Why does E = mc2 ?
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- Опубліковано 17 чер 2024
- Let's derive the most equation in physics, E = mc^2, intuitively. This is Albert Einstein's original 1905 derivation. Here we will see exactly where the c^2 in the mass energy relation really comes from. We will do each part step by step. We will also derive the expression for the relativistic doppler effect.
Chapters:
00:00 Introduction
00:27 Counting energy lost by the atom
03:31 Relativistic doppler effect animation
06:35 Recounting energy from moving frame
07:20 Discovering Mass - Energy connection
09:47 How mass - energy relation comes from constant speed of light!
12:43 Rearranging the equations - (1)
13:43 Deriving relativistic doppler effect equation - intuitively
20:05 Substituting in equation (1)
22:40 Summarising the result so far
23:19 Final substitution
26:25 The climax - E = mc^2 derived
26:50 The summary
If this is how maths and physics is taught in schools, we would be having many more scientists and humanity will achieve 10 times more in 30 years compared to last 100years… Hats off to Mahesh sir🙏
No scientists won’t need this simple explanations I just like how he has made it easier for dumb ppl like me to understand it
Let's face it, we haven't achieved much in the last 100 years. 🙄🙄🙄🙄🙄
@@guydude3320 Correct… thats why I said schools not universities 😊… dum
@@mkpatel981 schools are not there to make smart scientists and succesful people... its to train peoplpe to work a 9-5
@@guydude3320 Ehm, scientists still have to originate in the educational system. So yeah, this level of education would ignite the crave fro knowledge for much more people
Loved the video. Just wanted to point out that the use of the binomial expansion and limiting to first order makes it sound like E=mc^2 is an approximate equation. A more formal derivation shows that it is in fact exact and not an approximation. It appears you needed to use the approximation because you took kinetic energy to be 1/2mv^2 in your derivation. That is only true at low speeds. It is in fact your kinetic energy equation that is the approximation and not E=mc^2. The use of the binomial expansion simply reconciles E=mc^2 with that kinetic energy approximation. Actually, it is a very nice way of showing how 1/2mv^2 come about at low speed. A more formal derivation would use the full relativistic kinetic energy equation (derived from the work principle) and then you end up with E=mc^2 being exact. I hope you don't mind me mentioning it but I didn't want people to come away thinking E=mc^2 is not exact.
Very valuable comment! In fact, this was exactly the impression I had: The famous formula surprisingly only the result of an approximation. Not something one would expect from Einstein. Until I stumbled over your remark. Initial disappoinment eliminated now. Many thanks!
like @stolgos8964 I thank you for this precision
That was exactly my question, thanks. Any pointers on how to derive the relativistic kinetic energy?
@@Wouter10123 The derivation is straightforward in principle, but nasty in practice. Kinetic energy can be derived using the work-energy principle that says the change in kinetic energy of an object is the work done on it to take it from stationary to some velocity, v. You calculate the work as the integral of force over distance. You integrate Fds. But Force is also the rate of change of momentum, p, so you can integrate (dp/dt)ds instead. This is the same as (ds/dt)dp, which is vdp. Still not nice but using the product rule you can convert this to d(vp)-pdv, and integrate that. That is vp minus the integral of pdv. Relativistic momentum, p, is 'gamma'mv, where 'gamma' is the familiar 1/sqrt(1-(v/c)^2) term of relativity. Substitute that in and the final integral is ugly by doable. The answer is (gamma-1)mc^2. That is relativistic kinetic energy! Not at all familiar is it? However, by doing a binomial expansion of it and dropping the higher terms, you're left with 1/2mv^2 believe it or not! To keep things familiar and intuitive, Mahesh started with 1/2mv^2 so had to apply the same approximation to the left side of his equation (so to speak) to make them consistent. You can see the derivation and discussion in more detail on Wikipedia at en.wikipedia.org/wiki/Kinetic_energy#Derivation_2. Hope that helps.
