Derive Lorentz Transformations
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- เผยแพร่เมื่อ 12 พ.ค. 2018
- Can you Derive the Lorentz Transformations from the postulates of STR?
When two inertial observers look at a common event, their measurements of distances and time are related by transformation equations. Usually, we use Galilean transformation (GT) equations.
However, the GT are not compatible with the postulates of Special Theory of Relativity. It cannot predict that the speed of light is a constant. It also cannot accommodate relativistic phenomenon like length contraction, time dilation, etc.
For this reason, GT needs to be replaced with a new set of transformation equations that will be compatible with Special Relativity.
These are called Lorentz Transformations.
In this video, I derive the Lorentz transformations for a very simple case, where relative motion between both frames of reference is happening only in one direction.
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PLAYLIST ON Special Theory of Relativity
• Special Theory of Rela...
-----------------------------------------------------
1. History of Special Relativity ► • History of Special Rel...
2. Michelson Morley Experiment ► • Michelson Morley Exper...
3. Special Theory of Relativity ► • Special Theory of Rela...
4. Time Dilation (Thought Exp) ► • What is Time Dilation?...
5. Length Contraction (Thought Exp) ► • What is Length Contrac...
6. Lorentz Transormations ► • Derive Lorentz Transfo...
7. Relativity of Simultaneity ► • Relativity of Simultan...
8. Can you prove E=MC² ► • Can you PROVE the most...
-----------------------------------------------------
9. Special Theory of Relativity ► • Special Theory of Rela...
10. Length Contraction ► • Length Contraction (Sp...
11. Length Contraction of Inclined Rod ► • Length Contraction (& ...
12. Time Dilation ► • The Mind Bending Predi...
13. Muon Decay Experiment ► • The Mind-Blowing Proof...
14. Relativistic Velocity Transformations ► • Derivation of Relativi...
15. Speed of light in moving medium ► • Speed of Light in a mo...
16. Relativistic Doppler Effect ► • What is Relativistic D...
17. Relativistic Mass? ► • What is Relativistic m...
18. Relativistic Kinetic Energy ► • Relativistic Kinetic E...
19. Relativistic Force ► • Relativistic Force
20. Relativistic Energy & Momentum ► • Relativistic Energy an...
21. Magnetism arises from Relativity ► • The Hidden Connection ...
22. GATE Physics question ► • GATE Physics: Problem ...
23. TIFR Physics question ► • TIFR Physics: Problem ...
24. Question on Volume contraction ► • Volume Contraction in ...
25. JEST Physics question ► • JEST Physics: Solving ...
26. NET Physics question ► • CSIR-NET Physics Probl...
27. Spacetime Invariant Interval ► • SPACETIME Interval & i...
28. Minkowski Spacetime ► • Minkowski SPACETIME, H...
29. Eucledian Space & Minkowski Spacetime ► • 5 Main Differences b/w...
30. Spacetime Diagrams ► • Time Dilation, Length ...
31. Four Vectors in Relativity ► • What are FOUR VECTORS ...
32. Doppler Effect using 4-vectors ► • How to use 4 VECTORS t...
33. Compton Effect using 4-vectors ► • How to prove Compton e...
34. Particle Decay using 4-vectors ► • Particle Decay in Rela...
35. (SHORTS) Does Light experience time ► • Does light photon expe...
36. (SHORTS) Light for moving observer ► • What is the speed of L...
37. (SHORTS) Nothing can travel faster than light ► • Why nothing can travel...
38. (SHORTS) What is farther away ► • What is farther away, ...
PLAYLIST ON Special Theory of Relativity - Lecture Series
th-cam.com/play/PLRN3HroZGu2nqysla3fazpMbEprTGTZx3.html
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great question 😡@@manveitsok4990
I feel really bad when I see rubbish videos on TH-cam getting veiws and really good videos like you made get much less views, it frustrates me so much!! Believe me I like you're every video really talented youtuber you deserve a million likes.
