Relativity 103c: Galilean Relativity - Galilean Transform and Covariance/Contravariance

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@himme8471 3 жыл бұрын

You present so many small details that really hammer in the larger important concept. Really love your style of teaching.

@white4571 Жыл бұрын

So much better than how physics texts present the material. They assume you know the answer and just need a refresher. The repetition here is key.

@joeheafner2495 4 жыл бұрын

This is the most impressive treatment of Galilean transformations I’ve ever seen! This is precisely how physics textbooks need to present it so as to bridge the use of vectors in other topics and to properly set the state for general relativity. I think/hope I know where you’re going with this in special relativity. In special relativity, some types of spacetime diagrams use contravariant vector components and some use covariant vector components. It would be amazing to see a side by side comparison of the two in your presentation style. I can provide many references.

@eigenchris 4 жыл бұрын

Thanks. I wasn't planning on introducing covariant vectors until after SR. I'm not sure what their physical applications would be in SR. Is there any particular reason to use them in SR?

@frede1905 4 жыл бұрын

@@eigenchris Personally, I don't think that covariant vectors are too important to consider in SR because we know that the contravariant and covariant version of a vector differ by a factor of the metric tensor. And since the metric tensor can be given as a diagonal tensor with components -1; +1; +1; +1 in SR, we get that the covariant and the contravariant version will be the same, except for the 0 component, where they will differ by a factor of -1. Although you therefore usually won't have to worry about the difference between the two kids of vectors in SR, I have seen partial derivatives with either upstairs and downstairs indices in SR, and then it's important to remember the factors of -1 in the 0 component when going from one to the other.

@frede1905 4 жыл бұрын

@@eigenchris kinds*

@うみうし-c4u 4 жыл бұрын

@@eigenchris Are wave vectors covectors?

@joeheafner2495 4 жыл бұрын

@@eigenchris In the context of spacetime diagrams, different kinds of diagrams use different ways of reading off the coordinates of events. Brehme diagrams use covariant components while Loedel diagrams use contravariant components. This isn't something that is usually pointed out in relativity courses, but I think it's an interesting application of the difference between the two types of components.

@physics_enthusiast_Soorya Ай бұрын

Omgggg, this videos literally deserve wayyy more views than they do, and you deserve wayy more subscribers, because So far, I've understood the concept CRYSTAL CLEAR! and No doubts at all except, If Components and Basis vectors are opposite to each other, couldn't be have named either of them covariant or contravariant?

@eigenchris Ай бұрын

Yeah. The one you call "covariant" and the one you call "contravariant" is arbitrary. It's just a matter of convention.

@physics_enthusiast_Soorya Ай бұрын

@eigenchris thanks for the clarity

@Oh4Chrissake 3 жыл бұрын

Note to self (2:20): Remember, t_man refers to the _car's_ position relative to Einstein.

@navilistener 2 жыл бұрын

I think you meant to say x_man instead of t_man. Anyway, good note. I also got confused with the notation, as in the video the subscript (man/car) duplicates the information of the tilde (or its absence), which indicates the reference frame of the coordinates. In my opinion, it would be clearer and more intuitive if the reference frame was indicated only by the tilde (or lack of it) and if the point/object being described by the coordinates (Einstein, car, plane, etc.) was represented in the subscript. Thus, for example, x~_man would be the position of Einstein relative to the car's reference frame and x~_car would be the position of the car relative to the car's reference frame (which is always 0). The same would apply to the time coordinate t.

@jankriz9199 2 жыл бұрын

I just wanted to express my gratitude. I already had some gtr lectures but i often go back to your channel (used to with differential geometry at least) to fill in the details and build much stronger basic understanding and i gotta say - i am deeply moved by how much better than the books i have read to galilean motion this intro is - everything apparently aims to just mash up also the position basis vector properly to conserve spacetime separation vector consistant with constant speed of light. So clear, so elegant. Really thanks!

@eigenchris 2 жыл бұрын

Thanks. I'm glad to hear these Galilean Relativity videos are useful, even if it's an extra couple hours of material to study.

@mwerensteijn 2 ай бұрын

Thank you so much for the detailed video's, all for free available.. Thank you!

@MrDragonbol312 4 жыл бұрын

Hi Chris! Huge fan. I just have a question. Isnt it weird to make a "time unitary" vector out of other 2 unitary vectors with different units? by this I mean that is a little weird that e_t' is made out of e_t and e_x when e_t' is supossed to have the same units as e_t.

@eigenchris 4 жыл бұрын

Yeah, that's a good point. In special relativity, we avoid this problem by measuring time in distance units like meters. We do this by replacing the time variable "t" with "ct" where "c" is the speed of light (m/s * s gives m). You could also do that in galilean relativity if you want, but I thought it would be too confusing so I just glossed over it.

@patriciacosson144 4 жыл бұрын

Toujours des videos extraordinaires simples à comprendre et très bien faites félicitations pour votre travail qui je l'espère va continuer

@laaamedaniel4943 Жыл бұрын

2:17 why is it a subtraction? Car's position coordinate must be bigger, but it won't be so, according to the formula

@laaamedaniel4943 Жыл бұрын

I got it, xman is not a man's position it is car's

@cyrobarros.m 4 жыл бұрын

Thanks for another video, they're very helpfull and well done!

@nickosc88 3 жыл бұрын

This video series is brilliant , Thankyou !!!

@bigprogramming579 8 ай бұрын

I don't understand what the variables represent at 2:22

@eigenchris 8 ай бұрын

They are the spacetime coordinates of a given event according to the car and the man. So if you draw a point on the spacetime diagram, the coordinates of that point would be given by t_man and x_man (they are the t and x values of the point according to the man). The car would measure the points at a different set of coordinates t_car and x_car.

