an event are determined by measuring the distance and time intervals between the event in question and some reference event which has been chosen as the origin for the spacetime coordinates. Events which have the same time coordinate are said to be simultaneous wrt that observer. Events which have the same space coordinates are said to occur at the same location wrt that observer. Transformation laws allow spacetime coordinates of events measured by one observer to be transformed into the coordinates that would be measured by another observer for the same events.
The time interval between a pair of events (A,B) that occur at the same location wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (A,B) will also occur at different space coordinates wrt the second observer. The time interval between another pair of events (C,D) that occur at the same location wrt the second observer will also be measured to be longer by the first observer who is moving relative to the second observer. This is time dilation.
The distance between a pair of events (E,F) that occur at the same time wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (E,F) will also occur at different time coordinates wrt the second observer. The distance between another pair of events (G,H) that occur at the same time wrt the second observer will also be measured to be longer by the first observer. This is distance dilation.
We define the length of a moving object based on the positions of the end points of the object as they are measured to be at the same time coordinate. Simultaneous events (I,J) such as the end points of the object at a particular time coordinate, wrt an observer for whom the object is stationary, occur at different time coordinates for an observer for whom the object is moving. So by comparing the distance between the end points at the same time wrt one observer (I,J) with the distance between the end points at the same time wrt the other observer (I,K); we are no longer comparing distances between the same pair of events. This results in the length of moving objects being measured to be shorter along the direction in which it is moving. The same applies to the separation between bodies which are both moving at the same velocity. This is length contraction.
The density of an object and any other quantity that depends on the density will also be measured to be different depending on whether the object is moving or stationary wrt the observer. In a sense, this is all just an extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object wrt one observer to another depending on the ratio of their respective distances from the object. Measurements made by each observer are equally valid.
Al rats here's a👍 for your striving
Would you experience "teleportation" going close to the speed of light? Distances would appear shorter and time would grind almost to a halt.
I'm sorry what?
If not for your video, I could not have believed what I watched in Interstellar. Thanks for making Interstellar even better.
thanks, but could you speak faster?
U can always increase the speed of the video lol
I have 10% of an idea of what this whole series is trying to tell me, but i still like it!
I don't know how to do a time stamp, but at 3:29 my brain exploded, wiping out 97% of my intelligence and now I'm a Trump supporter. Thanks a lot!
Gotta shoehorn politics into everything, huh?
a trump hater that doesn't even know how to do a timestamp! WOW.
jk i don't care for trump either, but this is a science channel. leave that political bs elsewhere.
it's just a jk, chill
apple54345 too bad politics shape society more than science
Edited because "to" and "too" do not mean the same thing
97% of your intelligence? so like 9.7 IQ points? xD
Never get tired of watching these vids
I'm relativly first :3
LetsPlayCrazy the physics of youtube comments
I think we all are.
Best Lorentz transformation applications' explanation ever.
437secondsphysics
OK, this make my brain really grind, but, it makes perfect sense how you explain it all! Love this series.
math is radical.....
....get it?......
Why did you do this.
That's irrational.
Your Waifu Sucks No it isn’t.
goddamit, I need to watch all videos of this series again when you upload a new video
185th viewer. So nothing significant
Me too
Not from your time perspective.
Zyron
yeah.. In that case i'm always first
Hey there’s another portal paradox: what happens when a cube moving toward a portal stops half way? A.it stays put. B.it plops out. C. it shoots out but with half the speed?. make a video about that please!
too quick too slick. Slow down . explain.
I had to watch it at 0.75 speed.
@Robin Hack fine
Brilliant work. Thank you for your contribution. I want to point out a technical mistake in the lecture, at 3:55, the formula is not correct, the orange deltax and blue deltax are in wrong positions, I think. Could you please correct it to avoid confusion?