Spacetime rotations, understanding Lorentz transformations
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- Опубліковано 8 тра 2024
- What is a Lorentz transformation? How do we turn within space-time? Why is the speed of light invariant? All these answers in 15 minutes!
0:00 - Introduction
1:22 - Galilean Transformations
3:52 - Lorentz Transformations
6:56 - Hyperbolic Rotations
11:50 - Unifications
14:00 - Conclusion
This video is narrated by Octave Masson.
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Alessandro Roussel,
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To learn more :
en.wikipedia.org/wiki/Lorentz...
en.wikipedia.org/wiki/Rapidity - Наука та технологія
This channel is absolutely unparalleled! I've never encountered such clear explanations for these concepts.
Yes, they stick out
once the space-time graphics reach a certain point, I lose all clarity of visualization. It's the same for all such channels.
In this case, things are going OK, until... 5:46 . At that point the animation becomes _worse_ than stationary diagram, and moreover I cannot map the verbiage into it
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So it’s clear that gravity is a bent fourth dimension? 😂 Such stupidity.
never tired of watching videos about spacetime.
Never tired to infinite rapidity 🫣
Best!
Try the “ double slit test “ for a trip to the quantum side
I never get tired of existing in spacetime.
Yep. Can't get enough of it
Knowledge for free that previous generations couldn’t even have dreamed of. An amazing UA-cam channel.
Humans are unbelievable sometimes, amazing we know these things
@@garymceneny6114 for real, today while walking on the road I was wondering about like just the shear fact that most the things which makes humans so powerful (not in physical scene) over other animals is the fact that we are like these mages in games who can take advantage of the environment to the fullest
I am a physics major, and finished special relativity last semester. I had some ideas about the subject, and wanted to create some diagrams to explain it better. I was stuck in circular rotation, and i had completely forgotten about hyperbolic rotatios. THANK YOU VERY MUCH, AMAZING WORK!!
What physics books are recommended at uni for this subject and GR?
Create a specific simple geometric representation of motion that is taking place within space-time. This particular representation is composed of a Space-Time diagram that contains both length scalars and motion vectors that are combined or tied together. What you now have, is circular rotation, combined with change of direction. This simple geometry also allows you to quickly derive the special relativity equations, including the deriving Lorentz transformation editions.
Are u sure u weren't stuck in a hyperbolic rotation?
Special relativity end on a sphere because theory contains 1/2mv^2
oy vey...don't mention physics...what painful flashbacks.
You are by far the best science and physics channel on UA-cam imo! Greetings from Germany✌🏼
deutschland!
@@DascooleSchaf Ein Volk, ein Reich, ein Kommentarbereich!
@@DascooleSchafdeutschland
douchland!
jk jk
@😢
I love the way you explained this.
My dumb brain has always had trouble with spacetime diagrams and light cones, but this helped me to better comprehend the idea.
Thank you!
I think a really good follow-up to this video would be an exploration of the spacetime metric. Then you can introduce the flat metric tensor very intuitively. Finally, explore a uniformly accelerating frame of reference and show how the metric tensor suddenly isn’t flat, and you have a perfect foundation for GR.
Spacetime is still flat (curvature zero) in uniformly accelerating coordinates (aka Rindler coords.). But yes that would be a nice topic for next video.
@@imaginingPhysics am I not understanding something? An observer in the accelerated frame no longer sees the world with the standard Minkowski metric tensor. By the equivalence principle, this is identical to a uniform gravitational field, which by definition is a curved spacetime. Essentially, any metric tensor that is not a bunch of 1s along the main diagonal is “curved.”
