With any EM radiation like RADAR it falls off in strength pretty quick with that whole inverse square of the distance thing. Put a couple hundred of light years behind it and the strongest RADAR pules ever transmitted by earthlings gets lost in the interstellar static.
Yep, the "bubble" of radio emissions or the light-front from them is a "dot" that's roughly 200 light-years in diameter. A 200 light year sphere is the same size as the pixels/dots used to represent the stars in most CGI visualizations of the Milky Way galaxy.
The old DEW line radars are much more powerful than the first 19xx-whatever Marconi Morse code CW transmissions, but yes, even they will fade off really fast.
It's just at the borderline of feasibility that we could see "ourselves" at our rate of radio leakage at 200 light years with our best radio telescopes, if we knew where to look and on what frequencies. What everyone forgets is that the transmitting civilization needs to "beat" the Drake Equation too. And to take a serious stab at it, would probably require mining all matter in the Solar System, converting it into a Dyson Sphere, redirecting all the Sun's energy into radio broadcasts sweeping the plane of the galaxy, and maybe a few other nearby galaxies for best odds of detection, and then leaving the signal up and running, for millions, maybe billions of years to allow time for other technological species to evolve to even receive the message, much less reply.
http://i.dailymail.co.uk/i/pix/2012/02/27/article-0-11EF84AB000005DC-183_964x959.jpgAnd that's what the study that MechAg94 links to is about. The
assumption is that a long-lived technological civilization that's "made it" would also build a bunch of Dyson Spheres (or matryoshka brains) in either a distributed Kardashev Type II civilization, or Type III that actually harnessed it's whole galaxy. And instead of visible light, we'd see an increased spectrum of IR radiation leakage, because again the
assumption is such a civilization can't beat the laws of Thermodynamics and eventually heat/IR that's too low in energy to be worth the effort to capture it must eventually leak outward.
So after surveying several thousand galaxies and not seeing any with a super-civilization's macro/mega-engineering IR emissions, either there are no such civilizations, or if there are, they don't operate in that manner.
It's premature to say we're alone, we've only seriously begun to look with scientific instruments that have a
chance of detecting anything for roughly 50 years. We've been around for only 2 million to 200,000 years, depending on where you draw the line. But from the conservative side, that's only .00025% the length of our species existence. Add in geologic time, Solar System time, Galactic timescales, keep on adding zeros...
However, if we are alone, it's profound too. It would be a horrible shame if we didn't get as far in our Galaxy, or the Universe as we could.
My worries right now are that we find microbes or fossil evidence of life on Mars, Jupiter's moon Europa, in the ice fountains of Enceladus around Saturn etc.
Mars I can kind of handwave away, there's a good chance microbes hitched a ride on ejecta/rocks from meteor impacts between our worlds. Jupiter and Saturn's moons, not so much. If we find even one
other parallel genesis of life in our Solar System, it's likely the Universe is lousy with it. But that bodes badly for us, because statistically speaking, whatever filter or event that causes the "great silence" in the Universe lies ahead of us becomes more likely.
The list potential places the "great filter" for ETI's (and us) resides is something like the Drake Equation itself:
1. Stars? - Plenty of stars.
2. Planets? - Now exoplanet searches are showing we're lousy with planets.
3. Hospitable planets? - exoplanet search resuts still coming in, but the dice are being rolled billions of times. Some are in the liquid water zone of their stars now.
4. Hospitable planets with life? - James Webb space telescope will probably be able to pull O2/CO2/CH4 atmospheric spectra from nearby exoplanets around 2020 or so, and we can make a better guess.
5. Hospitable planets with complex life? - Dunno.
6. Hospitable planets with complex life that evolve intelligence? Dunno.
7. Hospitable planets with complex life that evolve intelligence who start expanding technology? Dunno.
8. Hospitable planets with complex life that evolve intelligence who start expanding technology that don't die out, or destroy themselves? Dunno.
We're not seeing anything like that. No Kardashev Type II or III civilizations.
But each time we check off something on the list towards the bottom, the odds go up exponentially each time that humanity is foooked.
Then we'd have to hold out hope that #4 is really rare, and we don't see any atmospheres with free O2 or CO2/CH4(methane) ratios that aren't explainable by anything but life. And/or #6 is really rare, because evolution is a blind process that does not have "goals", intelligence/tool-using is a fluke. Or that #8 is explained away that advanced civilizations operate in paradigms that aren't easily visible with traditional astronomy methods, or that it's unlikely we'd ever be visited.