Relativity 104d: Special Relativity - Velocity Addition and Relativity of Simultaneity

[@rktiwa]

Today it's teacher's day in India when we thank our teachers. I thank you my dearest teacher, Chris for having taught me tensor which eluded me for years.

[@eigenchris]

Sorry for the re-upload. Someone caught a potentially confusing typo, and I've learned it's better to fix those ASAP instead of leaving people confused a year from now.

[@gummybears6125]

What was the typo ?

[@eigenchris]

@@gummybears6125 Had some of the numbers in the velocity addition calculations correct on some slides and wrong on other slides.

[@freddupont3597]

Very good, thank you. When that happens, maybe you should indicate it in the title so it is immediately apparent that something changed?

[@attilauhljar3636]

Simply brilliant! So clear that even my guinea pigs could understand it, and now they're busy planning their escape using time dilation.

[@canyadigit6274]

“Hey I’ve seen this one before!” “What do you mean it’s brand new!”

[@eigenchris]

something something time is relative.

[@agelosbedini2627]

You doing such a great job. My favorite videos on GR. THANKS, A LOT. Soon when I make my credit card I will donate. You deserve it.

[@treena3956]

This is awesome as usual! Thanks for helping so many of us!

[@MarceloChaves1971]

Awesome explanation.

[@7177YT]

The lorenz transform matrices sure look pretty. Thank you! Keep 'em coming. (;

[@eigenchris]

They will look evem prettier in the next video when I explain what a hyperbolic rotation is.

[@ahsanhayat8035]

If you can understand Urdu, Ghalib would have said. دیکھنا تقریر کی لذت کہ جو اس نے کہا میں نے یہ جانا کہ گویا یہ بھی میرے دل میں ہے۔ It goes like this He speaks so beautifully and fluently that sometimes I think I already knew this.

[@owen7185]

You're a freakin champion Chris. I love every video on your channel, and have made me want to learn even moee

[@jakeobrien809]

Hey @eigenchris great videos. They're really helping me understand tensors/tensor calculus and im hoping they'll eventually help me understand general relativity. Is you background primarily in math or physics?

[@eigenchris]

My undergrad degree was "engineering physics".

[@JeanDAVID]

The best lectures ever

[@patriciacosson144]

What a beautiful video i hope you will make a video about the transformation of electric and magnetic fields thank you for your hard work

[@eigenchris]

Thanks. I might consider doing this late in 2021... but my main goal for now is to move forward to general relativity.

[@jigold22571]

Your fabulous thank You!

[@danielwalker5682]

Great explanations! Still can't say I totally get it, but your channel is going to help!

[@eigenchris]

You're welcome to ask me questions in the comments if you need help.

[@danielwalker5682]

@@eigenchris Thank you. I have been trying to come to terms with t' and x' for around 38 years. I find it intriguing and disturbing in roughly equal measure. I have been following various lectures including Susskind's and I came across yours which I also think are excellent. Concise and clear. You've gained one more subscriber. All the best. Keep up the good work.

[@mateuszanuszewski69]

would love to hear more about error correction codes from you, especially how Reed-Solomon is made up from Cyclic codes, or some basics of Galois fields the reason being you explain everything step by step pretty much flawless.

[@asmatminhas8644]

Great explain I appreciate your hard work

[@ekaingarmendia]

Well... This looks bad for Tenet.

[@jay1421]

Great Video, I had a small doubt though. Why is it that βu and βv are less than 1 in the first place?

[@eigenchris]

Any massive object you're familiar with will be traveling less than the speed of light, so the β factor will be less than one. I guess we've only proved that object traveling less than the speed of light can never go faster than light. If an object is already going faster than light, this formula doesn't prove anything. Although an object like this has never been observed, and would cause a lot of theoretical problems, since it could break causality.

[@jay1421]

Thanks, helped a lot

[@vitrums]

oof, this video is a real eye opener

[@Your_PI]

Wow 😳

[@allykid4720]

20:50. Is it correct to state that if two events are connected by line slower than light then there is no causal relationship? There still can be relationship which is undetectable by limited v

[@eigenchris]

There could be a causal relationship. The example of the gun shooting the vase would involve a worldline slower than the speed of light.

[@allykid4720]

@@eigenchris ok.

[@stevewhitt9109]

Love this series on Relativity. Watched all your videos on Tensor Calculus. All your videos make sense, but giving Lorentz a gun after Einstein stole his ideas ? :)

[@richardlinsley-hood7149]

