Deriving Einstein's most famous equation: Why does energy = mass x speed of light squared?

[@nmgreg11]

As a 61 yr old Mechanical Engineer, this channel has me addicted. The teaching style works. Please, keep future (what ever that means, relativistically ) videos coming.

[@PhysicsExplainedVideos]

Thanks! Plenty more videos on the way

[@hoekbrwr]

As I am even a little bit older now I do understand why I needed to learn all those rules of math in school! That's more than 50 years ago. As I ended up being a practical electric engineer and not done a theoretical job I catch just a tiny bit of it. I really get that marvelous feeling again of understanding all those math 'tricks' as I had to learn 50 years ago. Keep making these excellent videos!

[@daveanderson718]

@@PhysicsExplainedVideos You must be doing something right here. I see I am not the only "old" dude here who once was taught this stuff in a much more complex way.....and subsequently never used it my profession.....only to appreciate what you have done in 30 mins on KZbin. Rather than "whine about the loss", you inspire me to watch it again and your other videos as well. Bravo to you Sir!

[@tim40gabby25]

Jeesh.. anyone here under 60? Old UK duffer here, enjoying the ride :)

[@alirezanabavian771]

@@tim40gabby25 it takes a great deal of experience like decades of engineering to truly appreciate and dive into these equations and walk with Einstein discussing physics though for only a short period of time....yes Albert ..now I see where you're coming from....

[@DMBHomes]

When I studied physics I found it hard to accept equations that I had to memorise. It was as though my mind rejected anything that wasn’t proved to me. Learning how to derive an equation was my way of instilling it into my brain for ever and at that point I was able to leap forward. Fantastic video - Thank you

[@xxxalphaeverythingxxx8489]

Holy shit this is so relatable to me. I have this feeling of missing out or of not actually knowing something unless i can derive it myself in my mind

[@toughenupfluffy7294]

I'm the same way. I look up word roots for the very same reason, understanding of context allows for deeper learning.

[@User-jr7vf]

@@xxxalphaeverythingxxx8489 same. This is annoying at times but it is the way my brain works and I've come to accept it 😂

[@BD-np6bv]

People who simply memorized equations won't learn anything. It's people who question equations that will grasp the theories.

[@xxxalphaeverythingxxx8489]

@@BD-np6bv Couldn't agree more.

[@alextaws6657]

Thanks!!! I cannot tell you the amount and intensity of pure happiness of understanding and insight your videos give me! A huge part of that is using the actual math behind the concept (a rarity in educational videos) but didactically so well that I can get even concepts of which I would have never thought that I could! (a difference to, e.g., pbs spacetime)

[@atticuswalker8970]

I got one for you. E=ymc² where y is the Lorentz factor. Time is 1 dimentional. And spacetime stretches to accommodate the necessary interactions with the Higgs field to maintain mass.

[@acpwnd2020]

I'm so glad your channel exists. I've felt like the way physics is taught is wrong; we're just forced to memorize a bunch of equations. But your channel truly reveals the underlying beauty. Thank you. Don't stop making these videos, I bet they'll inspire many a future physicist.

[@PhysicsExplainedVideos]

Thank you so much!

[@Hampo03]

I’m just in the 2nd of 3 years in high school (in Sweden) so it’s not that advanced but my physics teacher is amazing at teaching both. He shows how somethings works and then how to get the equation for it, often using previously learned equations

[@am3rgam3r]

It very much depends on who your professor is. Physics is one of the most amazing and Fulfilling sciences and subjects in school today. ( my opinion )

[@BruceNitroxpro]

Totally and completely true. The simplicity of expression is a wonderment.

[@BboyKeny]

@@am3rgam3r I read the old books by the people of that made the theorems. I find their instructions to be often the best.

[@InfuZedShaDoWz]

It's just absolutely insane to me that the human brain is complex enough that it can work stuff like this out. It's like looking into the game files of life.

[@PhysicsExplainedVideos]

I know what you mean!

[@HR-yd5ib]

Only one in A Million brains though! 🤔

[@chrismadaj8751]

That is what I have gotten out from this we are so Superior with our brains but only a few of us can comprehend with mathematics. To come up with these equations But not necessarily saying they're smarter than the Average person. Common sense is a whole another thing.so cool though 😎

[@iancampbell4394]

Not life, my friend. Life is a fundamentally biological concept. This is like looking into the game files of the universe itself.

[@ibrahimkhatib6191]

@Chris Madaj The measure of smartness depends on the smartness frame of reference!

[@johnny14980]

These are the most intuitive and ground up videos I’ve ever seen. No glossing over concepts. Not missing a detail. Absolutely brilliant. Thank you for teaching physics the way it should be taught.

[@jasoncassidy492]

You are easily pleased, John, I find the explanations to be so obfuscated and trite as to be of no use.

[@nerdsunscripted624]

@@jasoncassidy492And you sir put a lot of effort to make your comment more obfuscated than it needed to be. If you think this is hard then maybe the oversimplified mildly incorrect explanations of physics are more for you

[@myzo247]

😊😊😊😊😊😊😊😊😊

[@hfarthingt]

I’m now an expert

[@jasoncassidy492]

​@@nerdsunscripted624 Nothing hard about it, time does not exist and energy has no relation to mass, therefore E= mc^2 is nonsense. F = ma makes perfect sense since a force applied to a mass can cause it to accelerate. However, E = mc^2 suggests energy can be converted to mass and vice-versa. We have no idea what energy is and we define it loosely as the ability to do work. When Einstein created that equation, he was talking about electromagnetic energy being converted to mass. He believed that and he was wrong. Can it also be applied to thermal, electrical, mechanical, and gravitational energy? Don't think so. Einstein lived in a time when these phenomena were just starting to be investigated. I fear he jumped to irrational conclusions.

[@jamesdavison6290]

When I was in high school, I read George Gamow's book "1 . . . 2 . . . 3 . . . infinity!" I read the "gamma" equation and plotted points, and read Heinlein's books about time compression, and tried to get my mind around Einstein's understanding of the universe. I even took courses in differential equations as an engineer and became familiar with the mathematical tools you used. But forty years later, seeing all the dots connected in your video was a personal discovery that I will remember long after tonight's hangover has worn off! Thanks!

[@PhysicsExplainedVideos]

Very glad to hear it, thanks for the comment and feedback

[@daveanderson718]

@@PhysicsExplainedVideos Obviously you are doing something right. Don't stop.

[@alirezanabavian771]

I feel the same way exactly after having been an electronics engineer for 40 years I have gone through the same revelation as you have....more power to him...the best I have ever known...

