The Maths of General Relativity (1/8) - Spacetime and Worldlines
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- Опубліковано 31 тра 2024
- In this series, we build together the theory of general relativity. This first video focuses on the notions of worldline, proper time, and coordinate systems.
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Alessandro Roussel,
For more info: www.alessandroroussel.com/en - Наука та технологія
Hi everyone ! This first episode is quite short, it's here to introduce the series and some fundamental notions we will use throughout the 8 videos. The videos will be published one each week starting now, I hope you'll enjoy it !
@Bhavesh sinha We will talk about the different tensors yes, but not from a differential geometry point of view (we will see them as matrices)
Thank you for translating this it's a really good series
Thank you for your dedication to fulfil my intellectual appetite. Your efforts are much appreciated!
Teach me daddy :3 Can't wait for the next episodes!
@@alphalunamare Well it's the same idea as describing vectors by column matrices, you represent a geometric object by projecting it on your coordinates. I agree this is not the most elegant way to approach GR, but it's in my opinion the most efficient for beginners if you don't want to go deep in the formalisms of diff geo etc. The metric tensor is actually closely related to matrix calculus and vector algebra since it represents a quadratic form.
Video: "We must forget everything we know."
Me: "Alright"
Vid: "In front of us us a sheet of paper."
Me: "What the hell is paper?"
Ahah well spotted 😂
like that spongebob episode where he forgot his name and he panicked
Hahahahah good
Could be "forget the physical theories we learned before"
Just forget about Newtonian physics would be enough!
This channel is going to be the 3 Blue 1 Brown of physics.
whenever I watch 3 Blue 1 Brown, it's just a matter of random time until I start hearing words without having any idea of what they were supposed to mean
@@ynntari2775 You should have patience. I watch them ten times until I get them.
This chanell is even better 🥰
@@omaralhafez5014 Yes, a monster has just born.
@@achyuththouta6957 that's spirit
Many can understand. But only a rare few can pass on that understanding to others.
This guy is a true teacher.
It’s probably bs why are you so gullible
Why in the world would you think general relativity was BS?
@@Vasectomyjohn
I always wanted a series on this in detail, this and math in quantum mechanics...PLZZ consider maths for quantum mechanics for your next series
Fb: #lock3dinthesh3d
That is exacly what i had on mind to, i know i it is too early to ask for topic for another series, but when this series will be finished, good next step would be quantum mechanics or even quantum field theory, i need to understand it better. This was good worming up.😊
take a look at ua-cam.com/users/ScienceClic to see what videos you can expect in the future
Let's not put pressure on the guy, not that I have any right to speak xD For now, I'd be grateful to have this series finished first
Your explanations are really the best. We all hope to learn not only the theory but also the maths behind them. Thanks for all the trouble.
256 people watched the premiere. The programmer in me is pleased with this.
The programmer in me would have been more pleased with 255.
@@RussellSubedi we don't want to start the HTML argument please lmaoo
@@mohammadelassal8079 Not the argument I had in mind, but let's not start any.
@@RussellSubedi 255 is not a round number, 256 is.
@@stephaneduhamel7706 Well, it's the difference between 100 and FF.
100 indeed is round but FF is neat on it's own - as it is the biggest 8-bit number.
general relativity is a topic that never ceases to amaze me; guess I just fell in love with your animations; I can't wait to see the part about tensors, geodesics, co-vectors, christoffel's symbols and curvature, all concepts I've been strugling to grasp
Let's appreciate how important the contribution of an apple in physics.
Great channel, btw, I have watched these from the first video up to this point in last 2 days.
Icebear was so hyped for this... Icebear is grateful
be like icebear
Ok icebear says Prateek Gupta
@@prateekgupta2408 Binod
good icebear
Icebear is happy to find more people who like quantum mechanics
This step is clear, I hope I will not lose my self later
how is it clear? It sounds like nonsense.
@@cecilmcintosh864 Up to now, ScienceClic just explains that objects travel not only in space but also in time. This travel is always present, sometimes they move more in time than in space and sometimes viceversa. Also that the time of the observer is different from the time of the object. The hard part is yet to come
@@MattiaConti I think these things are clear only if one chooses to accept them. However, i think when we use mathematics to model real phenomena we have to keep our assumptions logical in order for the model to be true.
