Why velocities don't add up? (Relativistic velocity addition intuition)
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- čas přidán 8. 02. 2024
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Let's explore why relative velocities don't just add up as we learnt in Newtonian mechanics. We will use the ideas of time dilation, length contraction, and relativity of simultaneity to intuitively derive the relativistic velocity addition formula.
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The final equation at 16:20 is not the same as the one at the beginning. Denominator ought to be 1+uv/c², yes?
i have said this before and i will say it again. i am so glad that you are giving so much attention to relativity of simultaneity. It's like everyone just goes wild over time dilation and length contraction but everyone ignores relativity of simultaneity
Yes!!! It’s fuelled by my own frustrations of understanding relativity :)
y = mx + b
everyone talking about m, nobody want to b.
I totally agree. I saw a lot of videos about relativity and all of them just ignored relativity of simultaneity. And because of that their explanations was hard to wrap my mind around.
With that missing piece the whole concept looks so elegant now, thanks to this channel
@@Mahesh_Shenoyto understand relativity. you have to abandon belief . just use observable fact. time and space are connected. where space increases density of mass. time increases its density. to match.mass in motion dosent change its shape . it changes the relative density of spacetime around it.
I say this about QM. Most people are very capable of understanding the concepts in QM. What prevents them from learning is they don't like or accept those concepts as true.
Your enthusiasm is infectious and makes your videos an absolute joy. Keep it up!
You answered a question I've not understood for decades until now... in just a few minutes. Thank you.
Good way to start 11th grade, with this topic
Even though its not in there ig
Yeah right
Ig? What is this meaning?
@@nicolasoltonig = i guess
How come you are starting 11th now? Boards exams aren't even complete
@@chicka-waiiamv9202 yeah, I meant after the boards exam r complete, this video will be a good way to set up the intuition, and feel towards the kinematics of 11th
Just when you thought this man was done expanding your understanding, he drops Wisdom at the end. You're cooler than the other side of the pillow, Cheers.
Thanks. Only for folks who stay till the end :D
i don't usually comment on socials but this time after a few months i'm watching your content i personally wanted to thank you for the quality of your videos and the energy you put into them
Wow, thanks a lot :)
Great content, but dissing of Newton was not necessary
That ending though... it was just perfect. You don't just say something profound just for the sake of saying something profound, you explain for 17 minutes why it's profound without that even being the main goal of the video, and then you point that out as a side topic at the end. I feel like I completely understand what you mean by that at a core level. The quality of your videos is simply incredible. And I've never found videos that explain concepts like special relativity so intuitively, you're amazing and deserve far more subscribers.
Been watching you for a few weeks now, and I have to say, your level of enthusiasm is contagious and so refreshing. The intuitive explanations of what are often deeply difficult subjects only serve to enhance the experience. Much respect 😊
Thanks a lot :)
Hello sir , I am Deen from Bangladesh and I wanna say that you are the best fluent teacher I have ever seen
Great to hear that, Deen :)
This level of enthusiasm, this style and oratory is usually never found in such a scientific and mathematical content ! Amazing 👏
Always a pleasure to like and comment on your videos.
You know ..such comments make my day :) Feel great about the community :)
@Mahesh_Shenoy I was taught simplified methods (much less than c) growing up and find your explanations challenging yet oddly complimentary to my understanding.
Mahesh is a good example of why India will soon be a superpower.
You are my favorite physics channel, and I've been looking for this exact content. Thanks a million!
Dividing relativistic effects to the second velocity *v* into 3 distinct components makes it really intuitive, while also leaving *u* unchanged. As in, *u* is observed directly while *v* has to be corrected. Very good explanation :)
Yup, that's a great summary!
Haven't seen videos of this guy before, but I love his passion for the topic, plus I learned something I'd never expected, great video!
The reason why I am watching is because you make me think about things I wouldn't normally think about and that fascinates me... and of course the T-shirts :)
Your drawing and animation skill have improved a lot!