@bigprogramming579 8 ай бұрын

@@eigenchris oh ok, thankyou so much sir

@homelesshendrix 2 жыл бұрын

'The car' or 'DesCartes'?

@porsgwen9562 2 жыл бұрын

Great explanation !!

@rupabasu4261 4 жыл бұрын

The only motivation, gr8 job 👍👍👍

@yq9hy6moon55 3 жыл бұрын

You're genius !!!

@richardsmith6488 4 жыл бұрын

What is the unit of the "t" dimension? Or asked another way, does the coefficient in 1t have velocity dimension.

@eigenchris 4 жыл бұрын

You can think of it as "seconds" if you want, but it could be anything like "minutes" or "hours". I didn't include specific units because I wanted to focus on the math, not the units.

@Physics_PI 4 жыл бұрын

Good lecture.. sir

@dansaunders6957 4 жыл бұрын

Great work!how would you define a time basis vector? is it a vector that is orthonormal to the 3 space vectors?

@eigenchris 4 жыл бұрын

There's no straightforward way to define what "orthogonal" means between the time and space directions in Galilean Relativity. For now just think of the spacetime plane as a 2D plane. The space vector always points right and the time vector can point in any other direction, as long as it points somewhat upward.

@ThisIsANameBruh 4 жыл бұрын

Hello and thanks for the video! I have a question: isn't it slight abuse of notation to write a row of basically columns since that's what the basis vectors can be represented as?

@eigenchris 4 жыл бұрын

It's an odd notation that I've never seen anyone else use, I agree, but I think it helps a lot to write it this way. I prefer to think of the basis vectors as their own symbols that can't be broken down further instead of thinking of them as columns. The column [1,0] can represent the vector 1ex + 0ey, but that doesn't mean it's equal to ex.

@biggiefrosty 4 жыл бұрын

It’s a special case of block matrix notation. There are rules on when it works and doesn’t work but it can be very powerful to help understand bases, as is done here. See en.wikipedia.org/wiki/Block_matrix

@edouardbertrand6666 4 жыл бұрын

Passionnant !

@DireSheep 4 жыл бұрын

beautiful!

@joeboxter3635 4 жыл бұрын

Why do the units of et = et-tilda + v*ex-tilda not match. You are multiply a space basis (unit less) by velocity (space/time), to get a et which should give you a unit-less basis vector. Something does not seem quite right. Your presentation style is much improved over just a couple of years back. Very much improved.

@eigenchris 4 жыл бұрын

I end up addressing this in the 104 videos on Special Relativity. The trick is to measure speeds as a fraction of the speed of light, v/c, which is unitless. You also measure time using ct, which has units of meters (x). In these 103 videos, I don't use this trick because I thought it would confuse people too much. As a result, you are correct that the units don't work out correctly. You can apply the above tricks to Galilean Relativity as well if you want consistent units.

@javierserra3461 2 жыл бұрын

@@eigenchris I also congratulate you on the series, from which I am learning much. But this particular analysis of Galilean relativity does not convince me because of the same remarks made by Dragonbold312 above and Joe Boxter here. Yes, in SR the units are homogeneous because you measure time as ct and speed as v/c and hence a dimensionless number. You say, "you could also do that in Galilean relativity" above or "you can apply the above tricks to Galilean relativity" here... but are you sure of that? In Galilean relativity c is not invariant (it cannot be if t is invariant) and c is not a speed limit (so v will not forcefully be a fraction of c). So you will have a hard time in trying to applyg the same tricks. This analysis of Galilean relativity where the time unit becomes a basis vector, is it something totally originally of yours or have you seen it as well any textbook? I would be very interested in learning that. For the rest, let me insist again that the series is great. I have seen many videos which people paint as fantastic but which in the end are not so clear. Yours are and that is precisely why one can, exceptionally, notice something to be challenged!

@eigenchris 2 жыл бұрын

@@javierserra3461 I meant to say you can pick any conversion factor you like and call it "c", and use that. Maybe suggesting the speed of light as the conversion factor was confusing. So you can define "c =1 m/s" (this is not the speed of light... it is just a conversion factor between time and space) and use the "ct" variable instead.

@javierserra3461 2 жыл бұрын

@@eigenchris Hhmm... That means that you are measuring time with meters, as you actually do in SR. But on what basis feel you authorized to do that? In SR you can and it may be long to explain why, but it is due to all the assumptions (later proved by experiment) that you are *not* making in the Galilean context. You cannot convert between units unless you measure one against another and find a fixed relationship between them, which only happens when you are in fact measuring the same thing, albeit with a different standard, like when you were measuring length with km and miles or temperature with Celsius and Fahrenheit... It is not an arbitrary decision: it is not so the choice of a specific conversion factor (even in SR, where c does act as a conversion factor, its numerical content is not arbitrary), but it is not so, either, the decision to use "a" conversion factor. Would you feel authorized to take *any* two units, fix any conversion factor between them and join them on a basis?

@eigenchris 2 жыл бұрын

@@javierserra3461 I don't think it's that big a deal what you use to measure time, whether it is seconds, hours, meters or kilometers. In Galilean Relativity, spacetime is automatically "sliced up" into objective time slices, so everyone in the universe in all reference frames will agree on whether or not two points are on the same time slice or not. What you use to label the time slices, be it seconds or hours or meters or kilometers or something else, isn't too important in my eyes. You just need a way of labeling which time slice is which in a consistent way. Unlike SR, the time slices in Galilean Relativity will never get mixed up when we change frames. In SR, the consistency of units between space and time is very important because spacetime is a single entity with no objective way to be sliced up. But in Galilean Relativity, the objective time slicing exists as part of the theory.