I was hoping someone would clarify this in the comments. That bit felt a bit disappointing after an otherwise excellent explanation. So thanks for the clarification!
You are a fantastic communicator of high-level concepts. I love your enthusiasm!
All his enthusiasm is not able to make this explanation rational. Like all of SR theory, its not rational.
the fact that he smiles and shows excitement about the subject is infectious.
Who wants Mahesh sir to upload more videos like this ? And increase the frequency of uploading videos.
Yes. Will do. Have a list of videos ready already
U can use Doppler effect to increase frequency 😂😂😂
@@sgiri2012 I typed velocity by mistake. (Don't take it serious)
Notifications ON!! Yes
Everyone 😅
I have never seen anyone explaining with this energy and so much interest.
Much appreciated :)
You’ve got to be one of the best science communicators on this website, every video I’ve seen of yours is so intuitive and as a biologist I sometimes worry about getting too deep into physics and math but your videos help with the pursuit for knowledge
This means a lot! :)
But the information he communicated is not actually real physics truth. Einstein's theories have been debunked many times already. But the easiest way to find why they are wrong is to read the ebook, Dave Vs Hal 9001. Anyone with any ability to think, can now see that Einstein's theories are nonsense. No math required, just logic and reason.
@@everythingisalllies2141Source:Trust me bro. Dave vs Hal 9001 is a fictional book not an academic book. Also, where on actual earth did you see that Einstein's theories have been debunked.
Edit: Ah, just checked your channel and found it's a book written by you. Self promotion.
@@everythingisalllies2141 Don lie bro. Einstein's theories have been proved over and over again.
@@NorthMavericks-ow7jk The lie is that they have been "proved" over and over. But you don.t care if this is true or not. Your mind is set like concrete. The theories have no real proof, not one scrap.
Mahesh sir always rocks ❤
You are doing an extremely good job and you have a good will. This will help the lot of learners around the world.
Hats off to you sir
Thanks a lot :)
@@Mahesh_Shenoy I have said that I will say again that in this whole concept one very important variable is forgotten and must be taken into account and that is ACCELERATION of the shot out particle from the atom. NOTHING and NOTHING happens in zero second? Can you run 100 meters sprint in zero seconds? Can you say a word verbally in 0 seonds? NO! Thefore, the particle shot out from the atom must be accelerated by force F and that is equal to ma. Therefore, the equation of kinetic energy KE=1/2mv squared is derived from FORCE applied to an object times distance it moves is equal to the change in its kinetic energy by ACCELERATION. And now the question? The particle does not ''move'' instantaneously from the atom. That's impossible. And where did the FORCE COME from? And why did the particle accelerate to c? In even simpler equation of momenta p=mv, the velocity is gained by acceleration. So, acceleration distorts the E=mc2 because as small as ACCLETERATION may be, it is NOT 0! Something does not jibe here because it looks like the finished product without pointing to the process of acceleration.
I may feel sad about many things in my life but I always, strangely, find peace in physics.
Big thanks for this beautiful video, I will keep coming back to it 🎉
Here we learn important topics of physics while having fun.
Keep making more videos like this sir.
Gladly!!
If that was any other video going through algebra I would have had to stop watching.
The way you explained it so clearly, so logically, keeping it tied to the reality of the original experiment, reminding us what we were trying to solve, reminding which formulas we'd already done. You actaully made it make sense to me, and I genuinely got enjoyment from following it. Thanks buddy. You're an amazing teacher
I grew up with the assumption that only a tiny group of elite physicists could understand the math of the Theory of Relativity. But you clearly go through the math so that it's comprehensible even to me (who struggles with very basic calculus). Your intuitive approach really brings the theory alive and makes it something we, like you, can marvel and wonder at, rather than regard it as too complicated and remote. Kudos to Mahesh!! (P. S. I was a librarian in Jerusalem and got to know the head librarian of Hebrew University, where the original manuscripts of the theory, special and general, are kept. She gave me the wonderful privilege of seeing the manuscripts in person. It was a very powerful experience, seeing these documents that fundamentally changed our view of the universe.)