There is a philosophical element to discovering the truth to reality. It is how our theories progress toward ultimately provable realities. If you start off with the wrong logical foundation you will invariably lead to a wrong theory. I fear this is yet another case. I believe Newton's theory is more sound than Einstein's because all his assumptions are logical and provable, and although his theory may be incomplete in explaining phenomena that we do not yet understand, it is not because the logic of his theory is inadequate, but it is because the reliability of our measurements are inadequate as well as our understanding of our material world. Newton's law does not explain bending light, because we do not understand the true nature of light, but if we did it would follow Newtonian physics in my opinion.
My struggle with the foundational assumptions with this theory is that we are taking a perception(time) and giving it a definite yet relative magnitude(a contradiction). When this does not exist in reality. With Newton's model, time only exists as a measurement and depends on the available equipment to measure. With general relativity it seems that we are giving time as an intrinsic magnitude to all matter. Well if that is the case then we should not be able to assume that time is intrinsically continuous. Because in the absence of matter that would suggest that time ceases to progress. And logically that should not be true if time is supposed to be a magnitude that must progress regardless of any other influence.
So if time is to be used like a magnitude or a dimension of reality(rather than a measurement), it needs to have a physical explanation or causation. Otherwise we are conceptualizing the cart before the horse. Things do not happen because time is passing, but time passes because things are happening. So to assume that all matter is in motion through time continuously is to negate the reality that matter is in motion continuously and that this is the only reason there is any concept of time at all. Time is propagated by the events of the consecutive changes in matter, which is dependent entirely on the representation of matter within space. If energy states did not affect the relative position of matter within space then there would not be any time at all. Just like Einstein postulated that gravity is not a force since you cannot tell whether you are experiencing it differently on the face of the earth vs. within an accelerating box in space, you cannot tell whether time exists without matter changing position within space. And because at the quantum level we see that matter does not really move but actually vibrates on a wave pattern, time is not linear but is cyclical and actually cannot be deciphered. Since, at a certain level the positions of a particle could be equally at two different positions at the same 'time' of measurement, so the position is unknown and equivalent to not having moved which means no time is passing at all.
This is why I believe this mathematical model appears to work, yet it doesn't. we will never be able to measure time in two different positions exactly the same, because we need to measure time with material devices. Space does not curve and neither does time, but the physical reality in an area densely populated with matter vs one that is sparse will have a gradient to it with regards to the experience of passing time. If you cool things down that is why you start to see some anti gravity like behavior. Though the matter is there, you start to see relatively low changes in material position relative to one another causing time to be experienced differently within that field of low temperature.
I am trying to understand these things as best I can, but i simply cannot accept General relativity in its current form of explanation, and maybe that is just my limitation, or the limitation of people teaching it, but it remains the same. But i love to discuss it and hope someone can help me see what I am obviously not seeing.
I am more apt to believe that the fluctuations in reality are memory based, as in the fabric of our universe is not space or time, but simply a record of information being registered as a data object, possibly a very complex tensor of information. At the quantum level this breaks down to an unknowable local, because it is in between the speed of transfer. Like when a computer program stores information the transfer rate is distinct and in between those time points the information could be any where and doesn't fully exist in a readable form. But at the poles it is either a 1 or a 0, which is eerily similar to a wave function. This fundamental limitation to the rate of transfer of information is what governs how we perceive reality. And i think there is a bandwidth to reality and the more matter that exists in a certain place the slower the rendering, which may lead to the differences in experiencing time and motion. In essence i don't think curving space has anything to do with gravitational attraction or trajectories. I think those things are functions written into this reality. Newton modeled the function, and we simply don't have a way to explain why it occurs the way it does, but his model is still the closest representation, in my opinion, to what is actually going on. There is an attraction between 'matter' registered with a magnitude of mass. I think this is still fundamentally true, and I don't believe General Relativity can replace that fundamental truth. And it may actually slow down our progress to think there is actually some mysterious fabric called space time that can be bent and manipulated.
@@cecilmcintosh864 man we are talking about a video on UA-cam ... not a universitary lesson!
