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]
Materialization
Through Einstein’s theory we came to understand how material can turn into energy, and vice-versa.[ii] Einstein’s formula, E = mc², tells us that a given quantity of energy E is equivalent to an amount of mass m.[iii] It takes 25 000 million kilowatt-hours of energy to produce one kilogram of material.
Different Kinds of Rays
Material is composed of subatomic particles like neutrons, protons, and electrons, listed in order from highest to lowest weight. Electromagnetic rays are the tracks of energy particles called photons.[iv] Photons can produce particles if the equivalent mass of the photons is at least as great as the mass of the particles. Since c² is a large number, we need very energetic photons to make even low-mass particles.
X-rays have the most energetic photons scientists can produce with laboratory equipment. Low-energy gamma rays are identical to X-rays, but the term “gamma rays” refers to rays from natural sources. Some gamma rays have photons that are much more energetic than the most energetic X-ray photons we can produce. To materialize, rays must be at least as energetic as the hard X-rays physicists make with cyclotrons or linear accelerators.[v]
Materialization in “Empty” Space
Light rays are visible and make other things visible. All other rays are invisible. They carry energy in darkness.[vi]
Since we can see the stars, we know that light can travel in space. We say that space is empty when it contains no matter, but empty space always contains the energy of heat and of any light or gamma rays in transit. We have never been able to make any space so cold and dark that it has no energy at all. Electromagnetic rays can exist in empty space, and there they can make material.
[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.
[ii] 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 accelerate electrons to very high speeds by whirling them round and round, each time a little faster. Cyclotrons and other instruments that accelerate particles have demonstrated repeatedly that energy can 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 talk about “thought experiments” but he left real laboratory experiments to others.
[iii] 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.
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.
[iv] The weight and the energy of a photon are directly proportional to the rapidity of vibration of the rays.
[v] A single ray cannot materialize all by itself. Two rays, or a ray and a particle, must collide to materialize. If there is a particle present then the space is not empty, so let us talk first about the collision of two rays. When gamma rays or hard X-rays collide, they convert some or all of their energy into particles. The particles may be components of atoms, such as protons, neutrons, and electrons, or other, less well-known particles. We cannot see atoms because atoms are 5 000 times smaller than light waves. Subatomic particles are even smaller. During the collision, some of the original energy may become kinetic energy, the energy of moving objects. If so, the particles will depart from the scene of their materialization at high speed. If any of the original energy remains, it will travel on as one or more photons of lower energy. The photons continue to collide and fracture until they lack enough energy to materialize.
Sufficiently energetic rays become visible when they collide, fracture, and partially materialize as particles. The particles must form atoms, and the atoms must combine in great numbers before there is visible material. The remaining energy may be soft X-rays, ultraviolet rays, light, or heat. Only the light rays are visible.
An electron has the lowest mass of the three most common subatomic particles. Its mass is equivalent to the energy of the hard X-ray photons we use for treating cancer, much more than the energy of the softer X-ray photons we use for medical diagnosis. Visible light photons are far too weak to make electrons, let alone protons or neutrons. Neither heat nor light nor ultraviolet rays nor soft X-rays can materialize.
[vi] When doctors make an X-ray picture, they send a powerful pulse of energy through the patient’s body. The X-rays expose the film, but the patient sees nothing. To the patient X-rays are dark.
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]
Materialization
Through Einstein’s theory we came to understand how material can turn into energy, and vice-versa.[ii] Einstein’s formula, E = mc², tells us that a given quantity of energy E is equivalent to an amount of mass m.[iii] It takes 25 000 million kilowatt-hours of energy to produce one kilogram of material.
Different Kinds of Rays
Material is composed of subatomic particles like neutrons, protons, and electrons, listed in order from highest to lowest weight. Electromagnetic rays are the tracks of energy particles called photons.[iv] Photons can produce particles if the equivalent mass of the photons is at least as great as the mass of the particles. Since c² is a large number, we need very energetic photons to make even low-mass particles.
X-rays have the most energetic photons scientists can produce with laboratory equipment. Low-energy gamma rays are identical to X-rays, but the term “gamma rays” refers to rays from natural sources. Some gamma rays have photons that are much more energetic than the most energetic X-ray photons we can produce. To materialize, rays must be at least as energetic as the hard X-rays physicists make with cyclotrons or linear accelerators.[v]
Materialization in “Empty” Space
Light rays are visible and make other things visible. All other rays are invisible. They carry energy in darkness.[vi]
Since we can see the stars, we know that light can travel in space. We say that space is empty when it contains no matter, but empty space always contains the energy of heat and of any light or gamma rays in transit. We have never been able to make any space so cold and dark that it has no energy at all. Electromagnetic rays can exist in empty space, and there they can make material.
[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.
[ii] 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 accelerate electrons to very high speeds by whirling them round and round, each time a little faster. Cyclotrons and other instruments that accelerate particles have demonstrated repeatedly that energy can 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 talk about “thought experiments” but he left real laboratory experiments to others.
[iii] 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.
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.
[iv] The weight and the energy of a photon are directly proportional to the rapidity of vibration of the rays.
[v] A single ray cannot materialize all by itself. Two rays, or a ray and a particle, must collide to materialize. If there is a particle present then the space is not empty, so let us talk first about the collision of two rays. When gamma rays or hard X-rays collide, they convert some or all of their energy into particles. The particles may be components of atoms, such as protons, neutrons, and electrons, or other, less well-known particles. We cannot see atoms because atoms are 5 000 times smaller than light waves. Subatomic particles are even smaller. During the collision, some of the original energy may become kinetic energy, the energy of moving objects. If so, the particles will depart from the scene of their materialization at high speed. If any of the original energy remains, it will travel on as one or more photons of lower energy. The photons continue to collide and fracture until they lack enough energy to materialize.
Sufficiently energetic rays become visible when they collide, fracture, and partially materialize as particles. The particles must form atoms, and the atoms must combine in great numbers before there is visible material. The remaining energy may be soft X-rays, ultraviolet rays, light, or heat. Only the light rays are visible.
An electron has the lowest mass of the three most common subatomic particles. Its mass is equivalent to the energy of the hard X-ray photons we use for treating cancer, much more than the energy of the softer X-ray photons we use for medical diagnosis. Visible light photons are far too weak to make electrons, let alone protons or neutrons. Neither heat nor light nor ultraviolet rays nor soft X-rays can materialize.
[vi] When doctors make an X-ray picture, they send a powerful pulse of energy through the patient’s body. The X-rays expose the film, but the patient sees nothing. To the patient X-rays are dark.