E equals m c squared

"Proof" of 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. 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.

"In light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alterations of confidence and exhaustion and the final emergence into the light -- only those who have experienced it can understand it."

Einstein's theories sprang from a ground of ideas prepared by decades of experiments. One of the most striking, in retrospect, was done in Cleveland, Ohio, by Albert Michelson and Edward Morley in 1887. Their apparatus was a massive stone block with mirrors and crisscrossing light beams, giving an accurate measurement of any change in the velocity of light. Michelson and Morley expected to see their light beams shifted by the swift motion of the earth in space. To their surprise, they could not detect any change. It is debatable whether Einstein paid heed to this particular experiment, but his work provided an explanation of the unexpected result through a new analysis of space and time.

When Einstein used his equations to study the motion of a body, they pointed him to a startling insight about the body's mass and energy.

The deep connection Einstein discovered between energy and mass is expressed in the equation E equals m c squared. Here E represents energy, m represents mass, and c squared is a very large number, the square of the speed of light. Full confirmation was slow in coming. In Paris in 1933, Irène and Frédéric Joliot-Curie took a photograph showing the conversion of energy into mass. In the photography, an invisible quantum of light carrying energy changes into mass --Two particles were created and curved away from each other.

Meanwhile in Cambridge, England, the reverse process was seen: the conversion of mass into pure energy. With their apparatus John Cockcroft and E.T.S. Walton broke apart an atom. The fragments had slightly less mass in total than the original atom, but they flew apart with great energy.