Asked and answered (almost) FINALLY!

Got some great responses to my question about "law", "theory", and "equation" so I guess it's about time I share my physics prof's answer to the question. But before I do, I really should restate the question as:

When is the difference between a "law", a "theory", and an "equation"?

UPDATE: We're zeroing in on it. Take a look at these examples:

Newton's Law of Universal Gravitation: F = G m₁ m₂/r²

Einstein's Theory of Mass/Energy Equivalence: E = mc²

Schrodinger's Time-independent Wave Equation: Hψ = Eψ

UPDATE: So close we can almost taste it. KG nails the basic idea, and Ricki and Julie get the time component (albeit in reverse order):

Setting aside the sense of the word "theory" that is more general than a single equation, all three words mean essentially the same thing and it was the discoverer who chose the word. To some extent, this is a stylistic choice but not completely so. Up to, and into, the 19th century, scientists tended to speak in terms of natural "laws" and their equations were so named. By the 19th century, they would more likely refer to them as "theories". In the 20th century, they came to be called simply "equations". Note that I threw in the word "model", though this would be more like the larger sense of the word theory (like the Theory of Special Relativity, rather than the Theory of Mass/Energy Equivalence.

But partly, the progression from "law" to "theory" to "equation" reflects a growing sense of humility on the part of scientists over time. That is, science progressed from finding God's laws in the natural world to explaining the natural world to (a little more realistically) describing the natural world.

Early "natural philosophers" actually thought they were discovering God's laws, and their theories were so called.

Later scientists realized that any "laws" they came up with would always be tentative and subject to falsification on new evidence (or probably more often, fresh views of old evidence).

I suspect that once quantum mechanics came to be viewed as possibly questioning the very concept of "existence" itself, physicists in particular began to simply use the word "equation" for equations such as these, reserving "theory" for the larger, logically coherent frameworks of equations.

And Bruce's little exercise was really meant to be only that: an exercise, not a serious philosophical discussion. But I hope y'all found it as interesting an exercise as I did.

Posted by Ken S at February 26, 2008 07:59 AM | TrackBack (0) |