Thank you :)
Your ad reads are as good as your content. I didn’t see it coming. And I absolutely love the jokes you throw in. Yes, and the physics is mind blowing too. Awesome work!
Thanks for noticing. I try. Ryan Renolds is the ultimate inspiration though.
The fact I am searching for these videos and you always post them only a few days ago is blowing my mind. Like if I wanted an answer a bit earlier i wouldn’t have found anything
What a clear explanation to this topic! I've seen dozens of videos trying to explain this, yet this video is simple and brilliant at the same time! (at least from my reference frame)
I like your videos so much. Watched only from recommendations, but now I subscribed. Thank you for a lot of great intuitive explanations and energetic, interesting delivery of information!
Hi, this video is amazing! You cover the things I've noticed a lot of other explanations miss!
This explanation is quite exciting and intuitive. This suggests that when velocities add up, nothing happens to 'u'; the whole change happens to 'v' ( velocity w.r.t moving frame). The length contraction, time dilation and relativity of simultaneity; all conspires here to ensure that added up velocities won't exceed 'c'.
How could you explain it so easily? Loved it. You just earn a subscriber.
I'm so glad that I had an insomnia and found your channel by accident in the middle of the night.
I love your level of enthusiastic and ability to explain topics in such a simple and energetic manner.
To me you have the best science channel on the platform
I've always wondered how much length contraction and time dilation contributed but this really helped clear things up, thanks!
Incredible and succinct summary. Brilliant
I did not knew that you are from Karnataka i am also from Karnataka specifically from uttara kannada.. i feel so great that your channel in one of the best in the world..
Dhanyawaadgalu :)
It's really amazing how you explaining/simplify these complicated concept, I really enjoyed watching this video
thanks a lot and keep going
Awesome video again Mahesh. Keep killing it my dude.
Congrats on your growth, but most importantly on your contagious enthusiasm. It's a joy to watch your videos. Regards
Mahesh, many thanks for taking a subject that is so filled with accepted formula, and breaking that down into visualisations that make it “almost” understandable to us mortals. Your delivery and enthusiasm are engaging, your personality comes across as personable and friendly, and I am humbled by the effort you are taking to bring difficult science to the masses. Again, thank you.
If I could go back and not drop out of college I’m sure it would have been my calling to go into sciences like this, I go so deep learning and watching all these kinds of physics videos but it’s really because of your amazing, easy to follow teaching style and explanation. Would do life again if I could have had teachers that were as amazing as the videos you put out. Thank you.
The most intuitive explanation i have ever heard ❤
I really apreciate this channel. Greetings from Brazil!!!
i knew it was something to do with time dilation and length contraction (coz they are always the reason) but i didn't know the exact derivation of that fresky looking formula. thank you soo much for explaining it in such a fun way!
I wasnt aware that all 3 factors can really be calculated separately. It felt to me thats is like several aspects for the same dilation/contraction Lorenz Factor.
Thank you further explaining this! 😎🇩🇪🙏
Can you make a video about how gravity slows time?
How can we observe black holes merging if it takes an infinite amount of time for an object to fall in from a distant perspective?
yeah, that's kinda weird. It's more like 2 dynamic event horizons reaching out and grabbing each other. And once it's one event horizon: game over. ring down.
Gravity slowing down time is coming up soon.
@@DrDeuteron yup that's the picture. and we don't need to see the black holes to see their gravity waves.
Observation frame is everything. The photons of light emitted near the event horizon take a long time to arrive "to our observation frame". They also become red shifted below our ability to detect them. The event still happened, and took place at the time we can calculate and expect. But in our observation frame, we will never see it. All we see is a slow fade to red and freeze in place that fades away as fewer and ever redder photons arrive to our eyes/detectors.
Can't believe you made Einstein and Newton's spirits talk to each other for months just for a video. Make sure to release them now.
