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When Albert Einstein posits that energy and matter are one and the same, and one can be converted into the other, most people could not wrap their heads around the idea. They can imagine burning a piece of wood (matter) to get heat and light (energy), but the workings of chemical reactions (in this case oxidization) is well-established. But the idea that the stuff of matter itself (neutrons, electrons, protons) is made of this ethereal, barely-understood thing called energy, flies in the face of conventional wisdom and reasoning.
We've come a long way since then... |
"Mass and energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind."
Albert Einstein, Atomic Physics (1948)
The equivalence of mass and energy is one of the things that Einstein is most famous for. It is a famous equation in physics and math that shows what happens when mass changes to energy or energy changes to mass. The "E" in the equation stands for energy. Energy is a number which you give to objects depending on how much they can change other things. For instance, a brick hanging over an egg can put enough energy onto the egg to break it. A feather hanging over an egg does not have enough energy to hurt the egg.
There are three basic forms of energy: potential energy, kinetic energy, and rest energy. Two of these forms of energy can be seen in the examples given above, and in the example of a pendulum.
Imagine a heavy ball hanging on a rope. Your pull the ball to the right side. When the ball is released it will move back and forth. It would do that forever except that the movement of the rope and rubbing in other places causes friction, and the friction takes away a little energy all the time. If we ignore the losses due to friction, then the energy provided in the first place is given to the ball as potential energy. (It has energy because it is up high and can fall down.) As the ball swings down it gains more and more speed, so the nearer the bottom it gets the faster it is going and the harder it would hit you if you stood in front of it. Then it slows down as its kinetic energy is changed back into potential energy. "Kinetic energy" just means the energy something has because it is moving. "Potential energy" just means the energy something has because it is in some higher position than something else.
When energy moves from one form to another, the amount of energy always remains the same. It cannot be made or destroyed. This rule is called the "conservation law of energy". For example, when you throw a ball, the energy is transferred from your hand to the ball as you release it. But the energy that was in your hand, and now the energy that is in the ball, is the same number. For a long time, people thought that the conservation of energy was all there was to talk about.
When energy transforms into mass, the amount of energy does not remain the same. When mass transforms into energy, the amount of energy also does not remain the same. However, the amount of matter and energy remains the same. Energy turns into mass and mass turns into energy in a way that is defined by Einstein's equation, E = mc2.
The "m" in Einstein's equation stands for mass. Mass is the amount of matter there is in some body. If you knew the number of protons and neutrons in a piece of matter such as a brick, then you could calculate its total mass as the sum of the masses of all the protons and of all the neutrons. (Electrons are so small that they are almost negligible.) Masses pull on each other, and a very large mass such as that of the Earth pulls very hard on things nearby. You would weigh much more on Jupiter than on Earth because Jupiter is so huge. You would weigh much less on the Moon because it is only about one-sixth the mass of Earth. Weight is related to the mass of the brick (or the person) and the mass of whatever is pulling it down on a spring scale – which may be smaller than the smallest moon in the solar system or larger than the Sun.
Mass, not weight, can be transformed into energy. Another way of expressing this idea is to say that matter can be transformed into energy. Units of mass are used to measure the amount of matter in something. The mass or the amount of matter in something determines how much energy that thing could be changed into.
Energy can also be transformed into mass. If you were pushing a baby buggy at a slow walk and found it easy to push, but pushed it at a fast walk and found it harder to move, then you would wonder what was wrong with the baby buggy. Then if you tried to run and found that moving the buggy at any faster speed was like pushing against a brick wall, you would be very surprised. The truth is that when something is moved then its mass is increased. Human beings ordinarily do not notice this increase in mass because at the speed humans ordinarily move the increase in mass in almost nothing.
As speeds get closer to the speed of light, then the changes in mass become impossible not to notice. The basic experience we all share in daily life is that the harder we push something like a car the faster we can get it going. But when something we are pushing is already going at some large part of the speed of light we find that it keeps gaining mass, so it gets harder and harder to get it going faster. It is impossible to make any mass go at the speed of light because to do so would take infinite energy.
Sometimes a mass will change to energy. Common examples of elements that make these changes we call radioactivity are radium and uranium. An atom of uranium can lose an alpha particle (the atomic nucleus of helium) and become a new element with a lighter nucleus. Then that atom will emit two electrons, but it will not be stable yet. It will emit a series of alpha particles and electrons until it finally becomes the element Pb or what we call lead. By throwing out all these particles that have mass it has made its own mass smaller. It has also produced energy.
