I believe I know why the RUclips science educators usually avoid this line of reasoning. It took you 30 minutes doing math at a speed which can't be followed along in real time and it requires the viewer to actually do follow along or else the result is "it just pops out of the math"
To be fair, PBS Spacetime does have a video that attempts to take a good swing at it. It’s actually the one that inspired me to make this. When I saw the original paper they cited, my jaw dropped at how simple it was.
I kinda agree, the math are quite hard to follow in a "youtube" fashion. Also, the peak of the presentation, the C = 300M m/s is kinda rushed and dropped like "If you experiment, boom there it is". What are the experiments ? does it involve light ? So why not just speed of light then ?
@@ThePiiX In my defense, the video is not exactly a proof that "c is finite." It's a proof that c has nothing to do with light. If you want to prove that final piece, we can absolutely do it. I just need another 20-minute video to get there. :(
@@AntiCitizenX, no no no it's not a critique of that, I was just overwhelmed by the math and the conclusion looked rushed. Like How do you find THAT particuliar number, you measure light ? There are other factors that just align ? G ? plank length ? May be I wasn't paying enough attention. I'll watch it again, well rested. I'd love to see more videos anyway.
Why c is called the speed of light is an artifact from the fact that this peculiar behavior was first noticed in Maxwell's equations, where c is the speed of the propagation of electromagnetic radiation, and that speed worked out to be identical to the speed of light. Thus, light was reasoned to be a form of electromagnetic radiation, and the name "speed of light" was attached to c. Ie, c was already the speed of light and then it was also found to be the speed of causality.
@@mrjdgibbs Yeah, but it wasn't attached to light because light is swift. C is also used for the speed of sound, if you're working in the context of acoustics or fluid dynamics. It is customary to denote the speed of wave propagation in a medium with c.
Do you think it is worth a video on how Maxwell’s Equations imply a universal speed limit? It would require a lot of vector calculus to do it justice. Not sure how the audience would react to that. “Take my word for it! These upside down triangles prove the existence of a universal speed limit!”
@@AntiCitizenX That depends on how deep you need to understand vector calculus. If you just need a good pair of waders, I say go for it, guiding the viewer through the thorny parts. It it's long and painful, then I think you'll need a few videos, with a few interesting partial results as stopping points - if you do it at all. If there are no interesting partial results, I'd say forget it and save the derivation for the advanced students.
@@AntiCitizenX Definitely .. though, of course, by convention of mere human assumption, I presume .. not infinitely. Indeed, I am not at all sure my ability to do sums would get me that far, let alone swiftly - measured at a constant rate, e.g. of falling sand grains or heartbeats. Yey! ;o)
Errata: Yes, I am fully aware that I played fast and loose with the special case of the Galilean transformation. The primary goal was to show that we can derive the Lorentz transformation out of basic assumptions, thus showing how the universal speed limit is not tied to the concept of light. However, I did oversell the case, and I fully acknowledge that. But it did give me an idea for how to handle it in a more convincing way. I think I may re-edit this video and upload a revision in the future that makes the case more convincingly. Stay tuned. Also, I screwed up a step early on. You cannot just swap denominators like I did. I thought I was applying the equality of mixed partials, but that doesn’t apply in this case. Instead, a far simpler proof is to just assume the homogeneity of space and time (which is arguably implied already by the principle of relativity). So the proof still works, but that step needs some fixing.
I think you did an excellent job that most people can not do in physics today and that is make it simple and easy to understand I understood every thing you are saying even though I know there are more complicated explanations
Because those complicated explanations are built on those basic principles present in your video and those basic principles are the backbone that many people fail to realize that are evident and in play when it comes to such difficult equations you got to start from somewhere and surely einstein did not just immediately write down his magnum opus without first consulting lesser equations that made him ponder
A lot of the criticisms on your video i have read are illogical and unfair and it is sad because they seem to know so much about this topic that I cannot see why they do not see the implicate simplicity in such a brilliant equation its really disappointing
I have a question here. Im not particularly trained in relativity but I understand basic Physics and advanced Math. In this video, you are using light/vision as the medium to make observations. If we imagine a universe with no light and only sound and we make our observations using sound, it looks like the speed of sound will be the speed limit. Also, how do we know that the speed of causality is the speed of light? If weve been making experiments with speed of light as the limiting factor then it will be the limit of our experimental results. How do we know we just havent found something faster?
There was a tricky assumption that I don't think was stated explicitly but still played a big role in the result: You replaced v₁F₂' = v₂'F₁ with v₁/F₁'= = v₂'/F₂'. By dividing by the Fs, you implicitly assumed they weren't 0, but _could_ they be 0? If we considered the case where they were both 0, then you would get the Galilean result derived at the end from an infinite speed of light, but without the dubious construction of inserting an infinite value into the equations. Interestingly, the case of a = +c² is the case where time behaves like a spatial dimension. This, along with Galilean relativity and Special relativity form the 3 possible geometries of a 2D system: spherical, flat, and hyperbolic respectively. As for _why_ Galilean Relativity was so widely believed, it's actually the same reason as why some people believe in a flat Earth. They both come from the same geometric source: the small-angle approximation. One is a very small spherical angle, and the other is a very small hyperbolic angle, but both are very difficult to discern from flat lengths at very small scales, and compared with the size of the Earth and the speed of causality, human scales are indeed _very small._
The special case is just the Galilean transformation, which was talking about in the end. It's also hardly an "assumption" to call it wrong. I just didn't want to spend another 20 minutes dealing with it, because it wasn't exactly the point of the video. I might rectify that in the future, though. I think I have a straightforward way to eliminate it.
🎯 Key Takeaways for quick navigation: 00:00 🌌 Introduction and Challenging Common Beliefs - Exploring the concept of the speed of light and questioning the common understanding of it. 04:43 📜 Four Assumptions: The Foundation of Special Relativity - Introducing the four fundamental assumptions that underpin Einstein's theory of special relativity. 10:28 🔄 Transformations and Matrix Notation - Exploring how coordinate transformations are essential and introducing the concept of matrix notation. 17:17 🌐 Transformation as a Mathematical Group - Discussing transformations and the mathematical group properties they must adhere to. 19:27 📡 Lorentz Transformation - Unveiling the Lorentz Transformation as the fundamental result in understanding the relationship between space, time, and motion. 22:55 🚀 Misnomer of the "Speed of Light" - Addressing the misconception about the "speed of light" and suggesting a more appropriate term: "speed of causality." 22:56 🚀 Velocity Addition Formula - Explanation of the velocity addition formula in special relativity. - Velocities do not add linearly; instead, they follow a specific formula. 25:12 🌟 The Universal Speed Limit - Introduction to the concept of a universal speed limit in the universe. - The value of the universal speed limit is approximately 299,792,458 meters per second (the speed of light). 26:06 🌀 Galilean Transformation - Discussion of the Galilean transformation as a simpler, intuitive answer that we might have expected. - The Galilean transformation is applicable when speeds are much smaller than the speed of light. Made with HARPA AI
I never got the impression of anyone telling me to suck it up and just accept the the speed of light exists or anything. Or that there wasn't a reason. Certainly not in the sneering, insulting voice you ascribe to them. It's just that for most discussions, that is a simplifying axiom.
@@AntiCitizenX people told you the sky is blue when you were a baby, did they even stop and derive the Rayleigh equations so that you could have a grasp of why it was ? What useless parents..
@@kalisticmodiani2613 I’m pretty sure that your average college student taking a first course in modern physics for scientists and engineers can handle a little calculus…
@@kalisticmodiani2613 If I was taking a physics course on optics and scattering, then yes. I would expect to see the equations. You seem to be under the impression that this derivation is both well known among physicists and yet too complex for college students to handle. That is simply false, my friend. It is very simple to follow, yet conspicuously absent from the textbooks. Your antagonism is therefore very confusing and misplaced.
My math is very rusty so I had a hard time following. I think an example with numbers that we came back to after every derivation would have helped illustrate what all the expressions mean.
I'd like to think my math isn't too rusty yet, but it still took me multiple slow watches to get it all right. Having gotten an understanding, I'm not sure a numerical example would be of any use. There's just a lot of details that he kinda glosses over. You just gotta think of it from the perspective of trying to eliminate all the unknowns by using cases where we can easily derive what the unknowns are.
Thank you, that was really well argued. While my math is too rusty to follow the details, I was able to follow the argument. As a science fiction writer, the only lattitued is to change the assumptions... ;-)
This has been one of my absolute favorite YT channels for years. Your philosophy series is a cross between Cooking For Engineers and Philosophy For Dummies and every installment is pure gold with the best signal to noise ratio in the community. Can't wait for what's coming next.
This video was utterly inspiring. Even so far as engineering graduate school, I never had a professor talk his way through the logical implications of a derivation. I watched mathamagicians move symbols on the wall, but nobody ever rationalized the process thus. Sadly, my brain is not one that derives a great deal of understanding from the raw algebra. It's nice to see that there is an alternative. Thank you!
Thanks for making this video. I remember watching PBS SpaceTime's video where he explains how Lorentz transformation is the only thing that makes sense and linked a paper in the description which shows how you can derive Lorentz transformation without assuming constant speed of light. Couldn't understand the paper at all but I've been curious about it ever since.
This is an elegant derivation of the Lorentz transformation. I really do like that it doesn't presuppose anything about the speed of light. There does seem to be one thing you've neglected in your presentation though, and that's experiment. We know this is correct (for appropriate contexts) not because the math is elegant or because it agrees with our assumptions but because it agrees with experiment. Furthermore, as strange as it may seem to presuppose the constancy of the speed of light, there is a good reason to do so. We had observed it. Physicists had expected the observed speed of light would depend on the speed of the observer relative to the source and found that not to be true.
@@AntiCitizenX prior observations can serve as the foundation for a theory, but the true test is how its predictions agree with experiment. We have a great many mathematically elegant theories of quantum gravity, all of which agree with prior observations. At most, one of them is right. Similarly, we don't believe special relativity because the math is elegant and it agrees with prior observations. We believe it is right (within the contexts for which it was developed) because it makes testable predictions that have been confirmed by experiment.
@@allanjmcpherson Please point out the exact moment in this video where it was ever said or implied that we should believe in special relativity out of respect for mathematical elegance, and NOT because of empirical data.
A few other related things: 1. The "speed of gravity" is equal to the "speed of light" to within an error of less than 0.00000000000001% based on the observations a pair of neutron stars merging by the GW170817 and GRB170817A events. 2. Lorentz, Poincaré, Fitzgerald, Larmor, et al. had figured out this transformation, length contraction, time dilation, and a constant propagation velocity for light waves from within a model of space being filled with a "motionless" incompressible dielectric material (that didn't effect the motion of planets and stuff) which could never be measured. It was a big complicated mess... which gave you the exact same results as Einstein later derived from the single assumption that the propagation velocity of light in the vacuum, when measured from an inertial reference frame, is the same for all inertial reference frames. All this tedious mucking about with an unobservable aether was unnecessary. I speculate that the reason why many popular explanations of Special Relativity are so muddled, is because for the first half of the twentieth century, all the popular explanations of Special Relativity were the same old explanations of Lorentz's aether theory with the word -aether- crossed out. Which immediately makes the listener ask: Why isn't there an aether? Relativity needs to be presented in its own terms to be understood without actually doing the math. (I have a long rant about how terrible most popular science explanations of Quantum Mechanics and Relativity are, but anyway...) (I'm trying to avoid writing a long explanation of Special Relativity right here in this comment.) 3. Looking at some of the other comments on this video, yeah everything is always moving "at the speed of light" in some amount of "space" and "time" which are not distant separate things... ok I'm going to try to make this comment short.... historically the concepts of space, time and velocity were kinda backwards. When you hear: "speed equals distance divided by time" v=dx/dt it makes you think that time and space are separable things, but the problem is that we can not directly measure either time or space; we can only measure "things moving around" and work backwards from the velocities to figure out what to call "time" and "distance". Earth goes around the sun, that's a year, pendulum swings back and forth, that's a second, fly from New York to London at some velocity in some amount of time you get distance, etc. etc. etc. There is *only* velocity. Velocity is a function of three variables, three of your favorite space-like coordinates, and one time-like coordinate. You only need four numbers to describe the motion of everything in the universe. You can put the motion of everything everywhere into one giant four dimensional block called "Spacetime". Every location in space is also a location in time. You know how when you mix eggs together with vegetable oil, you get mayonnaise. And given some mayonnaise, you can't tell which part is egg and which part is oil? Spacetime is like mayonnaise in this metaphor. Every location in space is located in the past (the negative time direction) of every other location in space. Your feet are about six nanoseconds in the past from your head, and your head is about six nanoseconds in the past from your feet. The Moon is about 1.3 seconds in the past from the Earth, and the Earth is about 1.3 seconds in the past from the Moon. Complex numbers are a clever hack to manage this... because... remember the Pythagorean theorem... you take the square root of a distance between two points... since all distances in time are in the negative direction, you'll eventually wind up with a square root of negative one. (But also, it's just the off diagonal terms of a 2x2 matrix.) This is getting long... I'm going to rush through this, reply with a question if you want me to elaborate... So... people always ask: "Why can't you go faster than light?" and to put it bluntly, all material objects, including the human body, are made (partially) out of light, and so (parts of) you already are, and always have been, traveling at the speed of light... and you can't go faster than yourself. The really interesting question that people should ask is: "Why does anything travel *slower* than light?" The answer is confinement, and it's where inertia (mass) comes from. It's also how Poincaré and Einstein derived E=mc² or, more precisely, E² = (mc²)² + (pc)² which is just the Pythagorean theorem in 3+1D spacetime... I need to get going and stop writing this comment soon, ask me if you want the long explanation of inertia. Some bullet points: Linear momentum and kinetic energy are the same thing expressed in terms for space or for time. No, you don't "gain mass" as you "go faster" (than some unspecified thing). Inertial mass is invariant. You are always moving at *ZERO* velocity relative to yourself. Velocity is meaningless unless you specify *TWO* things for it to be the relative velocity between. Gravity only "sees" inertial mass, that is the only thing that counts for gravity. If you rearrange (mc²) = E² - (pc)² you can see that any extra linear momentum will cancel out any extra energy. Momentum and kinetic energy are are relative, because they are functions of velocity which is relative. p=mv KE=(1/2)mv² Oh! I just remembered why I started this comment... 4. You know how "time is relative" and "space is relative"... do you know what happens to electric charge? NOTHING! This was the entire point of creating the Theory of Relativity in the first place! Well... the moving charges and magnets paradox to be more specific. This is the *actual* problem that Lorentz and Einstein (and Heaviside) were trying to solve and Relativity is the solution. (That's why it's the "Electrodynamics of moving bodies".) So many pop-sci explanations of Relativity completely leave out the entire purpose for the creation of Relativity was to make electricity and magnetism work consistently for all moving observers... And a side effect of electric charge being the same for all observers... is that electromagnetic waves are the same for all observers. That's right, the speed of light is constant! Also, just as energy and momentum are the same 3+1D motion just described in terms of either time or space. So too are the electric field and the magnetic field the exact same 3+1D field described in terms of either time or space.
Everything you said is pretty much spot on. The only thing I would add is that all of this is predicated on the Lorentz transformation being correct. In my experience, this is a major psychological hurdle, which is why I think it is very important to find intuitive derivations. It forces your brain to accept something that is very counter intuitive.
