Why does E = mc2 ?

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

[mkpatel]

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🙏

[robwilliams]

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.

[hectorgarcia]

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

[sgiri]

Who wants Mahesh sir to upload more videos like this ? And increase the frequency of uploading videos.

[PhysicsConcept-cdbi]

I have never seen anyone explaining with this energy and so much interest.

[mozzerellaman]

You are a fantastic communicator of high-level concepts. I love your enthusiasm!

[KMac]

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.)

[sgiri]

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

[HK_Musician]

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

[NOTFOUND-dqho]

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 🎉

[rajanvenkatesh]

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.

[corsaircaruso]

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!

[ritwiksahu]

Here we learn important topics of physics while having fun.
Keep making more videos like this sir.

[nikhildivakar]

His ability to talk to dead scientists is an unfair advantage

[philoldout]

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.

[tunes]

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.

[Bondvsbatman]

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! ❤

[seanspartan]

Your enthusiasm for this subject is contagious 😊

[Shaurya_II]

Damn Einstein and Mahesh conversations really go deep

[Devendr]

This has to be one of the best physics videos on YouTube