Ask A Scientist

What exactly do the letters mean in the formula e = mc2? How does this formula apply to every day life?

Asked by: André Wenzlik
School: Susquehanna Valley School District
Grade: N/A
Teacher: Mr. Richard T. Stank
Hobbies/Interests: Music, watching TV, outdoor activities
Career Interest: Carpentry

Answer from Carl Stannard

Professor emeritus of physics, Binghamton Universi

Research Area: Physics education and impact on the citizen, medical physics and infrared photoconductivity

PhD School: The Ohio State University

Family: Wife, Gay, and two adult sons.

Interests/hobbies: Retired but remains active on campus

E = "Energy", is probably the most useful quantity in physics. Something has energy if it can somehow exert a force acting through a distance on an object. When you throw a ball, you exert a force acting through the distance your hand pushes it. The chemical energy from your lunch has let you give the ball a form of energy, Kinetic Energy, the energy of motion. Or, if you lift it up to a shelf, your force – equaling its weight – acts through a distance – the height of the shelf, as your lunch’s chemical energy gives it Gravitational Potential Energy. One of the major threads, running all through physics is the examination of all the many different forms that energy can take, and how it is transformed from one form to another. For instance, if the ball with kinetic energy hits you, it will deliver its kinetic energy to your skin, as a force acting through the distance that it "squashes" your skin, maybe bruising you, but also causing your molecules where it hits to "vibrate" a bit faster: it warms your skin as it converts its energy to heat - vibrational energy of your molecules ("Thermal" energy). You can feel and even see some effects of this thermal energy when the electrical energy put into a stove burner is converted into thermal energy, making it glow red. In that case, you can see and feel the results of some of the thermal energy then being converted into radiant energy of visible light and infrared heat radiation emitted by the burner. These are only a few of the great number of forms of energy that we observe. Around the 1880’s, people observed that very fast-moving objects , such as the planet Mercury, did not move as expected. Other experiments showed to our surprise that if you were on a very rapidly moving vehicle (the Earth) and shine a flashlight toward a stationary person directly in your path, you would see the light that leaves the flashlight traveling with the same speed, as the stationary person sees it approaching them. Newton said that if you throw a ball from a moving car, a person on the ground would see the ball moving with the speed you threw it, added to the car‘s speed, and that that implied that light should behave similarly. Einstein brilliantly speculated, using his extraordinary insight, that Newton was slightly wrong: that a more accurate description would result if we assumed that the speed of light, would be the same constant speed, called "c", when measured in any system moving at a steady speed, even if different systems are moving relative to each other (like the car and the ground). With this revolutionary leap of intuition, and assuming that whatever the laws may be, they must be the same in all systems moving at constant speeds, Einstein showed mathematically that his hypotheses predicted unexpected new Principles of Special Relativity, which experiments have confirmed as true. Measurements of time and lengths now will depend on the speeds of motion of the object and the observer, and the kinetic energy of an object behaves as if its mass also depends on the relative speeds. Even more unexpectedly, when Einstein derived the form of the energy for a moving mass, surprisingly, he found it had two parts (or "terms"), one that exactly reduces at low speeds to Newton’s kinetic energy expression. The second term in the energy, however, does not depend on the speed of the mass, m. but is given simply by mc2 (the mass times the speed of light multiplied by itself). This suggests that Einstein’s expression for the total energy of a mass, m, represents a sum of its kinetic energy (as expected), together with a new form of energy, mc2, associated not with its motion, but only with its mass. Mass is a quantity that tells us essentially how much matter (basically how many protons, neutrons and electrons) the body contains. The body’s weight, the force of the Earth’s gravitational attraction, is directly related to its mass, so that the quantities weight and mass are often confused. Weight, however, decreases if the mass is carried up a mountain, or taken to the Moon, since the gravitational force decreases then. In deep space, with no planets or stars nearby, its weight will be zero! But the amount of material, the mass, m, will always remain the same, no matter what the gravitational force is unless, you cut a piece off. The new term in Einstein’s energy is a brand new form for energy – the so-called "rest mass energy". The mass itself now constitutes a newly recognized form of energy: a mass, m, has energy E = mc2 directly associated with its mass. This says mass is another form of energy and can be converted into energy, and energy can be converted into mass. Experiments have shown that if a Gamma Ray (high-energy light) has enough energy, it may suddenly vanish and a negative electron and a positive electron (positron) appear in its place. Or, when that positron gets too near an ordinary electron, they will "annihilate" each other and vanish, producing a gamma ray having energy equal to the sum of the mc2 for the masses of the two particles! Similarly, when anything burns in a fire, if we could measure all the masses involved before and after the fire, we would see a miniscule loss of mass, corresponding to the amount of energy released by the fire as chemical changes in atomic electron energies occur. But more spectacularly, if the nuclei of atoms change, for instance if a uranium nucleus is broken into two or more smaller nuclei (a process called nuclear fission), or if say, two hydrogen nuclei get so closely pushed together that they "fuse" into a single nucleus of perhaps deuterium or helium, (nuclear fusion), the total masses involved will decrease by amounts which although still small, are much larger than mass decreases for chemical fires, releasing enormous amounts of energy, but still given by E = mc2, where m is the amount of mass decrease. In the 1940’s, the United States produced bombs releasing energy by nuclear fission of uranium and plutonium – atomic bombs. And a few years later, they used atomic bomb explosions as "triggers" to get forms of hydrogen hot enough for fusion to occur, producing fusion bombs – (hydrogen bombs). Even more importantly for us, due to its enormous gravitation, the interior of the sun is so hot that hydrogen fusion is constantly occurring. The sun is acting as a continuous hydrogen-fusion bomb. This is the mechanism that releases energy in the sun, as its mass is slowly being converted to the radiant energy, which has made life on Earth possible!

Last Updated: 3/1/17