@@MattiaConti I got no where else to talk about it. Just looking for new explanations of why people agree with this theory. Everyone seems to though, and I'm fine with being wrong until proven right. I just like to discuss such things when i see an opportunity.
This is the kind of explaining I like😁👍. Not with Stretch fabric 🤬
I'm taken back by the amount of effort you have put into this. It's truly astonishing and I can't thank you enough. UA-cam is the greatest thing that ever happened to education.
Love the start of this series. Hope this series successfully achieves the goal of simplifying GR math for everyone with basic (no more than high school) math skills.
I watch a lot of science channels and informative videos, but yours is different in a really good way. It’s more engaging, animations are clean and to the point, nice voice, and the music makes it feel intense. Great job, sir
It's amazing seeing more and more science education channels going into the really interesting details of the physics.
His editing skills are improving video by video giving me goosebumps
So far, it makes perfect sense, love the awesome animations, clear description and (almost) hypnotic background music!
your one video is equal to 12 school lessons
its amazing how much i can learn from your videos, you make it so simple and easy to understand
This channel is absolutely amazing. I binge watched the whole thing in one sitting and plan to rewatch it again. Outstanding and elegant examples, keep it up.
Such an elegant, intuitive way of looking at relativity.
Not gonna lie your videos are pretty fascinating to watch
Keep making content. Your visuals and delivery are easy to follow. Now I'm off at light speed so these 8 weeks feel like nothing in my proper time. Until the next one
So far the best channel for visual effects on GR loved it ❤️
A great start. Can't wait for more :)
You deserve all the love you're getting.
I like this channel. The guy explains difficult topics in a straightforward manner.
The best explanation for my non physics mind I've come across, so far. Keep it up!
I love this channel. I know that your channel will be one of the big science pages on this website someday.
I am a big fan of ScienceClic, man. And it happens that a couple of months ago I started self learning GR from lectures by Leonard Susskind uploaded to youtube. I will patiently wait for part 2 of this series!
Hello I am a bachelor and this was the first time I formally study general relativity. I can say that your work helped me a lot! It was brilliant! I believe this is the best material on the internet to explore the concepts behind this subject.
Why is it that as UA-cam ads get so much worse, UA-cam recommendations get SO MUCH BETTER!!
They make money on the ads and spend it on improving the recommendations algorithm, to get more people watch stuff to make more money on ads.
@@milobem4458 "woah" - neo
this series starts with all the right attributes of a super exciting series
best explanation videos on normal and quantum physics. its so easy to follow, i love this channel so much.
These videos are breaking new grounds. Everyone interested like in GR must be very excited and grateful. Thank you very much!
Wow. What a fantastic introduction to what I'm sure will be a phenomenal series. I'm so excited for the rest! keep up the good work :)
Thankyou *so much* for doing this. I think I have a pretty good grasp of Special Relativity but GR is such a massive step up and I doubted any UA-cam educator would be willing to take it on. Even if I have to watch this series a hundred times over before I understand it, then that is what I will do. Cheers!
This is a pretty good piece of work. Can't wait for your next videos. Earned my subscription at the 2-minute mark.
Great initiative to explain a complex topic in a simplified manner. True value add.
Great video. I'm excited for the next 7 videos. Really looking forward to this as I understand the concepts of general relativity but I'm not a mathematician and when I looked at Einstein's equations I resemble a deer in headlights so, yeah, I really appreciate this video series you're doing.
"Objects all have a speed through spacetime. The only thing that can change is how this speed is distributed between the coordinates of space and time."
This has to be the single best explanation I've ever heard. I have a physics degree, and while I never did much on GR, we looked a lot at special relativity and made teeny points towards GR and while I've seen the spacetime invariance vector over and over this was the first time that actually clicked for me what it means that it's invariant. Simple 2 sentences but absolutely beautifully worded. 1 episode in and I love this series.
Congrats on the physics degree. Do you have a BS?
@@dritemolawzbks8574 Thank you! and Yeah it's a BS. Most insanely brutal accomplishment I've done so far, especially considering my horrible math background. Do want to pursue a PhD soon, too
@@coach_tae_ No I'm an odd ball. I started out as a math and physics major during my freshman year ONLY, but I changed it, following career from my employer.
