Einstein's original paper question

[18t]

Hi, by reading the Einstein's original derivation of the E=mc2 formula (http://www.fourmilab.ch/etexts/einstein/E_mc2/www/), Einstein does an
approximation by neglecting higher order derivatives before arriving at
E=mc2. But, as far as I know, E equals mc2 precisely. Does anyone know why Einstein didnt derive the equation precisely? I tried to play with the paper a bit to make it spit out the precise equation but didnt have much luck-I must be overlooking something. Could someone help me with this one?

 

[nakurusil]

Hi, by reading the Einstein's original derivation of the E=mc2 formula (http://www.fourmilab.ch/etexts/einstein/E_mc2/www/), Einstein does an
approximation by neglecting higher order derivatives before arriving at
E=mc2. But, as far as I know, E equals mc2 precisely. Does anyone know why Einstein didnt derive the equation precisely? I tried to play with the paper a bit to make it spit out the precise equation but didnt have much luck-I must be overlooking something. Could someone help me with this one?

The Sep 1905 paper derivation has been long superseeded by the modern derivation that uses 4-vectors giving the general formula:

[tex]E^2-(pc)^2=(mc^2)^2[/tex]

For p=0 you obtain [tex]E=mc^2[/tex] exactly

The above can be written a little nicer if we take c=1:

[tex]<E,E>-<p,p>=m^2[/tex]

where <,> represents the dot product. In the proper frame of the object p is 0 therefore E=m

 

[Entropia]

It is important to note that Einstein's original paper on the E=mc2 equation was published in 1905, at a time when his theory of special relativity was still in its early stages and he was working with limited knowledge and resources. Therefore, it is possible that he made approximations and simplifications in his derivation in order to make it more accessible and understandable to his audience.

Additionally, it is also important to keep in mind that Einstein was not the only scientist working on the concept of mass-energy equivalence at the time. Other scientists, such as Max Planck and Henri Poincaré, had also developed similar equations before Einstein's publication. It is possible that Einstein was influenced by these previous works and used them as a basis for his own derivation.

Furthermore, it is worth noting that Einstein's original paper was focused on the relationship between mass and energy, rather than the precise numerical value of the equation. It was only later on, through further research and experiments, that the exact value of E=mc2 was confirmed.

In conclusion, while it is true that Einstein's original derivation may have neglected higher order derivatives and may not have resulted in the precise equation, it is important to consider the context in which it was written and the contributions of other scientists in the field. Einstein's paper laid the foundation for further research and understanding of this fundamental equation, and his approximation did not diminish its significance or impact in any way.