# Einstein's original paper question

• 18t
In summary, Einstein's original derivation of the E=mc2 formula involved an approximation by neglecting higher order derivatives. However, the modern derivation using 4-vectors gives the general formula E^2-(pc)^2=(mc^2)^2. This can be simplified to E=m when p=0 and c=1. The reason why Einstein did not derive the equation precisely is not clear. Some sources suggest that he may have overlooked certain factors or made simplifications for the sake of clarity. However, the modern derivation is considered more accurate and has superseded the Sep 1905 paper derivation.
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?

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18t said:
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

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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.

## What is Einstein's original paper question?

Einstein's original paper question is: "Does the inertia of a body depend upon its energy-content?" This question was posed in Einstein's 1905 paper titled "Does the Inertia of a Body Depend Upon Its Energy Content?" which introduced the famous equation E=mc².

## What is the significance of Einstein's original paper question?

Einstein's original paper question was significant because it led to the development of the theory of special relativity and the famous equation E=mc². This theory revolutionized our understanding of space and time and has been confirmed through numerous experiments.

## How did Einstein answer his original paper question?

Einstein answered his original paper question by proposing the theory of special relativity, which states that the inertia (or mass) of a body is directly proportional to its energy content. This means that as an object's energy increases, its mass also increases.

## What impact has Einstein's original paper question had on science and society?

Einstein's original paper question has had a profound impact on science and society. It revolutionized our understanding of the universe and paved the way for further advancements in physics. It also led to the development of nuclear energy and weapons, which have had a significant impact on society.

## Is Einstein's original paper question still relevant today?

Yes, Einstein's original paper question is still relevant today. The theory of special relativity has been confirmed through numerous experiments and is still used in modern physics. The equation E=mc² is also widely used in various fields, including nuclear physics and astronomy.

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