Thanks a lot! I'm getting closer to understand it in an intuitive way! 👍🏽👍🏽
This content is truly awesome!!!
Thanks for making physics more accessible!
I really like how he is just as passionate about an average person understanding physics as he is with his passion of physics itself.
There's a special place in heaven for people who firmly believe that people are smarter than they believe themselves, and just need to be reminded from time to time.
You’re my discovery of the week!
Mahesh,
Your ability to bestow upon folks an intuitive understanding of what Einstein observed is truly amazing. Naturally, we are drawn to the impossible next. What is reality if we can alter our course through time and contract like characters in a movie, with the projector being moved closer and farther from the wall?
If space and time are relative, then what exactly are the things we see around us? Time, Distance, and their resultant Speed do not conform to our intuition. I wonder if the reason lies in our intuitive concept of self.
We raise our seemingly rock-solid fists in defiance at the preposterousness of Einstein’s outrageous ideas. Yet, we don’t stop to think that our fists are not rock-solid at all. They are composed of tiny particles so far apart that they cannot touch. But they are not merely particles; they are waves with no width, but with volume that can expand or contract.
Mahesh, I trust you can correct any inaccuracies in what I have said, and I eagerly await your taking it to the next step. Please continue to challenge our understanding!
An even better way of adding velocities correctly is regarding them truely as rapidities (angular speed).
For small velocities (tiny angles) its very close to just adding the values, but c is at an asymptotic 90 degree that cant be reached
SCIENCE ASYLUM made a nice episode for this.
Worth to look at what is different between speed, velocity and rapidity
Thank you so much for this in depth explanation. I'll be honest and admit I never thought of this possibility because I've always just blindly accepted the speed of light as a constant until just recently.
When I learned of the one way speed of c issue a few months ago, I started questioning a lot of things after that.
The level of efforts ur putting in your videos are highly appreciable, thanks for making such intuitive videos for us. It really helps students like me to understand higher concepts of physics without going to coaching classes. Dhanyawad 🙏
I love you sir, i am from Bangladesh ❤ I finished watching all your videos in 2 days. I really liked your style of explanation.❤❤
Awesome to hear that :) :)
that sponsor transition was smooth
This channel is so good. I strongly believe that people who regurgitate equations and present that as an explanation do not understand the material they're pretending to explain.
that is not true. people understand stuff in different ways. Some people understand through equations. equations are not some gobbledygook nonsense. They are just a way of representing some physical truth. It is when they regurgitate those equations to people who DONT understand through equations , that there is a communication and understanding gap.
when they regurgitate those equations to other people who understand equations, then there is no such issue. in that case, equations are able to succinctly communicate something that would have been much harder to communicate otherwise.
no, my video would be 5 seconds: velocities, v, don't add. Rapidities, w = arctanh(v/c), do. _Le Fin_ .
Doesn't mean I don't understand it.
@@silverrahulIf you can't translate equations into intuitive spoken language, or give demonstrative metaphors you do not understand the material. You understand high school algebra. Period.
@@joels7605 " _If you can't translate equations into intuitive spoken language, or give demonstrative metaphors you do not understand the material_ "
you are missing the point of an equation, if you are looking for a simple translation into spoken language. a picture is worth a thousand words. and an equation is worth a thousand pictures.
the whole point of an equation is to encapsulate all those words into a concise, short mathematical equation.
Like i said earlier, people understand stuff in different ways. One kind of people are not very comfortable with mathematical equations, so they understand it better in words and statements. whereas some people are more comfortable with equations and have a good understanding of the equation and the material behind it. But, they are not necessarily good at explaining it to the first kind of people in words and sentences or metaphors. that does not mean that they dont understand the material, just that they are not meant to be great teachers or communicators.
that is where teachers and communicators like mahesh come in. THey are good at explaining stuff. But thinking that those who are not good at explaining, do not understand it themselves is a huge fallacy.
