In my universe, FTL communication using entanglement SEEMS to have been achieved. I understand quite well from a layman's perspective how it's basically impossible without a complete overhaul of established physics. But since it's based on a far-fetched speculation, never turned into reality in the universe of my story, what possible alterations to physics could scientists postulate?
This is a use of the Quantum Mechanics Can Do Anything ⚠trope, and a “groaner” to an increasingly large number of readers.
The idea of corralation of distant observations emerges from the math of non-separable states. You can't just put nonlocal communication in without messing up the foundations of QM. So you can’t make a simple alteration to physics to make changes to one entangled particle cause its mate to be changed, as opposed to breaking the entanglement.
It makes for a smarter story to introduce a new, different effect, and give it any properties you want. For example, in The Metamorphosis of Prime Intellect, the “correlation effect” was clearly something different, and discovering it changed the universe.
If you’re looking for ideas in general, not trying to make QM do this, see Is there a scientifically plausible faster-than-light communication system? , Science-based FTL drive, Are there any ways to allow some form of FTL travel without allowing time travel?, and others already posted here.
By the Principle of Locality, this is impossible with currently known physics. As such, this might be one of the first things to be questioned.
Alternatively, it would be possible if something like wormholes were discovered, which would mean that it would be possible to warp spacetime to a large enough degree so that 2 arbitrarily far away points could be brought close together and what appears to be FTL communication could occur - that is, nothing's actually travelling faster than light, only space is being manipulated so that the 2 points are temporarily brought closer together and so, during that time, regular communications don't take as long.
Now, back in 2011, physicists thought that they had measured neutrinos travelling faster than light (it turns out that they just made an experimental error), but as a result of this, lots of papers (almost 200) popped up about how this might be possible. This list can be found here - if you want to read a paper, you need to open the link to arXiv, then remove the following part of the URL: "web.archive.org/web/[number]/".
A small number of examples of explainations are:
- An acceleration due to gravity
- Another fundamental speed limit > $c$
- Extra dimensions
- a result of Neutrino mixing
While accelerations due to gravity and neutrino mixing don't affect photons, if a classical signal could be sent faster than light (i.e. if neutrinos could travel faster than light), this would allow for communication-by-entanglement that is faster than light as a classical signal needs to be sent at some point in order for communication-by-entanglement to work.
Its hard to say what theories science will come up with without data, and obviously you're not about to give us a pile of fake data to analyze =) Science builds models to fit the data, so it won't do anything without them.
However, there are two very general directions scientists are likely to turn. The first is the topology of space. There would probably be at least a few theories suggesting space is getting bent or even tied into knots. The other approach would probably involve particles that travel faster than light. The "Atomic Principle" is very popular these days. This principle is an unprovable hypothesis that the entire universe can be fully understood as a set of indivisible objects, each of which has some state. This approach is very popular in the subatomic physics world, so I would expect many theoretical physicists to explore this direction.
Of course, it could get more complicated if we figure out how to apply this principle before we fully understand it. Then all sorts of interesting patterns may emerge, such a papers claiming Bumblebees can't fly because their wing to weight ratio isn't high enough.
FWIW, it is much easier to conceive of plausible beyond general relativity and Standard Model physics that would allow for FTL communication than it is to imagine any plausible means by which FTL travel would be possible.
For example, one fairly mainstream (although minority) school of thought on how we can solve the unsolved problem of quantum gravity in physics is called "loop quantum gravity."
In loop quantum gravity, the very concept of "locality" is an emergent phenomena. Fundamentally, in LQG, there are a bunch of points in space-time connected to a bunch of other points in space-time, and when those form networks that cluster together, you get an emergent sense of locality based on the average number of hops to get from points with close connections to point A to points with close connections to point B.
But, nothing in loop quantum gravity prevents a few stray connections between space-time points from connecting directly to point C which has an average number of hops to reach point A that is much, much greater than point B.
One possible connection to this concept in quantum mechanics comes from the propagator function for the photon.
You see, in Quantum Electrodynamics (QED), the probability of a photon going from point A to point B at a certain time in the future, is determined by considering all possible paths from point A to point B, including paths upon which the photon travels at slightly less than the speed of light or slightly more than the speed of light, although the greater the deviation from the speed of light, the less probable it is that a photon will take that path. If you only consider paths at exactly the speed of light when calculating the probability that a photon will end up at a particular place and time in the future, you will get the wrong answer.
One "realist" interpretation of this empirical fact about the photon propagator. Photons really move a fixed number of hops per second, but it reflects the LQG concept that locality is emergent and that the distance from point A to point B reflects merely the average number of hops across space-time points that it takes to get from point A to point B, even though different paths may actually involve moderately different numbers of hops, and in highly improbable circumstances, very different numbers of hops.
Thus, fundamental particle sized wormholes, rather than being the exception, are the fundamental nature of space-time from which an apparently continuous and smooth apparent space-time emerges because the number of hops involved in any macroscopic trip from a point A to a point B is so great that the law of averages obliterates any apparent distinctions due to random variations in the number of hops necessary to cross a particular small distance.
Since these non-local connections are ubiquitous, finding local ones that connect to distant places in the universe isn't necessarily so hard. But, the problem is bandwidth. A non-local connection could support only one fundamental particle (such as a photon) at a time. This works great for communication but is lousy for moving solid, macroscopic objects.