[@riazhassan6570]

Yes. As an interested layman, I found this helped to take me round difficult corners better than some treatises I read in the past

[@colinnewton7291]

@@alirezanabavian771 Ditto

[@gamer19591]

It's always such a bliss seeing you explain such complicated topics with ease. It helps me tie together the theoretical parts from my lectures with some perspective. Thank you for these magnificent videos

[@PhysicsExplainedVideos]

Great to hear!

[@everettmcinnis5858]

There are many people on this planet that are capable of doing all of the calculations in this video, but there are very few people that are capable of explaining this topic with the lucidity that you have. Thank you deeply.

[@beardydave926]

This is one of my favourite derivations in Physics. I remember doing the algebra at Uni and having to redo it so many times to get it right. The maths was brutal, but so satisfying :)

[@iamprox3690]

🤓😒🎃

[@iamprox3690]

l l i’ll lollll l i’ll l l l l l l l l l l l l l l p p p p p p p p p p p p p p p p l p p p p p p p p p p p p p p p p p p p p p i’ll p p p p p p p p p p p p p p p p p p p p p l l p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p l p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p i’ll 😢

[@steveolmore6091]

Thanks for explanation, helps.

[@lightningbolt4419]

@@iamprox3690 agreed. This guy is bullshitting.

[@jasoncassidy492]

Dave...another David...the physicist David Bohm... once stated that an equation with no reality to back it is garbage. Time has no existence and the use of it as the basis of a theory is beyond garbage. The irony is that so many people blindly accept Einstein's theories simply because of his appeal as an authority figure.

[@lakshaygupta9061]

Stop spoiling us with all the terrific content

[@larryzdanis5377]

As a mechanical engineer, I was always intrigued by the E=mc^2.. never knew where it came from, whereas 1/2mv^2 was easily derived. Refreshing and englightening tok see the whole picture, and the presentation was elegant. Thank you.

[@Jacob.Peyser]

I watched this video a bit over a year ago out of pure curiosity. But back then I hadn’t even taken physics or learned calculus yet. Now I’ve done both, and coming back to rewatch this video with the new knowledge/intuition of what the heck you’re talking about half the time has made me realize how profound and awesome relativity is. Thank you so much!

[@hareecionelson5875]

Same. First time I saw this I was a year 4 med student, did not understand the chain rule. But, after graduating and working, I reapplied for physics and did more math, now I can follow along and it's even better

[@jasoncassidy492]

Jacob...time to put on the thinking cap and re-evaluate. It took me years after studying electrical engineering to understand that time does not exist. I confirmed that with one of my physics profs years later. He replied immediately that humans invented time to keep tract of change. Physicist David Bohm has claimed the same thing, that humans invented time. If we invented time, which we did, basing it on the rotational period of the Earth, how does it dilate? Anyone can convince most people of anything using math, the trick is to explain what the math means. When you look closely at the math in this video, it's all based on a distortion of the human mind and its inability to keep tract of relative motion. It seems astounding to me that Einstein could have missed that mental issue in his analysis.

[@Jacob.Peyser]

@@jasoncassidy492 Whether or not time is a strictly invented or a discovered phenomenon, it along with all the other fundamental ideas in physics describe our observations of the universe with unparalleled accuracy. In my current opinion, if a theory like special relativity could so precisely describe reality, then surely its implications must be fundamental to reality itself. Now, I never took an official class in special relativity. Hell! In under 2 months, I'll be starting my freshman year at university. So I have a long way to go with my physics education, and my views have much room to change. However, I hold this particular view very tightly. With regard to your opinion, It seems as though you don't get what time dilation is. To argue that time cannot dilate or be relative because time is based on the rotational period of the Earth is almost nonsensical. The whole point of Einstein's special theory of relativity is that there is no universal clock. Every inertial frame has its own unique metric of time, thereby making changes in time relative between observers. Keep in mind that this principle of relativity is mathematically deduced by the constant nature of the speed of light (as laid out in the video) and this characteristic of light was justified experimentally after Einstein's insights. I think the confusion stems from the terminology of time "dilation". Time doesn't physically dilate; it is simply relative. That's it. Einstein was not perfect, but I bet he was a hell of a lot wiser and more intelligent than 99.9% of the average Joe (like you and me) and even the current physics community. Wow... that was some rant over a comment from so long back.

[@jasoncassidy492]

@@Jacob.Peyser Jacob....what else could time dilation mean? The basis of Einstein's relativity theory is that both time and length change as a mass approaches the speed of light. He got that idea from Lorentz who had hypothesized earlier that time and distance must change when transforming between two axes moving relative to each other, as velocities approach the speed of light. Louis Essen, who invented the atomic clock, pointed out the error in both views. Both Einstein and Lorentz changed reality to make their equations work. Einstein arbitrarily changed the definition of time, and that is not allowed in science without proof. He supplied no proof, his conclusions are based strictly on thought experiments. He also ignored the fact that we humans defined time based on the Earth's rotation.

[@pipertripp]

master class. This was loads of fun. The derivations were very clear and easy to follow. In fact, the bit about time dilation could be taught to kids in geometry call. "See, this stuff you're learning is important and can help lead to mind blowing discoveries."

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@theshibby1337]

The fact that my highest education is a trade and I can still understand this, is a tribute to your teaching style. Thank you

[@bangscutter]

It's truly amazing how seemingly unrelated concepts just "pop out" of the math and build on top of one another! For example, Maxwell's equations deals with classical electricity and magnetism waves, yet the speed of light pops out of it naturally. Then, the constancy of the speed of light is used to derive special relativity. Next, special relativity which is about massless light, when applied to an object with mass, the rest mass energy pops out naturally! After that, considering the momentum of a massless particle and equating with the photo energy from the photoelectric effect, we get the de Broglie wavelength! The mass particle duality consequence of this, then leads on to Schrodinger's quantum physics! The self-consistency of the math and physics is truly astounding! It's always been there all these while, just waiting for a brilliant mind to uncover it.

[@PhysicsExplainedVideos]

I totally agree!

[@tim40gabby25]

@@xiaoxiao-kg5np given that the set of um.. Kabbalists does not include Maxwell, then your "all" assertion is false, allowing for your house of cards gently to collapse. Wrong channel old boy, kindly meant :)

[@xiaoxiao-kg5np]

@@tim40gabby25 Maxwell was not in my set of kabbalists that "discovered" quackery. You tried to add him in. I also did not include Newton, although he was a bit of a believer in alchemy and such, as were many others of his day. So please keep the kabbalists in their own camp of numerology and pseudoscientific quackery. My house of made of solid rock, standing on rock.

