Relativistic Velocity Addition In Special Relativity (Why does relative velocity never exceed c?)

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Let's explore why relative velocities don't just add up in special relativity 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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[@Mahesh_Shenoy]

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[@Ni999]

The final equation at 16:20 is not the same as the one at the beginning. Denominator ought to be 1+uv/c², yes?

[@CVBrennan]

You answered a question I've not understood for decades until now... in just a few minutes. Thank you.

[@samcousins3204]

Your enthusiasm is infectious and makes your videos an absolute joy. Keep it up!

[@supermatteino8618]

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

[@Mahesh_Shenoy]

Wow, thanks a lot :)

[@johnc4957]

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.

[@Mahesh_Shenoy]

Thanks. Only for folks who stay till the end :D

[@starkindler1134]

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.

[@TheMarcsOv]

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 :)

[@Mahesh_Shenoy]

Yup, that's a great summary!

[@venil82]

Great content, but dissing of Newton was not necessary

[@X22GJP]

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 😊

[@Mahesh_Shenoy]

Thanks a lot :)

[@MichaelLPerry]

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!

[@Mahesh_Shenoy]

Thanks for noticing. I try. Ryan Renolds is the ultimate inspiration though.

[@alisavas9526]

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 :)

[@pavangaonkardonigadde]

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..

[@Mahesh_Shenoy]

Dhanyawaadgalu :)

[@StaticMotions]

Always a pleasure to like and comment on your videos.

[@Mahesh_Shenoy]

You know ..such comments make my day :) Feel great about the community :)

[@StaticMotions]

​@Mahesh_Shenoy I was taught simplified methods (much less than c) growing up and find your explanations challenging yet oddly complimentary to my understanding.

[@nicolasolton]

Mahesh is a good example of why India will soon be a superpower.

[@priyank5161]

Good way to start 11th grade, with this topic Even though its not in there ig

[@RudraforchildEducation]

Yeah right

[@nicolasolton]

Ig? What is this meaning?

[@AyushRawani_]

​@@nicolasoltonig = i guess

[@chicka-waiiamv9202]

How come you are starting 11th now? Boards exams aren't even complete

[@priyank5161]

@@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

[@safiulislam9146]

Hello sir , I am Deen from Bangladesh and I wanna say that you are the best fluent teacher I have ever seen

[@Mahesh_Shenoy]

Great to hear that, Deen :)

[@sandeepjoseph3754]

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'.

[@RajaBabu-ur5kf]

Your drawing and animation skill have improved a lot!

[@Mahesh_Shenoy]

Thank you :)

[@kriiistofel]

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)

[@Musi_012]

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

[@daveboulton3897]

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.

[@nickrondinelli1402]

I've always wondered how much length contraction and time dilation contributed but this really helped clear things up, thanks!

[@alfonsonava8548]

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!

[@samiraesmaili7021]

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 👍🏻

[@jherbranson]

You are my favorite physics channel, and I've been looking for this exact content. Thanks a million!

[@parthhooda3713]

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!

[@Kowzorz]

Incredible and succinct summary. Brilliant

[@amadeov5998]

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.

[@manasyadav1993]

Awesome video again Mahesh. Keep killing it my dude.

[@2DKot]

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!

[@Kuvina]

Hi, this video is amazing! You cover the things I've noticed a lot of other explanations miss!

[@tayyab1614]

The most intuitive explanation i have ever heard ❤

[@anotherme4638]

It's really amazing how you explaining/simplify these complicated concept, I really enjoyed watching this video thanks a lot and keep going

[@ryanisber2353]

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?

[@DrDeuteron]

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.

[@Mahesh_Shenoy]

Gravity slowing down time is coming up soon.

[@nmarbletoe8210]

@@DrDeuteron yup that's the picture. and we don't need to see the black holes to see their gravity waves.

[@jppagetoo]

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.

[@varshard0]

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.

[@ranjitinamdar]

This level of enthusiasm, this style and oratory is usually never found in such a scientific and mathematical content ! Amazing 👏

[@VascovanZeller]

Congrats on your growth, but most importantly on your contagious enthusiasm. It's a joy to watch your videos. Regards

[@Dr.RiccoMastermind]

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! 😎🇩🇪🙏

[@auriuman78]

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.

[@Dr.RiccoMastermind]

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

[@monstruonegro05]

Thanks a lot! I'm getting closer to understand it in an intuitive way! 👍🏽👍🏽

[@bishalthapa3154]

How could you explain it so easily? Loved it. You just earn a subscriber.

[@photon434]

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!

[@DheerChawhan_112]

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 🙏

[@jeremiestern]

To me you have the best science channel on the platform

[@joels7605]

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.

[@DrDeuteron]

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.

[@joels7605]

@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.

[@mrmoose1599]

I love how confident you are in this bias. Shows how bias you are 😂

[@guilhermesegalla9419]

I really apreciate this channel. Greetings from Brazil!!!

[@jmcsquared18]

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.

[@DrDeuteron]

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

[@jmcsquared18]

@@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).

[@jadermsantos]

This content is truly awesome!!!

[@ajeebmondal2955]

I love you sir, i am from Bangladesh ❤ I finished watching all your videos in 2 days. I really liked your style of explanation.❤❤

[@Mahesh_Shenoy]

Awesome to hear that :) :)

[@JorgeTorres-ek5qs]

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.

[@Kiv_rin]

Amazing video!

[@Tomyb15]

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.

[@leonard4134]

Great Video!

[@dwakeling38]

Thanks for making physics more accessible!

[@korakatk318]

This video is amazing!

[@farikacvi]

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.

[@mrhoho]

thanks for sharing.

[@baomao7243]

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.