1. We have the o1 frame, with the observer standing in the center/origin of the train1 2. We have the o2 frame, with the observer standing in the center/origin of the train2 3. We have the o3 frame or rest frame, with the observer standing in the center/origin and where both o1 and o2 are moving in opposite directions with speed v 4. In each of the 3 frames, at t=0 , o1, o2 and o3 are crossing past each other 5. Train1 has front1 and tail1. Train2 has front2 and tail2 6. There are various points in the rest frame opposite front1, front2, tail1 and tail2 at t=0 7. Light from o1 and o2 will reach their respective front and tail at E2train1, E2train2, E3train1 and E3train2 8. The distances in the rest frame will be the same to E2train1 and E2train2 as will the distances in the rest frame to E3train1 and E3train2 9. The times in frame1 that E2train1 and E3train1 occur will be the same 10. The times in frame2 that E2train2 and E3train2 occur will be the same 11. The times in the rest frame that E2train1 and E2train2 occur will be the same 12. The times in the rest frame that E3train1 and E3train2 occur will be the same 13. Although there is a relative velocity between o1 and o2 as seen from o3 there are no differences in distance (8) or time (11, 12) to the events E2train1 and E2train2, E3train1 and E3train2 as seen from the rest frame 14. If m1 is the mass of train1 and m2 is the mass of train2 and are equal then m1=m2 15. The rest frame can be considered to be the same as a center-of-mass (COM) frame 16. If force F is applied to m1 in frame1 and force F is applied to m2 in frame2, the accelerations of m1 and m2 in the rest frame will be identical 17. In the rest frame, the clocks in frame1 and frame2 tick at the same rate. 18. Spacetime of E1 is ({d, +ve}, t) in frame1 and the spacetime of E2 is ({d, -ve}, t) in frame2. 19. Spacetime of E1 is ({d, +ve}, t) and the spacetime of E2 is ({d, -ve}, t), both in the rest frame 20. E2train1 and E3train1, E2train2 and E3train2 are examples of the paired events, E1 and E2, discussed above

[@ultramadscientist]

On the last part about causality, technically doesn't the math allow for faster than light solutions, but just not crossing the speed of light? Faster than light allowed but it can't slow down past the speed of light and slower than light allowed but can't speed up past the speed of light? The d'Inverno text on relativity mentions tachyons (and that we've never found evidence of them) but that they're technically allowed.

[@eigenchris]

That might be correct, but I don't know enough about tachyons to comment on them.

[@subhasish-m]

15:12 There's something really hilarious about this image

[@aneikei]

Hi, if the bullet was traveling torwards Einstien traveling at .90c from the gun, what would Einstein see the bullet's speed as?

[@eigenchris]

Also 0.9c

[@asmatminhas8644]

Still waiting for next video,plz explain causality briefly

[@cerwe8861]

I saw a much simpler derivation on sixty simbols, there he just devided lenght by time to do this.

[@eigenchris]

Yeah, I agree there are simpler derivations of the velocity addition formula, but I also wanted to prove that composing two Lorentz transformations gives you another Lorentz transformation, and I don't know of a simpler way to prove that.

[@km8130]

Thank you for your help. I've been reading about the subject of two consecutive Lorentz transforms and read that this is not strictly a third Lorentz transform, but a Wigner rotation. Textbooks are sparse on this topic as mentioned here: core.ac.uk/download/pdf/25361588.pdf, I was wondering if you could explain a bit about what a Wigner rotation is?

[@eigenchris]

Two consecutive Lorentz Transformations in the same direction will produce a 3rd Lorentz Transformation in the same direction, with the velocity addition formula shown in this video. A "Wigner Rotation" is what you get when you do two consecutive Lorentz Transformations in non-parallel directions (so for example, an LT along "x" followed by an LT along "y"). I haven't studied these before so I don't have much to say about them. According to Wikipedia, you can always re-write a Wigner rotation as a combination of a single LT and a single spatial rotation.

[@km8130]

@@eigenchris Thanks for your response! It's definitely a complex idea so I don't think is covered even in most graduate maths/physics courses.

[@eduardkuegler3655]

Thank you so much for all your wonderful videos. Please bring also the limiting case β1=-1; β2=1 discussed by J. Schwinger (Spektrum d. W. ISBN 3-922508-84-7). Now, since a Nobel prize for entanglement was granted 2022, we should consider this special experimental situation, for comoving entangled fotons. Especially the experimental situation described by G. Fischer- a Student of A. Zeilinger (see Gerhard Fischer in kzbin.info/www/bejne/sKrSgHZnadqUhbs problem at 21:45). Schwinger stresses the experimental fact, that we always have to deal with waves (electromagnetic or wavefunction). Velocity should be replaced by a term he calls general velocity, because we cannot put a tag on the phase. Thus he points out, that the equation for the square of the generalized relative velocity between two particles is nothing but the product of the squares of the two generalized velocities of each particle. It is really amazing to see, that this product of squares (1+ β1)/(1- β1)* (1+ β2)/( 1- β2)= {[1+ β1* β2]+[ β1+ β2]}/ {[1+ β1* β2]-[β1+ β2]}= (1+ βrel)/(1- βrel) ends up in β rel=(β1+ β2)/(1+ β1*β2). For Schwinger you have a division 0/0 when using comoving fotons. I am speculating, whether this randomness 0/0 produces this weird „element of reality“, when Alice can definitely predict, what Bob gets in a typical entanglement experiment. I guess the above stated problem happens, because the square of the generalized relative velocity can equally well be described as a quotient or as a product. But anyway, the concept of generalized velocity seems to reflect experimental handicaps.