@AntiCitizenX you see there is subtle detail in general relativity that is usually skipped over. There is a difference between space-time curvature and a uniform gravitational field. You see a properly accelerating object has a non-zero magnitude of their four-acceleration. But an object in free fall under the influence of the curvature of space-time has a zero magnitude of their four acceleration. In fact it is the reason why the right side of the geodesic equation is equal to zero. The components of the geodesics equation are exactly the components of the four acceleration. The reason why they look complicated is because of the Christoffel symbols that incorporate the curvature of space-time. A properly accelerating object isn't the same as an object in free fall. You may say what about the equivalence principle that says an object in a uniform gravitational field is equivalent to an accelerating object. Well here is the subtlety, the word "uniform" is crucial because it means a local gravitational field which you get by taking the taylor series of the schwarchild Christoffel symbols to first order. Only then is a gravitational field equivalent to an accelerating object. Why, because an accelerating object has non-zero Christoffel symbols just like a uniform gravitational field. But globally a gravitational field is different from an accelerating object. Just because an object is accelerating and has non zero Christoffel symbols doesn't mean it is equal to the curvature of space-time. You can check this by calculating the Riemann curvature tensor for a properly accelerating object. The tensor vanishes identically meaning the accelerating object still lives in the flat minkowski space-time. While if you calculate the same tensor for an object in free fall, you get non-zero components for the Riemann curvature tensor. Meaning the object is in a curved spacetime affected by the presence of some mass-energy-momentum distribution.
@@AntiCitizenX you see there is subtle detail in general relativity that is usually skipped over. There is a difference between space-time curvature and a uniform gravitational field. You see a properly accelerating object has a non-zero magnitude of their four-acceleration. But an object in free fall under the influence of the curvature of space-time has a zero magnitude of their four acceleration. In fact it is the reason why the right side of the geodesic equation is equal to zero. The components of the geodesics equation are exactly the components of the four acceleration. The reason why they look complicated is because of the Christoffel symbols that incorporate the curvature of space-time. A properly accelerating object isn't the same as an object in free fall. You may say what about the equivalence principle that says an object in a uniform gravitational field is equivalent to an accelerating object. Well here is the subtlety, the word "uniform" is crucial because it means a local gravitational field which you get by taking the taylor series of the schwarchild Christoffel symbols to first order. Only then is a gravitational field equivalent to an accelerating object. Why, because an accelerating object has non-zero Christoffel symbols just like a uniform gravitational field. But globally a gravitational field is different from an accelerating object. Just because an object is accelerating and has non zero Christoffel symbols doesn't mean it is equal to the curvature of space-time. You can check this by calculating the Riemann curvature tensor for a properly accelerating object. The tensor vanishes identically meaning the accelerating object still lives in the flat minkowski space-time. While if you calculate the same tensor for an object in free fall, you get non-zero components for the Riemann curvature tensor. Meaning the object is in curved spacetime affected by the presence of some mass-energy-momentum distribution.
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6:12 A very important distinction here is that only the order of events which aren't causally related can be changed by a Lorentz transformation. In a sense, the order of these events is irrelevant to the universe and thus subjective to the observer. However, if one event causes another, then it can't be done away by a Lorentz transformation. All observers must agree on what order the events take place in. They might not agree on the length or the duration between those events, but the order is fixed. In fact, that is how time is defined. If the order weren't preserved, time wouldn't exist.
Damn, I just noticed that there's a way to see this visually. In the video, the angle made by the line joining the two events is > 45 degrees. Which means they are causally unrelated or spacelike. Which is why their order changes during the transformation. For causally related events, the angle would be
@@feynstein1004 Yes! It is, in fact, quite mind-blowing. It also implies that the concept of 'Relativity Of Simultaneity' is not truly about simultaneity but rather about non-causal events. This is because there is no time for light to travel between points A and B if they occur simultaneously!
if the interval of time between two events are greater than the interval of time that the light takes to travel to the point of space wich occur the first event to the other point of space, than the two events are causally unrelated that is, for the to events to be causally related they just need that the time between then to be smaller than the amount of time that the light in the point wich occur the first event takes to go to the other point of space wich occur the second event, is not needed that the first event cause the second.
Yeah what you realised is basically the argument for why information cannot travel faster than the speed of light, while it might not appear to violate causality for you, some other reference frame might see someone else act on the information you sent them before you even sent it.
