I suppose that according to a classical theory (?), that wave could be perceived simultaneously by different people in different places around the source.
That is indeed what the classical theory says. It is wrong. This is where the assumption that domain of the amplitude is continuous is a bad approximation.
So how would Many Worlds work in this case?
Quantum amplitude flows into separate configurations. For each detector, there is a configuration such that that detector was the only one to detect the photons. There are also configurations where no detector detected it. So, if in some configuration, a detector detects the photon, and goes to check on another detector, it will find that the other detector has not detected the photon, not because some instantaneous space spanning signal collapsed the wave function, but because in that configuration the photon did not go that way.
I see, so the photon left the source as a particle and the wave picture represents the idea that the particle could have been anywhere, until you know which world you're in.
But the mechanical-model-that-made-me-so-happy was that the photon was actually just the electromagnetic field trying to update. The electromagnetic field would have to update isotropically ... it couldn't just update along the route to a given detector.
- Eliezer Yudkowsky, Collapse Postulates
In the olden days of physics, circa 1900, many prominent physicists believed in a substance known as aether. The principle was simple: Maxwell's equations of electromagnetism had shown that light was a wave, and light followed many of the same equations as sound waves and water waves. However, every other kind of wave- sound waves, water waves, waves in springs- needs some sort of medium for its transmission. A "wave" is not really a physical object; it is just a disturbance of some other substance. For instance, if you throw a rock into a pond, you cannot pluck the waves out of the pond and take them home with you in your backpack, because the "waves" are just peaks and troughs in the puddle of water (the medium). Hence, there should be some sort of medium for light waves, and the physicists named this medium "aether".
However, difficulties soon developed. If you have a jar, you can pump the air out of the jar, and then the jar will no longer transmit sound, demonstrating that the wave medium (the air) has been removed. But, there was no way to remove the aether from a jar; no matter what the experimentalists did, you could still shine light through it. There was, in fact, no way of detecting, altering, or experimenting with aether at all. Physicists knew that aether must be unlike all other matter, because it could apparently pass through closed containers made of any substance. And finally, the Michelson-Morely experiment showed that the "aether" was always stationary relative to Earth, even though the Earth changed direction every six months as it moved about in its orbit! Shortly thereafter, the inconsistencies were resolved with Albert Einstein's Theory of Special Relativity, and everyone realized that aether was imaginary.
Shortly thereafter, during the 20th century, physicists discovered two new forces of nature: the strong nuclear force and the weak nuclear force. These two forces, as well as electromagnetism, could be described very well on the quantum level: they were created by the influence of mediator particles called (respectively) gluons, W and Z bosons, and photons, and these particles obeyed the laws of quantum mechanics just like electrons and mesons did. The description of these three forces, as well as the particles they act upon, has been neatly unified in a theory of physics known as the Standard Model, which has been our best known description of the universe for thirty years now.
However, gravity is not a part of this model. Making an analogy to the other forces, physicists have proposed a mediator particle known as the "graviton". The graviton is thought to be similar to the photon, the gluon, and the W and Z bosons, except that it is massless and has spin 2. I posit that the "graviton" is essentially the same theory as the "aether": a misguided attempt to explain something by reference to similar-seeming things that were explained in the same way. Consider the following facts:
And, with reference to the graviton itself:
So, what's really going on here? I don't know. I'm not Albert Einstein. But I suspect it will take someone like him- someone brilliant, very good at physics, yet largely outside the academic system- to resolve this mess, and tell us what's really happening.