[@ziqfriq]

@@xiaoxiao-kg5np You should probably check out Gabor Fekete, and get on his email spam list.

[@frankh4069]

@@xiaoxiao-kg5np add Heisenberg to the nope-list

[@alfredobeltran611]

This is, by far, the best physics channel on KZbin. Very well done. Thanks for posting this videos

[@jaredkiehlmeier6460]

I’ve been watching videos on relativity for years and this video has brought a lot of conceptual ideas together very concisely . 10/10

[@randomstranger2579]

I’m 15 and I think that if they tought us about the equations we have to ‘memorise’, most people would love physics as much as I do. Great video! EDIT: Now doing a Physics degree

[@PhysicsExplainedVideos]

Thanks!

[@jaimeduncan6167]

I am glad you love science, and I can see that you still have a lot of fait in humanity. I believe you are wrong, most people will be asking if it's going to be in the test, and eager to just learn how to calculate, get the grade and forget about it. If you stop to look at it, you will notice that it's not as bad as it seems. I for example, have little interest on following the last fashion, aldo, in a daily basis, it affects us. Even so, if one says "more" people instead of "most" people one will be correct (I am guessing here). Keep your curiosity and your hope, it's a privilege of young age and gives people the power to transform the world, even if it's a little bit, for the better.

[@arniedamaniac6206]

@@jaimeduncan6167 I’m 14 too and I agree with you

[@lillearnero2329]

@@jaimeduncan6167 This is the guy who posted the original comment on another account as I was rewatching the vid and happened to see it. I believe you are correct as I am 16 now and have just finished my GCSEs. A shocking number of people decided to burn their books and notes as soon as we finished which proves your point, I do not really understand the logic behind it but it is just how things are. Fortunately their are still those that learn for curiosity and passion, however few they may be, and so I keep hope that the future can be bright. Thanks for replying and good luck.

[@jaimeduncan6167]

@@frankdimeglio8216 you have no idea what you are talking about. Like no idea, there is plethora of experiments that show that you are wrong. Even more, most of the stuff we see and use in a daily basis will not work if you were correct. I am not saying that the current scientific understanding, that predicts stuff with 10 digits of precision is perfect, we know with certainty that the current models are incomplete but dude you are way off. You really need to study a lot more and be humble. Once you do that your creativity may push you in the right direction.

[@as007de]

Just finished binging all your videos yesterday! Ready for new content :D Best channel I discovered in a while!

[@PhysicsExplainedVideos]

Glad to hear it, thanks for the feedback

[@georgiiii1000]

I watch tons of educational KZbin videos (PBS space time, philosophy, history, etc) you have blown my mind with how simple you made this. I have a math background so I was able to follow every step of the way. I have never considered contributing to a patreon before but if you have one I’d donate. You are an excellent educator. Thank you.

[@vedantsridhar8378]

This is real physics. PBS Space Time is only physics as entertainment for the general public.

[@georgiiii1000]

@@vedantsridhar8378 totally agree, still interesting to watch.

[@blackstar2008]

“Which should be familiar to anyone .....................studying particle physics “. Thanks for not making me feel stupid 😀

[@toddmarshall7573]

Now that you don't feel stupid, consider this: 9:40 "we'll see the light take a zig zag path": I go off the rails right here. Imagine the train going around me in a circle at 300m/s and 1km away. I'm watching a tennis player riding in a glass boxcar hitting the ball against the wall repeatedly (i.e. your tic tok). I am standing on a rotating disk looking through a telescope such that my view is perpetually perpendicular to the train's velocity. I don't see any zig zag. I don't see any dilation. There is no warping of space or time. Further, if there is a glass box car on my disk with a tennis player doing the same thing as the disk rotates, and I have a split mirror allowing me to observe both simultaneously, their "tic toks" are in perfect sync. Now speed up the train to any velocity you like...say 300e6 m/s. And speed up my disk rotation accordingly. I still don't see any zig zag...yet I am stationary and the train is moving at the speed of light. Further, the tennis players continue to hit the ball (as observed by me) with no zig zag and in perfect "tic tok" sync. And they both have the same mass. The tennis player on the train doesn't enlarge to infinite mass...and if you like, extend the radius of the circle such that he doesn't get squashed by the centrifugal force...and I don't get dizzy with the spinning. There is no magic at the speed of light...or anything to suggest I can't exceed it. Further, a train running the opposite direction but same speed on parallel tracks would appear to approach at twice the speed of light...because it is...and we likely should expect a Doppler effect, just as we observe with sound. 25:88 Then you go on through all kinds of math and end up comparing energy. And you have this spurious mc^2 term that you begin to explain away. But let's start that other train in the opposite direction on parallel tracks. Both trains carry a mass of 1kg. They are both traveling at a velocity of v^2. The KE of those masses is 1/2 mv^2 each. Together it is mv^2. Now, when we get to v = c, just as the masses are about to pass each other in opposite directions, push one mass into the path of the other...taking virtually zero energy to do so (e.g. you moved the mass 5 m perpendicular to the v ...or you move both masses 2.5m ...one toward me and one away from me...while they each travel 300e6 meters in the one second it takes me to do the shoving). And bammo! The masses collide and their velocity adds instantly to zero. And their KE goes instantly to zero...and turns into heat as the masses vaporize. By the time they hit, I'm 150e6 meters away and just see the flash. How much heat? Well, it's 1/2mv^2 plus 1/2mv^2 or mv^2. And if v is c, then it's E=mc^2. Now where is the magic? Where in any of this does relativity come into play? And do you really want me to believe that one tennis player is aging more quickly than the other? Or that the tennis player goes to infinite mass? And you really want me to believe there are massless particles? Why? I'll bet Tesla would get it. I'll bet he wouldn't have to make up photons either.

[@enricolucarelli816]

@@toddmarshall7573 sorry, but all of your thought experiment is wrong from the very beginning, because special relativity only applies to INERTIAL FRAMES, and your frame of reference is rotating, thus anything but inertial. In a rotating frame of reference you experience accelerations, thus you would have to consider space-time warping according to the laws of general relativity.

[@toddmarshall7573]

@@enricolucarelli816 something's peculiar. I can find your reply on my phone but not on my computer.