There's what you obtain only when the light cones have a common point. If you can detect each other, starting from that point you can relate pairs of different reference frames.
This is a brilliant visualisation of Lorentz transformations and worldline diagrams! It gives a nice exposition of the relationship between energy and momentum, and why it's a valid approximation to add velocities together in classical physics. As someone doing a PhD in particle physics, this is a very helpful picture to have in my head when thinking about these concepts.
I would just like to clarify that the statement made at 11:24 does not literally mean that the speed of light is infinite (which would be in direct contradiction with statements made earlier in the video). Instead, from the perspective of a massive observer, reaching the speed of light becomes harder and harder the faster the observer is moving. The massive observer would require an infinite amount of energy to accelerate to the speed of light, so light can be thought of as infinitely fast, since no massive observer can reach its speed (even if they accelerated for a very long time).
but, from the point of view of the traveller, wouldn't his time to reach arbitrarly distant point get shorter and shorter, so - for him - it would be like accelerating to infinite speed? Like a mion created in collision in upper atmosphere from cosmic ray/air molecule interaction can reach Earth's surface, because it has no time enough to decay (in its reference frame)? Of course system at the distant point would evolve quicker and quicker, so when we arrive, it's like we were travelling slower than c, but for the traveller - it took only short time, like he was way beyond c?
I must admit that I find the explanation of why we cannot travel faster than light using relativistic dynamics quite unsatisfactory. I mean, it's not incorrect to state that we would require an infinite amount of energy, but we can demonstrate that rapidity becomes infinite without involving any variables related to mass or energy. It's solely dependent on velocity, distance, and time. The hyperbolic properties of spacetime dictate the velocity addition formula, and there is no input of energy in this formula whatsoever.
Light reaches any distance in zero time from its own perspective. The time dilation is infinite, all forward distances have shrunk to zero.
This is the first time I've encountered the concept of the electric field being a rotation through time, but that makes such perfect sense! I've never had much of a problem with Relativity, but I've always found electromagnetism to be a bit puzzling. This clarifies so very, very much about it! Thank you.
One thing this channel severely stands out compared to other educational channels is that it always answers the question "But how?" and in extra detail.
I think this is the best relativitity video on the channel by a mile. In all the stuff I've seen about relativity, I've never heard the Lorentz transformation described as a rotation, yet that simple notion makes its application and effects remarkably intuitive.
The greatest benefit comes from the two unifications described in the video. When the magnetic field is described as the reletavistic effects of the electric field, it makes sense but it seems to fold the magnetic field into the electric field rather than justify an electromagnetic field. However, the idea that the two are time- and space-domain versions of the same thing fully justifies the merged name - neither is the 'real' field.
I need more
Can someone tell me why my idea wouldn't be a good one? I assume it wouldn't be a good one because I have never heard anyone explain it like this.
To my mind, to explain relativity, one must first imagine what an atom looks like. It would be a combination of wave fronts originating from the various quantum fields. So, ignoring the Higgs mechanism for a second, I imagine an atom as "buzzing" incredibly fast, like you often see in animations. That "buzzing" is the atom evolving as it interacts with itself and other atoms. It evolves through time like this. Now, I imagine a molecule made up of atoms, which still has the "buzzing." So, imagine a massive object sitting still. It would just be buzzint about, evolving through time. The key is that these wavefronts all move at the speed of light. It is the combination that results in an atom that isn't moving at the speee of light. So, if you take that object, accelerate it close to the speed of light, those wavefronts can only move one speed, so the movement of the object borrows some of that speee for translational motion, with all atoms moving in the direction. So, less speed can be used for the "buzzing" or evolution of the atoms. So, when the object is close to the speed of light, the buzzing will actually slow down. At slow speeds, the buzzing barely slows rown because little of the constant speed of quantum field oscillations is being used for translational motion. But at high speess, the atoms all barely buzz or evolve through time, so the objects ages much more slowly. This visual image helps me tremendously. Does anyone else think of it like that?
