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 check it out then there's a 30-day free trial that you can take but the first 200 of you can get a 20% lifetime off on annual subscription all you got to do is follow this link www. 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 99.99999% at the speed of photons that's possible I need finite energy for that and then I would see the photon to be almost at rest almost no it doesn't work because of Einstein's postulate we already know that from any reference frame regardless of how fast that frame is traveling you should always see the speed of light to be C photons will always appear to be moving at the speed of light C and therefore I will never see it to be at rest I will never see it slowing down what does that mean mean oh this means that the photons do not have any rest energy all the energy of the photon is the energy of the motion and because they don't have any rest energy oh that's why they should have no Mass because they don't have any rest energy that's the reason why we say photons are massless but I promised you that we're going to look at it from different angles and there is a way to attack this using a counter argument let's do that now all right so Einstein you said that there is no such thing as mass right it's only the energy so am I not allowed to Define mass as I see fit so here's my alternate definition of mass what if I Define mass as the total energy divided by c² I Define it that way I don't care about rest energy and motion energy I Define it as total energy by C Square according to this definition that moving tennis ball will have more mass because it has more total energy and therefore it should have more mass and then according to this definition I should be able to say mass of the photon equals its energy divid by c² because look I'm no longer care about its rest energy and move energy Just Energy divid by c² my question to you Einstein is can I do it this way can I redefine my mass to make sure that photons have a mass like this and Ein says yes we can do it what really and Ein says in fact this is how we initially interpreted relativity a lot of scientists took this Viewpoint that when you're moving your mass increases Fineman also uses it in his lectures he thinks about how the mass of a body in increases with velocity and I'm like Einstein well then why do we not use this Einstein says we abandoned this idea today we don't use this notion and I'm like why this makes so much sense why do we why did we abandon this let's calm down a little bit Einstein says okay there's a problem what's the problem Einstein well remember how we said that when you accelerate an object to speed of light it will have Infinite Energy yeah but now according to this new definition it should also have infinite mass and I'm like cool so this means in this alternate definition mass goes to Infinity at the speed of light and I'm cool with that if energy can go to Infinity at speed of light Mass goes to Infinity at speed of light I'm cool with that what's the problem here Einstein well Einstein says but photons have mass according to this definition they have finite mass and they travel at speed of light they don't have infinite Mass oh my God that that's the problem there is a contradiction on one hand we are saying going at the speed of light should give you infinite Mass but photons can go at the speed of FL and they have a finite Mass according to this Viewpoint there oh oh my God is so there is a contradiction so this will not work is it Einstein Einstein says no no no mahes don't sell it short we can still make it work in fact the way to there is a way in which we can make this whole thing self-consistent the way to do that is we'll Define two kinds of mass rest mass and moving mass and then all we have to do is agree on two things one is that things which nonzero rest Mass like you me and donkeys get infinite moving mass at the speed of light and then things with zero rest Mass like the photon get a finite moving mass at the speed of light I'm like wait what I need a second dear folks feel free to pause the video oh like what is this and I sense is exactly this is the problem with using this wheelo it is too confusing you have to cook up two different kinds of masses and then you'll have to invent different rules for things that have zero finite m zero rest mass and things that have nonzero rest Mass it is just too Dar confusing in contrast Einstein says look at the other view point isn't that simpler where you just have just have one type of mass and that mass is basically the energy content of the system and that mass does not change with speed like isn't that more intuitive and isn't it just easier to say that photons don't have mass instead of defining these new rules because of this simpler Viewpoint we abandoned this idea and at this point I educates us and talks tells us remember Mahesh physics is not about understanding reality it's actually about creating models to simulate reality and sometimes we can have multiple models like you have in front of us and and even though they could be self-consistent both models are self-consistent some models are just too Dar complicated and we don't want that we want a simpler model that's the reason why we got away with this model that's why this has become now Obsolete and today we don't talk about moving mass and rest Mass we just talk about Mass that's it just one kind of mass and we say photons are massless that's the simpler Viewpoint wow that's that's beautiful although we have covered pretty much everything now I promised you we're going to look at it from all possible angles so Einstein I have one last question for you under this Viewpoint the simpler Viewpoint where we say that mass is the amount of rest energy in this Viewpoint can photons have mass and Einstein says yes what it's possible light can have mass if photons travel slower than C what photons traveling slower than the speed of photon how does that make what does that even mean and iand replies with something extremely vague he asks me mes what do you think will happen if I slap you don't do that Einstein but if you slap me my cheek will hurt now Einstein says him slapping me is the cause and my cheek hurting is the effect now it feels in this case as if the cause and the effect happen at the same time instantaneous but turns out according to relativity cause itself takes some time to go from one point in space to another cause itself has a speed and the speed of that cause which we call the speed of causality that is the ultimate speed speed limit in the universe and Einstein says that his theory of relativity is actually not about the speed of light it's about the speed of causality wait a second Einstein is that the reason why we have a c yes C is the speed of causality and so his postulate that nothing can travel faster than speed of light or you cannot travel at speed of light it actually means you cannot travel at the speed of cality and you know in all the different reference frames it's the speed of coal that stays the same but then I 10 why do we talk about speed of light all the time well he says because in this case the light is the one the photons are the one that are sort of like the carriers of the cause in most cases and therefore we think that photons travel at the speed of causality and therefore everything that applies to causality also applies to photons but what if that's not true what if photons are traveling slightly ever so slightly slower than the actual speed limit the speed of causality then all bets are off then you can travel at the speed of photon because you are still traveling slower than the speed of causality you don't need Infinite Energy anymore then you can find photons at rest and they will have rest energy and therefore they will have mass so does it make sense now why if photons travel slower than C they can have mass so you put it all together if you put it all together Einstein how can we summarize everything that we just learned and Einstein says we can summarize everything in just two sentences the first one is things traveling at speed less than C should be massive and now it makes sense because if you're traveling less than the speed of causality you can always find them at rest frame they will have rest energy and therefore they will have some mass and secondly things traveling at the speed of causality should be massless that also makes sense because if you're traveling at the speed of causality which we think photons do then they will never be able to become at rest and therefore they should always have zero Mass that's the reason why we say photons are massless we've now looked at things from all possible angles and that's it folks this is it did the video live up to the promise do you now have a much more profound understanding of why we say photons are massless let me know this is it from my side see you okay let's close this

Channel: FloatHeadPhysics

Views: 944,818

Keywords: floatheadphysics, floatheadphysix, Mahesh Shenoy, Mahesh shenoy khan Academy, Mahesh shenoy physics, Why are photons massless, Why is light massless, why light has energy but no mass, why light has no mass but energy, Does light have mass?

Id: wiBsfvW5AWY

Length: 21min 57sec (1317 seconds)

Published: Fri Nov 03 2023