I Do Understand Relativity

Entanglement (more correctly, wave-function collapse) cannot be used to transmit information. So there is a "spooky action at a distance", but there is no faster than light communication.

I find it's easier to understand if you assume that every entangled particle already "knows" what state it will be at the moment of entanglement. In theory it's called "hidden variables". John Stewart Bell has proven that there's no local hidden variables, but noone said about global variables. For example, in Superdeterminism it's all easy and clear.

PS: Physicists thet reject Superdeterminism only for philosophical reasons, there's no scientific reasons to reject it.

Both of you are right in slightly different senses.

There is no "global time clock" and hence in a philosophical sense there is no "common now".

However, the speed of light is constant in the universe and so you can calculate time based on distance traveled by light to you provided you are not moving at speeds comparable to speed of light. This means you can suppose a "common lightyear clock" for measurement.

But when the speeds are comparable to that of light, you have time dilation and length contraction and so even the "common lightyear clock" is invalid. This is the principle of "Relativity of Simultaneity".

The way to think about it is, Events happen in a Space-Time fabric and so in order to measure the interval between two events you have to consider both Space and Time w.r.t. object speed vs. speed of light. The universal invariant here is the "Space-Time Interval" between two events which will be the same for everybody whatever be their mass or speed.

If we assume that the question is valid, then I can ask the same question but instead of Alpha Centauri I'd ask about some more distant object. Like the galaxy MoM-z14 (redshift z=14.4, the farthest known object) -- we see it as it was 280 million years after the Big Bang. No they cannot see Earth as it was 13.5 billion years ago, the universe age was only 280 million years at that time.

The correct ways to ask the question would be:

1. If we send a signal (like a question "how to you see us") to the Alpha Centauri/MoM-z14 -- what response would we receive from them and when?

2. If we send ourselves aka observer (at the light speed or slower) to the Alpha Centauri/MoM-z14, how would we see Earth when we arrive there?

In both cases the answer would be "like the Earth is today, or later", not "how the Earth was N years ago".

So we cannot move ourselves, even imaginatively, to a distant place faster than speed of light. Otherwise we would be outside our light cone.