@@ElectronFieldPulse I don't think your idea is a good one because it fundamentally misunderstands the context relativity comes from/exists in. From what I gather, you're trying to invent a quantum, physical origin for something that is fundamentally not physical in that sense. Relativity isn't an effect of any physical process but rather an operating principle - its like a conservation law.
Relativity derives itself from a set of very simple principles/observations. Special relativity comes from two:
- The laws of physics are the same in all inertial (non-accelerating) frames of reference.
- The speed of light in empty space is the same in all inertial frames of reference.
With just those two ideas, one can derive all of special relativity, including all the geometry in this video, as they are the transformations that respect those postulates.
@mekafinchi - Yes, that is exactly what I am saying though. Light is an excitation in the electromagnetic quantum fields. Your body is made up of atoms which are made up of excitations in other quantum fields in addition to the electromagnetic fields. Those propagations in the fields all move at the speed of causality, or the speed at which field propagation travel with no mass. So, it is a conservation thing. Those field propagations, be it a photon or the gluon, will only travel at one speed. So, when you are sitting still relative to something traveling close to c, your field propagations are all evolving your body through time. But for the object traveling close to c , those field propagations have to move with the object, meaning most of their speed is used for translational motion of the massive object. The speed that is left over constitutes the "clicks" of the clock being slowed way down, because the wave only has a little bit of speed left to interact with other waves in the atom. The speed of causality will either move the atoms forward in time or forward across the universe, the only difference is one is a local interaction bound by the forces of the atoms, so that speed is entirely local and aging the atom. Do you get what I mean?
@@ElectronFieldPulse From what I gather you're trying to explain time dialation via quantum fields.
While what you're saying does make some sense, it still misses the point I was trying to make, that relativity is independent of the physical system it is constraining. Importantly, this means that the effects of relativity will apply regardless of the system, and do not originate from any part of that system.
I've been binge-watching Andrzej Dragan's videos for the past few days, and during that time, I was also searching for a visualization of hyperbolic rotation of spacetime, but unfortunately, I couldn't find any. And boom... here it is :) Thanks!
Fun fact: In ordinary conditions (as described by Galilean transformation), speeds simply add up, following the equation V = (v₁ + v₂). However, when employing Lorentz transformation, the speed calculation is more complex and given by
V = (v₁ + v₂)/(1+v₁v₂/c²).
Now, if we consider measuring the angular speed (rapidity) in spacetime, represented by tanh(θ) = v/c, we can derive the equation for rapidity is
θ = arctanh(v/c). As a result, we can express V/c as
V/c = tanh(artanh(v₁/c) + artanh(v₂/c) + artanh(v₃/c)+...), allowing for the addition of multiple speeds. Nevertheless, this sum will never reach V/c = 1.
this means if a spaceship moving at v₁ fly out another spaceship moving at v₂ then flying out the spaceship moving at v₃, each moving at half the speed of light relative to the previous spaceship, the total speed is only tanh(artanh(0.5)+artanh(0.5)+artanh(0.5))c = 0.9285714c
where did u learn this? does it mean that the thetas simply add up?
@@lucasf.v.n.4197 Exactly!
Although speed does not add up in the traditional sense under relativistic conditions, rapidity still does.
this is also why most of our formulas about speed, time and lengths don't work anymore/get inaccurate when we reach more than 1% of the speed of light.
on our slow speeds that human can reach on earth the distortion inside the space time diagram is so little that the inaccuracy in the measurment is bigger than the impact of the transformation and thus it get's simplified to a simple addition.
@@lucasf.v.n.4197 I learned it in the video title :
"The Speed of Light is Infinite... Kind Of" Science Asylum
for teachnical details, look for Minkowski's geometry.
Much like how adding angles can be simplified by multiplying complex numbers, adding hyperbolic angles can be simplified by multiplying split complex numbers. α(c + vj) = (c + v_1j)(c + v_2j), for some scalar α that can be found without too much difficulty from the magnitudes of the two inputs.
