Length Contraction and Time Dilation | Special Relativity Ch. 5
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- Опубліковано 20 вер 2024
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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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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
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 😂😂😂
I just want to say thank you to UA-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?
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?
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 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
Length contraction?
Nobody:
“When guys get into cold water”
You're not wrong
More known as shrinkage or the Costanza effect
@@mohamadalrashed9064 significant shrinkage !
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!
Me: Just sitting here pretending I understand everything being said.
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 UA-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.
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. 😶
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
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...
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.
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.
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 UA-cam
pup RL yes
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. UA-cam's one.
Wow, I've been thinking about the time contraction thing for days, wondering why it isn't mentioned anywhere. Brilliant explanation!
I suddenly found that physics is good YT topics. It requires many review.
THE PARADOX THAT DISPROVES SPECIAL RELATIVITY:
There is a triangle of lights which we will call A, B, and C. They flash simultaneously in the frame of reference that is at rest relative to these lights. There is someone moving at a high rate of speed from B to A. There is someone else moving at a high rate of speed from C to B. There is someone else moving at a high rate of speed from A to C. So A flashes first and then B flashes and then C flashes and then A flashes again. How can A flash twice? When A flashes has B already flashed or not yet flashed?
or
B flashes first and then C flashes and then A flashes and then B flashes again. How can B flash twice? When B flashes has C already flashed or not yet flashed?
or
C flashes first and then A flashes and then B flashes and then C flashes again. How can C flash twice? When C flashes has A already flashed or not yet flashed?
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
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?
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
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.
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!
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!
"let's imagine I've placed a lightbulb at every point in space"
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.
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...😃😃😃
Thank you, saved my night, I didn't get length contraction until I watched you explain that you need to wait to measure the second event. Now my math gets the expected results.
Always great videos!
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.
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
Too bad we're allowed only one like on a video, great one !
A good analogy for the mutual slowing would be this: it's impossible for two people to see each other shrinking, except if they are moving apart from each other.
Just another way to say it's a perspective effect^^
Then about length contraction, would it be ok to say that the cat looks shorter because its tail starts moving before its head due to simultaneity breaking ?
Cheers
Cedric
Wot
Sexy Pug you didn't understand a simple video explaining special relativity? don't worry me neither LOL
check out the video made by carykh on this topic
*in Animal Planet narrator voice* this is the sound humans make when they are faced with more information than they can process
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.
"the cat is six hundred million meters long"
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!
2:22 God, that's VERY long cat. I mean think about his nervous reaction system which will QUIET take some time to "respond".
minutephysics: I will explain things in an easier way unlike others who uses tough methods.
Also minutephysics: *explains in a tough method*
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. 😊
goddamit, I need to watch all videos of this series again when you upload a new video
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 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!
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.
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.
this series is literally covering the same thing as my physics class rn xD
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. =)
I wonder if he'll cover acceleration in SR. I'd love to see that.
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
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.
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.
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 :)
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
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.
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
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 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!
Man, I love the spacetime globe. I wannit!
Can anyone explain?
Suppose two people A and B. B moves with respect to A, according to relativity, *time for B should be slower than A.*
But why?
Because when B is "moving" with respect to A and A is in "rest" , we can also say that A is "moving" with respect to B and B is in "rest", since motion is a relative concept.
So this should mean that *time for A is slower than time for B.* But this contradicts the first statement.
How and why? I don't get this. :/
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
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.
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.
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!!
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
4:15 _"... length contraction ... is ... 'distance dilation' PLUS then changing the times at which we're comparing [the front and back of the 'dilated distance' because they are] no longer simultaneous."_ Henry Reich, you came very close to capturing and expressing a particularly intriguing feature of Lorentz compressed objects. Your Lorentz calculator shows visually that the object _is no longer simultaneous across its contracted length._ In seconds per meter in the direction of motion, the equation for the "age gradient" visible in your video is -v/c^2 in object-frame meters and -gamma*v/c^2 in rest-frame meters.
Since we "know" a single object cannot span multiple points in time, our minds tend to dismiss what's displayed right there on your calculator.
There's also a deep-physics reason why non-simultaneous objects are disturbing. To ensure non-simultaneous objects keep the same physics as their simultaneous versions, the idea of a fixed lightspeed c must be abandoned and replaced with forward-backward velocity pairs. The product of these pairs is always the speed of light squared. This pairing allows the backward lightspeed to approach infinity even as the forward lightspeed approaches zero. The properly weighted geometric sum of those velocities is, not surprisingly, the Lorentz factor.