@@AntiCitizenX It's also possible get Relativity from the principal of inertia (and conservation of momentum). It's basically how Galileo, Newton, et al. came up with Classical "Galilean" Relativity. Lorentz and Poincaré were trying to make electric and magnetic phenomena work with relative velocities. The solution that they came up with was time dilation... that is to say, that there is no longer a "universal absolute clock" as Newton conjectured. Even after Poincaré had deduced this theory (modification to Galilean Relativity), he still insisted that the must still be an unobservable, unmeasurable, absolute time (in the "rest frame" of the aether), which we would never know. Then Einstein was like: "The aether is unnecessary", and he gets all the credit now. As I was saying... Relativity is really about inertia. Inertia is really weird when you think about it. An object in motion will stay in motion, moving in a straight line, forever, or until a "force" changes the direction of the straight line path it moves along. Zero velocity is also a constant velocity, so something "at rest" is exactly the same as moving at a constant velocity.... And, things with inertia, resist having their straight line path changed. More inertia means more force is necessary for a particular amount of acceleration. Hang on, I need to do some stuff and can't finish writing a long reply right now...
Well, y'know, electromagnetism is the one massless field whose wave solutions we deal with on a daily basis (unless we work at LIGO), so it's understandable that this would get attached to light.
To help expand the separation between light and the speed of causality is why some things must travel at the speed of causality such as the propagation of massless fields, and massless particles.
Amazing video, this is another example of just how powerful first principles are. One thing, from16:25 onward, we might be able to derive Galilean relativity by setting both F1 and F2 to 0; this would satisfy the condition F1*v2=F2*v1 without having to deal with an "infinite speed of light" (this is mentioned in your source). Edit: I see you responded to an earlier comment about the same thing.
That was how I recall this kind of development going: you set some pretty broad postulates and it turns out that Einstein relativity and Galileo relativity are basically your two choices.
This video is extremely misleading. Relativity has nothing to do with light?! How do you think they made their measurements in the first place… oh yeah, they made them using light signals. 🤦♂️
@@se7964 At least in theory, they can use any kind of measurement. And the thought experiment doesn't assume a measurement method that confined by the speed of light. It is coincident that light travels at the speed of light. And yes, most of our measurement is done by light or electromagnetic waves. But even if we had something faster than light for measurement, we'll still end up with Lorentz transform and when you combine speed you reach a limit.
This is the best explanation of the basics of special relativity I've ever seen, I feel like I'm starting to actually get a bit of a grasp of it way more than with the traditional courses I've taken, amazing video!
"The Speed of Light has Absolutely Nothing to Do With Light" But... why the universal speed limit happens to be equal to the speed at which light propagates in vacuum?
It's been a few years since I took modern physics. Since you targeted this at the layperson, try actually sitting someone down and try to teach them this before making the video. The appeals to intuition you make in the script would probably work better that way.
TL;DW: "the speed of light" is not set because that's the speed at which photons travel but rather it's a sort of universal speed limit that logically emerges from a few basic assumptions that most people would agree with. Light just happens to be one example of a thing that moves at that limit
Thanks for going through the math. While the pop sci videos are great for conceptual analogies, the math is essential to understand too, and too few go through both.
In a nutshell: the speed of 'light' doesn't describe reality, 'reality' describes the speed of light and also the speed of all other events, e.g causality itself. It is just a consequence of historical events that EM waves were the first to describe this 'speed limit'. Technically, if we had had instrumentation to describe the speed of gravitational waves in the 1800s, we would probably call it 'the speed of gravitation' or something today
You sorta snuck something under the rug there. When you argued that v/F is a constant, you implicitly used that F is nonzero. F=0 would give a nonisomorphic group and a different theory, namely Galilean Relativity.
Kinda feel like I understood better when I was reading the blog post. Now I'm just watching numbers and variables flash by on my screen without really getting what's happening. Maybe it's because I read what I could understand in the blog post, but here you're spending time reading out all of the equations that I'm just not getting because I'm not familiar with matrices,* and also calculus despite reading about the theory of it :P I still wonder if I would actually have a use for learning about these sorts of mathematics if they didn't eventually appear in code I'm writing.** Would it be worth it to learn all about it just so I can understand the explanations in this video, or would it be better to just accept what you're saying and move on? And for that matter, would there be any mathematical fallacies or signs of duplicity I'd have to watch out for to make sure I don't fall for misinformation? (Only examples I know about at the moment are lying with visual proofs and lying with statistics, which I probably watched one video each on.) I think a lot of this stuff would be significantly more intuitive if it was also shown visually. Like, the way transforming a transformation creates a new transformation could be shown in two to four diagrams - or an animation (if you're feeling capable of that). I've also seen a lot of graphic animations about why you can't surpass the speed of causality, showing objects moving on paths on grids with one space dimension and one time dimension, and the grids being required to do Lorentz transformations in order to follow along, and the general idea came across to me much better in those than in this video. It seems to be more of a presentation of the mathematical technicalities of it, rather than such an intuitive explanation. So maybe I'm just not part of the intended target demographic for this thing. This video doesn't really make it clear from the outside that it's more math-oriented than graphic-oriented, though, so maybe that's why all the people watching this are getting confused, and why this video might have poor retention (if it does). *After having another look at the script and then checking the video, it turns out you did say I should look it up if I'm not familiar with it. Man I'm such a derp... Still, I supposed it blended in with the rest of the video since frankly, by that point, I was just watching it not being concerned about grasping the material anymore because it already seemed established that I couldn't really follow along without slowing right down and spending a bunch of days familiarising myself with the notation, as well as the points being made with them after that. **And it seems as though my code is still so stupidly simple, despite being long, protracted and doing what it's meant to do, that I often don't even get what people are saying when they talk about good coding practices - maybe just because I haven't had to handle data, server interaction or workflow tools before in any of my current projects - and I can barely follow along on some CSS and JS tutorials and StackExchange answers without asking ChatGPT to explain it in steps in English. For CSS, it could be because the code is long and full of irrelevant fluff I have to cut before I can understand the fundamentals. Also, code seems to be a bit easier to follow along than mathematics. Maybe it's because the variable names have to be longer for you to understand what the code means when it's unfamiliar. And it literally does what it says, meaning you can mess about with it a bit until you understand the relationships between the variables, statements and functions you put in it. Mathematicians prefer to keep things compact and trite. Also, not only am I the type of person to only learn things either when they seem interesting or when I need to know them at a particular moment, but since I got ADHD, I'm also the sort to just unload things from my mind if they're psychologically impertinent. And there's a lot of code I don't even need to understand, because it works and I just want to have a certain feature in my program. I guess I feel that way watching the mathematics in this video; generally, certain concepts are fairly important to grasp, but mathematics just do themselves.
Hey, hello again, wanted to ask you something out of curiosity; what do you think of epistemological historicism? I have a teacher who is pretty adamant about It and, although I find that It goes against pragmatism which, based on my understanding, I agree with, I also find It hard to formulate a simple example of why historicism is incorrect (which basically means I understand what you say on a rather superficial level)
I fell off the math ladder at college level calculus barring me from pursuing engineering and never really came up with any other professional category ..ended up marketing, statistics, packaging. The meaningless squiggles and f circle g etc remain the greatest feeling of lost in my life. I still avoid any thought of advanced math.
I was going to ask why we wouldn't have seen this earlier before we discovered special relativity - what assumption is violated by Galilean relativity? But you answered that at the end well - Galilean relativity is just a special case. Thus, we shouldn't necessarily *expect* to see a speed limit, since there's a possibility that the speed limit is infinity. But we also shouldn't be too surprised that one exists, I suppose.
@@Bendertherobot69420 Galilean relativity plus a finite speed of light _relative to the medium of the ether_ is in principle perfectly viable. But it implies that you should be able to measure a difference in the speed of light relative to an observer depending on the observer's movement relative to the ether, and no such differences could be detected despite physicists' best efforts.
It should be pointed out that Lorentz and others had been developing the mathematics of the transformations for close to two decades before Einstein published his first papers. In fact they were conceived while aether theory was still a thing, and the very name was coined by Poincaré in that same Einstein "miracle year".
The assumption was that F₁ and F₂' in the equation v₁F₂' = v₂'F₁ were non-zero. If they were zero, then dividing by them to get a common ratio would've been an invalid operation, but the resulting transformations at the end would've still worked perfectly fine. Since we checked for a = 0 and determined that it didn't make sense, then it would've been valid to instead use F₂'/v₂' = F₁/v₁ as the constant ratio rather than its inverse.
@@angeldude101 Yes. He simply assumed away the Gallilean case in the Lorentz derivation, without explanation. In fact, the Gallilean and SR transformations are each special cases of the derivation he showed. That is why Einstein *needed* to postulate invariant finite c to explain Michaelson-Morley.
Could you later make a video explaining what cosmologists mean when they say in the future we won’t be able to see some galaxies because we’ll be moving away from each other at “greater then the speed of light”?
the physics and math behind it are immensely complicated, but in short, space expansion doesn’t violate the… speed of causality, and thus space can expand unto itself at any ‘velocity’, ours being rn 67.5 km/s per every megaparsec, which means some object, let’s say 4 441 370 megaparsecs away, will move faster than the speed of causality from us but yeah, the trick is that space expansion doesn’t violate speed of causality, it’s kind of, beyond it on a conceptual level
It’s like a fish swimming upstream at The Speed of Fish (the absolute fastest that any fish can swim through water) in a river that flows faster than The Speed of Fish. Even though the fish makes progress relative to the water, the water’s motion more than cancels out the fish’s progress.
Expansion of the universe is not the event inside the universe, it's the event happening to the universe, hence the expansion rate doesn't have the same limit of causality c. From similar math it also has to have its own "speed limit" but we would need observations from frame of reference outside of our universe to find that value. Einstein described geometry of our universe. We need to guess or assume without any evidence a geometry beyond our universe to scale this thought experiment. And define what "observer" even means outside time-space. Measured expansion doesn't play by this rules, hence we rather assume it's "outside" because assuming otherwise breaks causality "within" violating the 5th assumption of this video.
16:25-16:35: One fun little side note: the assumptions listed still work if we assume F1 and F2 are zero. It’s just that, instead of getting the Lorentz transform, we get the Galilean one. It’s easy to forget we can’t always divide by whatever coefficients we come across in our maths, unless we can prove they are nonzero. I suppose an extra assumption (appealing to real world experiments) could rule out this possibility.
Maybe I’m being too much of a nit-picky mathematician, but it’s nice to know the “dubious” step of setting c to infinity, leads to a result that has some rigorous backing, as it can be reached by checking out the F=0 case.
Great video. The math took me back to my college Calc IV class - with the Linear Algebra, matrices, and such. Oh...eigenvalues eigenvectors, orthogonal(s) Haha. I remember toward the end of the course having a moment where I thought to myself, "why don't they teach some of these fundamentals earlier on?" Would've made 2 and 3 easier...'grasping concept wise'?? I guess. Longtime fan. BTW...did KnownNoMore ever publish his detective novel(s)? Then again, I do have the internets... Keep up the good work!
One of the best explanations I've ever seen. I wish this was the way to introduce this topic physics students like me. One observation, if I'm not mistaken, ignoring Assumption #5 leads to breaking causality i.e. consequences happening before their causes. I feel this part of the argument could've been made more explicit in the video.
The speed of light has absolutely something to do with everything, i.e. it "limits" the speed of everything, including light. The tricky thing to learn humans is not to formulate invalid logic, such as "has nothing to do with" when it actually has something to do with it.
The point is that the actual speed of light could be different from c, the speed of causality. It could be a little smaller and energy/frequency/wavelength dependent. It's actually worse than that: it could even depend on the polarization if the physical vacuum has a preferred crystallographic axis and shows birefringence.
i always wondered, what about if speed of causality is constant but not the same for every observer, or dependes of the distance the event is from the observer. What about if the speed of the causality is slighly different for too far events? Does relativity still applies?
HOLY SHITTING HELL SON WHERE A BEEN?!! I swear, your quick disappearance from Twitter and non-updating here, I was seriously more and more drawn into “I hope he didn’t get hit by a bus” Welcome back, whatever the form you take. 😘
@@electra_ Of course not, but it timed with a lack of RUclips updates, which happened shortly after the channel rebranding update, so… My “bus theory” fear seemed more and more justified.
At 16:31 you assume that F1 != 0 and F2' != 0. The Galilean group, with gamma = 1 and F1 = 0 is a perfectly valid solution. You get rotations with sheers, instead of rotations and Lorentz boosts. So, I'm sorry, but you cannot prove relativity without the assumption of a maximum speed, or something equivalent (for example conservation of the interval (ct)^2 - x^2 - y^2 - z^2 = tau^2).
That’s just the Galilean transformation, which is discussed at the end. It is also very fair to point out that we still have “two” possibilities, but I never claimed otherwise. It just requires you to assume infinite speed for the mysterious constant c. If you like, we can use Maxwells equations to prove that there indeed exists a universal speed for all frames of reference, but the video was long enough as it is. :p
TBF, it is probably more "mathematically rigorous" to say something like "There are two cases, either F = 0, or F != 0", just because having C = infinity is perhaps a little janky. Intuitively, it makes sense though that Galilean relativity is just the Lorentz transformation but with an infinite maximum speed. Either way, we get both as valid options, but we can experimentally confirm that the speed of light exists.
A somewhat pedantic point but I don't think it's quite fair to say you need a concept of 'infinite speed' to obtain the solution described here. If as odysseus suggests we take F=0 from the start, there is no need to go through the rest of the derivation and identify the dependency on a constant c. In this case it's nothing to 'trip over', early 19th c physicists could easily go through the derivation and take the 'intuitive' F=0 solution without giving a single thought to the possible alternative and still have a perfectly consistent theory. In a sense kind of like imaginary numbers, before the need for such a concept arose we had centuries of progress blissfully unaware of their existence or meaning
In essence, physics has it backwards, but it is reasonable. We studied light/EM waves (later photons) quite a bit before relativity, or better put, the nature of space and time. Thus, we associate the symbol c with how fast light travels in a vacuum. But the truth is, this numerical value that has units of a distance over time is just really connected intimately to how space and time work, and how observers translate what they see to each other. It just turns out that what we call light has that value for its speed in vacuum. We just had the order of discovery backward, as far as what is more fundamental.
Answer this: Maxwell calculated the speed of light using permitivity and permiability in a wave equation. Permiability is a magnetic measure, and therefore is a relitavistic effect of charge and permitivity, and it can be calculated from that. Now we find the speed of gravity waves the same, and therefore calculable from electrical phenomena. Should we be paying attention to this? Or, is there an analogous relitavistic gravitational effect that could be used in a wave equation with gravity and its penetration into space to independently calculate c? And might this relativistic effect account for anomalous behavior of galaxies and binary systems that have large rotating mass?
HOW I'M HEARING OF THIS FOR THE FIRST TIME. Thank you so much, I'm actually shocked as to how much sense this makes! I couldn't quite follow along with math, but I'll continue figuring it out.
Now it suddenly all makes sense. Without complicated maths. Special relativity and speed of causality is fundamental to a flat space time geometry. As simple as that. Or physics break apart. Beautiful.
OK this was a great video, but it took me until 25:40 to realise that you're trying to talk about the proof that there is *a* universal speed limit, not why we have that specific number 299792458 m/s. Can you include a clarification at the start of the video? That being said, is there an interesting work on this too?
