### An Abstract Reality

What IS energy; that you buy it, use it, have it and notice it in others? (“The kids have such energy!”) You never see it, never touch it. Never smell it or hold it. What is the nature of such a substance? Energy is not coal. Nor oil. Nor sunshine. Nor boys playing soccer. These are said to possess energy. But what is this energy that they posses?

Here is the remarkable answer: “It is a numerical quantity which does not change when something happens.” R.P. Feynman 1962

That energy is a “quantity which does not change” means that if it grows less in one form then it must increase in another. So that the total amount doesn’t change. When I pay, say, $.15/kilowatt-hour for electrical energy, my purpose is to see it transformed into mechanical energy to run my refrigerator and into light energy at night for my reading convenience. Energy is something that can be transformed from one form into another. The totality of it persists (is conserved) as its form changes.

Electrical energy is made from the mechanical motion of wires in magnetic fields. The mechanical energy driving this motion comes from the thermal energy of heat which in turn comes from the chemical bond energy stored in coal or oil. There is energy of motion. There is energy of position – say of an apple feeling the force of earth’s gravitational pull. There is chemical energy stored in the binding of atoms to one another. There is nuclear energy stored in the binding of the nucleons inside the nucleus of an atom.

*But what, then, is energy?*

*It is a mathematical attribute found to exist in nature.* That there is a quantifiable something called energy emerged from the mathematics invented to describe the physical world.

The concept was born about 1807 when Thomas Young gave the first quantitative formula for the energy that is to be associated with motion. It was wrong by a factor of 2 but soon corrected. The energy to be associated with a mass, m, in motion moving at a speed, v, is given by the formula mv^{2}/2. The energy of position (in the gravity field of the earth) to be associated with the same mass being at a height y above sea level is mgy, where g is a known numerical factor.

The genesis of the idea that such a thing as energy exists is exemplified in this joystick graphic. In it you see that a mathematical quantity is conserved throughout the turmoil of physical events.

You can *throw *or *drop* the apple by clicking on the appropriate button. The graphic numerically displays the apple’s attributes as they change with time; its speed (positive means ‘going upwards’, negative ‘going downwards’), its varying position and the time at which each is measured. (The actual time is displayed numerically but the motion graphic shows it slowed down for convenient viewing. A 1-second interval is viewed in 10 seconds.)

As the apple, in its motion, follows the laws of nature, its position (*height* above the ground) grows or shrinks drastically and its *speed* keeps changing all the time. But remarkably, an arithmetic function of its speed (the square) plus another function of its position is shown to be constant throughout the motion.

In the graphic, the sum shown is actually computed repeatedly from the two terms above it. This sum turns out to be the same number no matter what is going on in the motion. You may freeze the motion and check the computation at any stage of the trajectory. Then release the motion to freeze it again at another time – say 0.2 seconds later. You will see that although all the physically measurable quantities – speed, height, time; the ones above the summation line – have changed markedly, the mathematical construction combining them is constant. This mathematical construction is conserved! It doesn’t change with time even though so much is happening.

It was from the reckoning illustrated in this joystick graphic that an idea was born. The idea is that there exists an ethereal mathematical something called energy that is conserved in all physical processes. Any such process can only change the form of the energy – not its magnitude. In the falling apple, position energy changes into motion energy. Mathematical expressions soon followed describing electrical energy, magnetic energy, chemical energy, heat energy and all the other forms. Over a hundred years ago Einstein taught us that mass is a form of energy. The equation for mass energy is E=mc^{2}.

Afer a few centuries of hearing about it we have come to adopt, as something completely familiar, a mathematical relationship between measurable quantities. This mathematical insight brought a completely abstract and invisible property of nature into common acceptance. The word *energy* is popular with everyone. It has achieved recognition.