Why E = mc2

Brian Cox & Jeff Forshaw

What should all of us know and few do:  What is the meaning of "E=mc2"?  Our intellectual curiosity demands that we probe this conundrum and gain a handle on it.  Here is a book that will do precisely that for us.

Two professors of physics, at the U. of Manchester England, here combine to explain the vast wonders and implications of Einstein’s revolutionary equation (E=mc2). In a proverbial nut shell, E=mc2 means that energy=mass times the speed of light squared; which means that energy and mass are interchangeable and the exchange rate is the speed of light squared.  (The “c” probability refers to the Latin word “celer”, meaning speed.)  Think of the implications: energy and mass are interchangeable, albeit only when moving at 186,000 miles per second.  The acceptance of this startling principle opened the door to much, much more revolutionary data.

E=mc2 was conceived by Albert Einstein (1879-1955) on 1 March 2905, and, as you know, it is simply the most important equation ever postulated, because it tells so much about the creation and workings of our universe.

Cox and Forshaw take us by the hand and lead us into the arcane and esoteric worlds of geometry, physics and chemistry, and they do so in language that we can grasp, in spite of many enigmatic equations, of which we may fathom to some degree, if we noodle them sufficiently.  E=mc2, we learn, reveals that Mother Nature never ceases switching mass and energy back and forth. When we break mass (matter) down, enormous energy is created, which, potentially, can benefit man enormously. We owe it to ourselves to secure some form of handle on this formula that has shaped every human life since Einstein conceived it. Do give it a try; you will learn enough to make it well worth your time.

E=mc2 leads us to the conclusions that

* gravity is actually a force created by curving space, * the earth is actually “falling in a straight line around the sun”. * space and time do not actually exist independently, * but, rather,  exist only as a blend of the two ("spacetime"), and * everything exists in spacetime.

A key premise of physics is that, if a theory can’t be proved by experiment, it cannot be accepted. Einstein’s theories can be constructed almost entirely using the language of geometry. Equations express relationships (e.g., speed=distance/time) and are convenient and powerful shorthand ways of stating facts. (In equations, the parentheses ( ) are used to indicate which operations of the equation should be performed first.)

The book’s bottom line is this: Before Einstein, no one dreamed that mass could be destroyed and converted into energy (e.g., the atom bomb). Indeed, if we could unlock the energy contained in only three kilograms of material/mass, we could keep a city with 100K population supplied with electricity for 100 years! Nuclear power plants destroy mass to create energy. Mother Nature exploits E=mc2 to sustain the sun and the countless other suns throughout our universe. After Einstein, we had to accept that mass and energy are different manifestations of the same thing. So, you can increase energy or mass in one place, provided that you reduce them equally somewhere else.

We know things only in 3D. To grasp E=mc2, we must accept the 4th Dimension: spacetime.

E=mc2 also enables us to explain the creation of stars and our own life forms. “Fusion”, in science, means the creation of energy by fusing together two or more nuclei. Nuclei include two or more protons. Nuclear fusion generates huge binding energy, as compared to chemical fusion that creates electromagnetic force. The force (energy) released in a nuclear reaction is typically one million times the force released in a chemical reaction. Temperature is essentially the speed of things; to increase heat, we increase the speed of the atoms, e.g., inside water. A temperature of 10M degrees is necessary for nuclear fusion to begin. Fortunately for us, such temperatures exist in the hearts of stars.

Since the Big Bang, the universe has continued to expand and cool; the primordial gases fall in upon themselves under the influence of gravity, picking up speed as they rush towards each other; the faster that they rush towards each other, the bigger the clumps or balls they form and the hotter and more dense those balls become. The individual electrons and protons fall inexorably faster and faster into an ever-quickening collapse, ever hotter and hotter. When they reach temperatures around 10M degrees, something wonderful happens: they are transformed into magnificent sources of nuclear energy, becoming the very life and light of the universe: a star. In this process, precious biding energy is released, sufficient to resist and halt a further gravitational collapse, at least for a few billion years, which is long enough for rocky planets to be warmed, liquid waters to flow, animals to evolve and civilizations to rise.

The key to Einstein’s Theory of General Relativity (TGR) is this: All things fall to the ground with the same rate of acceleration (as Galileo was the first to assert). Drop a penny and a 10-pound ball and watch them reach the ground simultaneously (absent interference from the wind). This is called the Principle of Equivalence. Inside a falling elevator, objects are weightless; gravity just goes away, but it does so by warping or curving spacetime (the new “gravity”); spacetime is warped in the vicinity of matter and, since E=mc2, in the vicinity of energy.  So, TGR says that the warping of spacetime, not gravity, is what keeps the earth orbiting the sun; i.e., the earth orbits the sun because spacetime is curved. Spacetime is a 4D “surface”, while the earth’s surface is 2D. Thus, gravity has been banished in favour of pure geometry. Thus, all things move in straight lines in spacetime, unless knocked off course. Einstein’s TGR is considered by most physicists to be the most beautiful of all theories of nature. The concept is simple; the math is defiantly complex. Simply put, spacetime is warped by the presence of mass, and it affects all objects, even light.

