Can you PROVE the most Famous Equation in Physics?
ฝัง
- เผยแพร่เมื่อ 14 ต.ค. 2024
- 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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3. Special Theory of Relativity ► • Special Theory of Rela...
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5. Length Contraction (Thought Exp) ► • What is Length Contrac...
6. Lorentz Transormations ► • Derive Lorentz Transfo...
7. Relativity of Simultaneity ► • Relativity of Simultan...
8. Can you prove E=MC² ► • Can you PROVE the most...
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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
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!
Fantastic explanation! I was looking for something like this for a long time. Thank you for posting.
The example which is discussed here actually happened or not.
Plzz bro if you know that.
Thank you
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..
I've seen your videos on Geiger Muller counters and Scintillators. You have earned another subscriber. THANK YOU
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?
gravity is also a type of external force
@@jackming7972 what is the opposite reaction of gravity?
@@sumthinfresh If you are standing on the earth there is the gravitational force mg on you downward. The opposite is the gravitational pull you are making on the earth, upward. This is equal in magnitude but doesn't influence the earth much because of its great mass in comparison. (Using Newton physics here for simplicity)
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.
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
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
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?
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?
p=E/c comes from wave equations for radiation/light. p=mv comes from basic mechanical concepts for particles with mass. Both have separate origins. The genius of Einstein was to equate the energy of radiation to that of the mass of a particle/photon. In terms of equations, it's nothing significant, but in terms of physical concept that involves the matter-energy equivalence of light, its a great breakthrough.
@@FortheLoveofPhysics Thank you sir
By De broglie principle about matter lke electron or photon that display wave nature ........P = H/^ De Broglie relation
p= H/^ relationship between momemtum p and ^ wavelenght of particle
P=H/c/f..........................C = V=F^
p= HF/C
P = E/c ( E = HF.....by plank )
@@goriolaganiu403 In 1901 Plank developed his equation and in 1905 Einstein developed his Mass energy equivalence formula.. Then in1923 de broglie developed equation related to matter & wave.. Don't try to prove Einstein equation with plank and de broglie equations..
@@ishankashyap3350 I appreciate your objection. It's food for -fart- thought
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?..
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.
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).
at 13:30
1st, the mass associated with the motion of the light energy -- you are already assuming the mass becomes the light, then the light becomes a mass upon hitting the point B. one way to view for a matter to travel at the speed of light, then rematerialize itself
2nd how can the point B instantly move as a light is emitted from the point A?
at 15:26 ...CM is unchanged.., only because of the laws of physics momentum must be conserved FIRST. MV=-mC = M (x2-x1)/t = -m(L2 - L1)/t, Mx2 +mL2 = Mx1 + mL1 , not the other way around, with which simply gives MV = m L/t = m c = E/c
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
1.Why you ignore the mass of source emitting light?
2.Why have you assumed speed of container to be uniform ??
3.Why have you taken x2
Even if rest mass of photon is =0.
I think thar the speed is uniform because there is no force acting there so the aceleration=0.
When you doing that kind of thing ....I get motivet ...and also thought that do what you want .....such a nice effort sir....and also like the way you are express the physica in a intresting and easy ways
You are doing it with great professionalism. Good Job ! Keep it up ☺
i hope you reach 1M subscribers. you deserve it. thank you for all your videos, i hope you continue to make many many more
Thank you for giving such an informative and interesting lecture sir. But I have one question, doesn’t light have zero rest mass?
I have seen several videos that tried to explain about e=mc2, and i don't understand, until i saw this great video.
Very clear explanation. One tiny improvement is that the term intensity is not exactly equivalent to energy. Intensity has its own definition in physics. But all these is minor.
Marvelous! Simply Marvelous! With all the hundreds of videos on this topic I have seen, only this video clarified the concept!
Very good explanation. Thank you very much.
you're the best physics teacher I've ever had! thank you sir
Yeah its a very good derivation sir.
Although Its only valid for objects at rest.
Its still incomplete what u hv written.
Pls provide the full derivation E= gamma mc^2
Yes. The generalized formula with Momentum term.
I'm with you till end of the line sir, my first encounter with you sir was in the video related that an electron cannot stay in nucleus which has to be proved by using Heisenberg's uncertainty principle.
Good night sir.
Sir, what will happen if we perform this thought experiment in space after getting too kuch facilities...and during performing, photons couldn't push the container in backward
Will we prove Einstein wrong???
Great job explaining this most interesting thought experiment and how some basic physics reveals the Energy-mass equivalence (equation).
Will you ever do an electrodynamics series?
Great video. Can you help me understand why external forces are needed for something to move? If I replace the light pulse with a bullet from a gun, the box should move, then stop when the bullet hits the other side, right? There was motion without an external force. What am I missing?