[@toddmarshall7573]

@@enricolucarelli816 Todd Marshall 38 seconds ago @Enrico Lucarelli something's peculiar. I can find your reply on my phone but not on my computer. ...... and now "having replied on my phone" it shows up on my computer...so I can respond. " sorry, but all of your thought experiment is wrong from the very beginning, because special relativity only applies to INERTIAL FRAMES, and your frame of reference is rotating, thus anything but inertial." And I agree with you. The INERTIAL FRAME is physical...a body in motion tends to stay in motion...and its direction is constant unless acted on by another force...that's inertia. That being said and understood by both of us, and trains A and B moving in the same INERTIAL LINE, which of the following assertions are correct and which are false: (1) The speed of light is constant and the same for all observers. (2) The wavelength(s) of light is (are) constant and the same for all observers. (3) The speed of sound (in its ether of air) is constant and the same for all observers. (4) The wavelength(s) of sound (in its ether of air) is (are) constant and the same for all observers. (5) The length of a ruler is constant and the same for all observers. (6) The "appearance" of a ruler is constant and the same when viewed from all angles. (7) Light from a flash light on a train moving at the speed of light is the same for all observers (8) Two trains moving in the same inertial plane. Train (A) is moving at 80 miles per hour. Train (B) is moving at 80mph plus 150e6 meters per second. On train(B) the wavelength of light from train (A) appears to be twice as long as it really is. (9) In example (8), but train B moving at 90mph plus 300e6 meters per second, the light from train (A) is never observed on train (B) (10) Train (B) cannot move at 90mph plus 300e6 because it's mass grows to infinity at that speed (11) A ruler on Train (B) is a different length than on Train (A) at any speed greater than 80mph. (12) A ruler on Train (B), as observed on (B) is of zero length when moving at 300e6 meters per second (13) A ruler on Train (B), as observed on (B) is of infinite length when moving at 300e6 meters per second (14) A flashlight on Train (B), as observed anywhere has the same mass as on Train (A) My answers: 1-T; 2-F; 3-T; 4-F; 5-T; 6-F; 7-T; 8-T; 9-T; 10-F; 11-F; 12-F; -13-F; 14-T; "In a rotating frame of reference you experience accelerations, thus you would have to consider space-time warping according to the laws of general relativity." More correctly, in a "rotating frame of reference" I experience a force which causes the straight line of inertia to change direction...and that Force is equal to the Mass times Acceleration. That being said and understood by both of us, it suggests "no" change in any of the "rulers" taking measurement...be they space or be they time. And perceptions don't change that.

[@edwardjcoad]

Awesome! It's the simplicity of the explain which I enjoy so much. Its calm, smooth and seamless approach which i enjoy. I have a PhD in Physics and I learn alot from these videos especially about the initial stages of a derivation which I appreciate. Another great video.

[@PhysicsExplainedVideos]

Thanks for the kind feedback, I am glad you enjoyed it!

[@ksskaria361]

@@PhysicsExplainedVideos It's really wrong.

[@krzysztofciuba271]

? from 8:00 to 13:00 a typical junk on "time dilation"+ he (surprisingly) got a right conclusion on the "mass" but there is a more simple derivation: just multiply both sites of space-time "distance formula" by a constant "m".

[@JackyKou]

Great video! This channel is my favourite, and is what I rely on if I *really* want to understand some physics mathematically. By the way, at 20:32-21:11, I believe the minus sign in the middle of the green square bracket should be a plus.

[@Miftahul_786]

This was really confusing me then I went back and realised yeah it should’ve been a plus

[@qgxii]

yep, you are right.

[@lolerishype]

Thank you so much so much

[@m_bm_a7884]

I have one question please: At video time of 19:00 , we have : dp=m.v= m.(dx/dt°) dp=m.(dx/dt).(dt°/dt) =m.v.gama This means v=dp/dt°=dp/dt Is there mistake here??!!!

[@JackyKou]

​@@m_bm_a7884 Following your quote "dp=m.(dx/dt).(dt°/dt) =m.v.gama", I found from the video that it is actually "m.(dx/dt).(dt/dt°)", with the chain rule properly applied.

[@dankuchar6821]

Excellent work! The best derivations and explanations I have seen in my three decades of Physics.

[@PhysicsExplainedVideos]

Great to hear!

[@musicmakelightning]

Beautiful work. Utterly clear. This series of lectures is masterfully executed. There is much to learn and retain with the minutes spent on this series.

[@davidmthorley]

As a complete dunce when it comes to maths and physics I found your video surprisingly understandable. Very clear, well presented, and using examples that helped me visualise the concepts. Great work.

[@SeverusVergiliusMaro]

Oh, this is gonna be goooood

[@appleslover]

Say hello to daddy aang

[@obst3085]

Absolutely the same. Every time it's fascinating with how little assumptions and clever actions, such elementary principles can be unveilled (although their primary derivation are works of art by some of the most talented scientists out there *and* their true meaning are beyond grasp for most things still)

[@DLockholm]

I was about to say this same shit lmao

[@magnomaxx2010]

This equation, not was Einstein's creation, but of one italian cientist before.

[@junkbucket50]

Love this channel high level treatments of topics while equating them with other relevant things. Really good channel

[@PhysicsExplainedVideos]

Thanks!

[@albela0007]

Beautiful. I always thought the derivation of E=mc^2 involved complex math because I don't remember anyone teaching this in school and college. This explanation provides a straightforward derivation using calculus most people learn in junior high school and college. I don't understand why then this explanation is not included either in math/calculus books or books on physics/mechanics. One small correction I see for the green equation at 20:32. It should + instead of - between the two terms in square brackets.

[@vhawk1951kl]

When you verified for yourself the truth of what you call "E=mc^2" the energy of what were you trying to discover? All sorts of things can be called energy can they not?What exactly were the dtails of the experiment to test the truth of the assertion "E=mc^2"? Just as a matter of interest how did you measure the speed of light to use in the verification for yourself of "E=mc^2"?How many times did you measure the speed of light and was it always the same in both directions? I am of course assuming that you would dream of just believing what you were told like a rather slow childand thus insisted on verifying eveything you were told by experiment known as the scientific or not_religious method; science being be the verification of every supposition by experiment and were you just to accept without questionE=mc^2" that would be religion would it not? So no belief for you who insistn verifying everything for yourself do you not? In your experiment to verify " E=mc^2 the energy of exactly what was the same as its mass multiplied bythe speed of light which was what when you last measured it. In units of what were you measuring the energy of exactly what? When did you verify for yourself that "E=mc^2"? Was it simplicity itself for you to satisfy yourself so that you were sure that " E=mc^2, or was it a complex and elaborate experiment to verify for yourself that "E=mc^2"? Purely as a matter of anodyne academic interest why might the speed of something other than X(specifically light)have any bearing on the energy of X? One has visions of chaps all over the world saying:" I'm not going to tote that barge or lift that bale because light seems rather slow today." Presumably before you can say that the energy of X is its mass multiplied by the speed of invisible rabbits, you would have to devise some method of establish the energy of X *before you multiplied its mass by whatever to see whether or not they were the same. When you were using the scientific method of verification by repeatable experiment, the energy of exactly what was the same as its mass multiplied by the speed of light which you stablished *by experiment* to be what? How exactly*did*you go about discovering for yourself?

