Energy

• 1. Introduction

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  Energy is the quantitative property transferred to a body or physical system, recognizable in the capacity to do work and in the form of heat and light. It cannot be created or destroyed, only converted from one form into another. That single rule, the law of conservation of energy, governs everything from a swinging pendulum to the fusion burning inside the Sun. The word itself reaches back to the Greek energeia, a term that possibly appears for the first time in the work of Aristotle in the 4th century BC. Back then it meant something closer to happiness or pleasure than to anything a physicist would recognize today. How did a vague philosophical idea become a precise number measured in joules? Who first realized that a conserved quantity, distinct from momentum, was hiding in the equations of motion? And why does the same principle that lights a forest fire also drive earthquakes, hurricanes, and the slow death of the universe itself? Those questions are where this story leads.

• 2. From Living Force To Joule

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  In the late 17th century, Gottfried Leibniz proposed the idea of the vis viva, or living force, defined as the product of an object's mass and its velocity squared. He believed that total vis viva was conserved. To explain why moving things slow down through friction, Leibniz theorized that thermal energy consisted of the motions of the constituent parts of matter, though more than a century would pass before this was generally accepted. The modern analog, kinetic energy, differs from vis viva only by a factor of two. Writing in the early 18th century, Émilie du Châtelet proposed the concept of conservation of energy in the marginalia of her French translation of Newton's Principia Mathematica. This was the first formulation of a conserved measurable quantity that was distinct from momentum, the thing that would later be called energy. The vocabulary caught up slowly. In 1807, Thomas Young was possibly the first to use the term energy in its modern sense, in place of vis viva. Gustave-Gaspard Coriolis described kinetic energy in 1829, and in 1853 William Rankine coined the term potential energy. The missing link arrived in 1845, when James Prescott Joule discovered the connection between mechanical work and the generation of heat. His name now marks the SI unit itself.

• 3. A Quantity That Does Not Change

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  Richard Feynman, lecturing in 1961, called conservation of energy a strange fact rather than a mechanism. He said: "There is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes." His point was that you can calculate a number, watch nature go through her tricks, calculate it again, and find it the same. For years before this clarity arrived, scientists argued whether heat was a physical substance, dubbed the caloric, or merely a physical quantity like momentum. William Thomson, known as Lord Kelvin, helped formalize conservation of energy into the field of thermodynamics. That framework drove rapid progress, with Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst explaining chemical processes, and Jožef Stefan introducing laws of radiant energy. Clausius also gave entropy its mathematical form. The deepest explanation came later. Noether's theorem, stated in 1918, shows that conservation of energy is the direct mathematical consequence of the translational symmetry of time. Put plainly, the laws of physics do not change from one moment to the next. Yesterday, today, and tomorrow are physically indistinguishable, and that sameness is why the energy number holds.

• 4. Mass As Energy

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  Albert Einstein's 1905 theory of special relativity revealed that rest mass corresponds to an equivalent amount of rest energy, captured in the formula E equals mc squared. Every massive body must possess this energy even while at rest, in direct proportion to its mass. Because the speed of light squared is so enormous, a tiny amount of rest mass holds a staggering store of energy. One kilogram of rest mass is equivalent to 21.5 megatonnes of TNT. The conversion runs both ways and obeys the books exactly. In electron-positron annihilation, the rest energy of those two particles becomes the radiant energy of the photons produced. Matter and antimatter are destroyed and changed into non-matter, yet the total mass and total energy do not change. The photons carry no rest mass but exhibit the same inertia the original particles had. The reverse process, pair creation, builds the rest mass of particles from a sufficiently energetic photon near a nucleus. Einstein was not alone in circling this idea. Similar formulas were derived earlier by J. J. Thomson in 1881, by Henri Poincaré in 1900, and by Friedrich Hasenöhrl in 1904. The 18th century had treated conservation of mass and conservation of energy as two separate laws; relativity merged them into one.