Light is a symbiosis of electric and magnetic fields moving forward in perfect agreement. Light always streams away from us at the same speed, regardless how fast we are moving; the speed of light (SL) is constant to all things at all times, BUT absolute time does not exist. Time passes at different speeds relative to who is moving and who is observing, and the relative speed of each. Time actually slows down for moving objects.  Galileo identified and defined gravity for us, but Einstein explained its cause (the curvature of space). Galileo taught us to disgard the notion of absolute space, but he did not address absolute time.

So many fascinating, related facts are here revealed. To name a few, consider:

(1) A flash of light takes only 8 minutes to travel the 88M miles to the sun but 100K years to escape our Milky Way Galaxy (MWG), in which our solar system exists in a corner, and that same flash of light takes 2M years to reach our nearest galactic neighbour, Andromeda. The MWG has some 200K Million suns (stars).

(2) The earth was formed from a collapsing cloud of interstellar dust.

(3) The speed of light (186K miles/second) is “the cosmic speed limit”. When things approach the speed of light (SL), strange things happen. We are able to accelerate tiny objects to 99+% of SL with machines like the 27Km Haldron Collider at CERN (Center for European Research of Neurons in Switzerland, where Tim Berners-Lee created the first Internet switch in 1989, and, hence, where computers were first linked together to form the early Internet).  (See htpp://home.web.cern.ch.)

(4) If we could exceed SL, we literally travel backwards in time to any point in the past (e.g., Michael J. Fox’s priceless film, Back to the Future).

(5) Conversely, if we travel at SL, we could watch the earth oceans boil away, as the earth was fried by the sun (in about 200M years), and see the earth be sucked into the sun (in about 600M years), and see the sun die, thus leaving any remaining planets in our solar system to fade into total darkness and become ice balls like Pluto. We could also see planets formed from swirling dust clouds and possibly the birth of new life forms.

(6) Moving clocks tick more slowly than stationary ones; e.g., clocks on orbiting satellites tick more slowly than those on earth, and the GPS’ in our cars recognize that and calculate the differences.

(7) The earth moves at 67K mph, relative to the sun, and our solar system travels around the MWG at the rate of 486K mph.

(8) Due to the Big Bang and the diminishing pull of gravity that distance affects, the galaxies are racing away from each other, and the more distant they are, the faster they are receding.

(9) The tides of our oceans are caused by the moon’s gravitational pull. The moon moves away from the earth by 4 centimeters/year.

(10) On the moon, everything weighs 1/6 of its earth-weight.

(11) Particle physics is the study of the subatomic world.

(12) On a sphere, the shortest distance between two places is a curved line.

(13) The second most famous equation is Newton’s (1687) “F = ma”, meaning “force” = mass times acceleration.

(14) “Distance” is a special kind of object.

(15) Energy, mass and spacetime must be combined into a spacetime object.

(16) “Kinetic energy” is energy caused by motion; “kinetic energy = ½ mv2” which means energy caused by motion equals 50% of mass times speed squared.

(17) A triangle without a bottom or an upside down “V” in front of any other letter means “placeholder for that letter”, e.g. a placeholder for mass, speed, speed of light, etc. Placeholders are needed in equations as a substitute for unknowns.

(18) the equation “p = mv” means momentum equals mass times speed.

(19) Our sun, a middle aged star (about 4.5B years old), loses 4M tons of mass every second – a rate that is in accord with E=mc2, which defines the rate at which nuclear fusion takes place. Eventually, it will consume itself and go dark.

(20) Iron is the end point of fusion in the core of stars. There is a limit to how closely you can pack electrons together. Stars collapse until they are so large (and dense) that they preven any further gratitational collapse, becoming “white dwarfs” – slowly fading monuments to their once bright states, gradually fading fro0m view.

(21) Atoms are no longer viewed as the smallest components of matter; their electrons, protons and neutrons are composed of even smaller particles (which we call “quarks”); there are 12 known particles of matter: 6 types of quark, 3 types of “charged lepton” and 3 types of neutrons. Common sense is not a good guide to fundamental physics. Particles appear to have no substructure, i.e., are not divisble; they are said to be “pointlike”, but, someday, we find a substructure. All 12 of these particles are the “W” and “Z” particles, the “photon” and “gluon”, and these are responsible for the interactions between all other particles. W & Z particles are the ultimate building blocks of all matter and carry the force of interaction and even make visible light, radio waves, infrared, microwave, X-rays and gamma rays. Billions of W&Z particles (also called “elementary particles”) stream through all of us every second. We don’t feel them, because they have “weak force”. Only 4 of these 12 particles (up and down quarks, the electron and the electron neutrinop) are needed to build the universe.

(22) Every particle in the universe has an antiparticle; e.g., the electron’s is a “positron”, which has a charge directly opposite to the electron. PET (positron emission tomography) scanners are used in hospitals worldwide, everyday, to construct 3D maps of the human body.

(23) Spacetime is the same everywhere.

So, is this book worth the trouble? Absolutely! We-laymen can understand at least 80% of it, and it is only the last 20% or so that bends our minds into Gordian knots. Bravo to these Professors; not only do they grasp the topic, they can explain in language that laymen can enjoy. Clearly, the equation E=mc2 and Einstein’s Theory of General Relativity are so important as to demand our intentions.  "Time" is our enemy.  Carpe diem!