Your question is confusing. Action at a distance does not imply going faster than light, it means there is some sort of field connecting the two things.
Action at a distance means there is nothing connecting the two things. That's the "distance" part of action at a distance. Modern physics rejects the concept, saying instead that forces are carried by particles from a source to a destination, and the effect of the force is the result of local [opposite of "distant"] interaction with the particles carrying the force.
Compare wikipedia:
> Under our modern understanding, the four fundamental interactions (gravity, electromagnetism, the strong interaction and the weak interaction) in all of physics are not described by action at a distance.
> This is an alternative to the concept of instantaneous, or "non-local" action at a distance.
> The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.
You'll note that "action at a distance" does in fact specifically mean that information travels faster than light!
But this understanding would seem to be incompatible with the idea that the mass inside a black hole can interact gravitationally with anything outside the black hole.
I'm not seeing where any of this requires faster than light travel.
But here's something that might help: We'll use gravity for our example, and I'll be non-technical for ease of typing.
The gravitational force that leaves an object is constant and continuous, it never stops, and it never starts. It exists from before the beginning of time, and it will never stop. The only thing you can do with that force is move it. This is because it's impossible to destroy energy. If you move the mass (the energy actually if you want to be exact) then you have changed the location (but not the strength) of the gravitational force, and that CHANGE travels at the speed of light.
So the gravitational attraction of my hand has, right now, already reached the end of universe, out to infinity. When I move my hand, it sends a tiny gravitational wave that travels at the speed of light, indicating a change in where the force is.
So the gravity inside the black hole has already reached the end of the universe, when that matter starts to clump, a change in the location of the gravity is sent out saying "this gravity is now moving over here".
This is why it feels like it's moving faster than light - it's not, it's already there at the end of the universe.
This is also why the orbit of Mercury is different in relativity, the sun pulls on Mercury where it WAS in the orbit, not where it is (which would require faster than light travel). In Newtonian gravity it's instant (i.e. faster than light).
What part of your comment says something about gravity that is different from what I've already said about it?
How do you look at a quote stating explicitly that action at a distance is, by definition, instantaneous, and say "I'm not seeing where any of this requires faster than light travel"?
> So the gravitational attraction of my hand has, right now, already reached the end of universe, out to infinity.
And how has the gravitational attraction of your hand gone more than 200 light years from Earth?
> How do you look at a quote stating explicitly that action at a distance is, by definition, instantaneous,
I clicked to the Wikipedia article, I did not see this quote.
> And how has the gravitational attraction of your hand gone more than 200 light years from Earth?
My hand is made of mass collected on earth. Those atoms have been rearranged into the shape of my hand, but their gravity has existed since the beginning of the universe, just in difference shapes.
> I clicked to the Wikipedia article, I did not see this quote.
No need to go to that much effort; I pulled that quote in my comment.
>> This is an alternative to the concept of instantaneous, or "non-local" action at a distance.
> My hand is made of mass collected on earth. Those atoms have been rearranged into the shape of my hand, but their gravity has existed since the beginning of the universe, just in difference shapes.
So, as you acknowledge, zero information about your hand has gone much distance from the earth. Someone 1000 light years away who could resolve gravitational information into an image with perfect detail wouldn't be able to perceive your hand, you, or anything related.
>> This is an alternative to the concept of instantaneous, or "non-local" action at a distance.
Notice the word "alternative", instantaneous action at a distance is a concept that was suggested at one point in the development of physics and discarded once relativity was figured out. Action at a distance these days is always at the speed of light.
> So, as you acknowledge, zero information about your hand has gone much distance from the earth.
No, not zero. All the gravity from the atoms in my hand is already out there.
> Someone 1000 light years away who could resolve gravitational information into an image with perfect detail wouldn't be able to perceive your hand, you, or anything related.
Correct, they would see the location of the atoms that make up my hand today, as those atoms looked 1000 years ago. (Probably in plants, and water.)
But remember: They do see the gravity from those atoms!!! Meaning the gravitational force my hand exerts, already exists 1000 years away, just in a different shape.
> Because gravity isn't a non-local force.
Are you saying gravity is a local force? Because that's not true.