@@AntiCitizenX It's just that when I hear "speed of light" my brain automatically translates it to "300 million meters per second" so that I have a reference in my head to compare to
@@MenkoDany The term “speed of light” is kind of overloaded. There is the speed at which photons travel through space, and then there is the deeper meaning encompassed by the Lorentz transformation.
@@MenkoDany Yes, that’s technically correct, but it kind of misses the deeper meaning. It’s kind of like saying the speed limit on the highway is the fastest speed that traffic can flow. Technically true, but not really what it means.
Cool, but there is a subtle assumption that you didn't mention. 16:27 I can see that you divide both sides by F1F2, but you can only do that if you assume that neither F1 nor F2 are 0. You say that that the galilean transformation only works if you set a constant (c) equal to infinity, but the only reason you were able to have such a constant is because you already subtly assumed the galilean transformation is wrong! So it's not imposing a "dubious assumption of infinite value for a mystery constant". If you apply this logic, then it's "dubious" to have anything equal to 0. For example, say you solve a differential equation, and it ends up with some parameter a. You could easily be like "well let's set a equal to 1 over a mystery constant b. It's a dubious assumption to say b is infinite" and then that would completely ignore a potential solution to the differential equation!
In math you can't just set something equal to infinity. If F = 0, then there is no such constant c. So it's actually not logically identical. At the end of the video, you said that the galilean transformation is dubious because you have to use an infinity, but my point is that you only have to do that if you already assume it's wrong.
@@Kuvina I didn't "assume" it's wrong. I leaped head-first into the experimental fact that it's wrong. I did so because I didn't want to spend another 20 minutes arguing it from first principles. A bit of a mistake, in retrospect, because I thought of a really simple way to show it (see pinned comment).
Regarding the equation displayed at 18:47, I am trying to understand the dimensional analysis of the 2 terms v^2/a and v/a. In the determinant, one of the terms is -v, so presumably the 4 terms in the determinant are all in units of v. This would mean that "a" is dimensionless, as v/a needs to also be in units of v. Under the square root, v^2/a is added to "1", so presumably v^2/a is dimensionless, meaning that a has units of v^2. This seems like an inconsistency, unless I am misunderstanding something? I will also mention that you go too fast in certain places, equations just magically re-arrange and then disappear before I can digest what has happened. I need to understand the reason for the manipulation, and then the mathematical validity, and then the interpretation. You go at a speed that is suitable for someone who already knows the material, but not for someone who is learning it. This creates an anxiety that detracts from the experience.
The deduction has a flaw:, at 16:34 there is no discussion about the possibillity of Fand F2 being zero. This would have all equations fall back to the Gallilean Case. This case would also be equivalent that 1/c is zero, so the limiting speed is infinite. Az the whole video addresses to deduce that there must exist a finite limiting velocity, it fails to proove it, since it performs a 'division by possible zero'. So the Lorenz transformation deduced from the quite linear Maxwell's equations gives us a hint that F1 and both F2 is not zero.
By the way, despite the above details, the deduction is interesting, and the video quality is well done. It is well worth to fix the above mentioned issus.
Isn't this the definition of Minkowski spacetime? And I have a question: At 13:14, why does t=t'? Because physics are the same in both frames? But you're measuring the time takes for Alice and Jim's heart to beat 10 times? Or do you mean the same amount of time as measured in 2 different frames, for example, measuring 10 seconds using the same clock?
Minkowski spacetime is basically relativity without the gravity. So you’re basically correct. The t=t’ means that two ideal clocks will always remain synchronized, no matter how much you pick one up and move it around. In retrospect, this would also have made a great segue into the wrongness of Galilean relativity. You can actually measure the de-synchronization of clocks after literally picking one up and waving it about.
All good. I just not agree with the complains at the beginning. There are many explanations on WHY it is so. The full explanation is often skipped if the video is not focused on the question
I have yet to see any videos that explain the “why” question correctly. My experience is almost always just a bunch of “well the evidence says so.” None of them ever try to show that it is a logical consequence of very basic assumptions. Even my own college classes on modern physics did the same thing. But hey, if you know any good ones that take it to this level, I’d love to see them. I’m only basing this on my own personal experience with all the popular RUclipsrs and science shows.
1) ruclips.net/video/DGpwkWhnWAI/видео.html&ab_channel=SixtySymbols 2) ruclips.net/video/msVuCEs8Ydo/видео.html&ab_channel=PBSSpaceTime 3) also I was reading some popular science books, where was told, that the speed of light was derived from Maxwell equations (using algebra, not measured) I got that your complain is about always associating the speed of causality with speed of light. I don't think its the big problem :)
@@DjSapsan That first video from Sixty Symbols is a good example of what I'm talking about. They already presupposed the Lorentz transformation. That's a really big pill you need to swallow before getting into the details. So my main goal in this video is show derive the Lorentz transformation from first principles, and do so without appealing to "light." As for that second video from PBS Spacetime... that's actually the one that inspired me to make this one! :D
It's interesting how, going from the mathematical model needing the constant c to function, to it being a way to accurately calculate the speed of light, or the speed of causality. It seemed so arbitrary at first. But I still feel that it should be important to mention that the mathematical model is still an approximation of the real world. Of course we test it, but it never breaks reality in the way it is said it does, it just breaks the model that we have of it
Except any violation of this model must necessarily manifest as a violation of one of our assumptions. For example, in a gravitational field, the law of inertia doesn’t exactly work. That’s a very important insight.
Excellent. Inspired and inspiring. I had to watch a second time, and with pen and paper as suggested at 4:28, and do the math for myself. So it takes a modest "me do it" effort, but I get it -- I really get it.
Well, now I'm wondering why light travels at that speed if that speed has nothing to do with light. If I remember my physics classes correctly, the speed of light can be derived from Maxwell's equations as a combination of a few other fundamental constants describing the electric and magnetic properties of empty space. So why do these two numbers match?
Mass is the conversion factor between force and acceleration: F = ma The more massive something is, the more force it takes to accelerate. So if something has no mass (like light) it undergoes infinite acceleration and instantly moves at the fastest speed possible. All massless particles move at the speed of light.
@@APaleDot That makes sense. Does that mean the magnetic permeability and electric permittivity of free space are in some sense determined by the speed of causality?
Because Maxwell's equations show that electromagnetic radiation will always travel at the speed of light, without any restrictions on which frame you're measuring it in. Thus, based on the principle of Relativity (assumption 2), the speed of light must be the same in every frame of reference. And, if you plug the value c into the velocity formula, you'll find that it always transforms to c, regardless of the relative velocity of the two observers. Thus, the constant "c" used here must also be the speed of light.
Maxwell's eq have an invariant c. Lorentz shows that the non-Gallelean case has a single invariant velocity that is also the max velocity (if accelerating from below it). Therefore (given MichMor experiment) c is the max velocity.
There is an even simpler set of premises in which you can prove relativity. N. David Mermin proved in his paper Relativity Without Light, that you can prove it on 3 assumptions that basicaly boil down to "physics works the same no matter how you look at it." I read it for my college thesis in philosophy of physics back in 2003, then discovered he was teaching at Cornell, WHERE I WAS STUDYING! So I went to his office hours to talk about the paper and make sure I wasn't screwing up the physics in my philosophy paper. That was the first time I learned that top notch experts aren't actually that hard to reach and talk to most of the time, something I have used many times in my career studying law in the decades since.
I’d be interested to see these assumptions. My experience with reading the literature on this stuff is that authors tend to be a little fast and loose with their premises, often taking stuff for granted rather than make them explicit. I looked and found the paper, but it’s hidden behind a pay wall. Booo.
@@AntiCitizenX It is beyond my capabilities to restate the premises now. It was something like invariance due to rotation, invariance due to translation, and something else similar. But I could be misstating it and certainly even if I'm not outright wrong I'm at the very least being imprecise. I never fully understood his paper. That's why I wanted to interview him to ensure I was at least adequately understanding his premises and conclusions for the purposes of how I was using them in my thesis (which was to convince philosophers that it is safe to assume that relativity actually needs to be considered, not really a super high bar as most philosophers accept that anyway).
Wow I can’t believe I’ve found this channel again after YEARS. Was it called something else before, or am I just salted with a terrible memory? Either way I’m glad to have stumbled back upon it.
Dammit, I'd have to brush up on calculus to digest the video. Real science is not as easy as dipping apologists in the substance of their own toughts TwT
Here’s another misnomer performed by hadron collider, especially back about 20 is so years ago when I tried contacting someone there asking how is it possible if an object travelling on one direction (particles) colliding with another object travelling in opposite directions both at estimated to be near if not the speed of light give results equivalent to light speed when it should be results from a collision at C square, same as when testing vehicles in crash testing, when slammed against a stationary object at 50mph the results are that but if the target is also travelling at 50mph then the results are comparable to a collision at 100mph. Now the physics part. Not only would 2 objects at light speed produce results from a collision at c square but there’s other possible results from strathing, strafing, scraping and my favourite which doesn’t result in scatterings but skittering with finite possibilities and more plausible to say is what places like cern have been observing all along since a phenomenon is possible which occurs in the universe at anytime which is particles passing through particles without any detected results other then , if they could get their heads out their you know what, any other results then time. Not unlike neutrinos but possible. Possibilities are a particle of hydrogen would and could theoretically change to its previous or destine state ie reverse or advance it’s priori in that present time. It time traveled in a sense.
Don't get me wrong, I see your point here. But there is nothing in there that forbids c to be infinite in reality. In fact speed of causality being infinite seems like a reasonable assumption and the whole math works out just fine. So saying that it has to be this way, there has to be a speed limit c, seems little disingenuous. It just happens that in our reality assuming the c being infinite would be one too many assumptions.
@@AntiCitizenX - isn't this video trying to prove it's more than just experimental data though? When you say "it is therefore not a matter of hopping into a spaceship and firing the engines" you seem to be saying there's something special about this being logically derived not just the result of experiment - so falling back on experiment at the end seems odd.
@@WorthlessWinner The primary argument of the video is that you don’t need to postulate a universal speed to get relativity. It naturally falls out of the basic concept of space, time, and motion. If you want a further argument that c is finite, then we can do that as well. But it’s kind of an entire video unto itself.
Great argument… really liked it… I think what is left is only few words to add in order to land on the “speed of light”… with extending the concepts used in this video you should easily figure out a relationship between this constant and the energy of the object. Then another extension will yield a relationship between the energy of the object (and hence the c contestant) with its mass. Then the finale! Massless objects has to be travelling at this speed limit C. Hence the speed of light (or any other massless object)! Voila!
Fascinating. But what speed of causality could mean? Any speculations on that? Why is it limited to that value? What's the background of this value? What if speed of causality was 50 km/h? What kind of universe we would have?
@@LachieDazdarian I think you can argue that the absolute scale doesn’t mean anything. If c were “slower” then everything else, including time itself, would also get slower, and nothing would change.
I haven't seen this exact version before, but I have seen derivations of the Lorentz transformation that don't involve assumptions about the speed of light, so it's certainly not something that isn't found in textbooks or isn't taught at universities. I think it would be better to say that it's typically not taught at the undergrad level, even though it certainly could be, since this is all freshman year math (single-variable calculus and basic linear algebra). I suspect the reason it's only taught at higher levels is that a lot of people find relativity difficult on a conceptual level. I've never had that problem, myself, but I've heard plenty of people perfectly capable of handling the math of SR, say that it messes with their heads. SR! Yes, with an S. You read that right.
I have maybe a half-dozen textbooks on modern physics and even relativity specifically, and none of them take this kind of approach. I’m therefore really surprised to hear that you have books and courses that do attempt something along these lines. Would be interesting to know what books you use. For me, the hard part isn’t really the math. It’s getting my brain comfortable with the underlying premises themselves, plus the meaning behind the questions themselves (i.e., what are we asking, exactly?) So in my experience, using a first-principles approach like this is extremely helpful because to forces me to accept the outcome within a clear logical framework. It also forces you to stop thinking of light speed as literally the “speed of light.” It is the fastest speed that the very geometry of spacetime itself allows.
@@AntiCitizenX I can't recall if it was in a textbook or something a professor did on a whiteboard (now that I think about it, I suspect it was the latter). I do remember that in it, c was treated as an arbitrary constant. I think the idea was to show why c is the speed of causality, as you put it, and therefore just happens to also be the speed of anything with zero rest mass, including light.
@@Martymer81 That sounds more appropriate to me. Usually they just assume you’re comfortable with SR before revealing the “deeper” meaning. But that kind of assumes you’re already on board with the whole speed limit concept in the first place.
@@AntiCitizenX Yeah, well, this must have been in the context of SR, because I never took GR at uni. Next time I remember seeing the Lorentz transformation derived properly was in a GR textbook, Schutz probably, but as I recall, he does rely on the second postulate. I may misremember. It was easily a decade ago.
@@Martymer81 How do you feel about a follow up to this video that specifically addresses the possibility of c being infinite? I’ve looked high and low for an intuitive argument against it, but the best I can find is the appeal to Maxwell’s equations. It’s technically valid, but also kind of hard to explain to a lay audience. Plus it falls into the trap of associating c with “light.” I’d love to see a compelling argument that is more intuitively satisfying.
As a fun exercise, I would encourage you to research the Spacetime Algebra and re-implement the same transformations using multivectors in lieu of matrices.
yeah ive read that formulation.i have several of his papers saved in my browser favourites. hes tge real solo godfather of multivector spacetime algera. did he invent it? it does get used by more experimental physicists and chemists outside this relativity physics world though a physics professor hesa real outsider rebel for using the s[aceti,e algebtra multivector approach instead of vectors. also there is one that uses a quaternion formulation instead of the four vector minkkowski used to geometise relativity in 1907-8.that paper is surprisingly by some electrical engineer types from mulriple universities. allsi have that one saved in favourites. i]ll link them if anyone wants? plus there is one physicist, possibly the spacetime algebra godfather who uses this algebra for everything-with the multivectors. time ends up becoming the bivector and so a rotational entiity, which fits nicely with the idea that time was born at the t equals zero moment of the big bang, or the pre cosmic inflation period that preceded the hot big bang st ate that we find in the CMB 300,000 years after.
Thank you so much for this video. I remember somewhat recently going over the history of relativity and wondering "wait how do we know SoL is constant again?". I looked up experiments that would have discovered this and found nothing. Now I know why. It wasn't one big experiment, it was a lot of math regarding obvious assumptions.
@AntiCitizenX point is, this is not an easily googlable answer. So having a relatively (lol) short video explaining how we know this is something I've been looking for.
Look up the solution of Maxwell equations for an EM wave. Speed of light ends up being a function of universal constants, rather than any feature of a particular system. That's why, even if we didn't have SR, we would still know that the speed of light is constant. Michelson-Morley experiment is relevant here as well.
@@omgopet I'd heard about the Michelson-Morley experiments. They're definitely relevant, but it always seemed to me like the conclusion just kinda came out of nowhere. Now I know why.
@@Nuclearburrit0 The sad thing about the MM experiment is that it was completely unnecessary. Maxwell’s equations very clearly imply a speed that cannot change with inertial frames of reference. The alternative would be an electric and magnetic force that change in magnitude with time of day and time of year and location on Earth.