In most radioactivity, the entire mass of something does not get changed to energy. In an atomic bomb, uranium is transformed into krypton and barium. There is a slight difference in the mass of the resulting krypton and barium, and the mass of the original uranium, but the energy that is released by the change is huge.
There are three basic forms of energy: potential energy, kinetic energy, and rest energy. Two of these forms of energy can be seen in the examples given above, and in the example of a pendulum.
Imagine a heavy ball hanging on a rope. Your pull the ball to the right side. When the ball is released it will move back and forth. It would do that forever except that the movement of the rope and rubbing in other places causes friction, and the friction takes away a little energy all the time. If we ignore the losses due to friction, then the energy provided in the first place is given to the ball as potential energy. (It has energy because it is up high and can fall down.) As the ball swings down it gains more and more speed, so the nearer the bottom it gets the faster it is going and the harder it would hit you if you stood in front of it. Then it slows down as its kinetic energy is changed back into potential energy. "Kinetic energy" just means the energy something has because it is moving. "Potential energy" just means the energy something has because it is in some higher position than something else.
When energy moves from one form to another, the amount of energy always remains the same. It cannot be made or destroyed. This rule is called the "conservation law of energy". For example, when you throw a ball, the energy is transferred from your hand to the ball as you release it. But the energy that was in your hand, and now the energy that is in the ball, is the same number. For a long time, people thought that the conservation of energy was all there was to talk about.
When energy transforms into mass, the amount of energy does not remain the same. When mass transforms into energy, the amount of energy also does not remain the same. However, the amount of matter and energy remains the same. Energy turns into mass and mass turns into energy in a way that is defined by Einstein's equation, E = mc2.
The "m" in Einstein's equation stands for mass. Mass is the amount of matter there is in some body. If you knew the number of protons and neutrons in a piece of matter such as a brick, then you could calculate its total mass as the sum of the masses of all the protons and of all the neutrons. (Electrons are so small that they are almost negligible.) Masses pull on each other, and a very large mass such as that of the Earth pulls very hard on things nearby. You would weigh much more on Jupiter than on Earth because Jupiter is so huge. You would weigh much less on the Moon because it is only about one-sixth the mass of Earth. Weight is related to the mass of the brick (or the person) and the mass of whatever is pulling it down on a spring scale – which may be smaller than the smallest moon in the solar system or larger than the Sun.
Mass, not weight, can be transformed into energy. Another way of expressing this idea is to say that matter can be transformed into energy. Units of mass are used to measure the amount of matter in something. The mass or the amount of matter in something determines how much energy that thing could be changed into.
Energy can also be transformed into mass. If you were pushing a baby buggy at a slow walk and found it easy to push, but pushed it at a fast walk and found it harder to move, then you would wonder what was wrong with the baby buggy. Then if you tried to run and found that moving the buggy at any faster speed was like pushing against a brick wall, you would be very surprised. The truth is that when something is moved then its mass is increased. Human beings ordinarily do not notice this increase in mass because at the speed humans ordinarily move the increase in mass in almost nothing.
As speeds get closer to the speed of light, then the changes in mass become impossible not to notice. The basic experience we all share in daily life is that the harder we push something like a car the faster we can get it going. But when something we are pushing is already going at some large part of the speed of light we find that it keeps gaining mass, so it gets harder and harder to get it going faster. It is impossible to make any mass go at the speed of light because to do so would take infinite energy.
Sometimes a mass will change to energy. Common examples of elements that make these changes we call radioactivity are radium and uranium. An atom of uranium can lose an alpha particle (the atomic nucleus of helium) and become a new element with a lighter nucleus. Then that atom will emit two electrons, but it will not be stable yet. It will emit a series of alpha particles and electrons until it finally becomes the element Pb or what we call lead. By throwing out all these particles that have mass it has made its own mass smaller. It has also produced energy.
In most radioactivity, the entire mass of something does not get changed to energy. In an atomic bomb, uranium is transformed into krypton and barium. There is a slight difference in the mass of the resulting krypton and barium, and the mass of the original uranium, but the energy that is released by the change is huge.
Ponder this
Is dark matter and dark energy part of the mass-energy equivalence?
If certain matter loses mass from radioactivity, can they gain mass as well? Would this break the law of entropy?
Discuss
If matter and energy are equivalent to each other, does that apply to all forms of matter and energy? Consider the different states of matter and their relation to energy; and at the same time, consider the different forms of energy. How would they relate to each other?
Further readings
The Equivalence of Mass and Energy, a very comprehensive entry in the Stanford Encyclopedia of Philosophy.
"What is the significance of E = mc2? And what does it mean?", an elegant article on the subject.
"Scientists discover how to turn light into matter after 80-year quest", turning photons into positrons and electrons.