" _You understand high school algebra_ "
that is what it looks like to you, because you look at those equations and only see gobbledygook algebra. others look at those equations and are able to intutively understand what is behind those equations.
THANK YOUUUUUUUUUUU SOOOOOOOOO MUCH !!!!!!
it really increased my knowledge, 10/10
Make a video on potential difference
This video is amazing!
Amazing video... truly
Another great video. Relativity of simultaneity to the rescue again!
This video helped me to understand gravity better!!!
Simply brilliant 👌
BTW, the parting thoughts are very ver deep 🙏
I used to work as an engineer on large particle accelerator drive systems.
We had to factor in relativistic effects into both beam velocity as well as the beam trajectory in bending magnets.
Relativity is dream for both physicists and philosophers; it stretches the mind’s concept of reality. Super fun.
The Lorentz transformations do this so well it's absolutely beautiful.
One problem I gave my modern physics students is, a ball in the train is dropped, while another is thrown horizontally at the same height and same time. In the train frame, they hit the ground simultaneously, but not so in the frame watching the train go by.
Turns out, the horizontal component of its speed in the frame watching the train is precisely the relativistic velocity addition of the train's speed and the ball's thrown speed. Because it's moving faster, time dilation makes it fall slower than the ball that was dropped.
This is tricky, because you included gravity, which opens Pandora's GR box and gives you gravitation. In the train frame, there is a uniform gravitational field, E, from the mass (a flat planet, or infinite sheet of mass, idk), but the mass is moving relativistically and generates a graviomagnetic field, B, according to:
curl(B) = 4piG/c^2 J + (dE/dt)/c^2
so that the two balls feel different analog Lorentz forces:
F = m(E + 4v x B)
while I'm sure you're method works, there are some thought experiments where you need to consider this--I think the relativistic submarine doing an emergency blow is one of them, but I don't remember
@@DrDeuteron yeah I of course did this with the assumption of special relativity and Newtonian gravity only (bc these are undergrads and GR would be a nightmare at this level haha).
thanks for sharing.
I thoroughly enjoy and benefit from your videos but I think saying Newton's addition was wrong is wrong! What he said was perfectly correct for classical velocity additions. In real life and everyday engineering we rarely reach even a tiny fraction of the speed of light. Ultimately Einstein's equations become Newton's equations at low speed and low gravity.
Thanks for your great videos 👍🏻
i think it is accurate to say newton's addition is wrong. the only reason we use it is because it is APPROXIMATELY correct at low speeds, so it being wrong is not significant enough at low speeds
Amazing video!
Excellent! Thank you 😊
Sir please add caption it will help me a lot to understand better as my mother tongue is not English, please sir polite and humble request
Hi Mahesh I want to thank you first for the content you create because it is so helpful and I am sure a lot of people are grateful to you. I had been studying electric fields and I came across uniform electric fields. I don't understand how two plates and a single battery can create a uniform electirc field can you make a video on that, I would be very thankful.
Excelent and nice teacher
Really good video.
I feel like the only topics left in need for an intuitive explanation like this are length contraction and time dilation. Textbook derivations of the formulas are numerous but very few feel satisfying to me.
I remember reading in one textbook that length contraction is essentially the result of an outside observer measuring the moving object at different times from the pov of the moving observer and thus looks shorter (ie. they measured the front of the vehicle before the end). However when I try to derive length contraction from the relativity of simultaneity, I get that it contracts when moving towards you but it *lengthens* when moving away (which I understand isn't correct).
A satisfying and intuitive explanation of all these phenomena should be derivable purely from the relativity of sumultaneity in my opinion.
Great Video!
thanks! I understand!
You're vids are amazingly crazy multiplied by crazily amazing, because it's crazy how amazing they are. I'd like more vids into the very basics of movement and velocity, like, why objects have "inertia" or what does even mean that an object "moves" without any absolute reference frame. I mean, if theres infinite reference frames, then the object "moves" at infinite different velocities according to who is watching, which is a crazy thought. I would like to understand that better. If a moving object launches a photon, it's crazy to me to think that it causes time and length disturbances about the whole universe because every point in space is a reference frame. Or is it?
