Asking the right question
Asking the right question is a key to getting the right answer. So here is a question: when a physicist writes an equation like “F=ma”, does it matter how F, m or a were measured? And if not, why not?
Right now, laws of physics assume that the measurement does not matter, and that it always approximate some idealized value. For instance, most physicists would tell you that m in the equation above is a real number.
Among other properties, a real number has an infinite precision, it can be arbitrarily large or arbitrarily small. This seems true enough. We can measure 1kg, but we can as well measure 0.1kg, 0.0001kg, and 10000.000027kg. Therefore, it seems like F=ma has to work with any real value for m.
But let’s now push the reasoning to the absurd. Since it’s a real number, m can in particular be set to be ten times the mass of entire universe. What does the equation tell us in that case? Does it tell us anything at all?
Newton’s second law, F=ma, has since been replaced with more complicated equations in modern theories of physics. But the problem is not solved. These equations still use variables like x, y, z or t, as if there was no doubt that any choice of measurement necessarily follows the same laws.
What is the Question?
Saturday, November 18, 2006