You still need to understand the math in detail to do anything useful with it, but it's good to have at least an intuition of it rather than none at all.
Thats some cool stuff to see writing of such a person.
This is my first time on this channel, and I just wanted to share my excitement for the descriptions of the relationships among space, time, momentum, energy, mass, etc., the aesthetic feels genuine and I’m only just starting to understand how some of the relationships work, and I’ve little to no practice beyond algebra. I’m missing some details, but that’s what repeated viewings and further familiarization with the subject matter are for. Your intuition based delivery was a unique way to handle that whole area. Thanks so much!
This is actually, intuitively, very appealing! It is quite fascinating that Einstein should have derived this (and speed of causality mentioned in a pervious videos) purely on eliminating what cannot be and accepting whatever that remains! logic following intuition=genius. Thanks for making this video.
Thanks a lot for the feedback. Awesome to hear that.
"eliminating what cannot be and accepting whatever that remains!" Just like Sherlock Holmes!
"When you eliminate the impossible, whatever remains, no matter how strange, must be the truth.
I wonder if we could find more physics through this method but not eliminating other 'impossible'maths. Something about negatives and imaginary numbers comes to mind
Lucky students that have you as their teacher. Providing an intuitive understanding of the subject matter for students to take with them as they dive into the details is I am sure invaluable. Well done indeed.
Please keep these videos coming! These are so helpful in explaining concepts intuitively which is something I always look for and love the content you post! Recently came across this channel and have been hooked!
You are awesome, Mahesh! I've been watching all your videos since I found out about your channel. I love your excitement and your intuitive take on hard topics!
Your enthusiasm for this subject is contagious 😊
I came across your channel just recently and absolutely love it! It would be fantastic if you touched on the topic of time paradoxes, time travel and general relativity! Have a great day!
I love your enthusiasm, and the fact that you want to explain things intuitively, it really helps!
I love how you give an intuitive explanation. Please continue making more videos.
Ihv never seen such simplification of such a complex topic. Absolutely outstanding piece of work you've uploaded sir. 👏👍
I admit that I can barely follow because this is not my profession, but I was always interested in physics and I think it is a shame that most people do not get to know or understand these greatest achievements of humanity and I truly admire your work to teach this extraordinary relevant topics. I like your admitation and fascination for science and gave you a like and a sub. Please keep going! ❤
You can't even imagine how happy am I about finding your channel. You are educational genius, people like you are moving humanity forward and I sincerely dream I can be someone like you. You are giving people new conceptions about the world we live in, transforming information about it into knowledge about it's laws. Thousands of years people paid money for conversations with people who have looked a little bit further in the ways of understanding this world, but now we can listen you for free and I'm grateful for that.
If half of the people, who watched your videos will get new knowledge (not as information,but something they will understand) then you are making tremendous work for all the humanity.
This really shows how smart Einstein actually was!
Thanks for the explanation mate! This was a great video!
There was a point in time when I was satisfied deriving E=mc^2 only using four-vectors and calculus. Now I know how much of a fool I was back then. This is the most beautiful/intuitive reasoing behind the connection between mass and energy I have ever seen. Thank you so much for putting in all of this effort to make reality make just a little bit more sense for the rest of us.
That’s a really wholesome comment. Made the effort that much worthwhile:)
Functional equations are need, www.casanchi.org/fis/dinamicafuncionales01.htm
Such intuitive explanation. Such infectious energy. Kudos bro. You took simplifying complex physics concept to the next level. Keep up the good work 👍
It's all scam look it up make no sense
Thank you for showing me how to understand the formula intuitively. Your videos are well explained and unlike other videos you show every step intuitively and im waiting for your next video!
You've reignited my passions for physics, I watched a vid on a whim and i've been watching them one by one since, you've captured all the things that makes this topic so interesting and explain it so well!
Best physics channel I've seen so far!
Wow!! Really intuitive ❤
Never understood it this better! Thanks
Wow, awesome to hear that :)
I have a question about the final stage of your calculation Mahesh.
