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 believe I know why the KZfaq 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"

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.

“It was my understanding that there would be no math.”

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.

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.

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._

🎯 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

Bad form to take a shot at Matt, who is not guilty of what you claim here.

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... ;-)

Hey man, happy you're back. Always love your videos and have been watching for years. Hope you're doing well.

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!

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.

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.

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.

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.

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.

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.

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.

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.

"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?

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.

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

It's good to see your content. Thank you.

Wonderful video and excellent description of the Peliseto/Testa paper. Well done!

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.

Finally. Was worth the long wait.

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.

We need to check the assumptions. How do we know they are true?

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.

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

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 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.

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.

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!

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”?

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.

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!

really elegant; never seen it that way before; meaning: i never saw it _explained_ that way, AND I had never _visualized it_ that way

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).

I've finally understood how relativity emerges from simple assumptions and not an 'eureka' moment. Thank you very much for this video.

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?

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.

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?

Good explanation but it doesn't say why light travels at the speed of causality (the fastest possible speed)

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.

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

so in short, composite closure of Transformations and maintaining Causality, lead to special relativity without getting into maxwells equations and michelson moorley experiments and stuf.

Wasn't there a video on PBS Spacetime with this exact same title?

Well I certainly wasn't doing matrices in high school. Eek.

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.

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?

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.

NOTHING in this universe is constant. EVERYTHING decays including the speed of light

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 :)

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!

The speed of light isn’t constant. It’s speed depends on the amount of mass nearby.

You can't have any idea how incomprehensible this video is to many of your viewers. However, I at least got out of it at 10:39 that the relationship between all inertial frames of reference is defined with respect to the birth of Christ (delta=AD-BC), which I had hardly expected.

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.

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.

Annie must be related to Calvin...errr..."Spaceman Spiff"

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.

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!

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.

I wish this guy did a video on veganism/vegetarianism or transgenderism. It seems hard (for me, at least) to find concise and well thought out solutions to the problems these topics present. Of course, I have my own thoughts, but either way, finding this channel feels like stumbling into an intellectually stimulating treasure chest, so getting to know his perspective wouldn’t do harm.

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.

I think you did a better job than PBS Spacetime at explaining this. Fantastic job ❤

The road speed limit has nothing to do with cars. Except it does. It's the limit cars are supposed to drive

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.

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)

Fun fact: we ASSUME that the speed of causality is the same as the speed of light (or, should I say, the speed of massless particles) but it was never proven as far as I know, we just assume to be the case it would be impossible to go faster than masless elements. I.e. we know we cannot go faster than c but we have not proven that speed of light = c. Or am I wrong?

I'm surprised people are having trouble with the math on this one. Is it just that people aren't familiar with matrix algebra?

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?

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. .

SPD all the way. I've been known to walk on an occasional endless steep hill, up to a quarter of a mile at a time. And to walk around in stores and other venues without worry or guilt. And the double side clip-in hardly requires any conscious action. And I think extra play is less likely to cause injury than rigid motion control -- whether or not they're perfectly adjusted.

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.

Random question, but I want to know if you affirm metaphysical nihilism and empiricism, this is due to some past videos I watched

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.

Woah. Awesome. Still got lost in the matrices, but that was awesome

Extremely well presented.

I believe your claim about any high school student who knows a little bit of calculus will be able to understand your explanation is an exaggeration. Group theory is not a high school concept. Your explanation would surpass the knowledge of any high school student I've ever known. I'm actually an algebraist and have taught college calculus, and no Calc I student I know of would easily understand your explanation.

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.

My main objection with this video is that it supposedly illustrates how the whole relativity it just intuitive. However, I find assumption #1 quite unintuitive myself. If the transformation is a function of space AND TIME, it means you already suggest time is relative. I can never accept this as intuitive. Intuition leads someone to believe if everyone had perfect clocks, and we synchronized them once, we would observe one event at the same time. Or at least, we would observe differences of pairs of events having the same duration. ( I am not SURE about the validity of my statements, feel free to correct them). As soon as you accept time as relative, yeah, I admit the - now intuitive - notion of AVOIDING watching "bullets first, triggers after" naturally leads to the Lorentz transformation.

This is why I don't think relativity is truly relative. The only thing that is relative is your *perception* of the space, time and the speed of light. If there was some fundamental speed of causality through space, then all interactions (even at the quantum level), would be limited by the two way speed of this causality. This would force all the things you measure space and time with to be distorted in a way that altered your view of space and time. Your individual space and time would then be defined by your relative motion in regard to the wavefront of this "causality wave" (which would effectively be like an expanding light sphere). This is effectively the same thing as relativity... but this causal wave wouldn't be (and couldn't be) a *relative* effect. It would need to be a very real, absolute effect. It would define an absolute reference frame, even if it is hidden and no different than the rest. Your perception of space and time would still be relative, but this causal wave would have to be a real fundamental function of the universe. If this was the case, it raises the question of what property of the universe causes this speed of causality? Can it be altered? Can it be changed? This is how new physics will be found IMO.

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.

You also need to assume sufficient continuity in order to swap the order of the derivatives, would you not?

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.

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.

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 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.

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).

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

Without math, for those who slept through Calc I, why isn't this thing linier? I mean, why is 200 million m/s plus 200 million m/s not 400 m/s? No math.

16:30 by dividing F, you assumed F is non zero. What happened if F is 0?

Yup, your very simple blackboard equations made it plain as day. I thought that was the way it was all along. Even my wife had it figured out. However, I'm much more concerned about the 70mph speeders that frequent my street which has a posted speed of 30mph. I think it can be addressed by the police and lawmakers. I'm not so much concerned about the speed of light, because nobody seems to have jurisdiction.

How do we know that the speed of light and the speed of causality are necessarily equal?

Most physicists believe the speed of gravity waves is equal to c. Can you give a reason why they should be the same?

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.

I never took calculus...which means this entire video is incomprehensible to me. I just accept _c_ as the speed of causality (and light), and cannot be exceeded...that we know of. There's nothing wrong with simply accepting the absoluteness of _c_ .