Einstein himself hated the use of constants; he figured that any physical equation that required a constant was not fundamental. (Example: the equation we use to determine the gravitational force between two bodies relies on the gravitational constant G, which is 6.67300 x 10-11m3kg-1s-2. Which means, in Einstein's view, that the classical understanding of gravity is almost right, but not quite.)As I've said before: sometimes when I'm trying to get to sleep, I think about some of the intractable problems of physics and engineering that I've enountered over the years.
Sometimes I come up with some interesting ideas.
Gravity, though--that one's a puzzler. Unlike the other four fundamental forces of nature we can't get it from the standard model of particle physics. It's the weakest of the four, and its scale is far greater, extending farther than even electromagnetism can. (EM must obey the red shift limit; gravity does not.)
Einstein was frustrated that his theory of general relativity needed the Fine Structure Constant (which we abbreviate as "alpha") in order to work; he felt that mean that general relativity was almost right, but he couldn't figure out what was wrong with it and reduce it to a more fundamental equation, one that didn't require a constant.
His most famous equation, E=MC2, does not require any constant to function. You put in the mass and the speed of light, do a little math, and you know how much energy you get.
But what could possibly be missing from our understanding of gravity? Why is the constant necessary?
Well, if you look at electromagnetism, you find that you need a constant to determine the force between two charges...but this constant turns out to be the permittivity of the medium surrounding the charges. Vacuum, a piece of metal, water, whatever, but we usually consider the charges to exist in a vacuum and use the constant which corresponds to it.
And that constant is determined by the application of what we know about how electromagnetic waves behave; it's generated only by arithmetical operations on known values.
...getting into a discussion of whether or not a constant is "fundamental" would make for a major digression. My point is, a constant may take the place of a more fundamental understanding of the property in question.
If the gravitational constant ("G") is in fact necessary, it may itself be similar to the vacuum permittivity constant required by the electromagnetic equations.
But gravity is a very weakly-interacting force. It takes the entire mass of the Earth to hold a paperclip on the top of your desk and keep it from floating away; but a magnet no bigger than the tip of your finger can exert enough force to lift that paperclip against the force of Earth's gravity.
Gravity's weakness makes it hard to measure and very difficult for us to play with, in order to figure it out. Electromagnetism is strong enough that we could do all kinds of experiments and learn all its properties, thus giving us enough information to generate equations which describe all its behaviors--and six score years or so later we're doing incredible things with electromagnetism because it's so easy to play with and learn about.
Gravity isn't so convenient. One can imagine Cavendish tearing his hair in frustration because his careful measurements were ruined when someone's horse clopped by at the wrong moment.
No one has managed to build a gravity wave detector that ever detected any gravity waves. (Of course, the gravity wave detector is a type of interferometer, and a gravity wave changes the shape of space, so the laser light probably wouldn't notice...but that's an entire other discussion in itself.)
(As you can see, the gravity question is one I keep coming back to, time and again.)
It really is a shame that we can't seem to crack this one. Imagine how useful it would be if we could manipulate gravity the way we manipulate electromagnetism.