[@stefanoscintilla5225]

​@@vhawk1951klthe proof is in this video. The OP also never said he did it himself. The speed of light can be derived from Maxwell equation and we use them everyday to make the phone from which you wrote this dumbass comment work. Stop being delusional.

[@awolgeordie9926]

Again, simply brilliant. A level Physics teacher here - background in Electronic Engineering - your videos are immensely helpful. And enjoyable. Thank you. (Might be a small error at 20:40. The two terms in the green equation should be added - not subtracted.)

[@PhysicsExplainedVideos]

Thanks for the feedback, I really appreciate it. And thanks for spotting the typo!

[@lolerishype]

Thank you so much so much

[@Euquila]

Wow, you really did the whole derivation without cutting corners. Nice!

[@aliabdaal]

Amazing video ❤

[@kenpee6751]

❤

[@maybepatrick369]

what is bro doing here

[@SdjdidjeuDidjdjdkkd]

He getting flexed on by other yoo toobers

[@dmhouse1024]

Perhaps I misunderstood, but I didn't understand the logical leap at 23:18. Why is it the case that gamma*mc^2 can be interpreted as the total energy of the object?

[@bobwhite137]

I had same question - all but that point was fairly clear

[@DSeyit]

Yes that part is not clear to me either. Why total energy is not kimetic energy?

[@DonkoXI]

This step alone is responsible for ending up with E=mc^2, but he doesn't explain it. It's a critical flaw in this derivation.

[@kenhaley4]

What a great explanation! One point I would add for all viewers who get confused by Special Relativity and the common paradoxes. E.g., if moving clocks run slower in my reference frame, then wouldn't my clock run faster from the reference frame of the moving object? (and the answer is no; see 'twin paradox'). And the point is this: You cannot fully understand Special Relativity, unless you understand all three components: Time dilation (discussed here), Lorenz length contraction, and the relativity of simultaneity. Obviously, a deep dive into these topics is beyond the scope of this video, but I think it's worth mentioning, as part of your audience might be new to Special Relativity concepts.

[@derekgreenacre9530]

I have tried many times to understand these equations but it is only with this video was I able not only to understand the equations but to be able to derive them for myself now. This is wonderful the equations have an intrinsic beauty that transcends space and time and that of course is what they are all about.

[@PhysicsExplainedVideos]

Glad it was useful

[@narfwhals7843]

You really just wanted to say "the ticktock of the moving clock" as often as possible, didn't you? Great video :)

[@PhysicsExplainedVideos]

Hahahaha, I was thinking that as I was saying it

[@nobigbang825]

​@@PhysicsExplainedVideos Keep repeating the lie until becomes the truth. E=MC^2 was originally attributed to Olinto De Pretto, you and your cult of Einstein had destroyed physics. en.wikipedia.org/wiki/Olinto_De_Pretto "Physics explained" my .....

[@bixmcgoo5355]

@@nobigbang825 man i wish I was able to be so confident while also being so wrong

[@ayo9344]

@@bixmcgoo5355 Idk it does say on the page that Pretto's formula E = mv^2 (v is the equivalent to c by Pretto) precedes Einstein's E = mc^2 by 2 years. Did you see that part? I just think it's interesting, and tbh just not sure what to think about it.

[@bixmcgoo5355]

@@ayo9344 oh I didn't say that the guy didn't come up with an equivalent theory (which is honestly great, though it's worth noting that the ether stuff he was trying to prove was horseshit). I guess the issue is the previous responder saying that Pretto was the one to which E=MC^2 was originally attributed, which is simply not true. They came up with two essentially equivalent formulae, and the proper formula was attributed to the one who discovered it. It's very likely that Pretto's work wasn't taken very seriously further down the line because, again, his entire line of questioning was in reference to a fundamentally wrong idea that is "the ether"

[@JamesKaramath]

Can't thank you enough for these! Give them to my A level students as engaging beyond the course material knowing that they can follow along and enjoy their physics more! Please keep up the great work!

[@lucas411_]

There’s nothing more satisfying than watching a video for the first time and being completely lost, then going away and doing more learning, then coming back and understanding everything. I first watched this about a year ago and got completely lost once the calculus came in. I’ve now started calculus in school and all of a sudden I realise how simple and beautiful this equation is.

[@adogonasidecar1262]

Very, very well done. I have studied physics quite a bit for 50 years or so. Yours is one of the most accessible approaches. Of course, there was a quick cheat in the process of integrating, but this is physics, not maths!

[@djenning90]

This was a gorgeous and enlightening presentation. Brilliantly done! Very accessible and understandable to me.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@RN555-jw1tc]

A lot of lectures and videos all couldn't quite explain these concepts to me, but this video makes it so much clearer and more intuitive, thanks

[@sync4995]

This channel is actually MVP! Thank you sir for the detailed breakdown please keep doing what you do.

[@eddownzzz]

Wow, what a great video and clear derivation. Covered more depth on the subject than my 1st year of undergrad while still keeping it remarkably clear. Good job :)

[@FredTurak]

I'm late to the party, but I've watched dozens of similar videos and this is the first time I've written a response. Your explanations, particularly the formula substitutions and logic behind them, was excellent. Well done!

[@avihayasraf2404]

"Now we've arrived to this ghastly expression" sounds like my professor. (though you explain way better)

[@neil2444]

No other word in the english language quite describes a bad expression quite like "ghastly", am I right?

[@valerianepartenie1013]

Amazing presentation of Special Relativity! The best so far on KZbin! There is one typing mistake at min 20:33... in the green expression, between the 2 fractions there should be "+" sign not a "-" for the expression to be correct. Other than that, all is brilliantly done!

[@77bronc14]

Outstanding video...this is a similar model and description my physics professor used to describe the equation 47 years ago. Great job and brings back some good memories

[@kaanasker4914]

This channel is the best, the other channels that claim they teach physics commonly don't mention the underlying principles and derivations of equations; they are concerned with the view count, not physics. But you, my friend, tell us the derivations using simple approaches and make us understand these beautiful equations without memorizing them. Thank you!

[@PhysicsExplainedVideos]

Wow, thanks!

[@stevenschilizzi4104]

Once again, a brilliant, crystal clear and most inspiring video, presented in a way that would make the sleepiest student sit up and listen, intently. All teachers should take you as an example to emulate. Thanks heaps for sharing your talent, sowing seeds that will certainly bear fruit!