I have a law degree, and work in intellectual property (patents, trademarks, and copyrights). In order to get licensed, I needed a background in STEM or relevant professional experience. My undergrad was in mathematical economics, so I met the requirements by getting a master's in engineering management and the practical experience working for in semiconductor manufacturing.
I remember the requirements for a BS in Physics, so I have a lot of respect for anyone able to complete the mathematical requirements and the higher-level theoretical courses.
In my case, I wanted to be an astrophysicist, but it's a very difficult subject. There's also a high demand and financial incentives for physics majors to be switch to Electrical Engineering or Engineering Physics.
I didn't reach the senior-level courses but like you, I learned so much more about relativity (special and general) online from these videos and keeping my old modern physics textbooks.
I'm pretty nerdy myself, so I love knowledge and even love learning more about advanced-level Newtonian Mechanics and Gravity, Lagrangian Dynamics, and Galilean Relativity. I don't see how people even attempt to understand General Relativity with mastering Newton's Principia first.
@@dritemolawzbks8574 That's wild, bro. I actually started out as an electrical engineering major and swapped INTO physics. Probably not my smartest move. I love physics which is why I did it but I'd be making good money and have my own place by now at a decent job. But there's another value in accomplishing a goal that makes you happy and surviving what I would argue to be the most difficult undergrad program out there.
A BS in physics is essentially useless without anything else attached to it so that sucks. But my love is in the field so I'll have to make something work. I like to see your passion for studying it and it's people like you that I'm trying to reach out to for a website I'm in the process of making for self-learning math and physics. Hopefully to show people that it can be really enjoyable and rewarding as well as helping those already interested.
I really love how well explained your videos are! Amazing.
I can't wait until we get into some of the concepts of differential geometry! It will be cool to see how you depict some of the mathematics of it such as geodesics and the levi-cevita connection.
Awesome! Love these graphics! Very excited for this series!
These series are AMAZING! Looking to find people who are as passionate about this as I am! It’s like i stumbled into a gold mine
Part 1/8. I'm so excited
Thank you for this series. This is amazing. So well explained
So far, so good. I never was able to get a good intuitive understanding of the equations of GR, I hope this series can remedy that to some degree.
Another great piece. The duration is perfect - short enough to entice, but not so long as to overwhelm those just starting their journey into the subject. This is the kind of content the world needs to get people interested in how the universe works, without the often times pointless or weak analogies. Excited for the next one!
A great start. Can't wait for more :)
I have seen the general relativity videos in french version of your channel...its wonderful to have those videos in english,since i dont understand french.
Thanks a lot for the wonderful upload.
By teaching such a hard topic in very beautiful way ,you are doing a great job
I am loving this... Publish all of them now...!
I'm on my second year of physics, and I just had my mind blown by a realisation at the end ( the sidenote). Somehow, this observation has eluded me, as I couldn't have properly visualised the constant movement of stationary objects that move through spacetime at all times, because they are moving through the future.
These might seem silly to someone reading this, but I'm actually gobsmacked, as I've spent a significant time studying this issue, and only now, upon seeing this UA-cam video, have visually comprehended it in a way I couldn't have before.
Great explanation! Looking forward for the rest of the series
Great effort.... awesome..... easy to understand... thanks for the amazing visual and content.... From India-Tamilnadu 🇮🇳
Love the simplicity in the animation. Great content keep it up....
U are so hardworking. ... u will definitely become a renowned scientists some day and I wish for that
Good luck in explaining this complex topic. I will look forward to your future videos.
This is much better and understandable than what we did in school, by the way shout out to the Greek man, they started studying science and medicine and their letters are everywhere in these fields, plus most English words have Greek origins. cant wait for the next videos
Are you a teacher? I'm really impressed at how you created a video explaining such a difficult topic in such a compehensible, easy to digest way. Keep up the good work!
Thank you for making this series.
Thank u so much! This helps me a lot! This probably is the first useful video youtube ever has recommended me.
