Why light has energy, but no mass? (Understanding E = mc2)

this video is sponsored by brilliant. org more about them later in the video photons have energy and according to Einstein equals mc² so I thought that photon's energy can be converted into mass and so therefore they should have mass given by E by C squ but what I read and heard from everyone is that that's wrong photons are massless and I never understood why the reasons I under the reasons I got was because this equation doesn't apply to photons but why because pH travel at the speed of flight C what it felt like these were all disconnected empty statements I never got a true intuitive understanding behind what's really going on over here but then I understood the problem the problem was I hadn't really understood what equals MC square was but then I read up not finean lectures because fan lectures also didn't help and you'll see why towards the end of it but after reading a lot of it I finally understood what it was and then I got the complete picture and now I feel like I have a much deeper intuition for what's going on and I'm super excited to share that with you so the promise of this video is we will attack this problem from different angles and by the end of the video if I do this right you will walk away with a much more profound understanding of what's really going on so if you're ready for this let's begin so where do we start Einstein well Einstein is saying because we want to talk about light's Mass over here let's take a step back and ask ourselves the big question what exactly is mass well I tell Einstein will you know mass is just the amount of stuff and Einstein says there's a problem with this and I'm like why Einstein to answer this he asks me mes what is your body made of fundamentally well I say well it's made of atoms but he says Mahesh at the most fundamental level oh I say oh all right yeah yeah it's made of protons neutrons and electrons and he says Mahesh at the most fundamental level that's right protons and neutrons are made of quarks themselves so Einstein at at the most fundamental level my body is made of quarks and electrons now Einstein says okay now if this if a mass is the amount of stuff then my body mass must equal the mass of all the quarks and electrons right I say yeah but turns out that's not true turns out if you add it up then the quarks and the electrons add up to give about 1 to 5% of my total body mass and different papers site different numbers so I don't know exactly what percent percentage it is but the important thing is the total quarks and electrons only add up to give you give me a fraction of my body mass and so I'm asking Einstein where does the rest of my mass come from Einstein well Einstein says these quarks are held together by energy inside the atom and the quarks themselves are vibrating so they also have this kinetic energy so if you take all of that energy you add it all up and you you divide that energy by c² that gives you the rest of the mass Mo he says wait a second Einstein are you saying that that energy is converted to my mass and I says no no no there is no conversion business over here in fact what he's saying is that a better way to think about it is that there is no such thing as mass at all what we have been always measuring is energy divided by c² and I find that pretty mind-blowing because I used to think that energy converting into mass is mind-blowing but turns out the reality is much much more profound there is no conversion now it makes sense because there is no such thing as mass there's only the energy and you're always weighing you're always measuring the energy wow but wait we have some questions Einstein what about that 1% what about the mass of the quarks and the electrons themselves where do they get their their Mass from well Einstein says these quarks and electrons well it turns out that they interact with something called the hick field and that interaction gives them the energy so when you're measuring the mass of electrons and quarks what you're really measuring again is their energy divide by z s you are always even at the most fundamental level measuring energy no conversion no such thing as mass it's always energy divide by c² that's what his equation really means all right let's see if you're on the same page Einstein if I understand you correctly are you saying that if I take a spring and I compress it then compressing it gives it an additional potential energy and because of that it gets more mass and I says yes that's E equals mc² whoa all right what if I take a cold coffee and I heat it up does that heating gives it more vibrational kinetic energy and does that give it more mass and I says yes that's equal to MC squ w we're getting it finally similarly a moving tennis ball has more kinetic energy than a stationary tennis ball and therefore it should have more mass and I says no what no I thought we were understanding equals MC squ Einstein how is this different you said more energy gives more mass the moving tennis ball has more energy it has additional kinetic energy so why why doesn't it have more mass compared to a stationary ball and the answer that Einstein gives to this that is the final piece of the puzzle folks that is what we need to truly understand what equals MC square is and once we understand this everything else will logically follow so are you ready for this because this is it this is the climax all right let's do this Einstein why do you say that there is no more mass in this case well Ein say if we go back to the spring case when we compressed the spring we added more energy inside the spring some internal structure of the spring changed more energy in the spring that manifests as more mass the same thing happens with the coffee when I added more heat the internal structure of the molecules change in the sense they're now vibrating more there's more energy added inside the coffee and therefore there is Manifest at more mass but when the tennis ball is moving einan asks have we added more energy inside the tennis ball I mean think about the molecules of the tennis ball is that vibrating any faster now no the temperature is the same is there more potential energy in some sense inside the tennis ball no it's not so we haven't added more energy inside the tennis ball another way to think about what Einstein says is imagine you want to weigh this tennis ball now how how would you do it this tennis ball is moving you have a weighing scale how would you do it well one way to do that would be to run along the tennis ball with the exact same speed so that the tennis ball appears to be at rest with you and then you wait but now the tennis ball looks identical to that other stationary tennis ball in other words this kinetic energy that you have added to the entire ball does not add more mass to the ball because you're not adding more energy inside ins some sense inside the ball another way to put this all together Einstein says is think of it this way if you have a moving object its total energy has two components it has the energy at rest the energy that you see from the rest reference frame and then it has this additional energy of motion like the kinetic energy of this ball what really matters is the rest energy because that's the energy that's in some sense represent presents the energy that's confined inside that object the energy of the motion doesn't really matter when it comes to mass and therefore Einstein says what matters is this rest energy and that equals mc² not the total energy but the energy that's there in the rest the energy that's inside the object that equals mc² so now we have the tools needed to find the mass of any moving object first of all we need to figure out from the total energy how much of it is the rest energy and how do you figure out it's rest energy we'll just get it move along with it at the same speed and look at it from the rest frame and now calculate all the energy inside it that's the rest energy that equals to mc² and from there you can calculate its mass so now that we know how to calculate the mass of a moving object let's see if we can apply this to photons first of all can we see what we did wrong earlier with the photons when we earlier divided the photons energy by C Square we took the total energy of the photons and divide by the C Square that's why that was a mistake we need to figure out the rest energy of the photons divide that by C square that gives you the mass of the photon let's do that now let's do that all right okay let's move it over here here's our Photon I want to figure out what is the rest energy of the photon how do I do that well just like what we did with the tennis ball let's move along in the same direction as the photon at the same speed the speed of wait a second I will have to move at the speed of light for that Photon to be appear to be atress Einstein can I move at the speed of light with a weighing scale Einstein says no why not because according to special relativity Einstein says to accelerate any object to the speed of light you need to put infinite energy into it but wait why does moving at speed of light require Infinite Energy well you can actually derive this step byep using Einstein's postulates and what if I told you there was a fun and a free way to actually learn this introducing brilliant. org this video sponsor brilliant has amazing math science computers and data courses I love their cool interactive simulations because it makes things super intuitive I went through the advanced physics section and took their special relativity course I loved it because it started from the basic nean mechanics and then using beautiful interactive simulations I was able to build all the relativistic equations and even derive the famous E equals mc² and eventually I discovered why it takes infinite energy to travel at the speed of light I and my friends love brilliant I also recommend them to my students and if you want to 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brilliant. org float head physics the link is also in the description not only will it help you learn things deeply but you'll also support my Channel all right back to the video so you me or donkeys will require infinite energy to travel at the speed of light and therefore I cannot travel at the speed of photon I can't do the same thing as I'm doing with the with that tennis ball all right okay but Ein understand what if I don't travel at the speed of photons what if I travel at like say 99.