[@PhysicsExplainedVideos]

Thanks for the very kind words, much appreciated!

[@ruyewang8403]

In this video the math can be easily followed, and the physics underneath the math is clearly explained. This is the best derivation and explanation of E=mc^2 (and special relativity) among all popular science talks I have seen, most of which are merely some kind of handwaving in nature. I also enjoyed other videos by you such as the one about Schrodinger equation. I look forward to many more of such videos in the future on more advanced topics, such as general relativity. Although general relativity is based on much more advanced math, but I trust you can still do a better job explaining the theory than any other similar talks I have seen. Please keep producing such high quality videos! Thank you!

[@Craznar]

40 years after learning the rest + classical energy formula - I finally get it explained so I understand.

[@PhysicsExplainedVideos]

Glad to hear it!

[@DuncanIdaho1980]

Great work really, it's cristal clear, both physically and mathematically. I've taken classes in Special Relativity and an intro into Particle Physics this year, and it's quite exciting to see all those fundamental relations linked in a single masteful video. Double, triple like please. I'm pretty sure that it's been said before, but there's a typo at 20:50 in the green expression (a "-" instead of a"+" in the parenthesis).

[@vhawk1951kl]

Did you*believe* what you were told in the classes you mention or did you verify it for yourself by experiment or what some call " science" the physics of which particle hat you could identify as such was what? What exactly were the details of the experiment that you conducted to find out for yourself whether or not E=-mc2? the energy of what were you trying to discover by experiment? Have you yourself ever measured what is called " the speed of light" In your experiments to discover for yourself as opposed to believing what you were told , was the speed of light always *exactly* the same each time you measured it, and you measured it how?

[@wjiuvdjsvhsnsm]

This video is worth me to take screenshots for every page, and the explanation is worth me to listen for dozens of times. What an art work of teaching

[@appleslover]

I was hungry for such content

[@aliamjadrizvi]

This may be one of the best videos I’ve ever seen on KZbin. Thank you.

[@hansfijlstra5932]

I have never seen a better tutorial about relativity. I am very impressed how you manage to combine ‘complex’ formulas with a ‘simple and easy’ to follow narrative in such a way that you really feel that you understand what is presented. This kind of teachers are the ones that, as a kid, you will remember for the rest of your life. If you allow me one suggestion: consider (where possible) not spell out the same formula every time again because the listener is already reading it and is already familiar with the formula. But maybe that is only my preference and not that of other listeners. Thanks for your passion and effort to explain difficult matter in an easy way 👍!

[@tom23rd]

I never knew that very last point, and I'm dumbfounded. Thank you.

[@PhysicsExplainedVideos]

My pleasure! The idea that mass is an invariant quantity is often not emphasised in relativity lectures

[@robertmontague5650]

This is the best KZbin presentation on this subject I have ever seen--bar none! Hats off to you.

[@richardrood4151]

This is excellent. There is something that seems unstated at 23:16, E = KE + mc^2. I am interested in the reasoning that KE + PE + InternalEnergy + ... = (gamma-1)*m0*c^2. That is, how do we go from KE to total energy? I think I learned that E = gamma*m0*c^2 or that m = gamma*m0. Does this then suggest that time is not measured by a clock but as motion through a distance?

[@gmtoomey]

This is a clear derivation that demonstrates important concepts.

[@johnfaulkner5946]

Thanks, The best explanation I have ever seen.

[@PhysicsExplainedVideos]

Wow, thanks! Glad it was helpful!

[@cHVF]

Thank you for making this video. If only you and youtube existed when I was grinding my way through college physics in nineties.. I had a great time back then, but it didn't have to take semesters to 'see it'. You are so very good at explaining, I can only hope my kids in college get a chance to feel what I'm feeling now. ..and now, I'm going to rewind and replay and try to follow the math and enjoy every time you say 'when the dust settles', hopefully my scribbles end up in the same place. :)

[@tadeastkadlec15]

Amazong video! However I didn’t catch for what reason you set that equation at 23:15 equal to total energy. Did I miss something in the video?

[@baptistesirvente2697]

Looking for an answer to this, tell me if you find one

[@CaptainJuiccy]

This was absolutely beautiful... thank you! I view physicists as philosophers driven not just by the desire to describe existence, but by the pursuit to grasp the fundamental working mechanisms that allow it all to exist. Not "WHY are we here", but "HOW are we here".

[@novicapetrovic8026]

Absolutely love how you explained this, it was so clear and concise!

[@PhysicsExplainedVideos]

Glad you liked it!

[@l.h.308]

Ar 23.15, why does he say that the expression to the right, KE + mc^2, is the total energy, E? (In the absence of any potential energy - there are no gravitational or electric field here.) You could say, what else could it be, but there must be a better reason? At 19.07, p = m dx/dt_0. Why dt_0 here, not simply dx/dt?

[@PaulThatcher-iu5in]

I always sucked at Maths, but since I did Physics in high school, I have been determined to understand relativity. Explanations such as trains moving relative to each other, or the the photon clock, and popular science books by people such as Stephen Hawking and Michio Kaku have served pretty well: I would say I have a grasp of relativity and its implications. I remained 'intimidated' by the equations, though. This video, and the others in the series are the first time in 40 years (I'm 59) I've felt that at last I'm going to understand relativity and other aspects of Physics from the mathematics. This is excellent. Thank you.

[@eyebee-sea4444]

dp/dt -> enter tunnel -> rule x, trick y ... -> exit tunnel -> E=mc^2

[@deepfranz]

At 23:12 you say " ... and this expression (KE + mc²) is simply equal to E, where E is the total Energy of the object." But you don't give any reason for this claim.

[@baptistesirvente2697]

I was wondering the same thing, do you have an explanation?

[@qazwsx6340]

the way you introduced the formula for time dilation was amazing. I never thought it was as simple as just using the pythagorean theorem. It was always just told to me with little explanattion

[@madhunayak165]

I wish I could like this video a million times over. Your teaching style is just so simple and elegant. Wish I had a teacher like this

[@bierundkippen720]

Well, he's explaining it wrong to make it simple.

[@RageBabki]

@@bierundkippen720 what did he explain wrong

[@baptistesirvente2697]

At 23:15 I don’t understand why that expression is equal to E, isn’t that what we are trying to prove in the first place, that total energy is KE plus a constant term which is independant on the velocity?

[@m_bm_a7884]

I have one question please: At video time of 19:00 , we have : dp=m.v= m.(dx/dt°) dp=m.(dx/dt).(dt°/dt) =m.v.gama This means v=dp/dt°=dp/dt Is there mistake here??!!!