There were motion in both directions, net momentum = 0 all the time. So the systen as a whole is not moving.
It just occurred to me that the same thought experiment could be done with Muons. They travel in a vacuum with a velocity of about 0.98C, and their Mass is 1.883531627(42)×10−28 kg. Would I arrive at the same result, E=M² ?
The center of gravity should have shifted because the mass of light moved from one end of the box to the other. The mass of the box did not change. I trust that I did not hear incorrectly about the center of gravity. I find that this e=mc2 to be a relationship between mass and its internal energy since c is a constant. Since there is no external force applied to the light mass in this proof.
Brilliant explanation and clarity!
Sir, in one place I have doubt. Initially you said that light is emitted internally.But How light will emit inside a container automatically. If we one it remotely than it means externally is force is applied but you said no external force is applied. How???
In some forms of radioactive decay (I think gamma decay for example) a photon can be emitted.
So our emitter at point A could be some radioactive material that decays and therefore emitts photons "automatically", with no need for an external force.
Because the Sun is an Sphere ???
If you can make one more video on it, I would like to watch the original derivation by einstein.
I'm an aerospace engg and too enthusiastic for theoretical physics, since years I'm struggling to understand the relativity concepts and concepts of quantum physics, specifically uncertainty principle. Would like to watch an elaborated video covering mass, light, gravity and quantum phenomenon. Thank You.
I'm very impressed !
What is the location of X1 and X2 in your diagram? Thanks
Excellent, please keep posing such videos .
A brilliant teaching way 😀
I have clearly understood the equation
A very very thank you to you Sir 😊
The equation for kinetic energy, KE= 1/2 mv^2, is very similar to E = mc^2. Leave out the 1/2 and it's still a measure of energy. So then you have KE= mv^2 and E=mc^2. c is a velocity so the two equations are very similar. Is there a way to reason from one to the other?
No, because c is not a free parameter. It's not even a physical constant. The numerical value is completely dependent on choice of time and distance units. In any rational system of physical base units c=1, so all you are really left with is E=m.
Interesting, but sadly it is incorrect.
Let:
El = the energy of the photon
M = the mass that doesn't convert to a photon
m = the mass that converts to a photon
In the first moment, we have:
E1 = (m + M)c^2
Then, when the mass m converts to a photon, we have:
E2 = El + Mc^2 + Mγc^2
The term "Mγc^2" represents the kinetic energy of the mass that didn't convert to a photon.
We know that TOTAL energy is conserved, so:
E1 = E2
(m + M)c^2 = El + Mc^2 + Mγc^2
Thus,
El = mc^2 - Mγc^2
However, the video claims that
El = mc^2
I am not aware if somebody else pointed it out before me.
Can someone explain, why does the equations of the center of mass look like they do? Like are they derived from an already existing equation where different letters are put in there because the represent the letters at the already existing equation?
Fantastic explanation
One more thing: you considered everything only in one system of reference, namely the stationary one, you never switched to a moving system and never employed Lorentz transform. That's why there's a question: what relevance does it have to Special Relativity? Could Newton (or, Maxwell for that matter) have derived it?..
Good for you, brother... Very good presentation.
I am a data scientist (well, I'm TRYING to be); I never thought I see Einstein here. But, here he is (can't get rid of this guy. I love the guy. I just don't have that much IQ); calculating matrices, tensors, etc. So, I'd really appreciate if you did some videos on vectors, matrices, spaces and ...
Sir , without any external force how the photon was generated??
Easy e:mc² stands for energy is equal to mass times the speed of light squared
1 question, that m was "photon" mass, but the real equation m was rest mass of any object. So is there any error from this derivation? Or this was just a tale...
I like the way you teach..... please continue uploading videos covering more topics...
Gi sir we learn it a lot and enjoy your video thank you so much sir such a enlightening, knowledgeful, video providing for us I may feel your hard work behind this great work
I'm getting very confused at the part where you explain how the center of mass remains in the same place. You put out the equation (m1x1+m2x2)/m1+m2. I don't understand how you got there.
That is the equation for center of mass
Is the example you have told actually happened or not.
Plzz sir I am still confused.
But sir explanation is mind-blowing.
Thank you very much.
Sir,where can i get your printed notes?
Sir thank you so much I like the way you explain the concepts of physics
Most wonderful teacher
He teaches physics greatfully
I can prove it in 3 lines
E = hc / lambda ----(1) plank's eqn
Lambda = h/mc ---- (de broglie eqn)
= h/lambda = mc
Putting in (1)
E = (mc)c
=E = mc^2
But it should not be that easy sir please tell if there is a flaw in my proof
Its not about the equations. Its about the physics behind the equations.
