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:

$$E^2-(pc)^2=(mc^2)^2$$

For p=0 you obtain $$E=mc^2$$ exactly

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

$$<E,E>-<p,p>=m^2$$

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