[@phobics9498]

@@m_bm_a7884 You wrote it incorrectly and the interpretation would never make sense anyway. You wrote (dt°/dt) but it should be inverse. Also, dp/dt will never equal any v as it will always give you a force. I have no idea where you got "this means..." from even the incorrect equation honestly but you can probably clear the misunderstanding by yourself anyway now

[@ImSoUnbelievablyCooked]

Wow, this is really what i needed to truly grasp relativity, at least in terms of the path of motion

[@snorkfire]

SUBSCRIBED! That’s a fantastic presentation of the actual mathematical derivation. For my part, I really appreciate that first you’ve studied the topic and now’ve done an excellent, stepwise explanation of this amazing revelation. I’ve used the equation to grasp a nuke’s destructive power, but have always wanted to see the math that arrived at its richer meaning. Thank you very much.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@hareecionelson5875]

It's crazy that we learn these equations as separate nuggets when they are all linked together: Newton, Einstein, De Broglie all mixed together

[@feynmanschwingere_mc2270]

De Broglie is overrated

[@neil2444]

Honestly a little surprised we didn't see something from Euler.

[@justanotherguy469]

On the shoulders of Giants we stand!

[@hareecionelson5875]

@@feynmanschwingere_mc2270 We're enemies now

[@VKodryan]

I am blown away by your series of instructive videos. I have watched 3 of them so far, and the derivation of the Schroedinger equation was especially interesting. I appreciate that you painstakingly explain the math along the way and remind important building blocks of calculus and trigonometric equalities. Your presentation is vivid with different colors highlighting formulas, animated graphs, and frequent repetition of important points. Overall, it is very well done and a must-watch for anyone interested in physics even those who once studied physics and since then forgot so much (me :-)).

[@mohamedgharbi759]

This was just.. illuminating .

[@dhoyt902]

I'm confident you were illuminated no faster than c. Once you 'get' relativity, thinking about other things doesn't cut it...

[@__-1234]

Hi, thanks for a very nice video, it was really good to refresh this point. Only one thing I did not get, at 23:18, why can you say simply that E is the total energy of the object, which by the way sounds strange since it could have a potential energy too.

[@Miftahul_786]

Yes this is the only part that I don’t understand can someone help?

[@WyattScott]

Good lord, that was cool. Don’t understand most of the math, but it was still very educational.

[@justanotherguy469]

It is just amazing how Einstein was able to calculate the counterintuitive relationship between the energy, as expressed through the momentum of a massless particle, and how you are able to transpose and communicate that relationship, through words! Thank you sir.

[@juliankimmel6511]

Can't wait to watch this when i get home!

[@dgnash]

In sixty years this the first time my A level maths was useful and the first time I understood time dilation. This video actually made Einstein and Maxwell clear and simple.

[@olli343]

Absolutely fantastic video! Even though I'm a 3rd year physics student, I did not know that the derivations showed in the video were this simple (we did not learn this). So thank you! I do have a question though: At 23:12, you set the KE +mc^2 equal to the total energy of the system. But how do we know that this is true?

[@lakshaygupta9061]

I'm only a high schooler so I may very well be completely wrong here but here it goes. Since Einstein(and others before him) knew that there is some other form of energy for masses just as rest by the virtue of their mass, it's a fair assumption to theorize mc^2 as being that additional form of energy. Besides, it was experimentally proven in nuclear fission experiments later on. So my answer to your question would be that since physics drives on assumptions about the natural world, Einstein just assumed it to be true. Again I may be totally wrong.

[@hoekbrwr]

@@lakshaygupta9061 At least he could not find any other explanation!

[@PhysicsExplainedVideos]

Let A = gamma m c^2 Let B = mc^2 If KE = A - B Then A = KE + B > KE So it is reasonable to label A the ‘total’ energy because it is comprised of both the kinetic AND the rest mass energy.

[@olli343]

@@PhysicsExplainedVideos ... ,under the assumption that mc^2 is indeed the rest mass energy. Because - if it isn't - it could be the case that we're just *labeling* KE +something as the total Energy. It still seems arbitrary to me. Of course, there must be a flaw in my logic here, but I don't see it at the moment.

[@angelmendez-rivera351]

@@olli343 KE + mc^2 = E is true, because the fact that KE = γmc^2 - mc^2 holds is true even for free particles. For free particles, PE = 0, and since E = KE + PE by definition, it follows that E = γmc^2.

[@augijyotbali2131]

I literally watched special relativity by brian greene but i can't believe this is better than that . I dont want to believe this but i have to admit . Thank you so much 👍 . I wish you were my teacher .

[@PhysicsExplainedVideos]

Wow, thank you!

[@andrewmawanda5055]

This channel's explanation is much better

[@a.sanaie2460]

Amazing. I have been looking for a clear explanation of this for many years. Thank you so much 🥰

[@PhysicsExplainedVideos]

Glad it was helpful!

[@HDitzzDH]

It's very interesting to see that some of the most famous and important equations in the world is nothing but a combination of some logical thought experiments and some algebra and calculus.

[@tensor131]

and a teeny weeny bit of inspiration!

[@vedantsridhar8378]

Ohhh yeah I gotta learn calculus now to understand it.... That explains why it was so hard for me. I'm just a 9th grader and I was wondering how everybody understood it. But yeah that's the barrier, calculus...... My dad has to teach me it.

[@wpeck99]

Great stuff, but the statement at time 23:16, "...and this expression is simply equal to E" needs motivation and/or justification.

[@jamie.humphries]

Yes! I don’t know what this means, but it’s pivotal to the whole conclusion. What’s happening here?

[@sthamansinha243]

That's the definition of the relativistic energy of a particle. I'm surprised he didn't mention it and what caused Einstein to define it the way it is

[@sthamansinha243]

That's the definition of the relativistic energy of a particle. I'm surprised he didn't mention it and what caused Einstein to define it the way it is. I'd recommend reading through the section in the book written by Einstein himself which discusses this energy

[@timothyvanrhein5230]

I have a question: At 23:13 You say that the expression is equal to E (total energy). Why is that the total energy? I must be missing something. I also feel like one could, at that point, simply set the KE to zero for an object at rest and obtain the desired result immediately. Is that incorrect for some reason?

[@Richard.Holmquist]

Perfect. No hand waving, anywhere. No gaps.

[@EvanOfTheDarkness]

I think you did not look hard enough...

[@Richard.Holmquist]

@@EvanOfTheDarkness in copying (yellow to green) the second term of dp/dt he miscopies the + as a - but immediately corrects it (green to blue). I wouldn’t consider that either hand waving or a gap, just a momentary sign mistake everyone has made at one time or another. Other nontrivial errors?

