I recently got a proof of mass energy equivalence from my friend who claims to have it from a very famous professor of IIT , the proove is as follows , please help to find me if there are any errors or arguments .....

Let us consider a photon emerging from somewhere , assuming that there exists a point of time , when it has just emerged , when it's initial velocity is 0 , which we will later proove to be false when we have derived

\[E = mc^{2}\]

So, \[u=0\] where u is the initial velocity

And \[ v = c\] where v the final velocity is \[c\] , speed of light.

Let us assume the \[d\] distance when the photon reaches the speed \[c\]

Clearly the initial energy would be 0 ,and the energy gained by it would be the work done by it.

So, \[W=E\]

\[W=Fd\]

\[W=mad\] Force is equal to product of mass and acceleration.

\[W=m\frac{(v-u)}{t}d\]

\[W=m\frac{v}{t}d\]We took d/ t to be v because according to Maxwell's equation light shall not change its velocity ever ever.This realisation of Maxwell has occurred to us later here but for which we assume there be some distance d and some time t.

\[W=mv^{2}\]

\[E=mv^{2}\]

\[E=mc^{2}\]

As in quantum physics , energy here is referred as to travel at c so this proof relates and does not contradict Uncertainty principle or quantum mechanics either.

This was the explanation given by the professor , whose name shall not be mentioned, I hoped this would be liked by the brilliantines so decided to share this a matter of knowledge.

Please if any arguments or contradictions that may be raised tell me I may that professor who is my friend's relative

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## Comments

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TopNewestIn the latter half of the "proof" your instructor said: "We took \(\frac{d}{t}\) to be \(v\) because according to Maxwell's Equation light shall not change its velocity ever." But in the beginning, he said "...when its initial velocity is zero, which we will later prove to be false when we derive \(E=mc^2\)." Really, the instructor didn't prove much, he could have just as easily referenced Maxwell in the beginning and stated that the velocity must always be constant. Also, he arrives at \(E=mc^2\) under the assumption that the initial velocity is zero, which is erroneous as a light particle can never be static as he later claimed. Then if we follow his framework with this fact in mind, we get \(E=0\), which is wrong. Also, I believe Einstein's derivation of this is based on relativistic mass, which photons have. However, photons do not have mass in the normal sense, hence the substitution where \(W=Fd\) becomes \(W=mad\) isn't exactly correct either as this assumes that photons have rest mass. In short, I don't believe this is correct. However, I am not a professional and I could be completely wrong. If I am and someone knows why, I'd be interested to learn.

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And not to forget that you are excellent proof-writer , how do you do that?

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I would like to say that the same case is with me I am a student and new to this world. First of all you should consider this that this proof is in third person. Suppose a car is running on road , then we are the observer , observing in third person and the driver is the doer observing his actions in first person . It is not necessary that the observation of the doer and any other observer be the same. The initial velocity that we are saying is 0 , is our assumption that there be some point in time when the velocity is 0 , realistically or simply really not because we are observing it is not but because it is our very own assumption with no contradiction in it. Actually we being observers would not be able to distinguish for its speed should be same in every observation due to the slowness or fastness of time accordingly. So , in short , this is our assumption. In that case the energy would not be 0 in our reference that's all we want. Secondly, Maxwell told light has momentum but if light has no mass how could it be possible, it was made true by simply assuming that the mass is relative to its energy so substitution you are saying to be false is just true , entering the relative mass instead of original mass will give you value.

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I see what you're saying. I assumed the mass in the above proof was the rest mass. If it is the relativistic mass, then that part of it makes sense to me. As for the initial velocity, after re-reading the proof and your comment, I somewhat understand what you're saying in this context (it's an assumption that we, as observers, cannot prove to be true or false in our frame of reference, by my understanding).

I'm still learning relativity. For some reason, I find relativity to be much more difficult to understand than quantum mechanics (I do not claim to understand quantum mechanics extremely well either, I definitely understand it better than relativity though). Perhaps I should devote more time to it. Relativity was written by Einstein, inspired by the ideas of Lorentz, Poincare and a few others. Quantum mechanics is a field that has been developed by many, many people (including Einstein). The fact that the majority of Relativity can be attributed to one person astounds me, I think it's incredible. If you understand the concepts of relativity as you appear to, then congratulations, that's something to be proud of.

And thanks for the compliment on my proofs! I really appreciate it, glad to see that someone likes them.

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