No.
The Speed Of Light is Really the Speed Of Information Transfer
The speed of light isn't the speed of light, it's the fastest that information can be transferred across spacetime. Light travels at that speed because it has no mass. No information can be transferred faster than the speed of light. Note that there can be causes and effects which appear to violate this, but when you look at them closely you'll find that there is no information transferred.
Watch PBS Spacetime's video The Speed of Light is NOT About Light.
The Result Of Observing Quantum Entanglement Is Random
For simplicity's sake let's say our entangled particles can be spin up or spin down. If you observe one is spin up, the other must be spin down, and vice versa. But which spin a particle will be is random. You cannot predict, before you observe it, what spin your particle will be.
You also cannot influence the result. You cannot, for example, make your particle comes out spin-down to ensure the other particle comes out spin-up.
Observing One Does Not Collapse The Other
I believe the thinking is that when one particle is observed and collapses, the other particle simultaneously collapses, and Observer B can know when Observer A looked at their particle.
Again, no information can be transferred this way because Observer B cannot know their particle is collapsed without observing it which collapses their own particle's waveform. An observer cannot tell the difference between "the waveform collapsed because the other particle was observed" and "the waveform collapsed because I observed it". One observer cannot use entangled particles to signal to the other that they've observed their particle.
Quantum Entanglement Conveys No (New) Information
Quantum entanglement only appears to violate this constraint, but in reality no information can be gleaned from an entangled particle faster than the speed of light. You can't even know if the other particle has been observed.
For example, let's say you move two entangled particles and observers far apart. Then Observer A observes their particle A, and it is spin-up. When Observer B observes their particle B, it must be spin-down. Ah ha! The two particles must have communicated with each other! The jury is out the mechanism, see Bell's Inequality, but no new information was transferred between Observer A and Observer B. They already had it all, and it was transferred at or slower than light, because the observers had to carry the entangled particles with them.
Since the result of the observation cannot be predicted, Observer A cannot influence their particle to come up a particular spin and thus alter what Observer B sees. All they know is Observer A saw the opposite of what they saw. But even that conveys no new information, Observer A already knew Observer B would get the opposite result. Since the result is random, Observer A didn't influence Observer B's result either. Observer A doesn't know anything they didn't already know at the start, they've been carrying that information with them at conventional speeds.
Consider Two Envelopes
To see why, replace particle A and particle B with two sealed envelopes. Observers A and B are handed the envelopes and told that one says "1", the other says "0". Then they move apart from each other at (or near) the speed of light. Then Observer A opens their envelope and sees "0". Now they know Observer B got "1". Nothing special happened. The pair of envelopes, and information about their entanglement, were transported conventionally. Even if Observers A and B are light years apart, the envelopes, and the information about their entanglement, still had to start together and travel apart at less than the speed of light.
Most importantly, Observer A can not use the envelopes to send any information to Observer B. They can't predict what's in Observer B's envelope without opening their own, information which was contained in the envelope all along and carried with them conventionally.
They cannot influence what's in Observer B's envelope, that information was already set at the start (in reality it wasn't, read on).
They can't even use their timing of their opening to send a message. Observer B doesn't know that Observer A opened their envelope, just as with the particles Observer B doesn't know that Observer A observed their particle.
Yes, Spooky Action at a Distance. No, Hidden Variables.
The envelope analogy is good to understand why no information has been transferred, but it implies that the spin of the particles is predetermined. It turns out this is probably not true due to something called Bell's Inequality which states:
No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.
Local hidden variables are one of the ways to get around the "spooky action at a distance" in things like quantum entanglement. The claim is that the entangled particles have hidden variables, like their spin, which are only revealed by observations.
But experiments have shown this isn't true over longer and longer distances. The recent QUESS mission tested quantum entanglement, quantum encryption, and Bell's inequality in space for the first time over 1200 km. The results are still being analyzed.
So yes, it seems there is spooky action at a distance between quantum entangled particles. It seems they do influence each other's outcome instantly. But that's ok because no information is transferred. The universe appears to be weird like that, and the speed of light only applies to information transferred across space.
Veritasim explains Bell's Inequality and why it is most likely true in Quantum Entanglement & Spooky Action at a Distance.
A Note About "The Observer"
Just to be very clear, no, the "observer" isn't a person, unless it's these guys. There's no quantum woo here about consciousness.
Quantum "observation" means that two quantum systems have interacted causing the wave function to collapse. You are a quantum system, but so is a laser, a microscope, and a coffee table.
No Schrodinger's Observer
Let's try to transfer information. Observers A and B are in a suicide pact. They come together and generate a pair of entangled particles. One year from now the one whose particle is spin up will kill themselves.
One year later, and far distant, Observer A observes their particle and sees it's spin-down. They instantly know Observer B is supposed to kill themselves! Doesn't that transfer information instantly?
No, Observer A had the information with them all along. They had to communicate conventionally with Observer B to make the pact and get their entangled particle. They had to carry it with them, conventionally, the whole year. They could have, at any time, observed their particle. This is just like the pair of sealed envelopes.
Summary
- The entangled particles must be together when they're created.
- The entangled particles must be transported apart at conventional speeds.
- The result of the observations are random, they cannot be influenced.
- You cannot know whether the other particle has been observed.
The only information an entangled pair transmits is "we are paired" and that information is transferred at conventional speeds. Just because they happen to be observed when far apart doesn't convey any new information to the observers.
@before their username. $\endgroup$