[@fayezakhtar1155]

THANK YOUUUUUUUUUUU SOOOOOOOOO MUCH !!!!!! it really increased my knowledge, 10/10

[@thanoskorovilas8899]

Amazing video... truly

[@Narcissus833]

Excellent! Thank you 😊

[@adakot123]

Simply brilliant 👌 BTW, the parting thoughts are very ver deep 🙏

[@colson369]

that sponsor transition was smooth

[@curiousburke]

Another great video. Relativity of simultaneity to the rescue again!

[@Wild_Pernaja]

This video helped me to understand gravity better!!!

[@dragonbmgo]

❤️❤️❤️ Great job! ❤️❤️❤️

[@wilsongomes3360]

Excelent and nice teacher

[@krzysztofcukier4565]

You’re my discovery of the week!

[@shatfield725]

Great video 👍

[@Chrisymcmb]

Awesome man!

[@NoWheyHombre]

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

[@Mahesh_Shenoy]

Yes, thanks for the question :)

[@VertauePhysik]

Thank you for Mahesh sir, Enistine, Maxwell for the videos, btw congratulations🎉 for 110k subscribers

[@Mahesh_Shenoy]

Welcome, and thanks :)

[@VertauePhysik]

😊

[@gilbertengler9064]

thanks! I understand!

[@gigachadgogeta]

I dont study physics But all these time dilation, length contraction etc. seem to me are only trying to prevent anything getting faster than speed of light except light itself Physics is just trying to keep "Time" absolute Making sure we can never see the future, to keep time unidirectional

[@JT-hi1cs]

I suppose if all the universe suddenly goes to one direction at 90% speed of light we wouldn’t even notice. All calculations would still be valid as normal. Even the speed of light would remain “speed of light”, considering everything would be contracted (but unnoticeable for us inside the universe)

[@Robert-cd5zr]

Time and space, the fabric of reality itself, adjusts to ensure the speed of light isn't exceeded

[@Mahesh_Shenoy]

Actually. I think it's slightly deeper than that :)

[@RovingTroll]

​@@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.

[@Peregringlk]

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?

[@_Just_Try_0001]

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

[@Reaction1s]

@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?

[@thebetteryou8018]

Make a video on potential difference

[@oloyt6844]

Hi Mahesh, the only part where I’m struggling to understand is where it feels like we jump from the lack of simultaneity in the moving ship with the firecrackers bursting at different times to the observer, to where you say that this means events at the back of the ship occur first to an observer. I don’t really understand this logic without the light emitter in the center

[@PramochanYaan]

I love the word *INTUITIVELY*

[@roger7341]

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?

[@ronaldocabada7763]

I love your work, it would be great to have them translated into Spanish so we can make it reach more people.

[@TheMemesofDestruction]

Great Work! ^.^

[@planktonfun1]

if u and w are both close to the speed of light then uw/c^2 is close to 1, from then just use an approximation v≈(u+w)/2

[@edwardmacnab354]

matter has a time function , and at very high velocities it is easier to see. Most of the energy injected into the matter is used to slow time flow within the matter and only a little bit of energy goes to actual velocity. When the matter is stopped , the erroneous assumption is that most of the energy released is from an increase in mass when it really comes from the energy required to speed up the time flow within the matter from it's slowed state, not decelerate an increased mass.

[@kopi314]

Two Questions: 1. What is with energy preservation? 2. As the observer stays outside and these movements are relative to each other in their common moving coordinate system, compared to the observers stationary system, the observer won't observe time slowing down. And finally, how this can be fitted to our real life massed objects observations?

[@angeldude101]

Energy is simply momentum through time. This increases without bound as kinetic energy increases to compensate for the increased momentum through space, to keep the differences of their squares at a constant equal to the object's mass. (Difference of squares because they're hyperbolic rather sum of squares like when using a Euclidean metric.) Classical velocity is the perceived ratio between the velocity through space and velocity through time, and classical momentum is the same. These do possess an upper bound tied to the speed of light.

[@seetharamasvara7254]

Let us say A is at absolute rest (earth at max .001c can be taken as at rest) B moving at 0.6c w.r.t A and C moving at 0.8c w.r.t A. Assume A, B & C's clocks start from zero when all A,B, C coincide. Then speed for 1 sec in A clock B reads 0.8 sec and clock reads 0.6 sec. In other words for 1 sec in clock B, clock C reads 0.75 sec, i.e. clock speed of B : C is 1:0.75 . By velocity addition formula (here subtraction formula), speed of C w.r.t B is about 0.38c and corresponding clock speed of B : C will be 1: 0.923. How to explain this anomaly

[@nskhoo5143]

How did we get uv as the time delta from relativity of simultaneity?

[@jeremiestern]

This is great

[@HarpSeal]

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.

[@nirajbista27]

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?

[@yashwanthcb]

can you explain about warp drives?

[@SamratDuttabdn]

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.

[@bmuhammadthariqhumaid4670]

Can you content about quantum physics?? Love your channel❤

[@derwegweiser1177]

wow, i like these explanations. thank you. what still doesn't make sense to me though: lets say you have from one end light emitted towards the center and also from the opposite end light is emitted towards the center: why do the two light beams not move towards eachother at double the light speed from a resting observers perspective?

[@Mahesh_Shenoy]

From the observers perspective, the speed of light is speed of light. But, may be what you meant is the speed of one light beam with respect to another? I am answer that question in the next video. :)

[@derwegweiser1177]

ohh response from the creator himself :) hmm yeah maybe thats what i meant :p wow that's awsome!! 🙏@@Mahesh_Shenoy

[@dharmvirsingh4277]

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?

[@icreatesomethin3835]

"The Best Question with the Best Answer of the Year" award goes to :

[@heheboi5794]

Can you make a video on general theory of relativity