# Wondering e=mc^2 is derived from what equations

• karan1114
In summary, E=mc2 was first derived by Einstein in a 1905 paper, where he showed that mass and energy are equivalent. The equation can be derived without mentioning light, and the constant c can be interpreted as the maximum speed of causality. The equation is based on the concept of momentum four-vector, where the norm equals E2-p2c2 and can be interpreted as m2c4. When a particle is at rest, the equation simplifies to E=mc2.
karan1114
i was just wondering e=mc^2 is derived from what equations and is linked to which other.

FAQ: Where does E=mc2 come from?

Einstein found this result in a 1905 paper, titled "Does the inertia of a body depend upon its energy content?" This paper is very short and readable, and is available online. A summary of the argument is as follows. Define a frame of reference A, and let an object O, initially at rest in this frame, emit two flashes of light in opposite directions. Now define another frame of reference B, in motion relative to A along the same axis as the one along which the light was emitted. Then in order to preserve conservation of energy in both frames, we are forced to attribute a different inertial mass to O before and after it emits the light. The interpretation is that mass and energy are equivalent. By giving up a quantity of energy E, the object has reduced its mass by an amount E/c2, where c is the speed of light.

Why does c occur in the equation? Although Einstein's original derivation happens to involve the speed of light, E=mc2 can be derived without talking about light at all. One can derive the Lorentz transformations using a set of postulates that don't say anything about light (see, e.g., Rindler 1979). The constant c is then interpreted simply as the maximum speed of causality, not necessarily the speed of light. We construct the momentum four-vector of a particle in the obvious way, by multiplying its mass by its four-velocity. (This construction is unique in the sense that there is no other rank-1 tensor with units of momentum that can be formed from m and v. The only way to form any other candidate is to bring in other quantities, such a constant with units of mass, or the acceleration vector. Such possibilities have physically unacceptable properties, such as violating additivity or causality.) We find that this four-vector's norm equals E2-p2c2, and can be interpreted as m2c4, where m is the particle's rest mass. In the case where the particle is at rest, p=0, and we recover E=mc2.

A. Einstein, Annalen der Physik. 18 (1905) 639, available online at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

## 1. What is the meaning of "e=mc^2"?

"e=mc^2" is a famous equation known as Einstein's mass-energy equivalence formula. It represents the relationship between mass (m), energy (e), and the speed of light (c) in a vacuum.

## 2. How was "e=mc^2" derived?

Einstein's equation was derived through a series of thought experiments and mathematical calculations. It was first introduced in his 1905 paper "Does the Inertia of a Body Depend Upon Its Energy Content?" and has since been supported by numerous experiments and observations.

## 3. What equations were used to derive "e=mc^2"?

Einstein's equation is based on two other equations - the principle of relativity and the principle of conservation of energy. It also incorporates the famous equation E=hf, which relates energy to frequency, and the equation p=mc, which represents the relationship between mass and momentum.

## 4. Can "e=mc^2" be applied to all types of energy?

Yes, "e=mc^2" can be applied to all forms of energy, including kinetic, thermal, and potential energy. This equation is a fundamental principle of physics and applies to all systems, regardless of their size or complexity.

## 5. What are the practical applications of "e=mc^2"?

The practical applications of "e=mc^2" are vast and have revolutionized our understanding of the universe. This equation has been used in the development of nuclear energy, nuclear weapons, and nuclear medicine. It also plays a crucial role in our understanding of stars and other celestial bodies.

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