When you carry out the binomial expansion to finally determine that E=mc^2 you ignore the higher powers of x(v^2/c^2) as the velocity(v) is much smaller than the speed of light(c). Doesn't this mean that E=mc^2 is also an approximation and so would not hold for values of v approaching c?
I was a little worried people might think that when I saw the video. Be in no doubt, E=mc^2 is exact. It is not an approximation. In the video kinetic energy was taken to be 1/2mv^2. THIS is the approximation. Kinetic energy is only 1/2mv^2 at low speeds. What Mahesh was doing was using the binomial expansion to reconcile E=mc^2 with the kinetic energy approximation that we are all familiar with. In fact the binomial expansion is a nice way of showing that kinetic energy becomes 1/2mv^2 at low speed. If you use the full, relativistic kinetic energy (derived using the work principle) then you do not need the binomial expansion and E=mc^2 ends up being exact. I hope that puts your mind at rest.
@@robwilliams4773Thank you very much
@@robwilliams4773 Thank you
@robwilliams4773 Thanks.
I am still a bit confused. Does the atom have different energies when viewed from a rest vs. moving frame?
All observers , regardless of what frame they are in, will agree that the atom has intrinsic mass, m, with energy equivalence given by E=mc^2. The atom may be ascribed kinetic energy in addition to this due to its motion relative to individual observers. Kinetic energy depends on the relative velocity of the atom and therefore different observers will ascribe different amounts of kinetic energy. But they will all agree that the rest-mass energy must be exactly mc^2.
I hope your channel blows up my friend ur enthusiasm combined with story telling and clarity helped explain this concept in such a digestable way. I learned alot from this! :)
Great stuff! You are the best. I love the ongoing dialogue he keeps up between 'Mahesh' and 'Einstein'. 🙂
Damn Einstein and Mahesh conversations really go deep
Mahesh, please make a video on force upon a charge by a magnetic field. Hope you take any action, you may either make a short.
👍🏻✌️🤜🏽🤛🏼
i love your channel. i started watching you because i needed to for my e&m class, but you made me actually appreciate the subject. great content.
fantastic! I'm 59 and I've long understood the concepts, but never thought I could understand the underlying math.Now I do, thanks!!!!!
Love your videos!
Great to hear that!!
Your explanation of the relativistic Doppler shift is spectacular! But a subsidiary point of the video is a bit lacking. When you drive by a stationary sound emitter, you do indeed hear a change in pitch. Your presentation of the doppler effect for sound makes it sound like you wouldn't hear a pitch change.
Thank you! Yes, I noticed that. I wanted to put a small disclaimer at the bottom. But forgot to add that.
You are right, there is pitch change in sound as well. But, the pitch change is due to the apparent change in the velocity of sound. Not the wavelength. I think that’s the key point.
Could explain how the Doppler effect with light does lead to a drastic doubling in frequency versus in sound, only leading to a minor change in pitch
This is exactly what I was looking for! Very cool. Thank you , brilliant animations. So well executed
Just brilliantly delivered. You have a gift...thanks for sharing it.
High expectations.... The intro looks amazing... Lemme watch...
Let me know!!!
What about now 😂
@@Mahesh_Shenoyfrankly, I felt the video like casual physics lecture 😆. I'm so sorry to say this 🙏🥲.
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Let me watch it again in a free time 😅
@@Mahesh_ShenoyAmazing 🤩
Pls make a video on the derivation of length contraction
You are just amazing. And you deserve millions of subscribers! Thanks for all of your videos and surely for your passion.
I really enjoy your videos. Helps me understand. Things better than I ever had. Thank you.
Another doubt is that, in 9.04 part of the video, when you said the atom must have lost mass after it emitted out light, shouldnt the atom on the right (from the girl in rocket perspective) also lose mass after it emitted light?
