Gravity is arguably action at a distance. The sun's radiation mutates genes from a distance. Lightning has been said to be triggered by particles emanating from exploded suns in distant galaxies. — Anthony
disclaimer: I am no physicist and don't pretend to be an expert. I have never taken so much as a single physics course. I've only done some casual reading and thinking about physics. In the following, I might make mistakes. Take my position with a grain of salt. If you find an error, I'd be happy if you'd correct my misunderstanding.
Gravity as understood by Newton was sometimes thought to be spooky action at a distance. And Newton was notoriously unhappy with this state of affairs. His law of gravity only described mathematically how bodies move in relation to each other. It said nothing about why they attract one another. Newton on the matter:
It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.[4]
— Isaac Newton, Letters to Bentley, 1692/3
But Einstein seems to have solved the problem. His way of understanding gravity restored locality and removed any action at a distance.
One way to get some sense of how it works is the old trampoline model of spacetime. Understand that this is a very flawed analogy because it involves another gravitational pull downward. But put that concern aside for the moment. Put a heavy bowling ball in the center of the elastic sheet. Now put some marbles on the trampoline some distance from the bowling ball. Because the bowling ball makes a depression in the trampoline right where it touches it, the surface of the trampoline under each marble is tilted. So the marble starts to roll, as it would on any tilted surface. The bowling ball isn't magically pulling on the marbles at distance, without contact. The motion of marble is determined by geometric orientation of the surface underneath it. And the bowling ball only has an effect on the trampoline surface it is touching. Each small part of the trampoline surface is affecting its neighboring parts. So by a chain of little things touching their neighbors, the bowling ball has an indirect influence on the marble. Nothing nonlocal. It is like having a dog on a chain. When you pull the chain and yank the dog's neck, this isn't spooky action at a distance. One link pulls the next, which pulls the next, and so on. It is all local contact action. In Einstein's actual theory, it is all strictly geometric and local.
Isn't it interesting that we think of Einstein's theories as weird and Newton's as non-weird? If you look closer, it would seem that Einstein made things agree better with our intuitions! He restored some sanity to our picture of things!
Now, suppose I shoot an arrow at a deer. Is this nonlocal? No. I physically touched the arrow, imparted momentum to it, which carried it across space, whereupon it touches the deer.
Particles from the sun mutating genes can be thought of as being like the arrow situation. Not nonlocal. Neither the particle nor wave manner of modelling such things as photons arriving from the sun to influence atoms in cells is nonlocal.
Quantum entanglement is the most obvious reason why this proposition may be true. — Anthony
Quantum entanglement is often misunderstood. It doesn't let you send information faster than light. You can't communicate with it. If you could, you could violate causality and introduce contradictions into the world, thus violating the law of non-contradiction. You could do things analogous to killing your distant ancestor and thus not existing to kill your ancestor, in which case, your ancestor lives, in which case, your ancestor doesn't live...
If information can travel faster than light, effects can precede their causes and thus influence them.
See such things as a no-communication theorem:
link
We don't really understand deeply what is going on with quantum entanglement. For one thing, the Everett interpretation paints quite a different picture of what is going on with it than other interpretations. There, it really isn't one thing influencing another. Rather, it is more of a matter of how states of the universe are inherited from ancestor states. This happens according to certain rules that make it the case that certain correlations will naturally be observed.
It is similar to how, if you take a pair of gloves and put each in a box (you don't know which is in which) and you send one far away, if you open the one you have, you instantly know whether the distant glove is a left or a right one. The glove you have didn't affect the distant one in any spooky way. And you can't determine before you open the box whether your glove is left or right. And thus, you can't determine whether the distant one is left or right. Since you can't determine which glove you have, you can't determine which glove is found in the distant box. And thus, you can't use this system to communicate. The entanglement situation is somewhat like this.
In the Everett interpretation, you might think of it like the following. If you have an entangled pair of particles and you measure the spin of one, you simply are discovering that you happen to be in the branch in which your particle is spin up (another copy of you in another branch presumably finds his particle spin down), and the rules are such that in a given worldline, where one of the particles is spin up, by a law of symmetry, the other must be spin down. So you also know that the distant particle is spin down. But before you measure your particle, you don't know if your particle is spin up or spin down. From your standpoint, it is completely random. And you can't determine the state of your particle in order to determine the complementary state of the other. So this doesn't allow communication.
Disappointing, I know, right?
Things can only causally influence things in their light cone, and only by local means, via some kind of contact action, whether you are dealing with waves or particles, both of which are thoroughly local. The very nature of waves is that each part of the wave is affecting its neighbors. Consider imparting wave motion to a rope. What about EM radiation in a vacuum since people have dispensed with the aether? Unless we use the virtual particle model here, I don't know how to understand this, frankly. Maybe it has to do with the following curious possibility:
In Einstein's theories, as you approach the speed of light, distance contracts. At the speed of light, the distance crossed is zero. So when an electron drops to a lower energy level and emits a photon, the "distant" electron receiving that photon and jumping to a higher energy level isn't really distant! It is as if a certain quantum of energy is simply being passed directly, by touching, from one electron to another, perhaps not unlike one billiard ball losing momentum to another ball when striking it, the energy simply passing from one ball to another. It is as if the electron in the distant star has literally touched the electron in your retina when you see distant starlight. The star has touched your eye. But because of the way spacetime geometry is affected by speed, the star as it is "now" cannot touch your eye. But the star as it was long ago in the past can touch your eye. You must be in the light cone. Things outside of one another's light cone are causally isolated.