Call it whatever you want and it still won't change the fact that visible light (as well as all invisible magnetic radiation) is traveling at the speed of light for all of us stuck on earth(which is traveling quite fast through space but in comparison to speed of light we might as well accept that we're almost not moving at all. It's like comparing snail to an aircraft. Thus our reference frame is pretty close to that of a completely stationary object and for us speed of light is like 99.9999999999999999 add as many 9s you wish, of the actual speed of light.). Sure, if we were traveling infinitely close to to speed of light, from our reference frame we'd be traveling at many times the speed of light but light would still be faster than us and from anyone else's perspective we'd just be traveling at speed infinitely close to the speed of light but not faster than actual light. Respect to anyone who's actually still reading this :)
I'm 63 years old, and haven't had calculus since 1978. Never had matrix algebra at all. So it gets a bit difficult to follow that part of the discussion. Nevertheless, there is an interesting assumption made that may not be true. That is, time only moves forward. My understanding of Planck time implies that time can move backward for that extraordinarily brief blip. Is that true? What does this imply for the Lorentz transformation, and therefore Special (maybe General) Relativity?
Time is that which the clocks show. It's a perfectly classical quantity. There simply is nothing resembling time at the Planck scale. It's not that it could move backwards. There simply would be no way to measure it because a clock that measures time at the Planck scale would collapse into a black hole. The classical transition to that is fairly obvious: an ever faster oscillating clock movement has to become ever heavier (because of the additional energy needed to make it move faster), so it would show ever stronger gravitational redshift effects until it would simply freeze for the observer at infinity. Such a clock just stops.
@@schmetterling4477 Time is fundamental to Relativity. "There simply is nothing resembling time at the Planck scale." Say's who? You're just making things up.
C is the distance light fills before the next moment in time. Time is the number of interactions with the higgs field necessary to contain the energy as mass within the field of the atom. By maintaining the trong force. Spacetime stretches to accomodate the required interactions of each atom. Gravity is a relativistic force
Hey, you have made me think (again) about taking philosophy courses instead of Optimisation theory. Could you please make a video about what one will await in pursuing philosophy? I think there are not many people who do Stem and philosophy and I think it is kind of sad.
25:25 More accurately, it can't logically be any other way *if* our assumptions hold. That's why scientists still run experiments, even tho the experiments to date support the assumptions.
100% agree. In the broader sense, however, I think it's very important to emphasize the logical connection. When hucksters try to "debunk" relativity, we need to be very clear about what else they would necessarily debunk in the process.
Is it at all significant that the assumption made at 2:50 is not practically feasible? Given that to start 2 clocks at the exact same time at different points in space requires information to travel between them.
Good question. I actually think this is one of the selling points of the argument. We have made no attempt to account for the time delay of information flowing between observers. We just assumed outright that all observers have perfect knowledge of things happening far away. That means the effects we derive are necessarily fundamental to space and time, and they have nothing to do with the imperfections of our measurements.
@@AntiCitizenX I get what you're saying, but what we're doing here is trying to conclude things about our universe, without observation. (That's what deductions / mathematical derivations are) Which is a dangerous game to play. Our only safety line is the assumptions we're making, based on the universe we're in. But how do we know which universe we're in, and which assumptions are reasonable? Through out measurements and observations! So to say the conclusions we derive from mathematics has nothing to do with our measurements, can't be quite right, can it? Because we're building our mathematics on the assumptions we built out of generalizing our observations. Maybe I'm missing something here, but it seems like if the thought experiment is one that cannot be performed in reality, then you can't use it to conclude anything about reality. I feel the same way whenever mathematicians introduce the concept of infinity to explain some feature of our universe, when we've never observed anything infinite.
@@Google_Censored_Commenter it’s not at all dangerous if your assumptions are based on empirical observations. Like, the law of inertia isn’t just some random guess I pulled out of a hat. It is very much an empirical fact. The same with the principle of relativity. Experiments performed in North America in the Fall tend to repeat themselves when performed in China in the Winter. If the assumptions were invalid, we would absolutely be able to show it. If anything, this is just another selling point. We KNOW that these rules do not universally apply. For example, the presence of a gravitational field would necessarily violate one of our assumptions, and it is a basis for general relativity. Violations of our assumptions necessarily imply new physics to be explored and measured.
@@Bendertherobot69420 what do you mean by "close enough"? Any distance at all will be a problem. And if you assume there's no distance between the two points, that's mathematically indistinguishable from 1 point, since 2 points cannot occupy the same area of space.
@@Bendertherobot69420 okay, but in reality it's not practically feasible for there to be no distance between two things. To define distance you need the position of two points in space. And to define two separate points in space, you must be able to identify a difference between them, that allows you to identify them as two separate entities. But if they occupy the same space, this is impossible. I'm not sure how else to explain it.
At that point we've set up the equality Ax + T(t) = X(x) + Bt. Doing a little rearranging: Ax - Bt = X(x) - T(t) So, we have this expression which depends on 'x' and 't', but it can be decomposed into the form X(x) - T(t) where we have two separate functions which only depend on one of the inputs individually. In other words, T(t) shouldn't have any 'x's in it, and X(x) shouldn't have any 't's in it. Since, Ax - Bt = X(x) - T(t), it seems the only possibility is X(x) = Ax and T(t) = Bt.
Thank you for using inertial frame of reference. If you are accelerating all bets are off. But then again, the universe doesn't care about arbitrary coordinate systems or arbitrary units of measure.
Hmmm... Maybe the real reason is that the descriptor and descriptors of "space" are concepts relative to our concepts and perceptions of places and stuff (and all the stuff, the cosmos). That makes our concepts about "time" equally hypothetical. Now, this does not mean that is no stuff or place where movement (change of relative location) occurs. Nor does it mean that there is no duration of "events" (phenomena) and/or no mentality and no duration of mental phenomena (awareness, thinking, maths, etc.). Yet, it does mean that there are differences between a.) understanding, b.) knowledge, c.) descriptions & models, d.) the totalities of phenomena described & modeled, e.) concepts of "space" and f.) the magneto-dielectric "field" of hyper-frequency energy that enables and sustains all EM phenomena & subfields (including us). Likewise, the momentary totality of interactive flow phenomena involving the magneto-dielectric "field" (the basic universal energy) and its EM subfields always happens now, not in hypothetical mental phenomena (assumptions, presumptions, excuses, pontifications, etc.) in imaginary "space-time" (and spooky QM-creationist maths floating around in a nonexistent nothingness). BTW, FTL "space" travel could happen in a double vortex ("outside" the field/material frame of reference) caused ahead of a ship, but how to slow down and avoid little bits of stray debris (micro-asteroids, etc.) are immensely nontrivial problems.
Making a comment before watching. Maxwell's equations predict electromagnetic waves should travel at a constant speed, Einstein was just assuming the law of physics are the same in any inertial frame of reference. It is the first thing you learn about Reliability. .
The video is based on the assumption that space and time coordinates of different 'inertial' frames relate to each other up to a linear, first order relation (by removing zero order offsets.) Also, it builds upon Newton i, using the concept of inertial frames and their definition. However it misses to discuss the case if only space variables transform and time variables are the same everywhere. This case is a possible case mathematically, which covers the case 1/c is infinite, and the lower left element of the matrices shown being zero. The correct statement would be: We can not deduce mathematically that there exist a finite speed limit, because we arrived to that assuming 1/c is nonzero. (coming from direct physical easurements or via indirect mesurements leading to Maxwell's equations and Lorent'z transformation) THUS: The exsistence of a finite speed limit comes from phusical observations, mainly about propagations of light waves.
By the way, despite the above details, the deduction is interesting, and the video quality is well done. It is well worth to fix the above mentioned issus.
@@AntiCitizenX Assumption in terms of mathematical proof. You cannot provide a logical proof of the statement, but only empirical evidence, therefore it is assumed at the start of your proof.
That's exactly how my high school physics text books explained it. However it's still the speed of light because of more advanced physics. See permitivity and permeability of free space that set the coupling between electricity and magnetism. Light and the other massless bosons are the carriers of causality.
@krisrhodes5180 spacetime physics by Taylor and Wheeler. It's a very good book. ...my high school was a regular Texas public HS. Not a magnet or anything else. But Mr Gonzalez was a hell of a teacher who knew his sh-t. Out of all of my professors at Stanford, only Laughlin was better.
Anyone with a strong enough mathematical background to follow your math variables would probably know what you’re trying to tell them already. People such as myself who have spent decades with numbers that I’ve manipulated mathematically, I can only then understand the general case of using letter variable names. Once I have a solid grounding, and how the real numbers work. I would play with the numbers with the two fields of reference, moving at the same speed, and then slowly, give them diversion speed and direction to get a feel for it. Once I have played with these numbers for a long time then and only then could I now substitute letters for that which I had seen in numbers. No point in you only preaching to the choir when this idea of speed of light is an important one for, many more people to understand.
c is introduced late in the video as a factor in the Lorentz transformation. It would be clearer if you started with the Lorentz transformation, explaining exactly what is meant by c.
Relativity is solely a description of the gravitational field which couples to the matter fields. We take c=1 and the reason the maximum local speed cannot exceed unity is that world-line lengths must be real valued (there is no meaning to a line that has an imaginary length) with the shortest "world-line" having a length of zero, which seems to be the case for electromagnetic radiation and low-amplitude gravitational radiation (quotes around "world-line" as the photon/graviton do not have proper time affine parameterization, i.e. they don't have a history).
Very interesting. I could not follow the math used to arrive at the universal speed limit, but I understand the concept that nothing can travel faster than the universal speed limit... including light. My layman's knowledge of relativity tells me that matter cannot reach the universal speed limit because mass increases dramatically as it approaches the universal speed limit, thus dramatically increasing the amount of energy required to accelerate it. Basically, there's not enough matter and energy in the universe to do that. But photons and electromagnetic radiation can zip right along at the universal speed limit because they have no mass. The term 'speed of light' may not be technically correct, but I think it has practical applications, at least for us laypeople, such as explaining why we can see stars and galaxies as they existed billions of years ago. Also, I understand that galaxies are moving away from one another faster than C because the expansion of space itself is not bound by C. The Universe is a wonderfully weird thing.
I am familiar, but I haven't used matrix algebra for decades so everything does not just pop out from my head instantly. I would have certainly prefered to not use it since this can be very easily expressed with normal equations.
@@AntiCitizenX Have you considered the fact that most the people theyre trying to teach are not physics majors? or didnt even try to get into college? This is from someone who actually likes calculus and math. The amount of high school teachers who ive asked 'why is this e(or i, or sin, or log) letter on my calculator even there? what does it do?' and get an unsatisfying answer of 'its just useful, you'll learn it in college' definitely doesnt help anyone try to actually gain that basic understanding. It especially doesnt help that unless you actually are going into a major that specifically requires calculus, youre just encouraged to avoid it entirely in college else you risk failing and adding another semester of debt alongside the debt you already incurred. The story around calculus is unfortunately that its a complex subject and useless for the vast majority of people to do their jobs, which means most people will just refuse to learn it. "just a basic understanding of calculus" really is an unfortunately high bar for people to have, even if it didnt have to be.
@@Captain.Mystic I understand what you’re saying. I just fail to see what this has to do with the video. The mathematical foundations of this video are well within the grasp of a reasonably well-educated high schooler. I personally took AP calculus in high school, and there are lots of kids who even got ahead of me. I made no secret about the fact that you need a high-school understanding of calculus to follow along. If that’s not your jam, then that’s fine. But surely you can appreciate the logical beauty of it?
@@Chance57 They do not show you the derivation. They just sort of state the assumptions and then declare the conclusion. I’m not sure why you would find that a problem.
@@AntiCitizenX No but they don't take it for granted and they don't pretend like light is the cause of the "speed limit" either. Their video title is almost identical to yours. It's not like your point isn't true, but saying it while PBS space-time is on the screen is weird. Because it's not true for them specifically. I've had professors it'd literally be true of, including one who told me "because God's smarter than us." But just because they didn't derive it from base assumptions doesn't mean they were doing anything like what you implied taking it as some ineffable standard. That video isn't even the only time they bring it up, they bring it up constantly. I'd sound like jingle bells if I had a nickel for every time Matt explained why c is used to represent the constant and why "light speed" is directly correlated to space-time, not photons.
Well, the editor of the journal (the International Journal of Quantum Foundations) didn't think so. He has authored 4 books on QM and he thought my paper was 'interesting'. a compliment in physics I believe. @@AntiCitizenX
How do you distinguish between inertial and non-inertial frames of reference? If you define inertial frames as frames in which the laws of physics work, that'd be like a circular definition wouldn't it. "The laws of physics work in all reference frames in which the laws of physics work"
I believe I know why the RUclips science educators usually avoid this line of reasoning.
It took you 30 minutes doing math at a speed which can't be followed along in real time and it requires the viewer to actually do follow along or else the result is "it just pops out of the math"
To be fair, PBS Spacetime does have a video that attempts to take a good swing at it. It’s actually the one that inspired me to make this. When I saw the original paper they cited, my jaw dropped at how simple it was.
I kinda agree, the math are quite hard to follow in a "youtube" fashion. Also, the peak of the presentation, the C = 300M m/s is kinda rushed and dropped like "If you experiment, boom there it is". What are the experiments ? does it involve light ? So why not just speed of light then ?
@@ThePiiX In my defense, the video is not exactly a proof that "c is finite." It's a proof that c has nothing to do with light. If you want to prove that final piece, we can absolutely do it. I just need another 20-minute video to get there. :(
@@AntiCitizenX I'd love to watch that video actually.
@@AntiCitizenX, no no no it's not a critique of that, I was just overwhelmed by the math and the conclusion looked rushed.
Like How do you find THAT particuliar number, you measure light ? There are other factors that just align ? G ? plank length ?
May be I wasn't paying enough attention. I'll watch it again, well rested.
I'd love to see more videos anyway.
Why c is called the speed of light is an artifact from the fact that this peculiar behavior was first noticed in Maxwell's equations, where c is the speed of the propagation of electromagnetic radiation, and that speed worked out to be identical to the speed of light. Thus, light was reasoned to be a form of electromagnetic radiation, and the name "speed of light" was attached to c. Ie, c was already the speed of light and then it was also found to be the speed of causality.
C is short for celeritas, the latin word for swift. That's where the name comes from
@@mrjdgibbs Yeah, but it wasn't attached to light because light is swift. C is also used for the speed of sound, if you're working in the context of acoustics or fluid dynamics. It is customary to denote the speed of wave propagation in a medium with c.
Do you think it is worth a video on how Maxwell’s Equations imply a universal speed limit? It would require a lot of vector calculus to do it justice. Not sure how the audience would react to that. “Take my word for it! These upside down triangles prove the existence of a universal speed limit!”
@@AntiCitizenX That depends on how deep you need to understand vector calculus. If you just need a good pair of waders, I say go for it, guiding the viewer through the thorny parts. It it's long and painful, then I think you'll need a few videos, with a few interesting partial results as stopping points - if you do it at all. If there are no interesting partial results, I'd say forget it and save the derivation for the advanced students.
@@AntiCitizenX Definitely .. though, of course, by convention of mere human assumption, I presume .. not infinitely. Indeed, I am not at all sure my ability to do sums would get me that far, let alone swiftly - measured at a constant rate, e.g. of falling sand grains or heartbeats. Yey!
;o)
Errata: Yes, I am fully aware that I played fast and loose with the special case of the Galilean transformation. The primary goal was to show that we can derive the Lorentz transformation out of basic assumptions, thus showing how the universal speed limit is not tied to the concept of light. However, I did oversell the case, and I fully acknowledge that. But it did give me an idea for how to handle it in a more convincing way. I think I may re-edit this video and upload a revision in the future that makes the case more convincingly. Stay tuned.
