Einstein’s Mass-Energy Equivalence

In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energycontent. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant. This means (for example) that the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of massto units of energy. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled “Does the inertia of a body depend upon its energy-content?” The equivalence is described by the famous equation:    E=mc2

 

Before Einstein, it was known that a beam of light pushes against matter; this is known as radiation pressure. This means the light has momentum. A beam of light of energy E has momentum E/c. Einstein used this fact to show that radiation (light) energy has an equivalent mass.

Consider a cylinder of mass M (see accompanying figure-“energy”). A pulse of light with energy E is emitted from the left side. The cylinder recoils to the left with velocity v=E/(Mc). If the mass of the cylinder is large, it doesn’t move far before the light reaches the other side. So, the light must travel a distance L, requiring time t=L/c. In this time, the cylinder travels a distance x=vt=[E/(Mc)](L/c).

Einstein reasoned that the center of mass of an isolated system doesn’t just move on its own. So, the motion of the cylinder must be compensated by the motion of some other mass. Let’s assume the light has mass m. Then, Mx=mL, since the cylinder moves x to the left and the light moves L to the right. Substituting the expression for x given above, the equation can be simplified to E=mc2.

From the fact that light has momentum, Einstein showed that light energy has the characteristics of mass also. In other words, energy has inertia. It turns out that all energy has this feature. That’s because one form of energy can be transformed into another. So, if one kind of energy has this characteristic, all forms of energy do.

Einstein himself explains the meaning of E=mc2 in this sound clip .

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