Also worth mentioning is the small angle approximation: sin(φ) ≈ φ for very small φ. (This is why anyone could've ever been convinced that the Earth is flat.) This applies for hyperbolic angles as well: sinh(φ) ≈ φ for very small φ. This means that when far below the speed of light, speeds do appear to add like in Galilean Relativity.
Excellent video. I loved how you mentioned the connection between electric and magnetic fields and energy and momentum
Can someone tell me why my idea wouldnt be a good one? I assume it wouldnt be a good one because I have never heard anyone explain it like this.
To my mind, to explain relativity, one must first imagine what ah atom looks like. It would be a combination of wave fronts originating from thr various quantum fields. So, ignoring the Higgs mechanism for a second, I imagine an atom as "buzzing" incredibly fast, like you often see in animatioms. That "buzzing" is the atom evolving as it interacts with itself abd other atoms. It evolves through time like this. Now, I imagine a molecule, made up of atoms, which still has the "buzzing". So, imagine a massive object sitting still, it would just be buzzint about, evolving through time. The key is that these wavefronts all move at the speed of light, it is the combination that results in an atom that isnt moving at the speee of light. So, if you take that object, accelerate it close to the speed of light, those wavefronts can only move one speed, so the movement of the object borrows some of that speee for translational motion, with all atoms moving in the direction. So, less speed can be used for the "buzzing" or evolution of the atoms. So, when the object is close to the speed of light, the buzzing will actually slow down. At slow speeds, the buzzing barely slows rown because little of the constant speed of quantum field oscillations is being used for translational motion. But at high speess, the atoms all barely buzz or evolve through time, so the objects ages much more slowly. This visual image helps me tremendously. Does anyone else think of it like that?
Hi I make videos about science. If you are a science enthusiast too, please review my channel ❤
This is THE BEST video on relativity and Lorentz transformations. You have a remarkable ability to explain the intuition behind concepts in physics without sacrificing precision. Many analogies abandon the rigor in order to demonstrate an idea, but you manage to distill such difficult material into a simple and intuitive understanding so that when one DOES learn the mathematics, they know where it goes. Top-notch content, bro.
This is already the most underrated channel. But it just keeps on surprising me...
I think what this channel does better than any other, is to connect the explanations to the leaps of intuition, all in layman’s terms.
Best explanation of a spacetime diagram! I am speechless with how amazing and visually appealing it is! Your channel is like a 3b1r of physics.
At 8:53, I was genuinely shocked when I had long believed that "cτ" represented the spacetime interval. It wasn't until recently that I came to realize the spacetime interval does not signify the worldline; rather, it denotes a 4-position vector in spacetime. The magnitude of this vector remains constant along the hyperbolic path of an accelerated observer, while proper time continues to elapse in Rindler's coordinates.
Exactly, few of these science channels are actually scientific and do the topics enough justice explaining them in a relatively short time.
It's hard to come by these in the flood of entertainment-science shows and channels.
Your channel is the best science channel hands down. Nobody comes close to making these concepts intuitive in the way that you do.
I have watched every video you’ve made. This one was by far the most impactful. As a mathematician, doing the various transformations was trivial. But this is the first time I ever heard the word rapidity and it crystallizes everything in place in just a few seconds. Rapidity adds in spacetime. My goodness how grateful I am. Octave Masson’s voice is hypnotic.
Finally I understand the Lorenz Transformations we learned in class! Thank you so much, always a pleasure to see one of your videos!!
The animations make difficult to grasp concepts much clearer. I wish we would have had these animations back in my school days. Thank you for this great work!
Especially the part abt hyperbolic rotations is explained in a few minutes, taking the essence out of a rather complex mathematical problem, BRAVO !!
Science explanations don't get better than this! Even if another science presenter put an infinite amount of effort into their similar video about this topic (which itself is obviously impossible), it would only approach but never exceed the brilliance of this explanation. I just always feel sad when your videos get close to the end, and I wish for many more of them, as the entertainment derived from them does add up in a Galilean sense.