• 5. The Many Forms

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  Chemical energy lives in chemical bonds, while chromodynamic energy binds quarks together to form hadrons, and these are only two entries on a long list. Energy can be elastic, electric, gravitational, magnetic, nuclear, or radiant, among other types. All of them sort into two parents: kinetic energy, set by the movement of an object or its components, and potential energy, the stored capacity for motion based on position in a field. Convenient combinations earn their own names. Mechanical energy is the sum of macroscopic translational and rotational kinetic and potential energies, and nuclear energy refers to the combined potentials inside an atomic nucleus from the nuclear force or the weak force. Thermal energy sits in this scheme as the kinetic energy of the microscopic motion of particles, a disordered cousin of mechanical energy. Quantum mechanics reshaped how these forms are understood. The first evidence of quantization came from spectral lines observed in sunlight in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. In 1913, the Danish physicist Niels Bohr proposed quantized energy levels in his theory of the atom. By 1926, Erwin Schrödinger and Werner Heisenberg had supplied the full quantum mechanical explanation, where the solution for a bound system is discrete and gives rise to the concept of quanta. For light in a vacuum, energy ties to frequency through the Planck relation, and those energy states are the photons.

• 6. Measuring The Invisible

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  The joule is a derived unit equal to the work done in applying a force of one newton through a distance of one meter. In dimensional analysis its base units come out as mass times length squared divided by time squared. Power, defined as energy per unit time, is measured in watts, where one watt is one joule per second. From there the everyday units fall into place. A kilowatt-hour, the energy delivered by one kilowatt of power for an hour, equals 3.6 million joules. Older and regional systems persist alongside the SI. The CGS energy unit is the erg, while the imperial and US customary unit is the foot-pound. Specialized fields reach for their own measures, including the electronvolt, the food calorie, the thermodynamic kilocalorie, and the BTU. Energy is also slippery in a way distance is not, because it depends on the observer. Picture a ball struck by a bat. In the center-of-mass reference frame the bat does no work on the ball, but in the frame of the person swinging it, considerable work is done. The same event, two different energy accounts.

• 7. The Body As Engine

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  Ninety percent of the oxygen a human takes in is used by the mitochondria, the organelles that generate chemical energy for the rest of the cell. The currency they trade in is adenosine triphosphate, or ATP, continually broken down and rebuilt as part of cellular respiration. Nutrients such as glucose and stearin are oxidized to carbon dioxide and water, and some of that energy converts ADP into ATP while the rest becomes heat. The numbers reveal how little of this goes into visible work. A recommended adult intake runs from 1600 to 3000 Calories per day, taken mostly as carbohydrates and fats. Yet a sprinter gains only about 4 kilojoules of kinetic energy during a 100 meter race, and lifting a 150 kilogram weight through 2 meters stores just 3 kilojoules of gravitational potential energy, against a daily food intake of 6 to 8 megajoules. Living organisms are remarkably inefficient in the physical sense, and most machines manage higher efficiencies. To make the scale tangible, physicists use the human equivalent. If a body runs on average at 80 watts, a 100 watt light bulb burns at 1.25 human equivalents. For a few seconds a person can put out thousands of watts, many times the 746 watts in one official horsepower, but sustained all day the maximum drops to about 150 watts. The waste heat is not pure loss. It pays for order, letting tissue stay highly organized while a greater amount of energy spreads out as heat across the surroundings, exactly as the second law of thermodynamics demands. That tax on every metabolic step is the physical reason behind the pyramid of biomass in ecology. Of an estimated 124.7 petagrams of carbon fixed each year by photosynthesis, 64.3 petagrams, or 52 percent, are reconverted into carbon dioxide and heat by the metabolism of green plants alone.

• 8. Stored Since The Big Bang

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  More than half of the Earth's internal heat budget comes from the radioactive decay of atoms in its core, driven by the decay of Uranium-235, Potassium-40, and Thorium-232. That thermal energy drives plate tectonics and can lift mountains through orogenesis, a slow storage of gravitational potential energy that may later be released as the kinetic energy of landslides. Earthquakes release elastic potential energy stored in rocks, drawn ultimately from the same radioactive heat. Trace that heat back far enough and it was stored in heavy atoms since the collapse of long-destroyed supernova stars that created those atoms. The Sun runs on a different ancient store. Its fusion of hydrogen releases potential energy created at the time of the Big Bang, when space expanded and the universe cooled too rapidly for hydrogen to fully fuse into heavier elements. That leftover hydrogen is a reservoir, unlocked only when gravitational collapse of hydrogen clouds generates enough heat and pressure to start fusion. The most extreme energy transformations in the universe belong to stars, novae, supernovae, quasars, and gamma-ray bursts, all powered either by gravitational collapse of matter or by nuclear fusion of light elements. Even black holes leak. Hawking radiation is the emission of black-body radiation from a black hole, a steady loss of mass and rotational energy whose temperature is predicted to rise as the object evaporates, speeding the whole process toward its end.