Derivation of Relativistic Velocity Transformations: Simplified | Problem Solving
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- เผยแพร่เมื่อ 21 ก.ค. 2024
- Relativistic velocity transformations relate velocities of objects with respect to two different observers in relative motion, that is consistent with special theory of relativity.
In classical (newtonian) mechanics, velocity additions / transformations are very simple. However, special theory of relativity poses a problem, as it introduces speed of light as the universal speed barrier, i.e. no object can travel at velocities greater than the speed of light. Hence we need to derive new velocity transformations that are consistent with Relativity. In fact, what we derive will be the general velocity transformation equations, and our Galilean velocity addition theorem are a special case of those general equations.
00:00 Introduction
05:12 Derivation
16:13 Problem Solving
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Real talented Physics teacher... Hats off sir
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At 15:42, the numerators for inverse Transforms of uy, uz are slightly off!
Numerator for uy should have been uy(dash)*sqrt(1-v^2/c^2).
Similar correction for uz.
For the rest, the video is perfect! :)
I will never forget about the first video that I saw on your channel. I was looking for something about radioactive decayment. I was struck by the illuminating way you explained things. Thank you.
Sir, you have a really amazing time way of explaining things! I admire your teaching a lot and your videos very interesting as always!
Hope your channel reaches out to many more people!
May mass×acceleration always be with you! 🙏
Love the way u teach man. Making every bit very clear
sir your way of explanation is really amazing, your videos are clearing my all doubts related to relativity
Thanks a lot
Your whole relativity playlist is awesome..... ❤️❤️❤️❤️
I've just completed it.
I am so glad I listened to this video. Goes to explain the momentum equations in a later video.
Well explained sir.... 👏👏have understood it clearly.. Thank you so much!
Great video sir, Good detailing and Break down of Equations as well as presenting their significance, Really loved it. God bless you ❤
finally concept smjh agya, adbhut anand ki anubhuti horhi hai 🤩
Clear and to the point explanation .Thank you sir
The way you explain is great sir 👍
Thanks sir for this crystal clear explanation 🙏🙏🙏🙏🙏
Sir i understood lessons as well .thank you sir to help to us to improve our knowledge . I was amazing when you teaching .good luck.❤❤❤
great explanation. thank you
hey sir your teaching is really awsm!!
Good explanation.
Discovered your channel yesterday, and am currently studying the same topic. Waiting eagerly for Relativistic Doppler Effect as well as effect of medium speed, as these are the only things a bit confusing. Thanks for this clear and amazing lecture.
Interesting...Have not completed the video yet😅 but i know it is going to be interesting 😃
amazing explanations sir, thanks
You are great 🙏🙏
Nicely done video.🙏
If observer S1 was instead going in the same direction in velocity as the spaceship in question, and we agree that time dilates as we approach the speed of light, and we also agree that the speed of light is a universal constant; could we postulate that one could in fact proceed beyond the speed of light by maintaining that same velocity constant in a time dilation that also approaches the speed of light?
I’m not sure how to properly word the question that I’m asking.
Essentially this: if we exist at a speed approaching the speed of light, would we be able to tell since light behaves consistently in the dilation we exist in? And if not, could we use a relativistic speed in a specific frame of reference and then accelerate another object to a relativistic speed within that initial frame of reference? And if we could, would that object “slow down” or carry its time dilation with it? Somewhat of a supercavetation for space time, in theory?
Forgive me if you’ve dealt with questions like this or if they come across underinformed.
Perfect explanation sir
Great video...
Sir why sicronisation happen?
Why is that in velocity composition law if ux'=-v ux is 0, and undefined (0/0) if ux=c and v=-c?
Instead of reinventing the wheel, we can exploit the fact that
u’=γ (x-vt) and t’=γ (t-ξx) are parametric equations dependent on t s.t x’:t↦ x’(t) and t’:t↦ t’(t)
Now, consider
dx’/dt = (dx’/dt’)(dt’/dt) by chain rule
If dt’/dt :≠ 0 on some interval, then dx’/dt’ = (dx’/dt)/(dt’/dt)
Therefore dx’/dt’= u’= γ (u-v)/ γ (1-ξu) = (u-v)/ (1-ξu) where ξ = v/c^2 and u= u_sub(x)
❤️ best teacher
Thank u ❤️
There is a small error in the expressions of inverse velocity transformation for uy and uz shown at 15:18.
Thanks for such very knowledgeable videos. Got to learn many things from your videos that are difficult and time consuming if one goes to books. Thanks and keep going :-)
yes
Nice sir
Thanks for this.
Around 9:00-9:30, I don't understand how the following has to be the case mathematically:
If ∆t approaches zero when ∆t' approaches zero, then lim ∆x'/∆t' as ∆t approaches zero is equivalent to lim ∆x'/∆t' as ∆t' approaches zero.
Why is this.
I mean just because ∆t and ∆t' both approach zero, it doesn't mean that the limits above have to be the same, does it. If so, why would this be the case mathematically?
Thanks.
You are just awesome ❤️
This is good explanation of relative velocities, but how about the actual distances traveled?
How does length contraction and time dilation for UFO A and B play here?
Dear Sir,
What will happen S' frame is moving in Y direction with velocity V
Hi, I am also from IIT Kanpur physics PG 1972 batch. I wish to share a GeoGebra file showing Graphic Relativistic addition of velocities. Sliders are included for your students to have hands on feel for changes in frame & object velocities. Nice work by you
Thanks sir 🙏🙏
Thank you sir
Why the Space ships' velocities don't add 🤔, though it is true for light
as per my understanding I.e, 2c is not possible . What happens in the Hadron Collider where v is close to c ? I'm confused. Please enlighten me.
Sir I have a question. Rocket A started from a point 10 crores km away from a goal at velocity of 2 lakh km/second another rocket B started at the same time from middle point at the velocity of 1 lakh km/second in linear direction.what will be their relatve speed as per special theory of relativity ? Will they reach at the goal simultaniously or not ?
What would be if we have done this proof with length contraction and time dilation? If we do this proof with that way we will find another result. In that case we would find an equation which says the relative velocity of the object from the referance frame of the other moving object is smaller than the velocity of the object from the referance frame of the standing (which has no velocity) object. this is a contradiction.
Keep uploading
For instante, if we had this two objects going in opposite directions each with 100% of the speed of light, if we substitude in the transformation eqn, we will get u' = c.
Sir agr ap hindi mai pdate to pdne mai or bhi mja ata thanku so much sir
Doubt in problem solving section (16:14):Will it even yield the same result if I will attach s(prime/dash) frame with earth and s frame with a spaceship. I tried it but got wrong result. Ans in this scenario came out to be 0.72c
I would be really grateful if anybody could explain this. Thanks in advance
15:30
the inverse transformation for y and z are written wrong😅
When we derived Lorentz transformation, we assumed that the relative motion was happening only along x-dimension. Here however the object has a velocity component in all the three dimensions. Why are we using the same equations should we need not to derive a different set of equations for this case.
But S' frame is moving with v in only x direction.
15:25 the right equations are not correct. They are not simetric.
Anyway, you're great!
op
😭😭😭Ha u ka sekama re ka oela.
Plz try to speak in hindi
And you also😁🤣
Hmm