The "E" stands for "energy". How do we make that more than a vague word? It is a conserved quantity, meaning that if we know how to measure it, we can watch how it flows around from place to place. It also is the source term for gravity, so we can check whether gravitational effects agree with our calculated energies.
"M" stands for "mass". There are two somewhat different conventions about what we mean by "mass". The simplest in this context is the one meant by Einstein. Mass is the thing which you multiply by velocity to get momentum. Momentum is another conserved quantity, so there's a way of checking whether we've calculated it correctly.
Of course if M and E are always related by a constant factor, c2
, then really they're just exactly the same thing but measured in different units. If you somehow had different names for height, depending on whether it were measured in inches ("h") or feet ("H"), then you might someday discover that h=Hk, where k is a conversion constant, 12 inches/foot. But really there's just one quantity, measured in two different units.
(published on 07/29/07)