Also, I screwed up a step early on. You cannot just swap denominators like I did. I thought I was applying the equality of mixed partials, but that doesn’t apply in this case. Instead, a far simpler proof is to just assume the homogeneity of space and time (which is arguably implied already by the principle of relativity). So the proof still works, but that step needs some fixing.
I think you did an excellent job that most people can not do in physics today and that is make it simple and easy to understand I understood every thing you are saying even though I know there are more complicated explanations
Because those complicated explanations are built on those basic principles present in your video and those basic principles are the backbone that many people fail to realize that are evident and in play when it comes to such difficult equations you got to start from somewhere and surely einstein did not just immediately write down his magnum opus without first consulting lesser equations that made him ponder
A lot of the criticisms on your video i have read are illogical and unfair and it is sad because they seem to know so much about this topic that I cannot see why they do not see the implicate simplicity in such a brilliant equation its really disappointing
I have a question here. Im not particularly trained in relativity but I understand basic Physics and advanced Math. In this video, you are using light/vision as the medium to make observations. If we imagine a universe with no light and only sound and we make our observations using sound, it looks like the speed of sound will be the speed limit. Also, how do we know that the speed of causality is the speed of light? If weve been making experiments with speed of light as the limiting factor then it will be the limit of our experimental results. How do we know we just havent found something faster?
@@marmosetman 💯
There was a tricky assumption that I don't think was stated explicitly but still played a big role in the result: You replaced v₁F₂' = v₂'F₁ with v₁/F₁'= = v₂'/F₂'. By dividing by the Fs, you implicitly assumed they weren't 0, but _could_ they be 0? If we considered the case where they were both 0, then you would get the Galilean result derived at the end from an infinite speed of light, but without the dubious construction of inserting an infinite value into the equations.
Interestingly, the case of a = +c² is the case where time behaves like a spatial dimension. This, along with Galilean relativity and Special relativity form the 3 possible geometries of a 2D system: spherical, flat, and hyperbolic respectively.
As for _why_ Galilean Relativity was so widely believed, it's actually the same reason as why some people believe in a flat Earth. They both come from the same geometric source: the small-angle approximation. One is a very small spherical angle, and the other is a very small hyperbolic angle, but both are very difficult to discern from flat lengths at very small scales, and compared with the size of the Earth and the speed of causality, human scales are indeed _very small._
Nice points, nicely put.
The special case is just the Galilean transformation, which was talking about in the end. It's also hardly an "assumption" to call it wrong. I just didn't want to spend another 20 minutes dealing with it, because it wasn't exactly the point of the video. I might rectify that in the future, though. I think I have a straightforward way to eliminate it.
@@AntiCitizenX Good luck with that! I bet it is impossible to eliminate the case F = 0 using just your assumptions.
@@martijnbouman8874 you need a final piece of empirical data, and there are dozens to choose from. The hard part is keeping it simple.
@@AntiCitizenX Oh for sure, empirical data - such as data that shows that the speed of light is constant - should do the trick.
Hey man, happy you're back. Always love your videos and have been watching for years. Hope you're doing well.
🎯 Key Takeaways for quick navigation:
00:00 🌌 Introduction and Challenging Common Beliefs
- Exploring the concept of the speed of light and questioning the common understanding of it.
04:43 📜 Four Assumptions: The Foundation of Special Relativity
- Introducing the four fundamental assumptions that underpin Einstein's theory of special relativity.
10:28 🔄 Transformations and Matrix Notation
- Exploring how coordinate transformations are essential and introducing the concept of matrix notation.
17:17 🌐 Transformation as a Mathematical Group
- Discussing transformations and the mathematical group properties they must adhere to.
19:27 📡 Lorentz Transformation
- Unveiling the Lorentz Transformation as the fundamental result in understanding the relationship between space, time, and motion.
22:55 🚀 Misnomer of the "Speed of Light"
- Addressing the misconception about the "speed of light" and suggesting a more appropriate term: "speed of causality."
22:56 🚀 Velocity Addition Formula
- Explanation of the velocity addition formula in special relativity.
- Velocities do not add linearly; instead, they follow a specific formula.
25:12 🌟 The Universal Speed Limit
- Introduction to the concept of a universal speed limit in the universe.
- The value of the universal speed limit is approximately 299,792,458 meters per second (the speed of light).
26:06 🌀 Galilean Transformation
- Discussion of the Galilean transformation as a simpler, intuitive answer that we might have expected.
- The Galilean transformation is applicable when speeds are much smaller than the speed of light.
Made with HARPA AI
I never got the impression of anyone telling me to suck it up and just accept the the speed of light exists or anything. Or that there wasn't a reason. Certainly not in the sneering, insulting voice you ascribe to them. It's just that for most discussions, that is a simplifying axiom.
I was exaggerating, yes. But it is very common to introduce relativity by just postulating the constancy of the speed of light as a brute fact.
@@AntiCitizenX people told you the sky is blue when you were a baby, did they even stop and derive the Rayleigh equations so that you could have a grasp of why it was ? What useless parents..
@@kalisticmodiani2613 I’m pretty sure that your average college student taking a first course in modern physics for scientists and engineers can handle a little calculus…
@@kalisticmodiani2613 If I was taking a physics course on optics and scattering, then yes. I would expect to see the equations.
You seem to be under the impression that this derivation is both well known among physicists and yet too complex for college students to handle. That is simply false, my friend. It is very simple to follow, yet conspicuously absent from the textbooks. Your antagonism is therefore very confusing and misplaced.
My math is very rusty so I had a hard time following. I think an example with numbers that we came back to after every derivation would have helped illustrate what all the expressions mean.
I'd like to think my math isn't too rusty yet, but it still took me multiple slow watches to get it all right. Having gotten an understanding, I'm not sure a numerical example would be of any use. There's just a lot of details that he kinda glosses over. You just gotta think of it from the perspective of trying to eliminate all the unknowns by using cases where we can easily derive what the unknowns are.
It doesn't make sense to do integral, or derivative on constants.
And all the parametes will be on said constant.
Thank you, that was really well argued. While my math is too rusty to follow the details, I was able to follow the argument. As a science fiction writer, the only lattitued is to change the assumptions... ;-)
This has been one of my absolute favorite YT channels for years. Your philosophy series is a cross between Cooking For Engineers and Philosophy For Dummies and every installment is pure gold with the best signal to noise ratio in the community. Can't wait for what's coming next.
This video was utterly inspiring. Even so far as engineering graduate school, I never had a professor talk his way through the logical implications of a derivation. I watched mathamagicians move symbols on the wall, but nobody ever rationalized the process thus. Sadly, my brain is not one that derives a great deal of understanding from the raw algebra. It's nice to see that there is an alternative. Thank you!
“It was my understanding that there would be no math.”
The mistake is thinking there’s just one universal math.
Thanks for making this video. I remember watching PBS SpaceTime's video where he explains how Lorentz transformation is the only thing that makes sense and linked a paper in the description which shows how you can derive Lorentz transformation without assuming constant speed of light. Couldn't understand the paper at all but I've been curious about it ever since.
This entire video is basically a point by point follow along with that exact paper, plus a few cracks filled in.
This is an elegant derivation of the Lorentz transformation. I really do like that it doesn't presuppose anything about the speed of light. There does seem to be one thing you've neglected in your presentation though, and that's experiment. We know this is correct (for appropriate contexts) not because the math is elegant or because it agrees with our assumptions but because it agrees with experiment.
Furthermore, as strange as it may seem to presuppose the constancy of the speed of light, there is a good reason to do so. We had observed it. Physicists had expected the observed speed of light would depend on the speed of the observer relative to the source and found that not to be true.
How did I neglect experiment? Every single one of the assumptions is based upon some kind of observable data.
@@AntiCitizenX prior observations can serve as the foundation for a theory, but the true test is how its predictions agree with experiment. We have a great many mathematically elegant theories of quantum gravity, all of which agree with prior observations. At most, one of them is right. Similarly, we don't believe special relativity because the math is elegant and it agrees with prior observations. We believe it is right (within the contexts for which it was developed) because it makes testable predictions that have been confirmed by experiment.
@@allanjmcpherson Please point out the exact moment in this video where it was ever said or implied that we should believe in special relativity out of respect for mathematical elegance, and NOT because of empirical data.
A few other related things:
1. The "speed of gravity" is equal to the "speed of light" to within an error of less than 0.00000000000001% based on the observations a pair of neutron stars merging by the GW170817 and GRB170817A events.
2. Lorentz, Poincaré, Fitzgerald, Larmor, et al. had figured out this transformation, length contraction, time dilation, and a constant propagation velocity for light waves from within a model of space being filled with a "motionless" incompressible dielectric material (that didn't effect the motion of planets and stuff) which could never be measured. It was a big complicated mess... which gave you the exact same results as Einstein later derived from the single assumption that the propagation velocity of light in the vacuum, when measured from an inertial reference frame, is the same for all inertial reference frames. All this tedious mucking about with an unobservable aether was unnecessary.
I speculate that the reason why many popular explanations of Special Relativity are so muddled, is because for the first half of the twentieth century, all the popular explanations of Special Relativity were the same old explanations of Lorentz's aether theory with the word -aether- crossed out. Which immediately makes the listener ask: Why isn't there an aether? Relativity needs to be presented in its own terms to be understood without actually doing the math. (I have a long rant about how terrible most popular science explanations of Quantum Mechanics and Relativity are, but anyway...)
(I'm trying to avoid writing a long explanation of Special Relativity right here in this comment.)
3. Looking at some of the other comments on this video, yeah everything is always moving "at the speed of light" in some amount of "space" and "time" which are not distant separate things... ok I'm going to try to make this comment short.... historically the concepts of space, time and velocity were kinda backwards. When you hear: "speed equals distance divided by time" v=dx/dt it makes you think that time and space are separable things, but the problem is that we can not directly measure either time or space; we can only measure "things moving around" and work backwards from the velocities to figure out what to call "time" and "distance". Earth goes around the sun, that's a year, pendulum swings back and forth, that's a second, fly from New York to London at some velocity in some amount of time you get distance, etc. etc. etc.
There is *only* velocity.
Velocity is a function of three variables, three of your favorite space-like coordinates, and one time-like coordinate. You only need four numbers to describe the motion of everything in the universe. You can put the motion of everything everywhere into one giant four dimensional block called "Spacetime".
Every location in space is also a location in time.
You know how when you mix eggs together with vegetable oil, you get mayonnaise. And given some mayonnaise, you can't tell which part is egg and which part is oil? Spacetime is like mayonnaise in this metaphor.
Every location in space is located in the past (the negative time direction) of every other location in space. Your feet are about six nanoseconds in the past from your head, and your head is about six nanoseconds in the past from your feet. The Moon is about 1.3 seconds in the past from the Earth, and the Earth is about 1.3 seconds in the past from the Moon. Complex numbers are a clever hack to manage this... because... remember the Pythagorean theorem... you take the square root of a distance between two points... since all distances in time are in the negative direction, you'll eventually wind up with a square root of negative one. (But also, it's just the off diagonal terms of a 2x2 matrix.)
This is getting long... I'm going to rush through this, reply with a question if you want me to elaborate...
So... people always ask: "Why can't you go faster than light?" and to put it bluntly, all material objects, including the human body, are made (partially) out of light, and so (parts of) you already are, and always have been, traveling at the speed of light... and you can't go faster than yourself. The really interesting question that people should ask is: "Why does anything travel *slower* than light?"
The answer is confinement, and it's where inertia (mass) comes from. It's also how Poincaré and Einstein derived E=mc² or, more precisely, E² = (mc²)² + (pc)² which is just the Pythagorean theorem in 3+1D spacetime... I need to get going and stop writing this comment soon, ask me if you want the long explanation of inertia.
Some bullet points:
Linear momentum and kinetic energy are the same thing expressed in terms for space or for time.
No, you don't "gain mass" as you "go faster" (than some unspecified thing). Inertial mass is invariant.
You are always moving at *ZERO* velocity relative to yourself.
Velocity is meaningless unless you specify *TWO* things for it to be the relative velocity between.
Gravity only "sees" inertial mass, that is the only thing that counts for gravity.
If you rearrange (mc²) = E² - (pc)² you can see that any extra linear momentum will cancel out any extra energy.
Momentum and kinetic energy are are relative, because they are functions of velocity which is relative.
p=mv
KE=(1/2)mv²
Oh! I just remembered why I started this comment...
4. You know how "time is relative" and "space is relative"... do you know what happens to electric charge?
NOTHING! This was the entire point of creating the Theory of Relativity in the first place!
Well... the moving charges and magnets paradox to be more specific. This is the *actual* problem that Lorentz and Einstein (and Heaviside) were trying to solve and Relativity is the solution. (That's why it's the "Electrodynamics of moving bodies".)
So many pop-sci explanations of Relativity completely leave out the entire purpose for the creation of Relativity was to make electricity and magnetism work consistently for all moving observers...
And a side effect of electric charge being the same for all observers... is that electromagnetic waves are the same for all observers. That's right, the speed of light is constant!
Also, just as energy and momentum are the same 3+1D motion just described in terms of either time or space. So too are the electric field and the magnetic field the exact same 3+1D field described in terms of either time or space.
Everything you said is pretty much spot on. The only thing I would add is that all of this is predicated on the Lorentz transformation being correct. In my experience, this is a major psychological hurdle, which is why I think it is very important to find intuitive derivations. It forces your brain to accept something that is very counter intuitive.
@@AntiCitizenX It's also possible get Relativity from the principal of inertia (and conservation of momentum). It's basically how Galileo, Newton, et al. came up with Classical "Galilean" Relativity. Lorentz and Poincaré were trying to make electric and magnetic phenomena work with relative velocities. The solution that they came up with was time dilation... that is to say, that there is no longer a "universal absolute clock" as Newton conjectured. Even after Poincaré had deduced this theory (modification to Galilean Relativity), he still insisted that the must still be an unobservable, unmeasurable, absolute time (in the "rest frame" of the aether), which we would never know. Then Einstein was like: "The aether is unnecessary", and he gets all the credit now.
As I was saying... Relativity is really about inertia. Inertia is really weird when you think about it. An object in motion will stay in motion, moving in a straight line, forever, or until a "force" changes the direction of the straight line path it moves along. Zero velocity is also a constant velocity, so something "at rest" is exactly the same as moving at a constant velocity....
And, things with inertia, resist having their straight line path changed. More inertia means more force is necessary for a particular amount of acceleration.
Hang on, I need to do some stuff and can't finish writing a long reply right now...
Bad form to take a shot at Matt, who is not guilty of what you claim here.
Well, y'know, electromagnetism is the one massless field whose wave solutions we deal with on a daily basis (unless we work at LIGO), so it's understandable that this would get attached to light.
To help expand the separation between light and the speed of causality is why some things must travel at the speed of causality such as the propagation of massless fields, and massless particles.
Wonderful video and excellent description of the Peliseto/Testa paper. Well done!
Amazing video, this is another example of just how powerful first principles are.
One thing, from16:25 onward, we might be able to derive Galilean relativity by setting both F1 and F2 to 0; this would satisfy the condition F1*v2=F2*v1 without having to deal with an "infinite speed of light" (this is mentioned in your source).
Edit: I see you responded to an earlier comment about the same thing.