@@FortheLoveofPhysics
Remember, Debrogly generated his equation from first two.
I really like your video, but in the beginning at 4:00 you write p = E/c, and we know p = m*v=m*c, so this right away implies E=mc^2. So it seems that p=E/c implies E=mc^2 right away. Is there a way to prove E=mc^2 without relying on E=p/c?
what u derived first relyed on the eqn given by him
Light is massless (no rest mass). Einstein proposed this thought experiment in order to make the observation that light must be considered to have a ‘relativistic mass’ in order to satisfy conservation of linear momentum. Plugging ‘c’ in for the velocity in the equation p=mv would be meaningless without this thought experiment. The derivation is not entirely circular either because the equation p=E/c was made my Maxwell in the 1850s (predating Einstein).
When light hits B', will the momentum transferred make the isolated box to move to the right side ?
In space an object has to continue to move as no force is applied then how did the container came to rest after emission of light is not happening
Because the photon moving in opposite direction hit the container and cancelled its momentum
How does light have a momentum whats momentum is mass×velocity so light is Massless then why we measure momentum of light plzz sir answer it
What a nice explenation...👏👏👏
Excellent. I am now more clear on this. Thanks.
Great explanation sir but this is theory.....in practice does it work the same way? Following the laws of conservation of momentum - Why the Sun doesn't move back while radiating thousands of tonnes of energy per second. Kindly explain as I am still not able to visualize Einstein's mass/energy equation.
The sun does not move because it is emitted a roughly equal amount of radiation in all directions, therefore the effect cancels out.
Sir , Can you explain working principle of magnetron and klystron ? Thanks
Very Interesting. Explanation is very Clear. Thank you I am from Sri Lanka.
Wonderfull.Marvelous teacher
If I substituted p for mc in the expression p = E/c, I get the famous equation, because momentum is mass times velocity, where m is the associated mass of light. Why did Einstein have to do all this calculation? Why am I wrong?
So, i wonder why in the photon case, p = E/c. How to prove this? For in the case of an ordinary particle, p = 2E/v. Why this difference?
Sir energy is the capacity of body to do work ...then what will be the interpretation of this E in E=mc^2
Will the absorber at point B become warmer? If so why is not accounted for in the equation since it is also a form of energy?
You start by : p = E/c
And you have made a big round but for nothing when you have taken "m" as a mass of the photon! because it's not right!
If we can do this why we don't do it from the begining in the relation p = E/c! If "m" is the mass of the photon so p = mc => mc = E/c
So E = mc^2
But what I have done is wrong and idm for you too.
Sir, I'm a physics lover ❤️I'm in grade 11 now and I was just looking for this proof in each and every resources! The problem is that either they have mathematically derived with the help of differentiation and integration with no explanations or their explanation is highfy for me to understand! This is the best proof till now I have seen.. Salute to you sir ❤️
One more thing, I request you to please make videos on CBSE phy syllabus of 11th and 12th with deepest concepts! I really would love to learn from a teacher like you.. Best wishes...
Thank you. I am happy u found the video helpful :)
@@FortheLoveofPhysics Your welcome sir ☺️
I am in class 9
@Unknown Person • 14 years I m in 11 now
yeah OK - BUT!!! why doesn't the box return to its original position. Considering it is an enclosed box with no external forces, then all the energy and momentum must be conserved. So, yes the box will move when the light "fires" but should return to its original position when the light "beam" hits the opposite end? Surely?
Hi sir, Will you please explain why we have not considered the momentum transfer to the body when photon leaves the point A, Acc to the momentum conservation, as photon leaves point A, it will transfer the momentum to the point A just like it happens in rockets, plz clarify.
Is it possible to apply the equation to the entire universe? I am wondering if we go back in time far enough is it possible for a condition wherein m=0? Imagining the big bang, It seems to me that there may have been a point where the entire universe is devoid of matter, and comprised of energy alone. If that supposition is correct, would there be a need for space? If not, would time exist in that condition? I'm not sure about dark matter and energy and how they come in to play.
Thank you from a spirited laman.
If del x is equal to L then what's the need of centre of mass and all
U R mad genius Sir.
U got my respect.
I've to edit.
I'm an MSc Chemistry
Very nice video and clearly explained! However, I have a (possibly stupid) question. In the thought experiment why can't you replace the light beam with an object with arbitrary speed? Does it have something to do with the zero mass thing.