Yes, i have the same question
Yes, it lost mass. But we observed the mass at two different times, one before it emitted photons, and after it emitted photons. This is why we see a diffrence in mass
Nice 👍👍👍
Thanks so much Mahesh bhai!! Excellent video and explanation and your enthusiasm made it that much more special!!
You're my favourite UA-camr I found this year!
Yay!!!🥳
My body is ready, but my mind is not. See in a few days
See you soon 🔜
Here before this masterpiece gets viral❤️🔥
🤞
Man how I've been looking forward for this video! 😍
Dude...the craziest thing about this video was learning what Albert learned by himself way back in the day...in just under 30mins...this was amazing...
I really feel like I'll need a bit to get a hang of it. Really nice work sir ngl even a toddler in physics would understand this as you even try to explain the slightest of things.
I just want to know that if E/c2= ∆m is an approximation, so it won't be able to work for high velocities right? Like those approaching quite much the speed of light like an electron in a bohr's orbit or can it tolerate that much?
Lastly, really thank you for keeping me interested in physics even when on the verge of losing it 'cause of this rat race.
That’s super awesome to hear 🙌
@@Mahesh_Shenoy The question 😅
There is no such equation. The equation is E=m, which defines the mass in the zero-momentum frame. You can have ΔE=Δm in the absence of change in the 3-momentum. [note: c=1]
E=mc^2 is not an approximation. Be in no doubt about that. The derivation in the video uses 1/2mv^2 for kinetic energy. THIS is the approximation. It is this equation that only holds at low speeds. The use of the binomial expansion reconciles the derivation with this approximation. If you do the analysis using full relativistic kinetic energy (derived using the work principle) then E=mc^2 is exact. This would make the story a lot more complicated though and I can see why Mahesh didn't go there. The key idea in the video is jumping between frames of reference, assuming physics should behave the same from both points of view, and thinking about what that must imply if the speed of light is the same. That is relativity theory.
@@robwilliams4773 No. The accurate equation is
E = 'gamma'mc^2.
E = mc^2 only works for low speeds or when things are at rest. As mentioned, it's a first order approximation!
Can you also do the derivation of the complete mass equivalence equation[(E^2=(mc^2)^2+(pc)^2] intuitively....
This is total energy Et = mc²+ Ec
Ec = kinetic energy
The equation you're citing is called the Relativistic Dispersion Relation, which is the norm of the 4-momentum,||P||^2=P^ag_{ab}P^b, expressed in component form: m^2=E^e-p^2.
Lack of use and 50 years time since college physics hinders me, but I found your enthusiasm and explanations delightful. I had long forgotten how to resolve nothing travels faster than the speed of light versus Einstein's energy-mass conversion process being dependent on the speed of light squared.
Dude you're so good, I love this channel. Glad I found this
His ability to talk to dead scientists is an unfair advantage
But Einstein seems totally happy with that
Present sir 🎉
Nicee
The single most important physics video on youtube. Nothing else come even close. Thank you.
Thank you for this, it helped me understand this equation for the first time. You are a great communicator and teacher. I hope to see more videos from you.
Light is way cooler😎 when it is wave than it is as particle
🆒
If E=Expresso and M= Milk , C= Coffie, this is the formula of the “Macchiato” 😂
Haha!
I'm going to be absolutely honest, you're actually insane, first time watching ur video, but I love it!
You would be a great professor. Keep up the good work, your videos are phenomenal!
My man doing god’s work. I haven’t completely watched the video, but I bet it is fine!
Thank youuu
Gem of a video. Way more insight than just what the title says
Mahesh, i love how you interact with Einstein like you just left his lecture. It helps make this so engaging
Love this.. you've shown that a 9th grade student can understand appreciate and admire this without any crazy equations.. a great showman just shows the trick first for us to enjoy.. and then later goes into the making details.. love it
Excellent. I'm almost having as much fun as you. Thank you well done. I impressed myself when I realized something before you said it regarding the Doppler effect on light I saw the time dilation was needed then you said it. That was fun. So I'm leaning. Thank you . Looking forward to more.