Thanks for the support brother :)
Exactly۔۔۔
Agree bro
Was going to comment same stuff here
So thanks for Lowering my burden here. ❤
I am 65 years old and am a retired engineer. But let me address you as Guruji.
Thank you Guruji, for explaining Lorentz transformation in simple and clear terms. May God bless you...
No need sir. We are all students of physics afterall. The more I teach, the more i feel as an ever curious student. And thank you very much :)
I literally signed in just to leave this comment: you're a phenomenal lecturer, you improved my understanding of the Lorentz transformation. Especially the part about how an inertial frame shouldn't impart an acceleration when you go from one frame to another. It makes total sense, but I never realized it, so I couldn't understand why special Relativity assumes the homogeneity of space and time (what you gracefully call Linearity). Thanks mate, this video is exactly what I needed! Greetings from the US ☺️🙏🏽🎉
This comment summarizes perfectly what I felt with this video
But i have a doubt. He wants that accelaration should be same in both frames but indeed the final result gives that it is different in both frames of references. Also, he want a one-one correlation but linear function is not the only one-one function, why it can't be anything else
@@ritilranjan7369_"He wants that accelaration should be same in both frames"_ - he does not want the acceleration to be the same in both frames. He just wants to avoid the transformation itself introducing phantom accelerations that don't exist in reality. He explains that at 5:00.
_"why it can't be anything else"_ - to avoid phantom accelerations.
I searched Lorentz eqn and TH-cam came up with so many videos.I saw few but wasn't satisfied then I saw urs and i can't say how much happy I was becoz I was able to understand every bit of it.U have such a proficient English which helped a lot to understand with clarity.Nothing can be more fulfilling than getting a conceptual clarity.Thanku sir.
I am a retired Engineer as well. 9 yrs ago I read derivation of Lorentz transformation. Today I revisited again. I have to say I enjoyed your video.
Excellent video.
Sir, you are a Legend. My professor just told me some abstract way of doing this which no one in class understood. However this 26 minute video did what he couldn't do in 2 hours of lecture.
Best explanation I’ve found on TH-cam the argument you make for linearity is very clear and the rest of the proof is very easy thank you so much 🙏🏼
You explain everything in such a beautiful way that there's no contradiction or misconception left about the video at the end of lecture.. thank you Soo much ❤️.....love from Pakistan 🇵🇰
Hell a lot of videos on TH-cam regarding this derivation. I finally now understood the Thing. Thanks Sir.!
Thank you sir !
I tried to understand lorentz transformations from CONCEPT OF PHYSICS by A. Beiser , but you made it more elegant and simple .
I watched several videos on this topic and this one was by far the best. Thank you
this video is REALLY AMAZING!!! It is very helpful for me and for everyone. You are explaining everything very well. and telling the subject very well. thank you!!
"Are you understanding?" lmao.
No but thank you very much for this really helpful video.
I am understanding ;)
you are a talented man. the way you explain things is amazing. thank you so much for such an extraordinary explanation
What is Time Dilation?
th-cam.com/video/lBiAE4Lxy8g/w-d-xo.html
What is Length Contraction?
th-cam.com/video/Ajjf_rIufb0/w-d-xo.html
What is Relativity of Simultaneity?
th-cam.com/video/vOSIGViCT-s/w-d-xo.html
Why didn't you take the negative value of a when going from a^2 to a?
Very great explanation....!!!! It is very clear to me... I missed to watch this for a long
Very good and very clear. Deriving the Lorentz Transformation is nontrivial, but he achieves it in less than 30 minutes. Sure, you'll want to go back and review the steps, but that's to be expected for such an important result.
you explain complicated concepts in a very compelling and simple way. god bless you teacher ❤❤
Very detailed and articulate explanation. Thank you and please keep posting videos like this. Please make videos on relativistic electrodynamics
Thank you so much sir...... I was facing confusions and after watching your video..... It has all been cleared. 🙏🙏❤️❤️
Really a concept clearing video. Thank you very much
Thank you for this wonderful lesson on Lorentz Transformations.