Exactly! You can! If it wasn't a photon travelling from one wall of the container to the other but, say, a golf ball pushed by a spring attached to the left wall and being glued to the right wall upon arriving there, then the container would have also moved as a result in exactly the same way - because the center of mass of a closed system must remain stationary. It's the same physical process in both cases. What would have changed however is this momentum-energy relation (E=pc) which we used in case of photon and which is not valid in case if a material ball.
Thank you for this insightful lecture!
“Mass associated by the motion of light” was this his great insight in this paradox? That massless photons still can create momentum?
Sir i have a question....you said that the light or energy has mass thats why it shows recoil, that container slightly moved backward then why not the other side move forward where the light striked on the other end of container as light carries the mass😅
great sir , for the sake of celebration you are doing one more proof ! true love for the physics . and sir it was really very interesting to proof E=mc^2 in this way and the suspense you created in the video i was like how Einstein sir solved the problem 🤔
Thanks. I am glad u liked the video :)
For the Love of Physics , thank you so much. Great job. Please keep it up and educate the students around the world. Where do you work ? Please
@@FortheLoveofPhysics Greetings. Reply please.
WHY THE ULTIMATE, TOP DOWN, AND CLEAR MATHEMATICAL UNIFICATION REGARDING PHYSICS/PHYSICAL EXPERIENCE IS F=MA AS E=MC2, AS ELECTROMAGNETISM/ENERGY IS GRAVITY:
E=mc2 IS F=ma. Gravity IS ELECTROMAGNETISM/energy, AS the Earth AND the Sun are CLEARLY linked AND BALANCED opposites; AS E=mc2 IS F=ma. ACCORDINGLY, the stars AND PLANETS are POINTS in the night sky; AS the MIDDLE DISTANCE in/of SPACE is linked AND BALANCED to/with/AS what is the FULL DISTANCE in/of SPACE !!! This necessarily represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. ("Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY.) Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (The sky is blue, AND the Earth is ALSO BLUE !!!) Great. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. SO, time DILATION ULTIMATELY proves (ON BALANCE) that ELECTROMAGNETISM/energy is gravity; AS E=MC2 IS F=MA. It ALL CLEARLY makes perfect sense. Indeed, BALANCE and completeness go hand in hand. Great !!! TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=MC2 IS F=MA !!!
Gravity IS ELECTROMAGNETISM/energy. E=mc2 IS F=ma. Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. Objects fall at the SAME RATE (neglecting air resistance, of course), AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY !!! WHAT IS THE EARTH, WHAT IS THE MOON, AND WHAT IS THE SUN ARE clearly F=ma AND E=mc2 IN BALANCE !!! Again, this NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY ON BALANCE !!! LOOK around. Think !!! Great !!! ("Mass"/ENERGY IS GRAVITY. E=MC2 IS F=ma. ELECTROMAGNETISM/ENERGY IS GRAVITY.) The Earth (A PLANET) is a MIDDLE DISTANCE form that is in BALANCED relation to the Sun AND the speed of light (c), AS the stars AND PLANETS are POINTS in the night sky; AS E=mc2 IS F=ma.
By Frank DiMeglio
how can you prove newton"s first law wrong here as there must be some energy used up in emitting the light and hence an external force would be there, pls reply??
i subscribed 3 times since i have 3 gmails you deserve more
Thanks man :)
Fantastic explanation...!!!!!
Thank u for excellent explanation.
Superb Sir
It is looking now simple after your explanation
Good Teacher of Physics. Good wishes for him.
You are doing a very great work. Keep it up!
Time sorayudathinullil angeekarichekkunna kullan graham onnundallo ettugrahangal orupole suryane ore anupathathil valam vaykumpol orannam avasanathe 9ennathu evayudeyokke thalathirivayanu karangunnathu ethayirikanam samayam savarayudhathile chandran =minittusuchiyengil uraponnum ella sawrayudham 8secend suchiyayikum 9ennathu aaclockile agolavalaythinte udhaharanam ayirikum karyathil paranjal nammalupayogikunna clock pole anganeyagam orupakshe sawrayudam undayirikunnathu angane aagamo sir
sir i kindly request u please make a video on ' parity, baryon number, Lepton number, Isospin, Strangeness and charm, concept of quark model, color quantum number and gluons '.
Will do soon..
@@FortheLoveofPhysics plz do it
Brilliant explanation...
Very helpful...
This equation is true and it will be just because there is no environment without nothing, there is always something even in a vacuum. I believe the "speed" of light can be infinitely fast if there is really nothing to interfere with, and the energy in this case "E" have a much bigger background story.
Very talented and hardworking teacher
Thank u bro. It was really excellent class for me.
sir can you make a video on relativistic mass and rest mass . it's very confusing
I wish he had just used the device of a deficit of mass in the body rather than calling it a "mass of a photon" .
Sir, please create playlists for all videos....