It follows the free-space path loss equation, which is actually pretty easy to work with. https://en.wikipedia.org/wiki/Free-sp...

A typical high-power transmitter might be 80dBm. A good narrowband receiver will detect signals down in the -130dBm range. (By narrowband, we're talking about voice or low-speed data like GPS, not video or broadband.)

I've only used it for terrestrial links of a few miles. I just tried it for an FM radio station, and I get a range of only a few million miles. But I know the Voyager probes worked over billions of miles on just 10W. It must be loads of antenna gain in the terrestrial antenna. Maybe someone can explain how RF-based SETI is even possible. Just running the FSPL equation quickly appears to confirm what you said.

What a preposterous notion! The next thing you'll tell us is the box could show you where you were on the planet down to an accuracy of say four or five meters. Pure fantasy, it'll never happen!

I've read that regular radio waves propagate so poorly over distance that even by the time our signals made it to Alpha Centauri (4 light-years) they were indistinguishable from noise.

Finite power - transmitted in a vast spherical volume - diminishes to virtually nothing "very" quickly.

Which we will also have in just a "short" time. (100 years? 200?... 50?)

No doubt. I struggle with this very issue as I try to lay plot lines in a "future history" I'm working on. Eventually you just have to accept the limitation and just work the story. Beg the future for forgiveness.

Yeah, that's a good one.
But I take a more optimistic view myself.

Short term the graph rises and falls, but in the long view we are rapidly advancing.

Personally, I think we'll find alien life to be much closer to ours than anyone ever expected.
Evolutionary pressures will be duplicated time-and-time again, quite possibly resulting in similar outcomes.

I'm not saying Humanoid per se (though there should be many humanoid species - why would we be the only one?) but UNDERSTANDABLE - recognizable.

Except, of course, for those that aren't! (Also sure to be!)
Ha!

Mankind is limited by what it knows to be real, what it has devised a way to measure, and what it can categorize into its perception. As we venture further into the unknown of space we will no doubt see and experience things, incomprehensible things, that defy the structure of what we've defined as reality. While speculation is fun, the reality that we may have actually come across something mankind previously has not seen or even ever thought of is as exciting as its is intimidating.

So shortly after developing radio, they become dim, fuzzy microwave sources. This seems more efficient than broadcasting, so it fits.

I think about Arthur C Clarke's 3001. One technology he imagined 1000 years in the future (from the 1990s) was a box you could carry around and verbally ask it to look things up or put appointments on your calendar. It had a female voice called Miss Pringle. It's so hard to imagine even 1000 years ahead.

Yes. We started with a few 100,000 W radio stations. We're starting to use mostly the internet over low power links to base stations that cover a very small area and re transmit it to the wired backbone. I suspect a few large RF carriers sending continuous one-way programming would be easier to detect than our internet of things world without countless transmitters, mostly transmitting with a small faction of a watt.

This is the same with a typical public safety radio system. It used to be one tall tower that covered a whole metro area. Now it's a network of transmitters and receivers around town that each cover a smaller area.

I think this trend will continue and make us harder for aliens to detect.

"...because they very briefly use high-power radio..." That makes sense to me, maybe all advanced civilizations have cable?

Absolutely.
Whatever we might be in a million years, it won't be US - anymore than we are Lucy.
(I know, Lucy was more than a million years ago but you get the point,)

Maybe we don't see radio waves from other civilizations because they very briefly use high-power radio and then abandon it for repeater based systems or other communications media. That's happening on earth.

So then they don't become visible until they build something like this sliver of a Dyson sphere they're imagining. It's hard to get my mind around it. I imagine them developing long-lived probes that would go out and find civilizations, both living and long-gone. I imagine them still being confined to their solar system by Special Relativity but having very long lifespans.

I can imagine them getting data back sent from one of their probes. They haven't visited Earth yet. This data is from some civilization on a planet with a thin atmosphere and less gravity. They developed a gestural and written language (the atmosphere being too thin for speech), began to urbanize, and then plague followed by a glacial period wiped them out, leaving the planet to non-intelligent animals.

If such a civilization existed 1500 light years away and we're seeing something they were building 1500 years ago, are we on a list of Goldilocks planets to visit. There are no radio waves. They can't zoom in an see the Holy Roman Empire, Byzantine Empire, or the civilizations in the Americas. By the time their probes get here, maybe they'll find our own energy collecting system and a civilization of people linked together by artificial brain interfaces, living thousands of years. I can't fathom whether any future humans would be weird enough to set out and spend its 3000 year lifetime on a trip to see KIC in person once they know someone is there.

Point taken, I have seen the drakes equation stuff too. Maybe the ability to reason is what will cause us to snuff it. Always seemed rather pessimistic to me.

Modern humans (depending on who you read) have been around 40 to 100 thousand years. 10 thousand is possible. If our descendants make it a million years, I doubt they will still be the same species. Wouldn't expect evolution to stop.

It all comes down to faster-than-light travel. If it is possible - we could be in trouble. If it's not possible - then we have breathing room.

As to where THEY all are - it's all about the lifespan of species.
Even a rare thing will be plentiful if it lasts forever. But will be vanishingly scarce if short lived.

Will we last another 10,000 years? Another Million?
Neither is very long in ASTRO-nomical timelines (even greater than geologic time scales!)

From a hard science perspective, Where are all the aliens? It's called the Fermi Paradox, with billions of galaxies, each with billions of stars, why haven't we found sign of them yet?

Personally, I think they wouldn't care about us. I mean do you go up and try to communicate with every barking dog? Maybe the only way we would get their attention would be to show up on their doorstep. Even then, they might just call animal control. 😸