No way, I've been rewatching some videos now for an hour and a new one drops, nice
As someone who did not study a science degree but was always fascinated by astrophysics documentaries, thanks to this channel I have finally begun to truly understand those concepts, so beautiful but difficult to conceive in my mind as real things.
After having heard a thousand times talk about relativity in simpler terms, I feel that finally someone is helping me understand it in a slightly greater degree of detail and complexity. Thank you!❤
Always exciting when Scienceclic uploads (:
Man, wish we'd watched this video before we'd made our spacetime metric one, and were struggling to figure out what exactly the hyperbolic angles in the metric tensor were supposed to represent! Another compliment for your visuals -- they are rapidly approaching an art-form in terms of consistency of look, ease of digestibility, and conveyance of mood. (We know cause our visuals are always all over the place, lol.)
This is most supremely the mathematician's view of reality, and as such it carries the mathematician's elegance. But our ontological approaches are a little divergent, and our next video tackles a similar topic, but from the completely opposite viewpoint, so let's have at it 🙂. When you say it is shocking that the speed of light is invariant, may we ask why? To measure the speed of light, one first needs rods (distances) and clocks (time). But to have clocks one first needs light to define light-clocks, and to define rods, one first needs light to define two-way light measurements (one-way light measurements being highly problematic) from which rod-lengths can be deduced. So are we not measuring the speed of light via the instrumentation we defined through the speed of light? In this sense, would it not seem intuitively necessary that the speed of light be a given constant?
We also neglected to respond to your statement about the reality of spacetime in your last comment, so we'll tackle it here: the spacetime manifold is a collection of "world-events". Insofar as we perceive world events to be objective, the spacetime manifold constitutes the reality of all "happenings" and is therefore of course real. But as to the statement "space and time aren't real but spacetime is" this again seems to be linked to the problem of defining time through space. We define the ticking of a light clock based on how much space a light beam has to traverse in a given clock, and in different frames that amounts to a different amount of space. So if we want the ticking of a local clock (the spacetime interval) to be the most "real" thing, then naturally we have to relativize our judgements of space and time. But there are other viewpoints we could take, in which we could discard the idea that local proper time is the most "real" quantity, and so in which perhaps we don't need to make such judgements at all... hint hint, wink wink (a plug here for our next video).
Hey there. Big fan of your videos. Can't wait for more 😀
Infinite rotation makes sense when TIME is one of the dimensions involved. Since you can't "return" to the past, you keep rotating indefinitely and always end up somewhere different. It might be the same *place,* but it'll always be a new *time.*
If u truly got it, pls help me understand 🙄
1) How come the light slows in water, even though it has constant speed?! 🙄
2) If time inside a black hole is nearly frozen, does that mean the time in early universe was extremely slow too, which means the true age of the universe should be much bigger! 🤔
@@duran9664 When light enters a medium, the electrons in the medium are disturbed by the electromagnetic wave, leading to the exertion of forces on them. These forces cause the electrons to vibrate, and vibrating electrons act as accelerated charges. Consequently, they generate their own electromagnetic wave. This second electromagnetic wave combines with the electromagnetic wave from the source, resulting in a new electromagnetic wave with distinct properties. This phenomenon is known as wave superposition. The velocity of the individual wave is referred to as the phase velocity, which remains constant.
On the other hand, the velocity that is slower than light is the group velocity, representing the velocity of the combined wave, which moves slower. However, it is essential to note that the speed of light (phase velocity) does not slow down even in a medium.
Allow me to further elaborate on this concept. When scientists mention "the speed of light," they are referring to the maximum speed of causality. This speed is unrelated to light itself and represents the maximum rate at which information can travel, encompassing gravitational waves and gluons, which also move at this speed.
it seems your own understanding of physics has evolved with the years. your videos from the last couple of years are much better than your earlier ones. i guess you started run of the mill, but now your videos truly excel, in depth, insight and clarity. IMHO, yours are now among the very best of youtube. congrats and keep it up!
I already know all of the effects that you show in your videos, but you are always able to give me new details that I didn't know or could not connect properly. thanks for that!
