114
WHY DOES E=mc 2
have more mass. Is it that simple? Well, yes and no. Here on Earth, we can determine the mass of something by weighing it, and that is what everyday bathroom scales do. Everyone is familiar with the idea that we “weigh” in kilograms and grams (or pounds and ounces). Scientists would not agree with that. The confusion arises because mass and weight are proportional to each other if you measure them close to the surface of the earth. You might like to ponder what would happen if you took your bathroom scales to the moon. You would in fact weigh just over six times less than you do on Earth. You really do weigh less on the moon, but your mass has not changed. What has changed is the exchange rate between mass and weight, although twice the mass will have twice the weight wherever it is measured (we say that weight is proportional to mass). Another way to define mass comes from noticing that more massive things take more pushing to get them moving. This feature of nature was expressed mathematically in the second most famous equation in physics (after E = mc 2, of course): F = ma, first published in by Isaac Newton in his Principia Mathematica. Newton’s law simply says that if you push something with a force F , that thing starts to accelerate with an acceleration a. The m stands for mass, and you can therefore work out how massive something is experimentally by measuring how much force you have to apply to it to cause a given acceleration. This is as good a definition as any, so we’ll stick with it for now. Although if you have a critical mind you might be worrying as to how exactly we should define “force.” That is a good point but we won’t go into it. Instead we will assume that we know how to measure the amount of push or pull, a.k.a. force.