That was how I recall this kind of development going: you set some pretty broad postulates and it turns out that Einstein relativity and Galileo relativity are basically your two choices.
This video is extremely misleading. Relativity has nothing to do with light?! How do you think they made their measurements in the first place… oh yeah, they made them using light signals. 🤦♂️
@@se7964 At least in theory, they can use any kind of measurement. And the thought experiment doesn't assume a measurement method that confined by the speed of light. It is coincident that light travels at the speed of light. And yes, most of our measurement is done by light or electromagnetic waves. But even if we had something faster than light for measurement, we'll still end up with Lorentz transform and when you combine speed you reach a limit.
This is the best explanation of the basics of special relativity I've ever seen, I feel like I'm starting to actually get a bit of a grasp of it way more than with the traditional courses I've taken, amazing video!
Thank you!
Check out the book by Hobson
@@everythingisalllies2141 😆😆
@@everythingisalllies2141
This video: mathematically precise deduction based on empirically verifiable premises.
You: ThAT’S pSEudoSCienCE!!! Duurrrr!
Read my top most post "Relativity Crisis" in the comments, you will se that things are more complicated, yet simpler!
"The Speed of Light has Absolutely Nothing to Do With Light"
But... why the universal speed limit happens to be equal to the speed at which light propagates in vacuum?
Because all massless particles travel at that speed, as well as gravitational waves.
It's been a few years since I took modern physics. Since you targeted this at the layperson, try actually sitting someone down and try to teach them this before making the video. The appeals to intuition you make in the script would probably work better that way.
TL;DW: "the speed of light" is not set because that's the speed at which photons travel but rather it's a sort of universal speed limit that logically emerges from a few basic assumptions that most people would agree with. Light just happens to be one example of a thing that moves at that limit
Yup!
It's good to see your content.
Thank you.
Thanks for going through the math. While the pop sci videos are great for conceptual analogies, the math is essential to understand too, and too few go through both.
In a nutshell: the speed of 'light' doesn't describe reality, 'reality' describes the speed of light and also the speed of all other events, e.g causality itself. It is just a consequence of historical events that EM waves were the first to describe this 'speed limit'. Technically, if we had had instrumentation to describe the speed of gravitational waves in the 1800s, we would probably call it 'the speed of gravitation' or something today
That gravity analogy is actually pretty good. I like it.
Wasn't there a video on PBS Spacetime with this exact same title?
Similar. Yes. It’s what inspired me to make this video. They explain the assumptions, but they do not actually take you through the details.
You sorta snuck something under the rug there. When you argued that v/F is a constant, you implicitly used that F is nonzero. F=0 would give a nonisomorphic group and a different theory, namely Galilean Relativity.
How is it sneaking under the rug when it was acknowledged it openly at the end of the video?
Kinda feel like I understood better when I was reading the blog post. Now I'm just watching numbers and variables flash by on my screen without really getting what's happening. Maybe it's because I read what I could understand in the blog post, but here you're spending time reading out all of the equations that I'm just not getting because I'm not familiar with matrices,* and also calculus despite reading about the theory of it :P
I still wonder if I would actually have a use for learning about these sorts of mathematics if they didn't eventually appear in code I'm writing.** Would it be worth it to learn all about it just so I can understand the explanations in this video, or would it be better to just accept what you're saying and move on? And for that matter, would there be any mathematical fallacies or signs of duplicity I'd have to watch out for to make sure I don't fall for misinformation? (Only examples I know about at the moment are lying with visual proofs and lying with statistics, which I probably watched one video each on.)
I think a lot of this stuff would be significantly more intuitive if it was also shown visually. Like, the way transforming a transformation creates a new transformation could be shown in two to four diagrams - or an animation (if you're feeling capable of that). I've also seen a lot of graphic animations about why you can't surpass the speed of causality, showing objects moving on paths on grids with one space dimension and one time dimension, and the grids being required to do Lorentz transformations in order to follow along, and the general idea came across to me much better in those than in this video. It seems to be more of a presentation of the mathematical technicalities of it, rather than such an intuitive explanation. So maybe I'm just not part of the intended target demographic for this thing. This video doesn't really make it clear from the outside that it's more math-oriented than graphic-oriented, though, so maybe that's why all the people watching this are getting confused, and why this video might have poor retention (if it does).
*After having another look at the script and then checking the video, it turns out you did say I should look it up if I'm not familiar with it. Man I'm such a derp... Still, I supposed it blended in with the rest of the video since frankly, by that point, I was just watching it not being concerned about grasping the material anymore because it already seemed established that I couldn't really follow along without slowing right down and spending a bunch of days familiarising myself with the notation, as well as the points being made with them after that.
**And it seems as though my code is still so stupidly simple, despite being long, protracted and doing what it's meant to do, that I often don't even get what people are saying when they talk about good coding practices - maybe just because I haven't had to handle data, server interaction or workflow tools before in any of my current projects - and I can barely follow along on some CSS and JS tutorials and StackExchange answers without asking ChatGPT to explain it in steps in English. For CSS, it could be because the code is long and full of irrelevant fluff I have to cut before I can understand the fundamentals. Also, code seems to be a bit easier to follow along than mathematics. Maybe it's because the variable names have to be longer for you to understand what the code means when it's unfamiliar. And it literally does what it says, meaning you can mess about with it a bit until you understand the relationships between the variables, statements and functions you put in it. Mathematicians prefer to keep things compact and trite. Also, not only am I the type of person to only learn things either when they seem interesting or when I need to know them at a particular moment, but since I got ADHD, I'm also the sort to just unload things from my mind if they're psychologically impertinent. And there's a lot of code I don't even need to understand, because it works and I just want to have a certain feature in my program. I guess I feel that way watching the mathematics in this video; generally, certain concepts are fairly important to grasp, but mathematics just do themselves.
really elegant; never seen it that way before; meaning: i never saw it _explained_ that way, AND I had never _visualized it_ that way
Hey, hello again, wanted to ask you something out of curiosity; what do you think of epistemological historicism? I have a teacher who is pretty adamant about It and, although I find that It goes against pragmatism which, based on my understanding, I agree with, I also find It hard to formulate a simple example of why historicism is incorrect (which basically means I understand what you say on a rather superficial level)
Sir, this is a physics video…
I fell off the math ladder at college level calculus barring me from pursuing engineering and never really came up with any other professional category ..ended up marketing, statistics, packaging.
The meaningless squiggles and f circle g etc remain the greatest feeling of lost in my life. I still avoid any thought of advanced math.
I was going to ask why we wouldn't have seen this earlier before we discovered special relativity - what assumption is violated by Galilean relativity?
But you answered that at the end well - Galilean relativity is just a special case.
Thus, we shouldn't necessarily *expect* to see a speed limit, since there's a possibility that the speed limit is infinity.
But we also shouldn't be too surprised that one exists, I suppose.
That’s a great way to put it. It’s technically possible, but we kind of had to stumble over this other solution to get there.
@@Bendertherobot69420 Galilean relativity plus a finite speed of light _relative to the medium of the ether_ is in principle perfectly viable. But it implies that you should be able to measure a difference in the speed of light relative to an observer depending on the observer's movement relative to the ether, and no such differences could be detected despite physicists' best efforts.
It should be pointed out that Lorentz and others had been developing the mathematics of the transformations for close to two decades before Einstein published his first papers. In fact they were conceived while aether theory was still a thing, and the very name was coined by Poincaré in that same Einstein "miracle year".
The assumption was that F₁ and F₂' in the equation v₁F₂' = v₂'F₁ were non-zero. If they were zero, then dividing by them to get a common ratio would've been an invalid operation, but the resulting transformations at the end would've still worked perfectly fine. Since we checked for a = 0 and determined that it didn't make sense, then it would've been valid to instead use F₂'/v₂' = F₁/v₁ as the constant ratio rather than its inverse.
@@angeldude101
Yes. He simply assumed away the Gallilean case in the Lorentz derivation, without explanation. In fact, the Gallilean and SR transformations are each special cases of the derivation he showed. That is why Einstein *needed* to postulate invariant finite c to explain Michaelson-Morley.
Could you later make a video explaining what cosmologists mean when they say in the future we won’t be able to see some galaxies because we’ll be moving away from each other at “greater then the speed of light”?
That would require a LOT of intermediate videos to work up to that. :P
the physics and math behind it are immensely complicated, but in short, space expansion doesn’t violate the… speed of causality, and thus space can expand unto itself at any ‘velocity’, ours being rn 67.5 km/s per every megaparsec, which means some object, let’s say 4 441 370 megaparsecs away, will move faster than the speed of causality from us
but yeah, the trick is that space expansion doesn’t violate speed of causality, it’s kind of, beyond it on a conceptual level
It’s like a fish swimming upstream at The Speed of Fish (the absolute fastest that any fish can swim through water) in a river that flows faster than The Speed of Fish. Even though the fish makes progress relative to the water, the water’s motion more than cancels out the fish’s progress.
Expansion of the universe is not the event inside the universe, it's the event happening to the universe, hence the expansion rate doesn't have the same limit of causality c. From similar math it also has to have its own "speed limit" but we would need observations from frame of reference outside of our universe to find that value. Einstein described geometry of our universe. We need to guess or assume without any evidence a geometry beyond our universe to scale this thought experiment. And define what "observer" even means outside time-space. Measured expansion doesn't play by this rules, hence we rather assume it's "outside" because assuming otherwise breaks causality "within" violating the 5th assumption of this video.
16:25-16:35: One fun little side note: the assumptions listed still work if we assume F1 and F2 are zero. It’s just that, instead of getting the Lorentz transform, we get the Galilean one. It’s easy to forget we can’t always divide by whatever coefficients we come across in our maths, unless we can prove they are nonzero. I suppose an extra assumption (appealing to real world experiments) could rule out this possibility.
Maybe I’m being too much of a nit-picky mathematician, but it’s nice to know the “dubious” step of setting c to infinity, leads to a result that has some rigorous backing, as it can be reached by checking out the F=0 case.
Finally.
Was worth the long wait.
Great video.
The math took me back to my college Calc IV class - with the Linear Algebra, matrices, and such.
Oh...eigenvalues eigenvectors, orthogonal(s)
Haha. I remember toward the end of the course having a moment where I thought to myself, "why don't they teach some of these fundamentals earlier on?" Would've made 2 and 3 easier...'grasping concept wise'?? I guess. Longtime fan. BTW...did KnownNoMore ever publish his detective novel(s)?
Then again, I do have the internets...
Keep up the good work!
One of the best explanations I've ever seen. I wish this was the way to introduce this topic physics students like me. One observation, if I'm not mistaken, ignoring Assumption #5 leads to breaking causality i.e. consequences happening before their causes. I feel this part of the argument could've been made more explicit in the video.
The speed of light has absolutely something to do with everything, i.e. it "limits" the speed of everything, including light. The tricky thing to learn humans is not to formulate invalid logic, such as "has nothing to do with" when it actually has something to do with it.
The point is that the actual speed of light could be different from c, the speed of causality. It could be a little smaller and energy/frequency/wavelength dependent. It's actually worse than that: it could even depend on the polarization if the physical vacuum has a preferred crystallographic axis and shows birefringence.
i always wondered, what about if speed of causality is constant but not the same for every observer, or dependes of the distance the event is from the observer. What about if the speed of the causality is slighly different for too far events? Does relativity still applies?
HOLY SHITTING HELL SON WHERE A BEEN?!!
I swear, your quick disappearance from Twitter and non-updating here, I was seriously more and more drawn into “I hope he didn’t get hit by a bus”
Welcome back, whatever the form you take. 😘
I wouldn't be shocked about anyone dissapearing from Twitter at this point
@@electra_ Of course not, but it timed with a lack of RUclips updates, which happened shortly after the channel rebranding update, so…
My “bus theory” fear seemed more and more justified.
At 16:31 you assume that F1 != 0 and F2' != 0. The Galilean group, with gamma = 1 and F1 = 0 is a perfectly valid solution. You get rotations with sheers, instead of rotations and Lorentz boosts. So, I'm sorry, but you cannot prove relativity without the assumption of a maximum speed, or something equivalent (for example conservation of the interval (ct)^2 - x^2 - y^2 - z^2 = tau^2).
That’s just the Galilean transformation, which is discussed at the end.
It is also very fair to point out that we still have “two” possibilities, but I never claimed otherwise. It just requires you to assume infinite speed for the mysterious constant c. If you like, we can use Maxwells equations to prove that there indeed exists a universal speed for all frames of reference, but the video was long enough as it is. :p
TBF, it is probably more "mathematically rigorous" to say something like "There are two cases, either F = 0, or F != 0", just because having C = infinity is perhaps a little janky. Intuitively, it makes sense though that Galilean relativity is just the Lorentz transformation but with an infinite maximum speed. Either way, we get both as valid options, but we can experimentally confirm that the speed of light exists.
A somewhat pedantic point but I don't think it's quite fair to say you need a concept of 'infinite speed' to obtain the solution described here. If as odysseus suggests we take F=0 from the start, there is no need to go through the rest of the derivation and identify the dependency on a constant c. In this case it's nothing to 'trip over', early 19th c physicists could easily go through the derivation and take the 'intuitive' F=0 solution without giving a single thought to the possible alternative and still have a perfectly consistent theory. In a sense kind of like imaginary numbers, before the need for such a concept arose we had centuries of progress blissfully unaware of their existence or meaning
In essence, physics has it backwards, but it is reasonable. We studied light/EM waves (later photons) quite a bit before relativity, or better put, the nature of space and time. Thus, we associate the symbol c with how fast light travels in a vacuum. But the truth is, this numerical value that has units of a distance over time is just really connected intimately to how space and time work, and how observers translate what they see to each other. It just turns out that what we call light has that value for its speed in vacuum. We just had the order of discovery backward, as far as what is more fundamental.
Answer this: Maxwell calculated the speed of light using permitivity and permiability in a wave equation. Permiability is a magnetic measure, and therefore is a relitavistic effect of charge and permitivity, and it can be calculated from that. Now we find the speed of gravity waves the same, and therefore calculable from electrical phenomena. Should we be paying attention to this? Or, is there an analogous relitavistic gravitational effect that could be used in a wave equation with gravity and its penetration into space to independently calculate c? And might this relativistic effect account for anomalous behavior of galaxies and binary systems that have large rotating mass?
HOW I'M HEARING OF THIS FOR THE FIRST TIME. Thank you so much, I'm actually shocked as to how much sense this makes! I couldn't quite follow along with math, but I'll continue figuring it out.
Bear in mind that I made a couple of mistakes. I’ll post a correction at some point, but they don’t affect the conclusion in any serious way.
I've finally understood how relativity emerges from simple assumptions and not an 'eureka' moment. Thank you very much for this video.
Relativity was our second asumprion though.
Now it suddenly all makes sense. Without complicated maths. Special relativity and speed of causality is fundamental to a flat space time geometry. As simple as that. Or physics break apart. Beautiful.
OK this was a great video, but it took me until 25:40 to realise that you're trying to talk about the proof that there is *a* universal speed limit, not why we have that specific number 299792458 m/s. Can you include a clarification at the start of the video?
That being said, is there an interesting work on this too?
Actually I was just showing that the speed limit itself has nothing to do with light. But I got carried away. :)
@@AntiCitizenX It's just that when I hear "speed of light" my brain automatically translates it to "300 million meters per second" so that I have a reference in my head to compare to
@@MenkoDany The term “speed of light” is kind of overloaded. There is the speed at which photons travel through space, and then there is the deeper meaning encompassed by the Lorentz transformation.