Powerful stuff 💥
Yes, this video lived up to its promise. Each time I watch it it gets better. Genius. Thank you.
I never knew that I could derive E=mc^2 without even holding a pen and paper and just by visualizing things looking at a youtube video. Just amazing. Loved it~
Loved your video huge support❤❤ we want more physics videos like this ❤❤ will be excited for next one
Thank you so much, Mahesh! This explanation is super useful and clear ❤
I love how you simplify very complex subjects, and "ask" the questions we all have to get to the answer. Would you please do one on the "twin paradox"? Also, would you please explain in a "thought experiment" how someone in a spaceship moving at a constant velocity can measure the speed of light moving in either forward or backward direction to be "c"?
I love your passion!!! Makes learning so fun
I was never good at math , science . I'm into accounting. But with this kind of videos on UA-cam my interest in science has grown and I'm fascinated by this. I sleep most of the time while the video is playing in the background sometimes. It's kind of calming strangely.
just found the channel. love the enthusiasm. absolute goldmine, will be binging
Recently discovered ur channel sir..loved it so much that i watch 1-2 vdos daily after my college...btw im a undergrad phy honors studuent...so i love it 💖💖
That was so good!!!!!!! Mind unexpectedly blown while eating lunch. Epic
Amazing video. Thanks!
Your excitement and explanations are the best! 👏👏👏
Your excitement when talking about this is great. I enjoy your videos.
Super awesome to hear that :)
I like it. Amazing!
You did a massive help to me to break-in that was a puzzle to me always (for a long time). I am to explore a lot and a lot with my resources!
THANKS A LOT.
Amazing explanation and enthusiasm!!
LOVE your energy in this video!
You have a gift of going into detail and can explain in a way that many viewers can relate to. I appreciate that. I also understand that you have a comical and conversational way of presenting. But I cannot help saying that, in invoking great names such as Albert Einstein and Richard Feynman in the dramatic conversations and more importantly in your intonations, they do not come out in quite the respectful way toward the two great geniuses as probably all scientists would do. Even in a dramatic conversation when invoking such towering personalities, the intonation should not sound like you and them are equals. They did everything, and they dedicated their lives to doing so, you are just re-telling their findings in a way many people may find easy to understand. But for this important point, that I could not help pointing out, everything else is good! So, please keep it up!
In other words, the science deities are beyond humanizing, right? We must all bow down in supplication in their presence,yes? Yours is the attitude that has got high energy particle physics & cosmology into the mess they are both in.
Sir. Thanks for your amazing content. Its given me a lot of joy to understand things like theory of relativity and other stuffs and your videos have helped me alot in the process. Keep it up. Your videos are amazing.
Mahesh, I love your videos! I want to study quantum physics and love your intuitive videos and I am happy to tell you that I share your passion for physics!
Great video! Your enthusiasm is contagious and admirable. Simple and rigorous proof.
That was a beautiful video. It helped me clearly understand so much more of the details. Thank you for patiently walking me, baby step by baby step. Very well done.
wow - I have never witnessed someone so excited about things wayyyy beyond my abilities - your are amazing - I love listening to you - even though I have NO idea - thank you
Really great and impressive, specially your way of teaching
This is the only way i understand this stuff thanks man this is the most interesting part of physics to me tbh
you really make things so easy, thank you sir
Excellent explanation. Thank you very much!!
Really Loved all of your videos broo. ❤️❤️❤️❤️
Mahesh, this is the most intuitive physics channel I have encountered so far! Big Gratitude!🎉 Perhaps could you please at some point make videos about AI/ML topics?
Super clear and fantastically explained thank you!
Took put a paper and pen and wrote the hole thing, i never understood the calculation of dubbeler effect mathematically thank you for that. Totally wirth the subscription ❤
This is so great! The intuitive explanation at the beginning (up to 10:35) is so close to an explanation simple enough for people who don't even understand kinetic energy or why energy is proportional to frequency. If you could come up with intuitive ways to understand those two concepts you could help so many more people by letting them understand this magnificent theory!