The search for extra-terrestrial life -- and their search for *us*

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I'd like to preface the following with my firm belief that what I'm about to present is *not* an original, ground-breaking thought, but something that in all likelihood has been thought of and discussed before -- but that I hadn't heard it myself. I am not so arrogant.

What I'd like to present is a reason why the Fermi Paradox exists.
The nearest star to our own is 4 lightyears away. Therefore, obviously, any observations we make of the Alpha Centuri system are all 4 years old by the time we see them.
We haven't noticed any signs of life or civilizations, on any wavelength, from that system.
However the likelihood of our *nearest* neighbor harboring a technological civilization? Vanishingly small. At best there might be some life but not anything we could detect.
Meanwhile there are billions of other star systems in our own galaxy. Surely, statistically-speaking, there could be life on at least a few of them, potentially a technological civilization, yes? That's the assumption, and the heart of the Paradox: we haven't seen a single sign of that.
However: what I'd like to point out, is that many, many of those star systems, are far enough away, that *their* observations of *us* could be *so old*, based on the distance, that what they're observing *doesn't show any detectable signs of human civilization simply because, from their distant perspective, there ISN'T ANY CIVILIZATION THERE*.
Therefore: if any alien, techonological civilization exists in our galaxy, and they would not detect any civilzation here due to the distance, *why would they bother trying to send us any sort of signal*?

How do you say 'Fermi Paradox' in {alien language}? ;-)

As I stated in my preface: I doubt this is an original thought. But I've never seen it presented before.