Excellent! Best explanation that I've seen.
One of the best explanations i have seen about Lorentz transformations, academically accurate and user friendly at the same time.. I also subscribed to PBS Space Time, i gathered more data from there but never at this simplicity level.
I saw basically all videos to find good intuititive ideas about the topic. Your video is the only making such a polite and yet powerful analogy for special relativity in EM (E field as hyperbolic rotations... wow man, that's what I still missed yet after all this time researching). I really appreciated it
Man, you're the best! All those professors talking stuff which I can barely grasp, but you're bringing clear animations. Excellent 👌
This channel is literally among the 3 best physics channels (next to Kurzgesagt and Veritasium) if not the best at explaining really hard and complex topics in an easy way, so everyone with or without a physics background could get a grasp about all these amazingly interesting facts! 🤓👏👏👌
Please never stop 🛑 teaching us to comprehend a little better our wonderful universe 😁👏👏👌
This was an awesome video. You have the best animations of these concepts that I've seen anywhere.
Absolutely brilliant!! Your explanations are so thorough and yet so accessible!! Thank you!!!
Applause for educating... requesting to do video on condensed matter (Visualizing it, with quasiparticles)
I agree
Thank you for your wonderful animations! It helps me build an intuition for the math that stands behind it. Good work!
As someone who's always been curious about the fabric of spacetime and how it behaves, this video has been an absolute eye-opener. The visual aids and clear examples helped me grasp the essence of these transformations better than any textbook ever could. Kudos to you for making advanced physics concepts accessible to curious minds like mine. Can't wait to dive deeper into this mind-bending realm and explore the wonders of the universe! 🌌💫
great admiration also to the narrator! excellent voice, perfect english and accent/tone! perfect combination of expertise, narration and perfect music type/volume/vocal balance
I now see how poorly I previously understood these concepts. Thank you for these intuitive descriptions.
finally you made the video I was waiting and asking for for years. thank you.
This is the best description of this topic I've seen. Nice work.
This has to be my favorite channel on UA-cam. I just wanna say you guys are awesome, remarkable. I love your visuals and LOVE the background music! I show my family your videos all the time and continue showing them even though they don't understand half of it LOL. Your video about what we would see approaching the speed of light is my favorite video on the internet, so awesome and fascinating! Superb work guys!
Nicely done! I’m normally a stickler for every nit picky detail I can find in these videos, but this one was absolutely perfect.
If u truly believe it’s absolutely perfect, pls help me understand 🙄
1) How come the light slows in water, even though it has constant speed?! 🙄
2) If time inside a black hole is nearly frozen, does that mean the time in early universe was extremely slow too, which means the true age of the universe should be much bigger! 🤔
@@duran9664 The phrase “speed of light” is kind of misleading. It really means “speed of light in a vacuum.” Also, light technically has nothing to do with it. It’s more like a “speed of causality,” which all massless particles happen to travel at. But it’s the maximum speed at which anything can ever appear to causally influence another.
@@duran9664 As for black holes, that’s a General Relativity question which extends beyond Special Relativity. But for what it’s worth, I’ll give it a shot…
You can’t think of time as this fixed, universal thing. There is only the apparent flow of time as measured by clocks in various frames of reference. When we speak of the age of the universe you have to imagine a clock floating in space, ticking away since the Big Bang. If such a clock existed, it would indicate about 13.7 billion years having passed.
I cannot stress how much I love your channel. As a 16 year old with limited access to advanced courses these are like having the teacher I never had. Thank you.
To fully understand time and space, I have been watching this channel for many months, although I didn’t like physics at school. the music and voice of the narrator of this channel makes videos filled with fascinating mystery and a mind-boggling understanding of the mystery of the universe. I going watch this video again tomorrow
Love this! Clear and concise explanations with meaningful animations. Thank you.
After watching this video you should need a few minutes to gather yourself while the flood of revelations begins to subside from your mental illusions being blown away by a tsunami of enlightenment.