@@AntiCitizenX I've been taught that "speed of light" is just "speed of mass-less particle"
@@MenkoDany Yes, that’s technically correct, but it kind of misses the deeper meaning. It’s kind of like saying the speed limit on the highway is the fastest speed that traffic can flow. Technically true, but not really what it means.
Cool, but there is a subtle assumption that you didn't mention. 16:27 I can see that you divide both sides by F1F2, but you can only do that if you assume that neither F1 nor F2 are 0. You say that that the galilean transformation only works if you set a constant (c) equal to infinity, but the only reason you were able to have such a constant is because you already subtly assumed the galilean transformation is wrong! So it's not imposing a "dubious assumption of infinite value for a mystery constant". If you apply this logic, then it's "dubious" to have anything equal to 0. For example, say you solve a differential equation, and it ends up with some parameter a. You could easily be like "well let's set a equal to 1 over a mystery constant b. It's a dubious assumption to say b is infinite" and then that would completely ignore a potential solution to the differential equation!
You do realize that F=0 is logically identical to setting c to infinity, right?
In math you can't just set something equal to infinity. If F = 0, then there is no such constant c. So it's actually not logically identical. At the end of the video, you said that the galilean transformation is dubious because you have to use an infinity, but my point is that you only have to do that if you already assume it's wrong.
@@Kuvina I didn't "assume" it's wrong. I leaped head-first into the experimental fact that it's wrong. I did so because I didn't want to spend another 20 minutes arguing it from first principles. A bit of a mistake, in retrospect, because I thought of a really simple way to show it (see pinned comment).
Regarding the equation displayed at 18:47, I am trying to understand the dimensional analysis of the 2 terms v^2/a and v/a. In the determinant, one of the terms is -v, so presumably the 4 terms in the determinant are all in units of v. This would mean that "a" is dimensionless, as v/a needs to also be in units of v. Under the square root, v^2/a is added to "1", so presumably v^2/a is dimensionless, meaning that a has units of v^2. This seems like an inconsistency, unless I am misunderstanding something?
I will also mention that you go too fast in certain places, equations just magically re-arrange and then disappear before I can digest what has happened. I need to understand the reason for the manipulation, and then the mathematical validity, and then the interpretation. You go at a speed that is suitable for someone who already knows the material, but not for someone who is learning it. This creates an anxiety that detracts from the experience.
If you’re struggling to follow along, feel free to just pause and rewind. Or hit the slow motion button.
The deduction has a flaw:, at 16:34 there is no discussion about the possibillity of Fand F2 being zero. This would have all equations fall back to the Gallilean Case. This case would also be equivalent that 1/c is zero, so the limiting speed is infinite. Az the whole video addresses to deduce that there must exist a finite limiting velocity, it fails to proove it, since it performs a 'division by possible zero'. So the Lorenz transformation deduced from the quite linear Maxwell's equations gives us a hint that F1 and both F2 is not zero.
By the way, despite the above details, the deduction is interesting, and the video quality is well done. It is well worth to fix the above mentioned issus.
Why do you say there is no discussion when there is absolutely a discussion at the end??
Isn't this the definition of Minkowski spacetime? And I have a question: At 13:14, why does t=t'? Because physics are the same in both frames? But you're measuring the time takes for Alice and Jim's heart to beat 10 times? Or do you mean the same amount of time as measured in 2 different frames, for example, measuring 10 seconds using the same clock?
Minkowski spacetime is basically relativity without the gravity. So you’re basically correct.
The t=t’ means that two ideal clocks will always remain synchronized, no matter how much you pick one up and move it around. In retrospect, this would also have made a great segue into the wrongness of Galilean relativity. You can actually measure the de-synchronization of clocks after literally picking one up and waving it about.
All good. I just not agree with the complains at the beginning.
There are many explanations on WHY it is so. The full explanation is often skipped if the video is not focused on the question
I have yet to see any videos that explain the “why” question correctly. My experience is almost always just a bunch of “well the evidence says so.” None of them ever try to show that it is a logical consequence of very basic assumptions. Even my own college classes on modern physics did the same thing.
But hey, if you know any good ones that take it to this level, I’d love to see them. I’m only basing this on my own personal experience with all the popular RUclipsrs and science shows.
1) ruclips.net/video/DGpwkWhnWAI/видео.html&ab_channel=SixtySymbols
2) ruclips.net/video/msVuCEs8Ydo/видео.html&ab_channel=PBSSpaceTime
3) also I was reading some popular science books, where was told, that the speed of light was derived from Maxwell equations (using algebra, not measured)
I got that your complain is about always associating the speed of causality with speed of light. I don't think its the big problem :)
@@DjSapsan That first video from Sixty Symbols is a good example of what I'm talking about. They already presupposed the Lorentz transformation. That's a really big pill you need to swallow before getting into the details. So my main goal in this video is show derive the Lorentz transformation from first principles, and do so without appealing to "light."
As for that second video from PBS Spacetime... that's actually the one that inspired me to make this one! :D
We need to check the assumptions. How do we know they are true?
The easiest way to think about it is massless particles can only travel at light speed and particles with mass can never reach light speed.
It's interesting how, going from the mathematical model needing the constant c to function, to it being a way to accurately calculate the speed of light, or the speed of causality. It seemed so arbitrary at first.
But I still feel that it should be important to mention that the mathematical model is still an approximation of the real world. Of course we test it, but it never breaks reality in the way it is said it does, it just breaks the model that we have of it
Except any violation of this model must necessarily manifest as a violation of one of our assumptions. For example, in a gravitational field, the law of inertia doesn’t exactly work. That’s a very important insight.
Excellent. Inspired and inspiring. I had to watch a second time, and with pen and paper as suggested at 4:28, and do the math for myself. So it takes a modest "me do it" effort, but I get it -- I really get it.
Well, now I'm wondering why light travels at that speed if that speed has nothing to do with light. If I remember my physics classes correctly, the speed of light can be derived from Maxwell's equations as a combination of a few other fundamental constants describing the electric and magnetic properties of empty space. So why do these two numbers match?
Mass is the conversion factor between force and acceleration: F = ma
The more massive something is, the more force it takes to accelerate. So if something has no mass (like light) it undergoes infinite acceleration and instantly moves at the fastest speed possible.
All massless particles move at the speed of light.
@@APaleDot That makes sense. Does that mean the magnetic permeability and electric permittivity of free space are in some sense determined by the speed of causality?
@@origamiswami6272
No idea
Because Maxwell's equations show that electromagnetic radiation will always travel at the speed of light, without any restrictions on which frame you're measuring it in. Thus, based on the principle of Relativity (assumption 2), the speed of light must be the same in every frame of reference. And, if you plug the value c into the velocity formula, you'll find that it always transforms to c, regardless of the relative velocity of the two observers. Thus, the constant "c" used here must also be the speed of light.
Maxwell's eq have an invariant c. Lorentz shows that the non-Gallelean case has a single invariant velocity that is also the max velocity (if accelerating from below it). Therefore (given MichMor experiment) c is the max velocity.
There is an even simpler set of premises in which you can prove relativity. N. David Mermin proved in his paper Relativity Without Light, that you can prove it on 3 assumptions that basicaly boil down to "physics works the same no matter how you look at it."
I read it for my college thesis in philosophy of physics back in 2003, then discovered he was teaching at Cornell, WHERE I WAS STUDYING! So I went to his office hours to talk about the paper and make sure I wasn't screwing up the physics in my philosophy paper. That was the first time I learned that top notch experts aren't actually that hard to reach and talk to most of the time, something I have used many times in my career studying law in the decades since.
I’d be interested to see these assumptions. My experience with reading the literature on this stuff is that authors tend to be a little fast and loose with their premises, often taking stuff for granted rather than make them explicit.
I looked and found the paper, but it’s hidden behind a pay wall. Booo.
@@AntiCitizenX It is beyond my capabilities to restate the premises now. It was something like invariance due to rotation, invariance due to translation, and something else similar. But I could be misstating it and certainly even if I'm not outright wrong I'm at the very least being imprecise. I never fully understood his paper. That's why I wanted to interview him to ensure I was at least adequately understanding his premises and conclusions for the purposes of how I was using them in my thesis (which was to convince philosophers that it is safe to assume that relativity actually needs to be considered, not really a super high bar as most philosophers accept that anyway).
Wow I can’t believe I’ve found this channel again after YEARS. Was it called something else before, or am I just salted with a terrible memory? Either way I’m glad to have stumbled back upon it.
Saddled*
Good explanation but it doesn't say why light travels at the speed of causality (the fastest possible speed)
Dammit, I'd have to brush up on calculus to digest the video.
Real science is not as easy as dipping apologists in the substance of their own toughts TwT
Here’s another misnomer performed by hadron collider, especially back about 20 is so years ago when I tried contacting someone there asking how is it possible if an object travelling on one direction (particles) colliding with another object travelling in opposite directions both at estimated to be near if not the speed of light give results equivalent to light speed when it should be results from a collision at C square, same as when testing vehicles in crash testing, when slammed against a stationary object at 50mph the results are that but if the target is also travelling at 50mph then the results are comparable to a collision at 100mph. Now the physics part. Not only would 2 objects at light speed produce results from a collision at c square but there’s other possible results from strathing, strafing, scraping and my favourite which doesn’t result in scatterings but skittering with finite possibilities and more plausible to say is what places like cern have been observing all along since a phenomenon is possible which occurs in the universe at anytime which is particles passing through particles without any detected results other then , if they could get their heads out their you know what, any other results then time. Not unlike neutrinos but possible. Possibilities are a particle of hydrogen would and could theoretically change to its previous or destine state ie reverse or advance it’s priori in that present time. It time traveled in a sense.
Don't get me wrong, I see your point here. But there is nothing in there that forbids c to be infinite in reality. In fact speed of causality being infinite seems like a reasonable assumption and the whole math works out just fine. So saying that it has to be this way, there has to be a speed limit c, seems little disingenuous. It just happens that in our reality assuming the c being infinite would be one too many assumptions.
Nothing except experimental data.
@@AntiCitizenX - isn't this video trying to prove it's more than just experimental data though? When you say "it is therefore not a matter of hopping into a spaceship and firing the engines" you seem to be saying there's something special about this being logically derived not just the result of experiment - so falling back on experiment at the end seems odd.
@@WorthlessWinner The primary argument of the video is that you don’t need to postulate a universal speed to get relativity. It naturally falls out of the basic concept of space, time, and motion. If you want a further argument that c is finite, then we can do that as well. But it’s kind of an entire video unto itself.
Great argument… really liked it… I think what is left is only few words to add in order to land on the “speed of light”… with extending the concepts used in this video you should easily figure out a relationship between this constant and the energy of the object. Then another extension will yield a relationship between the energy of the object (and hence the c contestant) with its mass. Then the finale! Massless objects has to be travelling at this speed limit C. Hence the speed of light (or any other massless object)! Voila!
Fascinating. But what speed of causality could mean? Any speculations on that? Why is it limited to that value? What's the background of this value? What if speed of causality was 50 km/h? What kind of universe we would have?
@@LachieDazdarian I think you can argue that the absolute scale doesn’t mean anything. If c were “slower” then everything else, including time itself, would also get slower, and nothing would change.
@@AntiCitizenX so is it about consciousness? I'm trying to wrap my head around it.
I haven't seen this exact version before, but I have seen derivations of the Lorentz transformation that don't involve assumptions about the speed of light, so it's certainly not something that isn't found in textbooks or isn't taught at universities. I think it would be better to say that it's typically not taught at the undergrad level, even though it certainly could be, since this is all freshman year math (single-variable calculus and basic linear algebra). I suspect the reason it's only taught at higher levels is that a lot of people find relativity difficult on a conceptual level. I've never had that problem, myself, but I've heard plenty of people perfectly capable of handling the math of SR, say that it messes with their heads. SR! Yes, with an S. You read that right.
I have maybe a half-dozen textbooks on modern physics and even relativity specifically, and none of them take this kind of approach. I’m therefore really surprised to hear that you have books and courses that do attempt something along these lines. Would be interesting to know what books you use.
For me, the hard part isn’t really the math. It’s getting my brain comfortable with the underlying premises themselves, plus the meaning behind the questions themselves (i.e., what are we asking, exactly?) So in my experience, using a first-principles approach like this is extremely helpful because to forces me to accept the outcome within a clear logical framework. It also forces you to stop thinking of light speed as literally the “speed of light.” It is the fastest speed that the very geometry of spacetime itself allows.
@@AntiCitizenX I can't recall if it was in a textbook or something a professor did on a whiteboard (now that I think about it, I suspect it was the latter). I do remember that in it, c was treated as an arbitrary constant. I think the idea was to show why c is the speed of causality, as you put it, and therefore just happens to also be the speed of anything with zero rest mass, including light.
@@Martymer81 That sounds more appropriate to me. Usually they just assume you’re comfortable with SR before revealing the “deeper” meaning. But that kind of assumes you’re already on board with the whole speed limit concept in the first place.
@@AntiCitizenX Yeah, well, this must have been in the context of SR, because I never took GR at uni. Next time I remember seeing the Lorentz transformation derived properly was in a GR textbook, Schutz probably, but as I recall, he does rely on the second postulate. I may misremember. It was easily a decade ago.
@@Martymer81 How do you feel about a follow up to this video that specifically addresses the possibility of c being infinite? I’ve looked high and low for an intuitive argument against it, but the best I can find is the appeal to Maxwell’s equations. It’s technically valid, but also kind of hard to explain to a lay audience. Plus it falls into the trap of associating c with “light.” I’d love to see a compelling argument that is more intuitively satisfying.
As a fun exercise, I would encourage you to research the Spacetime Algebra and re-implement the same transformations using multivectors in lieu of matrices.
yeah ive read that formulation.i have several of his papers saved in my browser favourites. hes tge real solo godfather of multivector spacetime algera. did he invent it? it does get used by more experimental physicists and chemists outside this relativity physics world though a physics professor hesa real outsider rebel for using the s[aceti,e algebtra multivector approach instead of vectors. also there is one that uses a quaternion formulation instead of the four vector minkkowski used to geometise relativity in 1907-8.that paper is surprisingly by some electrical engineer types from mulriple universities. allsi have that one saved in favourites. i]ll link them if anyone wants? plus there is one physicist, possibly the spacetime algebra godfather who uses this algebra for everything-with the multivectors. time ends up becoming the bivector and so a rotational entiity, which fits nicely with the idea that time was born at the t equals zero moment of the big bang, or the pre cosmic inflation period that preceded the hot big bang st ate that we find in the CMB 300,000 years after.
Thank you so much for this video. I remember somewhat recently going over the history of relativity and wondering "wait how do we know SoL is constant again?". I looked up experiments that would have discovered this and found nothing.
Now I know why. It wasn't one big experiment, it was a lot of math regarding obvious assumptions.
Well... obvious assumptions, plus lots of big experiments. :D
@AntiCitizenX point is, this is not an easily googlable answer. So having a relatively (lol) short video explaining how we know this is something I've been looking for.
Look up the solution of Maxwell equations for an EM wave. Speed of light ends up being a function of universal constants, rather than any feature of a particular system. That's why, even if we didn't have SR, we would still know that the speed of light is constant. Michelson-Morley experiment is relevant here as well.
@@omgopet I'd heard about the Michelson-Morley experiments. They're definitely relevant, but it always seemed to me like the conclusion just kinda came out of nowhere. Now I know why.