Thank you for Mahesh sir, Enistine, Maxwell for the videos, btw congratulations🎉 for 110k subscribers
Welcome, and thanks :)
😊
I love the word *INTUITIVELY*
Great video 👍
Can you content about quantum physics??
Love your channel❤
This is nearly the exact question I asked in one of your last videos. So thank you for, I assume, making a video just to answer me
Yes, thanks for the question :)
Wtf channel has this much subscriber only, it should have in millions😢
You are the best I know in You Tube.
I would call you the physics 3blue1brown guy, thanks for your quality content!
Can you make a video on general theory of relativity
But if you have two photons 3 lightseconds from each other and they are moving excactly toward each other on the same line, after one second, they will be separated by 1 light second, no?
Can you also do a video on mass variation. There is a much confusion about it. Lately physicist are avoiding that thing. What about transverse and longitudinal mass variation?
How did we get uv as the time delta from relativity of simultaneity?
Awesome man!
Sir I have a question. rocket A started from a point 20crores km away from a goal with a velocity of 2 lakh km/second another rocket B started from middle point at the same time with velocity of 1 lakh km/second in linear direction.What will be the relative speed of A&B as per special theory of relativity? Will they reach at the goal simultaneously or not?
Time and space, the fabric of reality itself, adjusts to ensure the speed of light isn't exceeded
Actually. I think it's slightly deeper than that :)
@@Mahesh_ShenoyBecause the speed of light has nothing to do with light. It's the rate at which cause and effect propagate. Massless particles such as photos just happen to travel at that speed. Hell I'd venture to say that "travel" is the wrong word to describe the behavior of photos.
I love your work, it would be great to have them translated into Spanish so we can make it reach more people.
@1:28 beyond dimensional analysis, light can draw from all dimensions because of its wave properties. That is why c2. Does that mean a c3 particle will appear? Can a c3 transformation be repressed? Why can they seemingly disappear?
❤️❤️❤️ Great job! ❤️❤️❤️
PLEASE Make Video on " The Kardshev Scale - Human Civilization Types ".😊
the way he says from different point of views makes his videos even better
Thank you :)
The CERN Large Hadron Collider is able to accelerate particles in opposite directions to within about three m/s of the speed of light in a vacuum. If two sets of particles are approaching each other in opposite directions, each traveling at about 299,792,455 m/s, what is their relative velocity at the instant of impact?
How do you get from the proper distance x to a velocity v in the train?? 🤔 v should not stand for a distance
Great Work! ^.^
Why wasn't the velocity of the train at 0.87c also divided by the 3 factors that contribute to velocity addition? It's also moving in our frame of reference.
For 2 spaceships, one moving forward and another moving backwards... Is the same formula used?
For example, in my reference frame (outside the spaceships), one spaceship is going to the right at 80% the speed of light, and the other is going to the left with 90% the speed of light... How fast will a spaceship pilot see the other spaceship moving?
Ahh...that's not how it works. You have to start from a rest frame. So call the ships L, M, R (you are M). In L's frame, you are moving right at 0.8 (by symmetry, no formula req.). Now you see R going 0.9, so L sees R going: (0.8 + 0.9) / (1 + 0.8x0.9) = 170 / 172 = 85/86
Now you asked about flipped sign, which was boosted out of the problem, so suppose R was going -0.9, then L sees:
(0.8 - 0.9) / (1 - 0.8x0.9) = -10 / 28 = -5/14.
Note that any spatial ordering of the ships is irrelevant.
Just , use variable -v ( since second ship is going to left ) for how fast ship pilot will see other ship moving.
then use u = .8c
then solve the equation , for value of v.
.9c = ( u - v )/ ( 1 - uv/c^2)
This is great
can you explain about warp drives?