[@SanderKonijnenberg]

@@Richard.Holmquist For me, I'd say at 18:32 something happens that may be regarded as hand waving. Why is momentum defined as p=m dx/dt_0, and the force in the integral for W as F=dp/dt? Why is force not defined as F=dp/dt_0, or momentum as p= m dx/dt?

[@Richard.Holmquist]

@@SanderKonijnenberg p=m dx/dt doesn’t allow for the momentum of massless particles.

[@SanderKonijnenberg]

@@Richard.Holmquist But then the momentum of massless particles should be a starting point of the derivation, not a conclusion as is presented here, no? Moreover, the question still remains: why not F=dp/dt_0?

[@saeedalvandkoohi6269]

At 23:15, E appeared out of nowhere as the total energy of an object! Why???

[@ulfschack]

Yup. The only hickup for me too. Calling it E out of the blue. Why is that so obviously so?

[@GHTorell]

The best video I've seen on this subject so far! And relatively ;-) easy to derive the equation with only special relativity. A while ago I thought we needed the general theory of relativity for that. Too complicated math for me, so I never bothered. Thanks! (Just in case someone have missed it: There are massive objects receding from us at velocities higher than c. But those very distant galaxies are "riding on the expanding space". Einstein's speed-limit of c (below c) between any objects with mass is meant for "local space". In fact, quite naturally, before the 1920:s most people including Einstein presumed a "static universe". He was certainly aware of the possibility of an expanding or retracting universe of course, considering his famous cosmological constant, see wikipedia.)

[@cederveltman]

Amazing video! Thank you for the incredibly detailed explanation! only this missing is how momentum works without mass, you told us that is was, but not why, maybe subject for another video? Just found your channel, this stuff is awesome!

[@PhysicsExplainedVideos]

Yes, I think I could have gone into a bit more detail there. Would make a good video!

[@Voron_Aggrav]

Brilliant video, just left me with one question, how fast would a person need to travel for Time Dilation to become measurable,

[@florianba922]

If my math isn't completely wrong, you can solve the equation at 12:01 for v. You can then put in the times t and t0 you find out that if you want one year for a stationary observer to be one second shorter for a moving observer, the moving observer has to be traveling at around 75 000 m/s. If time is supposed to travel one percent slower, the observer has to travel at around 42 000 000 m/s or about 14% of the speed of light.

[@florianba922]

Also, sorry for my bad English. Here the formula solved for v: www.wolframalpha.com/input/?i=solve+for+v%3A+t%3D%28t_0%29%2Fsqrt%281-v%5E2%2Fc%5E2%29 And here a few different values: t = 365d and t0 = 364d 23h 59min 59s, v = 75 497*m/s = 0.00025*c t = 24h and t0 = 23h 59min 59s, v = 1 442 373*m/s = 0.0048*c t = 60min and t0 = 59min59s, v = 7 065 685*m/s = 0.023*c t0 = 0.99*t, v = 42 290 930*m/s = 0.14*c t = 60s and t0 = 59s, v = 54 505 826 = 0.18*c t0=0.5t, v = 259 627 884*m/s = 0.86*c

[@Voron_Aggrav]

@@florianba922 Ty for the Effort, I Understand it even if I'm still incapable of reading it :D nothing to do with your English, just my math

[@craigwall9536]

It has been measured with atomic clocks on airliners, if that answers your question.

[@Voron_Aggrav]

@@craigwall9536 certainly helps me visualise it better ty

[@RichardKCollins]

At 19:56 the ? is the time derivative of the gravitational time dilation which has terms for gravitational potential, velocity potential, and electric and magnetic potential. For satellites (GPS/GNSS) velocity and gravitational potential are used. And it changes constantly. Now there are gravimeters, gravity gradiometers and various sensors that can measure it. Lots of groups using many methods. Usually it is more intuitive if you multiple by the speed of light top and bottom. That gives c/sqrt(c^2 + 2*GM/R - V^2 + magnetic and electric terms) All the terms in the square root have units of potential (Joules/kg) But these simple equations are never used. You go to the groups doing the measurements and see what models and data they use for real. Look for time dilation, combined effect of velocity and gravitational time dilation. These are big effects with today's sensor networks. The magnetic fields needed are hundreds of Tesla, but that too is routine now with high harmonic gain lasers and accelerator beams. G and mu0 are simply related in energy density terms to convert from acceleration to magnetic units. LIGO ought to measure these things and share in geophysics research and solar system efforts. But they ignore it and call it "Newtonian noise". A few people still keep trying there. But it is taking them decades to do things they could do in a short time, because they ignore the earth's really large signals and groups. You miss a big opportunity for teaching by only talking about things, and not giving tools, data and community. Talking does very little. Richard Collins, The Internet Foundation

[@Bill-em9zn]

This video is awesome!

[@PhysicsExplainedVideos]

Thanks!

[@SvetlinTotev]

23:00 you just added mc2 to both sides of the equation and said it is equal to the "total energy" without showing in any way why any of the sides should be the total energy or what that total energy even is. You basically "derived" E = mc2 from E = mc2 while hiding the whole thing in a big pile of differential equations that confused your viewers enough for them to not call you out on it. You didn't derive what you said you will, though you did derive a lot of the relevant equations needed for the proof of E = mc2. But you skipped one of the most important parts.

[@jonathanrivera6724]

I had a similar issue and actually found this video to try to figure out what exactly was going on. In a textbook of mine, the author gets to the same point in the derivation and then *defines* _E = mc^2_ and leaves it at that. I think it may be the case that E was defined this way in order to provide a good reference, or 0 point, for energy. In classical mechanics no such 0 point is defined in the theory. Another "benefit" of defining E this way is that it prevents any observer from seeing negative energies. I'm not too sure though and I cannot find much more information online.

[@ernst9100]

So Schrondiger wave equation which gave us hell in campus come was derived from Einstein's equation ? So many of us , who never had youtube channel really suffered to comprehend Einstein and Schrondiger's Relativity and Wave theory equations.....oh..current generation are really spoon fed. Thinkers belonged to 19th. 18th. 17th centuries

[@wayneyadams]

28:30 What is mind blowing is thinking about the tremendous amount of energy in the universe bound up in matter. This was a nice high-level presentation that university Physics students should be able to follow.

[@Kanbei11]

Of course in their frame of reference the muons heading towards earth experience length contraction as time would tick normally on their clock

[@PhysicsExplainedVideos]

Indeed!

[@ralfsbelohvosciks7466]

This came in clutch as I have a physics exam tomorrow