Well, and converted them to sound waves. But yes, you can find sound files of, say, simulated neutron star mergers online. They start off low, then chirp high, and abruptly cut off.
So gravitons (and photons, etc.) follow the shortest path and the longest path possible? Could this be the answer to the GR question of inertia- every object’s virtual gravitons are interacting with the rest of the universe?
It’s really more proper to say “stationary” action (my bad) rather than minimal/extremal/etc, although it’s really not a point worth worrying about. Basically the action must either be a minimum or a saddle point, but the action is never actually maximized. When you calculate the trajectory of a particle using the principle of stationary action, you do it by finding a path for which the action is stationary. Whether that path happens to maximize or minimize (or is just a saddle point of) the action is not really relevant. It is not trivial to make a general statement about when a path of stationary action will be a minimum/maximum/saddle-point, but it can be proven that it is never a maximum. It is also difficult to find simple examples (I think – maybe someone here knows one) where the action is not minimized. I can think of one. Put a particle on a sphere. Pick two points on the sphere. There are two paths of stationary action. One is the path of shortest length: an arc along a great circle connecting the two points. The second path is also along a great circle connecting the two points, but going around the “long way”. Both paths minimize the action, and indeed, we know the particle could just as well take the shorter or the longer path: either way it would be travelling in a straight line. But you’ll notice that the longer path is not “the path of maximum length,” because we could have added wiggles to the path to make it as long as we wanted, but those paths would not have stationary action.
I gave a simple example of a (local) maximum: reflection from a sufficiently convex spoon (the curvature has to be greater than that of a paraboloid). What is so hard about that?
I don’t get it. How can it be a local maximum if you can always add wiggles that make it larger?
Well here is an example that occurs all the time in daily life. Whenever you look at an object in a mirror and you also have direct line of sight to that object, you are presented with two different paths, one(direct line of sight) is minimal and the other(through the mirror) is not. However they are both locally minimal.
An aside about gravitons: since we don’t have a good quantum theory of gravity, what we surmise about gravitons is more or less by default of what we guess has to be true. Since quantum theory holds that all energy has to be quanticized, gravity is presumed to be too. And simply to not contradict the known behavior of gravity, gravitons would have to have zero rest mass, be electrically neutral and be bosons with a quantum spin of 2. But all this is simply by way of all the alternatives being ruled out; we don’t have a positive theory yet that predicts them.
Well, maybe. The reason why the String Model first started getting any attention is that versions of it which accounted for all of the Standard Model particles also all turned out to predict the existence of a massless spin-2 particle, despite that not being one of the things they were designed to predict. Of course, there’s very little real progress in the String Model.