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I've read that asking "what's happening right now on a planet P that is N light years away from Earth?" is a non-sensical question due to time-dilation at great distances.

But I wonder about the following:

If we send a message to planet P, that will take N light years to reach the planet, and when received, that message will light up a red bulb on that planet,

then,

N light years from today, if X were to ask Y: "What is happening on planet P right now?" couldn't Y then answer: "A red bulb is being lit up on planet P right now" and wouldn't that be a sensical/meaningful answer ?

And likewise, if a person standing on planet P, N light years before the red bulb was lit, exclaimed: "A message was emitted from Earth just now" wouldn't they also be saying something meaningful/accurate ?

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I think it's more accurate to say that there is no UNIVERSAL notion of "now". The reason why is that, in general relativity, we are always free to define a new time coordinate:

$$T = T(t,x,y,z)$$

so long as $\nabla_{a}T\nabla^{a}T < 0$, and since the theory can't tell between one coordinate system and another, it can't tell whether "now" means "at a constant T" or "at a constant t".

That said, you can work out a convention, like you seem to be trying to do above, to create agreement between two observers (another choice: define T relative to the "comoving coordinates" of the Hubble cosmology). But you have to understand that this is just a convention, and isn't "fundamental" to the physics.

Zo the Relativist
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It's not that the questions or answers have no meaning, it's that they have too many meanings.

Human language is not a good way to describe something like this. Almost all the words are ambiguous. "now" is just one example of many. The words and language evolved to describe an everyday existence that is almost (but not quite) perfectly described by Newtonian physics, where "now" is a very simple concept. Most humans will never need more than that.

That's why we use the language of mathematics to handle these things. That is not ambiguous (when a proper set of definitions are made).

StephenG - Help Ukraine
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