Fascinating! Plz make sure u can keep it so illustrative and clear like this episod. Also when u het to more mathematical parts plz don’t over simplify it, a bit challenge is ok. I became your fan after watching your video on “everything moves at the speed of light” for the first time I understood why there is a maximum speed when I saw the circle of spatial and temporal speed. Well done and many thanks.
this channel will become the 3brown1blue of physics
I'm glad I caught the first part video. Looking forward to the rest. You have my sub.
Looks very promising! I'm still following, waiting for part 2.. GOGOGOGOGOGO
omg i was so ready for the next episode and i realised that this first has just been released!!!... @sienceClic English this is some pretty good content, i might subscribe to your patron... there are plenty of people like me that we did engineering or other field that used advance maths, but after years of not using it like in university or doing or thesis, we don't remember as good as before any more.. .so this is great tool for ppl like me!
Nice to have you guys back.
Fantasctic. This is Physics, not lost in Maths. Well done.
Great video, I hope I can understand the topic through this series.
Always wanted video like this
I SO love this channel!!!
I just wanted to say thanks for translating these!
Mind blowing explanation, of theory to the imagination of example..🔥🔥 great. 8 episodes are lit🔥
We are about to be treated with absolute gold and I can't believe how lucky we are. Thank you so much.
This is pure gold, really really well explained, this for me is the maximum exponent of human intelligence and ultimately shows our ability to work together through time to get to comprehend highly deep concepts about how the very fabric of our universe works 💪🤓⚡👌
Very cool video! The explanation is absolutely top notch. Thanks for making this! :)
Thank you for the dissemination effort. Ciao!
Thank you for doing this. This is certainly going to open this complex topic to the general public
Everything is explained in a very clear manner, 10/10
So SO excited!!!
Thank you for this! From the bottom of my heart.
Actually, I've got another question if you don't mind.
I've heard people say many times that there is no global time in GR. But then I've had it explained that the spacetime interval is a number that all observers can agree on and that can be used to show a concrete ordering of events. Why don't we just call that time?
The "spacetime interval" is basically what we call "proper time". It is the physical "length" between two points of spacetime. But this time is only experienced by an observer that would be moving along these points.
@@ScienceClicEN Answering questions in YT comments? that is commitment. Respect.
The video is pure gold to me. Thanks
Subbed, can't wait to see the next parts.
Thanks alot, waiting for the next one.
I love this channel
Couldn't believe that we would be waiting for the next episode of an educational series like this like we would for a GoT ep.
Whatever this music is, it keeps us at the edge...hooked..
Amazing.. One of the best channels
This is BEAUTIFUL!
I see a bright future for this channel.
I’m so glad this channel showed up on my wall
Esperaba el video con ansias, muchas gracias ! Saludos desde Chile 🇨🇱
Since I'm early for class, I have a question:
Is gravity simply and directly caused by the presence of energy?
Like, if you have a photon or a proton at a certain position does it just pull spacetime towards it in a uniform sphere?
@Bhavesh sinha yeah. Thats partially why we couldn't unify both yet
Long answer: Gravity is not completely understood. For example, a quantum theory is still elusive. So... no-one knows.
Short answer: Yes.
I suppose we should qualify some this. Mass or Energy of any type contributes to the stress-energy tensor. So, the prescence of your photon or proton at a certain position does influence the Stress-Energy Tensor. This goes on the right hand side of Einsteins field equations. The left hand side of these equations then shows us how spacetime must curve. The curvature is determined by the metric of spacetime, so knowing that there is curvature we know something about the metric. Schwarzschild provided a solution for the metric that describes your situation perfectly. Specifically, it is spherically symmetric about the gravitating source and this is the sense in which I interpret your phrase "it pulls spacetime towrds it in a uniform sphere". To be very precise, it is spherically symmetric with regard to the SPACE co-ordinates (the time co-ordinate is a bit different but to keep it all simple, we'll say the matric is static, it doesn't change with time but instead just depends on position). OK, so that's simple enough... yes the prescence of a single photon or proton does exactly what you said.... however we have needed to be very fussy about exactly what you said... we are assuming that your particle was the ONLY source of matter or energy in the entire Universe. The Schwarzschild solution is only valid in the region of space outside the gravitating source AND assumes that this space is just a vaccum. In the real Universe, the Schwarzschild solution seems to be a good APPROXIMATION when you are well away from other gravitating sources.
