Can you PROVE the most Famous Equation in Physics?

A Simple proof of E=mc2 can be shown by a thought experiment, which goes as follows :

Imagine a container floating in deep space away from any external forces. If a light bulb inside it emits a beam of light, the container should experience recoil, as the light beam carries momentum. This is necessary for the Conservation of Linear Momentum. However this sets the container in motion which cannot be; as it will violate Newton's First Law which says that isolated bodies at rest will be at rest until an external force acts upon it. So, Einstein proposed a solution that the motion of light (which has momentum) is also associated with the motion of a small amount of mass, so that the final Center of Mass of the container+photon system does not change. Doing necessary calculations lead to E=mc2

E=mc2 or the Mass-Energy Equivalence Principle is probably The most famous Equation in all of Physics. It gives a quantitative relationship between Energy and Mass. Anything that has mass, will have an equivalent energy associated with it and any form of Energy will have mass associated with it. Converting one from the other is an experimental problem. The Equation merely states that the relationship between them when such a conversion happens, what should be the necessary relationship.

Here, in this video I discuss the simple yet elegant thought experiment of Einstein that can be used to show that E=mc2

#thoughtexperiment

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PLAYLIST ON Special Theory of Relativity
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[yairraz]

This guy is an absolutely great physics teacher, he focuses first on relying the underlying ideas and only later on the mathematical formalism. and has the very rare talent of explaining deep ideas in a straightforward manner, i would be great full to you if you could do some videos on quantum field theory

[shashidharnrao]

Fantastic explanation! I was looking for something like this for a long time. Thank you for posting.

[Marek-ztfy]

Love your voice, accent, videos, explanations, and how crisp, short and on-point all of your videos are. Great work man, really educational and entertaining!

[priyankalochab]

Many congratulations on completing this milestone.. wishing you more success in the future.. You are building a wonderful channel where anybody can learn physics from good quality videos.. thank you for taking out time to make these highly educational and useful videos.. we really appreciate you..

[Ihab.A]

I've seen your videos on Geiger Muller counters and Scintillators. You have earned another subscriber. THANK YOU

[bhavyaramakrishnan]

Please provide the initial assumptions for the isolated system.
1. No gravity
2. No heat dissipation
3. Container at rest
4. Free from external force
Anything else?

[mayankjoshi]

Sir, I would like to clear a thing. Consider a big ball and a car placed inside that ball, if the car is accelerated inside the ball the ball moves too. That means the force acting on the ball is external force. you gave an example about isolated box which has a light emitting beam inside it. So, when the light emits it puts some recoil on the box can call it as a force. The force acting on the box is external force not an internal force to be clear. If the light emission is putting recoil force on box that is an external force. And coming to internal forces there are only inter molecular, inter atomic forces acting. So the light emitting producing recoil force is truly an external force.

[winkychannel]

I have seen several videos that tried to explain about e=mc2, and i don't understand, until i saw this great video.

[biswajeetnayak]

I have been watching ur vdos, when u have less than 5k subscribers, now u have more than 100k subscribers, keep growing & keep educating us

[jackflash]

I am assuming that when the photon is absorbed by B, that B's energy has increased and it has therefore increased it's mass by the same value of the mass of the moving photon (because the rest mass of a photon is zero).

[blissfulbeing]

When you doing that kind of thing ....I get motivet ...and also thought that do what you want a nice effort sir....and also like the way you are express the physica in a intresting and easy ways

[FortheLoveofPhysics]

If you liked this video, here are a few more suggestions :)

[aravindrpillai]

absolutely awesome.. one small q. When exposing the Center of mass, why are we taking the initial points of container and the light as x1 and x2. Both starts from point x1 right?

[gaHuJIa_Macmep]

Actually, what you have derived is a relation
m = P/c
where m is a mass of a moving object (a ball or a photon), c — its speed and P — momentum of a container (and of a ball/photon respectively, due to momentum conservation). It suffices to put P = E/c for photon to get what you want (or another relation for massive particles in case you have one). It has Newtonian form (p = mv where v is substituted by c) although you are dealing with special relativity here. Does it constitute a problem?..

[fizykaliceum]

p=mv m-relativistic mas. For light v=c so for light p=mc . If you assume that E= mc*2 then p/E=mc/mc*2 p/E= 1/c p=E/c You are using equation E=mc*2 to derive equation E=mc*2

[shubhambeniwal]

You are doing it with great professionalism. Good Job ! Keep it up ☺

[Tzadokite]

here is an interesting derivation using the time dilation expression of STR: we have t(v)=t(0)*(1-v^2/c^2)^1/2. we write this as frequency 'f', which is defined as frequency = 1/time. hence we have f(v)=f(0)/(1-v^2/c^2)^1/2. for constant 'v' we have df=df(0)/(1-v^2/c^2)^1/2. we have dE=dP/dt *dx or dE*dt=dP*dx=k. this gives us dE*dt=k and dP*dx=k. from these one can obtain the heisenberg's uncertainty expressions. however, if we take dE*dt=k and write it as dE=k/dt we get dE=k*df, because df=1/dt as frequency = 1/time and for frequency = df we have df = 1/dt where dt = time. from dE=k*df we obtain E=kf+C where C is the integration constant. if when f=0 we have E=0 then C=0. hence, E=kf. of course from we can shown that k=h and obtain the general expression E=hf of which the planck expression for energy quanta or photon is a special case. hence E=kf(0)/(1-v^2/c^2)^1/2. from E=kf we get E(0)=kf(0). hence, E=E(0)/(1-v^2/c^2)^1/2. again for kinetic energy E(KE) we have E(KE)=E(v)-E(0) or {E(0)/(1-v^2/c^2)^1/2 } - E(0) = E(KE). for v<<c we have E(KE) = (1/2)*(E(0)/c^2)*v^2. but we know from classical physics that E(KE) = (1/2)*m(0)*v^2. comparing the two expressions for E(KE) we see that E(0)=m(0)*c^2. and from E(v)=E(0)/(1-v^2/c^2)^1/2 we get E=m(0)*c^2/(1-v^2/c^2)^1/2. this gives the relativistic mass expression m(v)=m(0)/(1-v^2/c^2)^1/2. the most important point in this derivation is to consider 'frequency' as the fundamental physical and dynamical quantity rather than 'time' which is a purely kinematical quantity. physical processes are dynamical and not kinematical which require that mass=0. making the kinematical time dilation expression of STR into the dynamical relativistic frequency expression one can obtain dynamical expressions such as E=MC^2, E=hf and uncertainty equalities from STR!

[williamolenchenko]

At time 08:35 velocity v of the container is written as a constant DeltaX/Deltat. That would imply infinite acceleration and infinite impulse. In reality, it will take some finite amount of time for velocity to go from zero to v. This should have been addressed.

[ishankashyap]

I really appreciate the teaching, great video!!
But I have one question. Initially you said the momentum is given by, p=E/c, but momentum is mass*velocity, ie mc (because c is the velocity here). Then we get mc=E/c => E=mc^2. So are we indirectly using E=mc^2 to prove E=mc^2. Isn't that circular reasoning?

I am not a student of physics, but a student of economics, so I might be mistaken about momentum etc. How would you clarify this doubt?

[Ihab.A]

Marvelous! Simply Marvelous! With all the hundreds of videos on this topic I have seen, only this video clarified the concept!