Amazing explanation⚡⚡.... You explain everything very clearly,
Thankyou sirfor this wonderful video 💫💫
Thank you very much!! I'm so glad I found your channel!
I saw many videos of lorents transformation but only this video is best
Really good and simple to understand ..thank u sir fr this wonderful video
I completed full playlist 😁 at the same night 🤠 thank sir❤️🔥🔥
Thanks for your videos. simple and easy to understand
Thank You Very Much Man. Wish You Grow More N More.
Fantastic presentation, no words to say.
Nice handwriting good explanation
Amazing.. very useful lessons
I really like your videos .. Please keep going ..
All respect
👍👍👍
Thank you so much :)
thank you so much for this explication i understand well now thank youuuuu from Morocco
This.Is.Excellent. THANK YOU SO MUCH
Dude, why you are so underrated?
How can to spherical light bulb gave the same origine for static frame and moving frame ?
Thank you very much, Sir!
You are really awesome. Very nice explanation
[@ 12:10 / 26:19 ] What does each observer perceive the wavelength of this "flash" to be (different or the same)?
Hello,
Brilliant. You make it all work by saying:
x = ct
x'= ct'
for a light pulse radiating from the origin of each reference frame. Pure genius. I'm 68 and this is the best derivation of the Lorentz Transformation I have ever seen.
All the best and many thanks,
Peter Nolan. Ph.D.(physics). Dublin. Ireland.
Thank you,
I wonder why can’t we obtain this equation
x=x’/γ+vt from the first equation and how is that contradictory to Einstein’s postulates of relativity.. pls answer
To derive reverse transform at 10:53 is assumed that the event happened at x=0 at the origin of the S frame. For S' frame, it is x'=-v*t. When x'=a*x+v*t is used for this, I got x=(x'+v*t')/a not x=(x'+v*t')a. What is wrong?
thank you sir very clear derivation!
Thank you for your contribution to my understanding of this and other relativity subjects.
Why we take ax+ bt positive in linear equation while the equation is x-Vt help ??
are all contractions(time, lenght,mass) "linear" to eachother? i mean at a given speed near of speed of light, when the length decreased by 50%, does the timedilatation also decreasaed by 50%? (and also the mass increased by 50%?)
great job , I learn a lot in this lesson , Thx.
I do appreciate that you wrote Lorentz Transformations in a horror movie font
i really wish they taught us like this in the university.
Nice explanation...i got it very well sr
outstanding, thank you for this video
Fantastic teaching.....Keep it up.
Thank you, this is very helpful
at min 19:52 where did the square root go on the left side? it can't just dissappear
Excellent video
Thanks a lot sir!
thankyou so much that was really a nice explanation
For Lorentz transformation of time are these expressions correct?
(1) t = t'.sqrt [(c+v) /(c-v)] and
(2) t' = t.sqrt [(c-v) /(c+v)]
How can you write x= a(x'+vt') given that x'=a(x-vt)? More specifically, I mean how can you 'assume' the coefficients a & b in the equation x'=ax+bt equal to coefficients a' & b' in the equation x= a'x'+b't' ?
Very simple and best....thank u.....😎
Very nice 👌👌👍..thank you so much...
Excellent sir i understand very well
Woow. Thank you so much.
Great, much appreciated
Great job
Great effort.
Well explained sir..😇
the best lecture
Well explained 💯💯
sir can you please make some videos for IIT JAM
Could you explain the quantum physics
thank you sir
Thank you
If it is the postulate of Special relativity that there is no resting frame in the Universe; it means it is not possible to determine which inertial frame is stationary and which frame is moving, then it means clock Paradox remains unsolved.
nice explanation
Thanks
Thank you for the clear and concise explanation! I have one doubt in this though. How can we assume the constants in both the Lorentz and inverse Lorentz transformation equations to be the same "a" ? I know it is the same but what's our reasoning behind the assumption?
