Deriving equations on Einstein's 4th paper

In summary, the conversation is about deriving equations related to the inertia of a body and its energy content. The individual is seeking help and direction on where to start and what transformations to use. They also mention being confused about the emission of waves of light and other factors. The speaker suggests looking into the theory of relativity and the relativistic Doppler effect for more information.
  • #1
Xeniebop
3
0

Homework Statement



I need to derive some equation that are on the paper "does the inertia of a body depend on it's energy content". http://www.fourmilab.ch/etexts/einstein/E_mc2/www/" I just don't know where to start and if someone can point me to the right direction, it will be so much help.

The first is,
eq1.gif

I know that this was derived using the theory of relativity but I don't know where to start and transformations to use.

The second is,
eq2.gif

The emission of waves of light and other stuffs just confuses me more, and is these just using the above relationship?

Thank you very much.
 
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  • #2
You can find the details of derivation of formulas like that under the heading of 'relativistic doppler effect'.
 

1. How did Einstein derive his famous equation, E=mc^2, in his 4th paper?

Einstein derived the equation E=mc^2 by first postulating that the speed of light is constant in all frames of reference. He then used this postulate to derive the special theory of relativity, which states that energy and mass are equivalent and can be converted into each other through the formula E=mc^2.

2. What other equations did Einstein derive in his 4th paper?

In his 4th paper, Einstein also derived the equation for the transformation of energy and momentum in special relativity, as well as the equation for the transformation of length and time. He also introduced the concept of four-dimensional spacetime and derived the famous equation for time dilation.

3. What was the significance of Einstein's 4th paper in the field of physics?

Einstein's 4th paper, titled "On the Electrodynamics of Moving Bodies," is considered one of the most significant papers in the history of physics. It introduced the theory of special relativity, which revolutionized our understanding of space and time and laid the foundation for modern physics. The paper also introduced the famous equation E=mc^2, which has had a profound impact on our understanding of energy, mass, and the universe.

4. How did Einstein's 4th paper challenge traditional Newtonian physics?

Einstein's 4th paper challenged traditional Newtonian physics by introducing the concept of relativity, which states that the laws of physics should be the same for all observers in uniform motion. This contradicted Newton's laws, which stated that there is an absolute frame of reference in which all physical laws are the same. Einstein's theory also challenged the idea of absolute time and space, which had been a cornerstone of Newtonian physics.

5. Are there any practical applications of the equations derived in Einstein's 4th paper?

Yes, the equations derived in Einstein's 4th paper have numerous practical applications. The most well-known is the equation E=mc^2, which is the basis for nuclear energy and has been used in the development of nuclear weapons. The equations for special relativity also have practical applications in areas such as GPS technology and particle accelerators. The concept of four-dimensional spacetime has also been applied in various fields, including cosmology and astrophysics.

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