The equivalence of mass and energy

This chapter starts with four pages of algebra, that is designated as "Can Be Omitted." It translates the classical concepts of force, momentum, and energy into relativistic terms.

We included this chapter in the book because, out of these results came the principle of the equivalence of mass and energy, which surprised even Einstein.

When his theory led him to suspect that there may be this equivalence of energy and mass, Einstein confided to a friend, Conrad Habicht, "...This thought is both amusing and attractive, but whether or not the good Lord laughs at me concerning this notion and has led me around by the nose -- that I cannot know."

There is much misunderstanding about the equivalence of mass and energy

"Equivalence" means they are the same. It does not mean that one can be converted into the other. They do not need to be converted; they are both mass and energy at the same time.

Imagine that there is a box that is green on one side and red on the other.

The box is both green and red, depending on which way you look at it.

We are accustomed to looking at the mass aspect of objects, and to look at the energy aspect of quantities like heat and motion or the stretch of a spring.

You don't convert a green box into a red one by walking from the green side around to the red side.

It does indeed seem like such a strange thing. Mass is a bunch of stuff; energy is what you have when you run. How can these be the same?

The equation for this equivalence is derived in this chapter. It is the famous equation, E = mc2, where c is the speed of light. This is an equivalence equation, not a conversion equation.

Here are some things that are true and one that is not:

• TRUE One can describe the mass of a 1kg (2.2lb) bag of sugar in energy units. One simply applies the equivalence equation, E = mc2. The energy of that 1kg of sugar is 90,000,000,000,000,000 Joules. That is 25 billion Kilowatt hours.
• TRUE One does not need both kg and KWh as units. You can say this is a 25 billion Kilowatt hour bag of sugar. You can see why units of mass are used. Buying sugar by the KWHr, at a price of \$1.50 for 25,000,000,000 KWHr could get messy.
• TRUE Particle physicists commonly describe the mass of particles like muons in units of Energy called ElectronVolts.
• NOT TRUE In nuclear reactions in Uranium reactors and in nuclear bombs mass is not converted to energy. It was energy all along.
• TRUE The mass that the Uranium loses during the nuclear reaction is the mass of the binding energy that is lost as the nuclear particles rearrange themselves to bind more tightly, which they do in the fission products.
• TRUE The same thing happens when you release a spring. The spring loses a small amount of mass, which is the mass of the spring potential energy when the spring was stretched.
• TRUE Early nuclear physicists were able to know that there is enormous energy locked up in these nuclei, by the difference in the total atomic weights of isotopes with their bonds arranged differently. Chemists had know this for a long time as the "mass defect."
• TRUE This understanding of the "mass defect" did aid the emergence of nuclear technology. Whereas you can find how much energy can be released by burning an ounce of gasoline by just doing it and measuring the heat released, it is quite hard to do the same on a try-and-see basis with nuclear reactions.

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