Motion being relative and there is no absolute motion in space except light the constant a is same in both equations
The reference frames are symmetrica.. exactly the reason k1 and k2 are same for both references at timestamp 23:50
Super sir.....😇
Plzz could you tell me a numerical ,lorentz transformation , to find t'is equal to ?? You have x ,v
21:06
But i have a doubt. He wants that accelaration should be same in both frames but indeed the final result gives that it is different in both frames of references. Also, he want a one-one correlation but linear function is not the only one-one function, why it can't be anything else
I have problems with formula 4, the reversed transformation. It seems to me that we should not use the same a and b constants for this different scenario. (10:45)
a and b have to be the same for reverse transformation too because of symmetry. S' is moving at velocity v relative to S. This means S is moving at velocity -v relative to S'. Therefore, to get reverse transformation, we should interchange x and x', interchange t and t' and replace v with -v. We should not make any other change. th-cam.com/video/Ba-GvGMcgEY/w-d-xo.html
good video
while taking square root why can"t a(the constant) be -ve of the expression in square root ?
Suppose S' is moving to the right of S and some particle is moving to the right of S'. Then, the particle must be moving to the right of S also. This rule cannot be satisfied if a is negative.
Thankfully yours is the only video I opened after this topic was started in my physics class in college.
Thankyou
Hello Sir, your method of explanation is very good. However I have a query, which is......
Force for both the Fs of R will be the same and since acceleration is a result of force if a`=0 then a=0 ( at 6:58 in the video).
However mass will take different values in S and S` so acceleration also can be different??????
Yes, acceleration depends on frame of reference. However, if acceleration is zero in one inertial frame, it is zero in any inertial frame. This is because, when force is zero, then for any mass, acceleration will be zero. But if you use non-linear equations in derivation of Lorentz transformation, then it is possible acceleration will be zero in one inertial frame and non-zero in another inertial frame.
th-cam.com/video/Ba-GvGMcgEY/w-d-xo.html
why at 07:32 is it + and not - ? doesn't the galilean transformation say that it is - ? I greatly appreciate any clarification from anybody
As you can see in further steps, the value of b is negative. See if the following video is clear. th-cam.com/video/Ba-GvGMcgEY/w-d-xo.html
Sir, please make a video about einstein field equation
Sir plz faucault pendulum p video bnaye ?
Sir can you please describe the significance of this transformation in particle physics? Like when we discussed Hadrons leptons. You are doing great work keep it up sir
Hi, while discussing motion of subatomic particles, we do need to take relativity into account especially if velocity is very high. For example in particle collisions, when high energy protons or electrons collide, the relativistic mass energy needs to be calculated. Traditional conservation of energy and momentum needs to be replaced by their relativistic versions. In other examples, Path of motion as well as time of motion experience contraction/ dilation when particles move, as i explained in my time dilation video.
@@FortheLoveofPhysicsthanks sir for such help and keep it up as I'm your subscriber and from your lectures I am earning great knowledge
Thank you sir۔۔۔
Amazing video sir , i understood Lorentz transformation of equations. Plz sir create a whatsapp grup so that we students can share prblms with u. Hope u will respond me soon.
Tnq you sir
Hello hello , please recognise the following
In the example of fire cracker taken by sir in the video can't have relativistic view of the observers
That is , both will send it at the same time as it emits light and we know that the speed of light is constant..
Those who agrees please like and sir if you too agrees please give a heart and if I am wrong please reply and explain ,🙏🙏🙏
Excellent presentation.. however it does not clearly show what Einstein did differently. That the speed of light is a constant is seen here too. But yes clear presentation. I also understand the of this video is explain laurentz transformation.
5:20 Units are wrong... 😕
In those cases, you'd need constants
with appropriate units to make up for it.
BTW are you from Hansraj ?
❤❤great
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