I've been studying this stuff for 50 years and this was the most lucid explanation of spacetime that I have come across. Absolutely wonderful. Thank you!
This analogy works one-to-one with math itself between trig functions for circles and hyperbolic trig functions for hyperbolas, especially when complex numbers are used.
These videos put mindblowing concepts into such understandable visualizations.
I tell everyone I can about these!! Thank you so much!!!
This was very good. Especially the way you walked us through the history of Galilean transformations towards Lorentz. These things are always easier to understand if there's a historical context - the logical steps from one realization to the next makes more sense.
YESSSSA my favorite science channel back at it again, explaining the most convoluted concepts in extremely intuitive way.
So excellent ❤
Wow... I like it, you introduced concepts which are never shown in others GR/SR videos. Rapidty, how energy can be "viewed" as time, momentum as space, electric and magnetic fields.... Really nicely done. Huge applause!
Amazing animations. Amazing and simple.
🎉🎉finally new video
this and Arvin Ash are by far the best UA-cam channels on these subjects. thank you for the work you do, and the knowledge you share. much love.
Idk how I've never heard of this channel but y'all are top tier.
Best graphical explanation I've ever seen (and I've seen quite a few). Added to "Favorites".
Dichronauts by Greg Egan really helped me visualize this
How about the speed of light in an expanding universe
filthy
Hi 👋👋
Thx a lot for the videos
They gave me motivation to pursue physics research
Today I am starting my college
Thx again for showing me the treasure physics has to offer
😊😊
Nice I’m starting out my physics degree at college this year too good luck to you
@@deananderson7714 good luck to you too 👍👍
Your channel is literally the best on UA-cam, for real!
Best visual representations of the subject so far, truly incredible work!
Finally my wait is over !
I think it’s time to migrate your slides and graphics to dark mode. Some of us love watching your content in bed at night
Probably the best science channel on UA-cam
Superb presentation - especially the second half and the section relating to rotations and unifications... On my watch again list! Many thanks for posting👍!
You are criminally underrated...
You need to upload more often
For me personally these videos are a spiritual experience
Exactly what I needed to hear today! Brilliant job! Well done! Thank you for sharing.
You have a deep sense of the fundamentals… its exciting to watch… the second half over n over n over.
Wonderful
Love these videos
要知道你在中国🇨🇳也有粉丝！❤
谢谢，我很开心你喜欢我的视频！
This channel is AMAZING!
These animations are truly amazing! What a great channel
STOP CENSORING
What do you mean?
OMG! After a lifetime of trying to understand this stuff, your video is like someone turning the lights on in a room I didn't know was dark! Thank you!
ABSOLUTELY CLEAR AND SIMPLIFIED TO UNDERSTAND
Never had such an intuitive explanation of relativity. These explanations are so powerful to visualize the geometry of spacetime
Science is so easy when you understand what and why equations represent.
such a clear and simple explanation
Short and deep. Loved it!
Brilliantly explained. These guys and Dialect are all you need.
Incredible animations and simulations! I love all your videos and can't wait to watch the next ones.
I'm blown away by this channel every single time!
I'm blown away at how well detailed this video is, especially the hyperbolic info graph regarding 'rapidity'. This channel always contains great content 🤯🔥
Alessandro your videos have taught me so much through the years and I just wanted to say thanks, looking forward to many more
PERFECT!
This channel has the best videos on the entire internet!
This video was incredible! I love this channel.
Brilliant video with tremendous animations! Thank you!!
You guys use excellent graphic representations that significantly increase my understanding. Thank you.
Beautiful videos and explanations!
Thank you for explaining it in a way that it's easier to understand.
Fascinating! Between the pictures and the way it's explained, I understood everything. This channel rocks!
Absolutely fantastic visualisations. Really useful for someone like me who has trouble with the equations, being able to picture these transformations in this way really helps.
Kudos to the people/person who made these graphics. This must've taken a long time to wrap their heads around the concept THEN visually make a graph that clearly represents what the heck is going on. This is mind bending.