Transformations between Matter and Energy
If material and energy both have mass and weight, can one be transformed into the other? Are they really different forms of one substance? Some philosophers before Einstein thought that some single substance underlies both material and movement, but they couldn’t prove their ideas. Einstein foresaw ways to convert energy into matter and back again. He told us just how much energy we need to make a given amount of matter, and how much energy we can obtain from matter. He presented his idea as follows:
The most important upshot of the special theory of relativity concerned the inert masses of corporeal systems. It turned out that the inertia of a system necessarily depends on its energy-content, and this led straight to the notion that inert mass is simply latent energy. The principle of the conservation of mass lost its independence and became fused with that of the conservation of energy.[i]
[i] Einstein, Albert, “What is the theory of relativity?”, The London Times, November 28, 1919, reprinted in Albert Einstein, Ideas and Opinions (New York: Wings Books, 1954), p. 230.
Through Einstein’s theory we came to understand how material can turn into energy, and vice versa.
This conversion does not happen in chemical burning or in nuclear fission. In those reactions, binding energy is released. There is another kind of nuclear burning, fusion, that combines small nuclei into larger ones. Some fusion reactions turn certain subatomic particles completely into energy. Also, physicists invented cyclotrons, machines that whirl electrons round and round, each time a little faster, and accelerate them to very high speeds. When sufficiently high-speed particles crash into others the particles may disappear completely and release energy as very energetic X-rays. Cyclotrons and other instruments that accelerate particles have demonstrated repeatedly that energy can turn into matter (materialize), and that matter can turn into energy. The theory is abundantly confirmed and has become a law of nature. We continue to say Einstein’s “theory” of relativity because Einstein himself did not do the experiments that confirmed it. He liked to propose “thought experiments” but he left real laboratory experiments to others.
Einstein’s formula, E = mc², tells us that a given quantity of energy E is equivalent to an amount of mass m.
This formula is easier to understand if we leave c² out, as physicists sometimes do. The equation is then just E = m. That simply means that energy is equivalent to material, or the amount of energy E is equal to the mass m of the material. The simplified equation without c² is correct when physicists measure energy and mass in the same units. If people always did the same, then we could go to the bakery and ask for 25 000 million kilowatt-hours of bread. But would the baker know we wanted a one-kilo loaf (or two one-pound loaves)? Or perhaps the light and power company, instead of billing us for 500 kilowatt-hours, would ask us to pay for 20 micrograms of electricity (the prefix “micro” on a unit of measure means “a millionth of” the following unit).
To work in units people know, we need Einstein’s full formula. The constant c is the speed of light, exactly 299 792 458 meters per second. The square of the speed of light is 89 875 517 873 681 764 meters squared per second squared. If we measure the mass in kilograms and the speed of light in meters per second, the energy will be in watt-seconds.
A watt-second is the energy required to keep a one-watt lamp lighted for one second. Usually a power utility bills us for electricity in kilowatt-hours. A kilowatt-hour is 1000 watts times 60 minutes per hour times 60 seconds per minute. That multiplies out to 3.6 million watt-seconds, the amount of energy needed to keep ten lamps of 100 watts each lighted for an hour.
To work in units people know, we need Einstein’s full formula. The constant c is the speed of light, exactly 299 792 458 meters per second. The square of the speed of light is 89 875 517 873 681 764 meters squared per second squared. If we measure the mass in kilograms and the speed of light in meters per second, the energy will be in watt-seconds.
A watt-second is the energy required to keep a one-watt lamp lighted for one second. Usually a power utility bills us for electricity in kilowatt-hours. A kilowatt-hour is 1000 watts times 60 minutes per hour times 60 seconds per minute. That multiplies out to 3.6 million watt-seconds, the amount of energy needed to keep ten lamps of 100 watts each lighted for an hour.
It takes 25 000 million kilowatt-hours of energy to produce one kilogram of material.