@@Nuclearburrit0 The sad thing about the MM experiment is that it was completely unnecessary. Maxwell’s equations very clearly imply a speed that cannot change with inertial frames of reference. The alternative would be an electric and magnetic force that change in magnitude with time of day and time of year and location on Earth.
Call it whatever you want and it still won't change the fact that visible light (as well as all invisible magnetic radiation) is traveling at the speed of light for all of us stuck on earth(which is traveling quite fast through space but in comparison to speed of light we might as well accept that we're almost not moving at all. It's like comparing snail to an aircraft. Thus our reference frame is pretty close to that of a completely stationary object and for us speed of light is like 99.9999999999999999 add as many 9s you wish, of the actual speed of light.). Sure, if we were traveling infinitely close to to speed of light, from our reference frame we'd be traveling at many times the speed of light but light would still be faster than us and from anyone else's perspective we'd just be traveling at speed infinitely close to the speed of light but not faster than actual light. Respect to anyone who's actually still reading this :)
I'm 63 years old, and haven't had calculus since 1978. Never had matrix algebra at all. So it gets a bit difficult to follow that part of the discussion.
Nevertheless, there is an interesting assumption made that may not be true. That is, time only moves forward. My understanding of Planck time implies that time can move backward for that extraordinarily brief blip. Is that true? What does this imply for the Lorentz transformation, and therefore Special (maybe General) Relativity?
Time is that which the clocks show. It's a perfectly classical quantity. There simply is nothing resembling time at the Planck scale. It's not that it could move backwards. There simply would be no way to measure it because a clock that measures time at the Planck scale would collapse into a black hole. The classical transition to that is fairly obvious: an ever faster oscillating clock movement has to become ever heavier (because of the additional energy needed to make it move faster), so it would show ever stronger gravitational redshift effects until it would simply freeze for the observer at infinity. Such a clock just stops.
@@schmetterling4477 Time is fundamental to Relativity. "There simply is nothing resembling time at the Planck scale." Say's who? You're just making things up.
@@dannutley931 We tried teaching you that "time is that which the clocks show" when you were five years old. That lesson clearly never stuck. :-)
C is the distance light fills before the next moment in time. Time is the number of interactions with the higgs field necessary to contain the energy as mass within the field of the atom. By maintaining the trong force. Spacetime stretches to accomodate the required interactions of each atom. Gravity is a relativistic force
I think you did a better job than PBS Spacetime at explaining this. Fantastic job ❤
Only Dialect
It’s worth noting that they did devote an episode to this topic, so maybe not earning a leading spot on the Bad Educators list.
Well I certainly wasn't doing matrices in high school. Eek.
Hey, you have made me think (again) about taking philosophy courses instead of Optimisation theory.
Could you please make a video about what one will await in pursuing philosophy?
I think there are not many people who do Stem and philosophy and I think it is kind of sad.
You will work for a carpet laying company, get fired, marry a lawyer, have 2 kids, get divorrced and die young from drinking, like my brother.
This guy thinking we took calculus in height school😂
25:25 More accurately, it can't logically be any other way *if* our assumptions hold. That's why scientists still run experiments, even tho the experiments to date support the assumptions.
100% agree. In the broader sense, however, I think it's very important to emphasize the logical connection. When hucksters try to "debunk" relativity, we need to be very clear about what else they would necessarily debunk in the process.
Is it at all significant that the assumption made at 2:50 is not practically feasible? Given that to start 2 clocks at the exact same time at different points in space requires information to travel between them.
Good question. I actually think this is one of the selling points of the argument. We have made no attempt to account for the time delay of information flowing between observers. We just assumed outright that all observers have perfect knowledge of things happening far away. That means the effects we derive are necessarily fundamental to space and time, and they have nothing to do with the imperfections of our measurements.
@@AntiCitizenX I get what you're saying, but what we're doing here is trying to conclude things about our universe, without observation. (That's what deductions / mathematical derivations are) Which is a dangerous game to play. Our only safety line is the assumptions we're making, based on the universe we're in. But how do we know which universe we're in, and which assumptions are reasonable? Through out measurements and observations! So to say the conclusions we derive from mathematics has nothing to do with our measurements, can't be quite right, can it? Because we're building our mathematics on the assumptions we built out of generalizing our observations.
Maybe I'm missing something here, but it seems like if the thought experiment is one that cannot be performed in reality, then you can't use it to conclude anything about reality. I feel the same way whenever mathematicians introduce the concept of infinity to explain some feature of our universe, when we've never observed anything infinite.
@@Google_Censored_Commenter it’s not at all dangerous if your assumptions are based on empirical observations. Like, the law of inertia isn’t just some random guess I pulled out of a hat. It is very much an empirical fact. The same with the principle of relativity. Experiments performed in North America in the Fall tend to repeat themselves when performed in China in the Winter. If the assumptions were invalid, we would absolutely be able to show it.
If anything, this is just another selling point. We KNOW that these rules do not universally apply. For example, the presence of a gravitational field would necessarily violate one of our assumptions, and it is a basis for general relativity. Violations of our assumptions necessarily imply new physics to be explored and measured.
@@Bendertherobot69420 what do you mean by "close enough"? Any distance at all will be a problem. And if you assume there's no distance between the two points, that's mathematically indistinguishable from 1 point, since 2 points cannot occupy the same area of space.
@@Bendertherobot69420 okay, but in reality it's not practically feasible for there to be no distance between two things. To define distance you need the position of two points in space. And to define two separate points in space, you must be able to identify a difference between them, that allows you to identify them as two separate entities. But if they occupy the same space, this is impossible. I'm not sure how else to explain it.
Annie must be related to Calvin...errr..."Spaceman Spiff"
at 9:20, why is x'=Ax+Bt the only solution? struggling to understand how that is easy to see
At that point we've set up the equality Ax + T(t) = X(x) + Bt.
Doing a little rearranging: Ax - Bt = X(x) - T(t)
So, we have this expression which depends on 'x' and 't', but it can be decomposed into the form X(x) - T(t) where we have two separate functions which only depend on one of the inputs individually. In other words, T(t) shouldn't have any 'x's in it, and X(x) shouldn't have any 't's in it. Since, Ax - Bt = X(x) - T(t), it seems the only possibility is X(x) = Ax and T(t) = Bt.
Thank you for using inertial frame of reference. If you are accelerating all bets are off. But then again, the universe doesn't care about arbitrary coordinate systems or arbitrary units of measure.
16:30 by dividing F, you assumed F is non zero. What happened if F is 0?
You get the Galilean transformation, which is identical to letting c -> infinity.
@@AntiCitizenX i see, so the basic assumptions do include galilean transformation as a solution. thanks.
Hmmm... Maybe the real reason is that the descriptor and descriptors of "space" are concepts relative to our concepts and perceptions of places and stuff (and all the stuff, the cosmos). That makes our concepts about "time" equally hypothetical. Now, this does not mean that is no stuff or place where movement (change of relative location) occurs. Nor does it mean that there is no duration of "events" (phenomena) and/or no mentality and no duration of mental phenomena (awareness, thinking, maths, etc.). Yet, it does mean that there are differences between a.) understanding, b.) knowledge, c.) descriptions & models, d.) the totalities of phenomena described & modeled, e.) concepts of "space" and f.) the magneto-dielectric "field" of hyper-frequency energy that enables and sustains all EM phenomena & subfields (including us). Likewise, the momentary totality of interactive flow phenomena involving the magneto-dielectric "field" (the basic universal energy) and its EM subfields always happens now, not in hypothetical mental phenomena (assumptions, presumptions, excuses, pontifications, etc.) in imaginary "space-time" (and spooky QM-creationist maths floating around in a nonexistent nothingness). BTW, FTL "space" travel could happen in a double vortex ("outside" the field/material frame of reference) caused ahead of a ship, but how to slow down and avoid little bits of stray debris (micro-asteroids, etc.) are immensely nontrivial problems.
Making a comment before watching. Maxwell's equations predict electromagnetic waves should travel at a constant speed, Einstein was just assuming the law of physics are the same in any inertial frame of reference. It is the first thing you learn about Reliability. .
The video is based on the assumption that space and time coordinates of different 'inertial' frames relate to each other up to a linear, first order relation (by removing zero order offsets.) Also, it builds upon Newton i, using the concept of inertial frames and their definition. However it misses to discuss the case if only space variables transform and time variables are the same everywhere. This case is a possible case mathematically, which covers the case 1/c is infinite, and the lower left element of the matrices shown being zero. The correct statement would be: We can not deduce mathematically that there exist a finite speed limit, because we arrived to that assuming 1/c is nonzero. (coming from direct physical easurements or via indirect mesurements leading to Maxwell's equations and Lorent'z transformation) THUS: The exsistence of a finite speed limit comes from phusical observations, mainly about propagations of light waves.
By the way, despite the above details, the deduction is interesting, and the video quality is well done. It is well worth to fix the above mentioned issus.
It’s not an assumption when it is evidently and demonstrably correct, my friend.
@@AntiCitizenX
Assumption in terms of mathematical proof. You cannot provide a logical proof of the statement, but only empirical evidence, therefore it is assumed at the start of your proof.
@@APaleDot for the second time, it is hardly an "assumption" when it is evidently and demonstrably correct, my friend.
@@AntiCitizenX
Different meaning of the word assumption.
That's exactly how my high school physics text books explained it. However it's still the speed of light because of more advanced physics. See permitivity and permeability of free space that set the coupling between electricity and magnetism. Light and the other massless bosons are the carriers of causality.
Sips water "That's exactly how my high school physics text books explained it." spits water
@krisrhodes5180 spacetime physics by Taylor and Wheeler. It's a very good book. ...my high school was a regular Texas public HS. Not a magnet or anything else. But Mr Gonzalez was a hell of a teacher who knew his sh-t. Out of all of my professors at Stanford, only Laughlin was better.
NOTHING in this universe is constant. EVERYTHING decays including the speed of light
You also need to assume sufficient continuity in order to swap the order of the derivatives, would you not?
Anyone with a strong enough mathematical background to follow your math variables would probably know what you’re trying to tell them already.
People such as myself who have spent decades with numbers that I’ve manipulated mathematically, I can only then understand the general case of using letter variable names. Once I have a solid grounding, and how the real numbers work. I would play with the numbers with the two fields of reference, moving at the same speed, and then slowly, give them diversion speed and direction to get a feel for it. Once I have played with these numbers for a long time then and only then could I now substitute letters for that which I had seen in numbers.
No point in you only preaching to the choir when this idea of speed of light is an important one for, many more people to understand.
The speed of light isn’t constant. It’s speed depends on the amount of mass nearby.
c is introduced late in the video as a factor in the Lorentz transformation. It would be clearer if you started with the Lorentz transformation, explaining exactly what is meant by c.
Relativity is solely a description of the gravitational field which couples to the matter fields. We take c=1 and the reason the maximum local speed cannot exceed unity is that world-line lengths must be real valued (there is no meaning to a line that has an imaginary length) with the shortest "world-line" having a length of zero, which seems to be the case for electromagnetic radiation and low-amplitude gravitational radiation (quotes around "world-line" as the photon/graviton do not have proper time affine parameterization, i.e. they don't have a history).
Very interesting. I could not follow the math used to arrive at the universal speed limit, but I understand the concept that nothing can travel faster than the universal speed limit... including light. My layman's knowledge of relativity tells me that matter cannot reach the universal speed limit because mass increases dramatically as it approaches the universal speed limit, thus dramatically increasing the amount of energy required to accelerate it. Basically, there's not enough matter and energy in the universe to do that. But photons and electromagnetic radiation can zip right along at the universal speed limit because they have no mass. The term 'speed of light' may not be technically correct, but I think it has practical applications, at least for us laypeople, such as explaining why we can see stars and galaxies as they existed billions of years ago. Also, I understand that galaxies are moving away from one another faster than C because the expansion of space itself is not bound by C. The Universe is a wonderfully weird thing.
I'm surprised people are having trouble with the math on this one. Is it just that people aren't familiar with matrix algebra?
Yeah, I guess so
I am familiar, but I haven't used matrix algebra for decades so everything does not just pop out from my head instantly. I would have certainly prefered to not use it since this can be very easily expressed with normal equations.
@@RandomGuyOnRUclips601
Harder to explain the inverse transformation, I would think.
"I dont know why this isnt taught more, anyone with a basic comprehension of calculus-"
thats why.
Contrary to popular opinion, plenty of people do know calculus. Most physics majors, in fact.
@@AntiCitizenX Have you considered the fact that most the people theyre trying to teach are not physics majors? or didnt even try to get into college?
This is from someone who actually likes calculus and math. The amount of high school teachers who ive asked 'why is this e(or i, or sin, or log) letter on my calculator even there? what does it do?' and get an unsatisfying answer of 'its just useful, you'll learn it in college' definitely doesnt help anyone try to actually gain that basic understanding. It especially doesnt help that unless you actually are going into a major that specifically requires calculus, youre just encouraged to avoid it entirely in college else you risk failing and adding another semester of debt alongside the debt you already incurred.
The story around calculus is unfortunately that its a complex subject and useless for the vast majority of people to do their jobs, which means most people will just refuse to learn it. "just a basic understanding of calculus" really is an unfortunately high bar for people to have, even if it didnt have to be.
@@Captain.Mystic I understand what you’re saying. I just fail to see what this has to do with the video. The mathematical foundations of this video are well within the grasp of a reasonably well-educated high schooler. I personally took AP calculus in high school, and there are lots of kids who even got ahead of me. I made no secret about the fact that you need a high-school understanding of calculus to follow along. If that’s not your jam, then that’s fine. But surely you can appreciate the logical beauty of it?
Showing PBS spacetime like they don't have a video titled "The Speed of Light is NOT About Light" is certainly a choice.
@@Chance57 They do not show you the derivation. They just sort of state the assumptions and then declare the conclusion. I’m not sure why you would find that a problem.
@@AntiCitizenX No but they don't take it for granted and they don't pretend like light is the cause of the "speed limit" either. Their video title is almost identical to yours.
It's not like your point isn't true, but saying it while PBS space-time is on the screen is weird. Because it's not true for them specifically. I've had professors it'd literally be true of, including one who told me "because God's smarter than us." But just because they didn't derive it from base assumptions doesn't mean they were doing anything like what you implied taking it as some ineffable standard.
That video isn't even the only time they bring it up, they bring it up constantly. I'd sound like jingle bells if I had a nickel for every time Matt explained why c is used to represent the constant and why "light speed" is directly correlated to space-time, not photons.
@@Chance57 Okay. But simply "bringing it up" is not really an explanation. It's an assertion.
I wrote a paper on this topic claiming the fractal does the same as light, quantum and all; that light may be a fractal. No one has got back to me.
Probably because everything you said was logically incoherent.
Well, the editor of the journal (the International Journal of Quantum Foundations) didn't think so. He has authored 4 books on QM and he thought my paper was 'interesting'. a compliment in physics I believe. @@AntiCitizenX
Woah. Awesome. Still got lost in the matrices, but that was awesome
How do you distinguish between inertial and non-inertial frames of reference? If you define inertial frames as frames in which the laws of physics work, that'd be like a circular definition wouldn't it. "The laws of physics work in all reference frames in which the laws of physics work"
Obedience to the law of inertia.
But then is inertia a universal law of physics, or is it just an artifact of how we choose to select reference frames?