@@colfrancis9725 Oh wow, that's a fantastic answer. And yes, it's a fair point that a static proton would produce a cylinder in the time dimension since by being static it's moving forward in time. Would it be in principle correct to think of that cylinder as a line of infinite spheres? Or is time genuinely pulled in a different way?
@@docopoper Hmmm... complicated and it seems clear to me that you know more about the topic then you first let on. Your geometrical interpretations may actually be right and I had never thought of it this way. Thank you very much for that. I'm going to side-step a direct answer by suggesting that, whether or not the geometrical interpretation is right, it doesn't necessarily help to explain the fundamental nature of spacetime. In particular you ask (or throw out an idea in the guise of a question) "is time genuinely pulled differently" and I have to be very careful how I answer this so as not to imply that time is an any sort of absolute quantity. The time you're talking about is just one co-ordinate time we could use.
If the proton wasn't static but was instead found to be moving at constant velocity with respect to our given co-ordinates, then the co-ordinates are the problem and that is all. We would introduce new co-ordinates so that the proton was stationary in those co-ordinates. In the new co-ordinates, everything is identical and we get the Schwarzschild metric again. You could apply a tensor transformation to the Schawrzschild metric tensor to see what it looks like in the old, original co-ordinate system (i'm not going to try and write the Maths out here in this limited text box). If you do examine the metric in the old co-ordinates then your geometrical ideas turn out to be quite reasonable. Let's do this briefly: For the standard Schwarzchild co-ordinate system we see that the metric depends only on spatial position (x,y,z) and not on the time co-ordinate t. Indeed, if we put a test mass at the fixed spatial position (x,y,z) then the distance or relative position to the gravitating source doesn't change as time passes and we have no reason to think that the value of the metric should change with time. In the old co-ordinate system, however, when we put a test mass at a fixed position and allow time to pass, it would appear that the gravitating source has moved away as time passed and so we would fully expect that the metric has changed its value. More generally it does appear that the time dependance of the metric radates outward in the time dimension, assymptotically approaching a flat minkowski metric as t--> infinity. This is exactly the same sort of dependance on time that the usual Schwarzschild metric shows with the distance from the gravitational source. However, it's equally important to note that the movement of the proton doesn't change the nature of the metric at all PROVIDED we use appropriate co-ordinates. So, I would say that time isn't "pulled differently" in this case provided we use sensible co-ordinates. Going back to our original discussion then, it's just that time is a bit different to the spatial co-ordinates which is important. The Schwarschild metric is spherically symmetric in the spatial co-ordinates but it is static (totally unchanging in time). How or why is time treated any differently or "pulled" any differently to space is still a very good question. I'm the sort of person who prefers algebra to geometry, so I would reach for an algebraic difference straight away: Time is treated differently to space because the metric has a SIGNATURE. The signature of a metric is a very special, untouchable algebraic property of the metric that cannot be changed by any (permissable) co-ordinate change no matter how hard you try. The signature of the metric tells us that vectors through time and vectors through space are not the same because they produce different eigenvalues. That's enough for our purposes, we don't have to assume time is exactly the same as space and it's perfectly reasonable to state that your proton (or photon) pulls spacetime so that the metric is spherically symmetric in the spatial co-ordinates but not in the time co-ordinate.
A more complicated situation: Suppose the gravitating source, the proton, wasn't moving at a CONSTANT velocity but was instead ACCELERATING with respect to the given co-ordinate system. It's going to be hard to find an inertial frame that makes the proton look stationary and you may realise that an acceleration could be the same as having another gravitational effect in the region. I'm not going to claim any expertise in this area but instead recommend you consult with experts on frame dragging. The ball is in your court, can you answer this one?
Very great video!
So pedagogical!
Eagerly waiting for the upcoming videos
I'm competent at math and have always wanted to be able to do general relativity calculations or at least understand the principles of it better. This looks really promising!!
Great video!
You know it’s going to be an adventure with a video is 1 out of 8 😆🙌👍
Amazing! Well done!
Great lucid explanation, can't wait to watch the other 7 parts.
Speaking of lucid, the physics channel Science Asylum, hosted by Nick Lucid, is probably the best for learning Relativity.