Variable light velocities are visible in your Lorentz calculator as the constant-area rectangles that grow thinner and longer as objects approach relativistic speeds. The shorter rectangle sides correspond to increasing backward light velocities, and the longer sides to decreasing forward velocities.
thanks, but could you speak faster?
U can always increase the speed of the video lol
@5:55 "But if you have a spacetime globe..." Oo, good idea, ill buy one-... er...
437secondsphysics
Thank you for the "Dreadnaught" pan over shot from The Last Jedi there in the opening 2 seconds.
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
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.
I'm relativly first :3
LetsPlayCrazy the physics of youtube comments
I think we all are.
This was the most lucid explanation of length contraction and time dilation as ever got!!!! Thanks for putting in so much efforts.
math is radical.....
....get it?......
Why did you do this.
That's irrational.
Your Waifu Sucks No it isn’t.
I’m guessing that time dilation is more extreme near speeds of light because of the Lorentz transformations? Because it takes more distance to move to its perspective when it’s closer to the constant speed of light, so the measurements of time relative to something else get closer and closer to each other. Does that make sense?
185th viewer. So nothing significant
Me too
Not from your time perspective.
Zyron
yeah.. In that case i'm always first
Mark Rober is the real MVP here.
And maybe some credit to the longcat.
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
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!!!!!!!!
too quick too slick. Slow down . explain.
I had to watch it at 0.75 speed.
@Robin Hack fine
The way I learnt both are:
The vector components in a spacetime diagram change under a change of basis vectors, and such, vector components change under changes of reference. So, the time components would change under a change of basis vectors, and that results in time being different and dilated.
For length contraction, I learnt it as, since reference frames have different position axis, you can’t measure a straight line on one reference frame since on another frame, it would be travelling in time. So, the line needs to be on an angle, and such, the lengths would be different.
Is this the new vsauce channel?
No, Vsauce is a 10minute of jumping from random thing to another while the episode is about a Very strange question and in the end you somehow have the awnser now?
Vsauce hasn't posted a free video in awhile
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!
Your videos have been sparse lately. What's up? Anything wrong?
Glen M These new and longer videos take more time to make...I think.
Quality > quantity
was a 7 minute vid with a 1 minute ad. I do get quality is difficult though.
He doesn't pick the length of the ad, and the ad will change upon each viewing.
No he meant the brillant ad at the end
Length contraction; If I tilt a pole lying horizontally on the ground twenty feet away from me perpendicular to my line of sight, through 45 degrees in the horizontal plane it will look shorter. It doesn't get shorter, it just looks shorter. If It is rotated a further 45 degrees, it will look like a dot - but its still a full length pole. We don't need an incomprehensively complex toy to tell us that.
Time is an arbitrary measure of rate of change. As you can't give me an inch, you have to give me an inch of something; as with time you can't give me a second, you have to show me a second's worth of change in something - like the finger on a clock face.
Time dilation and length contraction are how things look, not how they are - especially at .near-light speeds.
This video is brilliant! I'm trying to learn special relativity on my own during the summer and was stuck for like two weeks on how it comes that length shrinks while time expands, when they both have practically the same lorentz transformation.
The one thing im still not understanding is when the event actually happens, no when we perceive it to happen. In the combusting box example from the last video- do the boxes only combust at different times because the light takes longer to reach us for one box? But, from an external observer, they will always combust simultaneously
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!
Well thought out, and presented. But this doesn't end up supporting your point. Key question- is direction relevant to time dilation? I.e. time would very logically appear to dilate while objects move away from eachother.... but you'd have to flip your device yo illustrate deceleration. It would have to follow an exactly opposite curve, meaning regardless of what appears to happen when objects are moving relative to each other, they would catch up and again be synchronized if they were to come to the same reference point.
... If you were yo suggest that direction were irrelevant and that deceleration should be treated as acceleration in the opposite direction... imagine your device only able to move in one direction. Every time you accelerate, time should slow a bit. Decelerating would have time slow a bit more. Every time you started and stopped, time would increasingly and irrevocably become slower. This clearly doesn't happen.
Every episode my mind gets reblown. Blown up again, that is. And everything else in-between. An open non-dilated fully contracted unbent curve of blow.
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
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
Best Lorentz transformation applications' explanation ever.
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!
OK, this make my brain really grind, but, it makes perfect sense how you explain it all! Love this series.