Relativistic Velocity Addition In Special Relativity (Why does relative velocity never exceed c?)
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- Опубликовано: 4 окт 2024
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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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The final equation at 16:20 is not the same as the one at the beginning. Denominator ought to be 1+uv/c², yes?
You answered a question I've not understood for decades until now... in just a few minutes. Thank you.
Your enthusiasm is infectious and makes your videos an absolute joy. Keep it up!
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 :)
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 :)
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
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 :)
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!
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.
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!
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 :)
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!
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 :)
Hi, this video is amazing! You cover the things I've noticed a lot of other explanations miss!
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.
Incredible and succinct summary. Brilliant
Your drawing and animation skill have improved a lot!
Thank you :)
You’re my discovery of the week!
This level of enthusiasm, this style and oratory is usually never found in such a scientific and mathematical content ! Amazing 👏
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'.
The most intuitive explanation i have ever heard ❤
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 👍🏻
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)
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
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.
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! 😎🇩🇪🙏
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.
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!
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
I've always wondered how much length contraction and time dilation contributed but this really helped clear things up, thanks!
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.
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.
I love how confident you are in this bias. Shows how bias you are 😂
This video helped me to understand gravity better!!!
Awesome video again Mahesh. Keep killing it my dude.
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
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.
How could you explain it so easily? Loved it. You just earn a subscriber.
It's really amazing how you explaining/simplify these complicated concept, I really enjoyed watching this video
thanks a lot and keep going
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.
To me you have the best science channel on the platform
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 :) :)
I love the word *INTUITIVELY*
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 a lot! I'm getting closer to understand it in an intuitive way! 👍🏽👍🏽
Congrats on your growth, but most importantly on your contagious enthusiasm. It's a joy to watch your videos. Regards
the way he says from different point of views makes his videos even better
Thank you :)
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!
I really apreciate this channel. Greetings from Brazil!!!
THANK YOUUUUUUUUUUU SOOOOOOOOO MUCH !!!!!!
it really increased my knowledge, 10/10
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.
This content is truly awesome!!!
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.
Thanks for making physics more accessible!
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!
You are the best I know in You Tube.
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 🙏
that sponsor transition was smooth
Thank you for Mahesh sir, Enistine, Maxwell for the videos, btw congratulations🎉 for 110k subscribers
Welcome, and thanks :)
😊
I would call you the physics 3blue1brown guy, thanks for your quality content!
Another great video. Relativity of simultaneity to the rescue again!
Wtf channel has this much subscriber only, it should have in millions😢
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.
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 :)
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
Make a video on potential difference
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
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.
❤️❤️❤️ Great job! ❤️❤️❤️
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.
Simply brilliant 👌
BTW, the parting thoughts are very ver deep 🙏
This video is amazing!
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?
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.
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.
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.
Amazing video!
Hi, I wanted to add onto your understanding by simplifying it to a different way of thinking.
If we assume that light expands it's container in order to allow it to fit then it also explains each inconsistency. It states that the size of the train is changed when she throws the ball because there is now more energy within the train than there is energy outside the train. This limitation exists to prevent things from achieving the speed of light because if they did then they would collide with the dimensional boundary of their container collapsing the entire space.
This understanding explains all inconsistencies between newton and einstein's theories of gravity by making it dependent on the law of thermodynamics and creating 2 God particles, light as the collection of all current dimensional matter in its highest energy state and vacuum which is different dimensional matter in its lowest energy state. All other processes can occur as a result of recurring this over and over.
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
PLEASE Make Video on " The Kardshev Scale - Human Civilization Types ".😊
Excellent! One quick remark: in minute 5:21, you say “in the moving frame”, but I think you mean “in the rest frame”.
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)
First!
Ok fine maybe I was a bit late but amazing content Mahesh!
Haha 🤣! Thanks, Pranav :)
@silverrahulit will happen sooner than later! We discussed it recently.
It may or may not involve degeneracy pressure 🤐
Here's a question I have now. Two space ships start at Earth. Ship A accelerates to .9 c in one direction relative to Earth and ship B accelerates at the same rate to .9 c relative to Earth in the exact opposite direction as ship A went. What happens to ship A from ship B's perspective? Will light from ship A simply stop reaching ship B (and vice versa) once both ships exceed .5 c relative to Earth?
This is the same question of spaceship A stationary, Earth leaving at .9c relative to A and B at .9c relative to Earth. It's the same .9c+.9c problem.
Spaceship A will see B receding at the relativistic sum (less than c) as will B see A. Due to conservation of energy light from each ship is seen to be redder and dimmer.
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?
thanks for sharing.
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
Good video, I aways tought the relativity to be visible only through long distances, howerver this animation made me imagine this scenario:
If there are 2 people in the train moving like 9.99% light speed, the guy in the front would see the guy in the back in slow motion and almost stop, and if he decided to move to back he would see the guy in the back move very fast and gets older and older if he keeps walking in the direction of the back of the train
why? if they are both on the train, for them everything on the train and both people look normal. They are basically in the same frame of reference.
that would only work if there were an absolute rest frame, and there isn't, so it doesn't work like that.
Thanks, guys. I was being stupid, I forgot that if you are moving, you carry the momentum. This scenario will only be possible if you accelerate.
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.
Can you make a video on general theory of relativity
"The Best Question with the Best Answer of the Year" award goes to :
Great video 👍
Velocities correspond to saddle/fix points based on the flow gradient. Maxwell with GR doesn't cut it. Your theory is a nonlinear electrodynamic theory, which involves non commutative or simplectic geometry. Spacetime emerges from 0 d mirror ray spaces to an Infinite dimensional projective hilbert spaces. This form a lense or optical spacetime. You may want to research this direction.
Great content, but dissing of Newton was not necessary
2:03 😂😂
Mahesh sir was like:😎😎
😃
Amazing video... truly
I found Minkowski diagrams very helpful to illustrate this.
I don't know how else to explain it, but the how much slower it is than the speed of light multiplies.
At and after 13:03, you talked about how and when two objects that are a distance of a unit apart and moves ~1 times the speed of light, then the object behind would be slower. But but but, we can only say that by imagining the space as whole as well moving ahead right? (just like the example you gave of a train, where the behind object will read more time than the object ahead) But for that to be true, we need to prove that the space is moving ahead and in the direction of the ahead object and if we can't then how does any object know about which object is ahead?
p.s., A really great video and explanation! Love the whole process of digging down the problem and solving it from the fundamental level. Keep the good work going!
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?