Einstein's Derivation of E=mC2: English Translation

In summary, Einstein derived the famous equation E=mc^2 in his second article on special relativity in 1905. The original paper was published in German, but there is an English translation available. The equation can be derived by taking the integral of P=mv\gamma, where \gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}} and c is the speed of light.
  • #1
Iraides Belandria
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¿How did Einstein derived that E=mC2?. ¿ Can I find an english translation of his original paper?.
 
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  • #2
Iraides Belandria said:
¿How did Einstein derived that E=mC2?. ¿ Can I find an english translation of his original paper?.

See
http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf
(there is translated in english the second article Einstein published in Annalen der physik about special relativity -thanks dex, i missed last- in german)
 
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  • #3
It was his second article on SR in 1905 and the IV-th overall in that year.

http://www.aip.org/history/einstein/chron-1905.htm

Daniel.
 
  • #4
thanks Rebel and dextercioby for the required information
 
  • #5
You can simply take this integral and you'll get [tex] E = mc^2 [/tex]

[tex] \int^c_0{P dv} ; [/tex]

where [tex] P = mv\gamma [/tex]

and [tex] \gamma = \frac{1}{\sqrt{1 - (\frac{v}{c})^2}} [/tex]

[tex] \int^c_0 {\frac{mv}{\sqrt{1 - (\frac{v}{c})^2}} dv = mc^2 [/tex]
 

FAQ: Einstein's Derivation of E=mC2: English Translation

1. What is the significance of E=mc^2?

E=mc^2 is the famous equation developed by Albert Einstein in his theory of special relativity. It states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared. This equation revolutionized the field of physics and is considered one of the most important equations in the history of science.

2. How did Einstein derive the equation E=mc^2?

Einstein derived the equation E=mc^2 through a series of thought experiments and mathematical calculations. He first recognized that the speed of light is constant and independent of the observer's frame of reference. He then used this concept to show that mass and energy are equivalent and can be converted into one another.

3. Can you explain the English translation of Einstein's derivation of E=mc^2?

In his original paper, Einstein wrote in German. The English translation of his derivation can be summarized as follows: First, he established the principle of relativity, which states that the laws of physics are the same for all observers in uniform motion. He then introduced the concept of the invariant speed of light and showed that the laws of physics must be the same for all observers, regardless of their motion. Finally, he derived the formula E=mc^2 to explain the relationship between mass and energy.

4. Is E=mc^2 a proven equation?

Yes, E=mc^2 has been proven through numerous experiments and observations. The most famous example is the release of energy in nuclear reactions, which is a direct result of the conversion of mass into energy. This equation has also been confirmed by the accuracy of various technological applications, such as GPS systems, which rely on Einstein's theories of special and general relativity.

5. How has E=mc^2 impacted modern society?

The equation E=mc^2 has had a profound impact on modern society. It has led to advancements in nuclear energy, which is used to generate electricity and power various forms of transportation. It also plays a crucial role in modern technology, such as medical imaging and nuclear medicine. Additionally, E=mc^2 has significantly influenced our understanding of the universe and has led to new theories and discoveries in physics.

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