e=mc^2
We've all heard it: Energy equals mass time the speed of light squared. Many scientists consider this one of - if not the - most elegant and important formulas ever discerned by humankind. In fact, some believe that short of universal singularity, no other expression will ever do as much for scientific advancement as the five little characters that unlocked the door to atomic power.
Certainly we owe (one must suppose) a debt of gratitude to Albert Einstein who first proposed the mass–energy equivalence in 1905. The work of a genius? No doubt. And yet for all its power, e=mc2 remains unbelievable simple; so simple that virtually anyone who's ever taken basic math and science course could have figured it out.
Now, before I'm assailed by the scientific zealots and Einstein-ian devotees of the world, I'll be the first to concede that simply creating the formula is entirely different that understanding the implications of the formula. But one can certainly see the sun, without understanding nuclear fusion. And such is the case with e-mc2.
Let's go back in time to junior high. Go ahead, take a minute or two and work through the memories of your 7th grade heartthrob...now let's get to work.
Throughout that year, you were probably introduced to many basic concepts of algebra and physics. One such formula you may have encountered was this: Momentum = Mass (x) Velocity. You remember; your teacher explained how either a 100lb weight or a penny could crash through a table. It was just a matter of getting the penny moving fast enough; such as being dropped off the top of the empire state building.
At this point your teacher probably mumbled something about the limiting effects of environmental conditions and terminal velocity, but quickly returned to the principle that speed and mass are inherently related when considering the energy of an object in motion. At which point you thought, "yep - that makes sense." Class was dismissed, and you returned to delusions of grandeur about your heartthrob between classes.
Right then, right there - hidden in plain site - was the secret to atomic power and you missed it. I did it too. So did your teacher. Heck we all did. Even Einstein did - for years. So just for fun, let's go back one more time and see what we missed...
Many years ago, a scientist conducted tests with heavy metallic spheres and clay. She would take a metal ball, elevate it above the clay, drop it, then measure the depth of the indention. By changing the weight of the metal balls, and the height of the drop, she began to discern relations between weight and height; or more accurately, between mass and velocity at the point of impact. She refined these ideas into a forumla: Energy = Mass (x) Velocity^2. And that is pretty much where things stayed for quite a while. It was clean, elegant and logical. But it wasn't quite finished.
The formula only worked on items that were in motion. (And yes that had mass too, but that goes without saying.) For instance, a 10lb bag of flour sitting on the floor has - according to the forumla - no energy. But raise the bag up 100ft off the floor, then cut it loose and boom; it hits the ground with quite a bit of energy. Where did the energy come from? The pull of gravity? Or the act of lifting the bag to the 100ft height? Was it there all the time? Would it have more energy if lifted to 1000ft? What if the same test were repeated on the moon? Or in space? Would the energy be the same? The questions abound.
Let's review the formula again: Energy = mass (x) velocity^2
For any given mass, the faster the velocity, the more energy. Drop a penny from the top of a house, it gains a little speed, and you get a little "energy." Drop it from the top of the Empire State building, it gains a lot more speed, and therefore more "energy." Melt it down, make it into a bullet and shoot it from a gun, and you get quite a bit more speed and "energy."
As you can see, the key to everything is velocity. Of course this wasn't lost on good 'ole Albert either. He simply looked at the formula and said, "well, if velocity is the key, what's the maximum velocity possible? Whatever it is must be the maximum expression of energy." Of course the fastest velocity we know of is the speed of light (at roughly 186,000 miles per second.)
Once he realized using any velocity slower than the speed of light was not a complete expression of energy, Einstein did something very simple - so simple any of us could have done it. He changed one value in the formula from observed velocity (v^2) to maximum theoretical velocity (c^2). In doing so he changed the question from how much energy is expressed, to how much energy is ultimately possible, and that changed the world forever.
As I thought on this today, I began to wonder what I'm missing. Is there something right in front of me; day by day; that I take for granted but know in my heart to be not quite right; something that with one little tweak could forever change my world, or the lives of those I love? Whatever it is, if it is there, I pray I don't miss it.
