the thread on what would happen if we discover a planet with life:
http://boards.straightdope.com/sdmb/showthread.php?threadid=195308
got me thinking of just how far could we send a reliable, usable signal into the void? what about a signal that is detectable but not inteligable.
I know we’ve beamed a signal to one of the Megellanic Clouds and that’s supposed to take something like 40,000 years to get there. So, assuming they knew that the signal would survive that long, then it’s at least 40,000 light years.
I dunno—how good is their reciever?
I was gonna say “15 billion light years, + or -, but whether or not anyone could detect it is a different matter”, but you sort of walled that one off with your limiting factor of “reliable, useful…[at least] detectable”.
OK, attempting a serious answer. I think it has to do with signal strengh (duh!) but also signal duration, because if your interstellar aliens are way far away the signal degrades and you only get bits and pieces of it – but if it were broadcast over and over in a loop you could maybe record a couple hundred of those loops and let a computer clean it up and make sense out of it using statistical math & such.
I don’t know enough about how signals degrade as a function of distance but I suspect is has something to do with a sphere and its surface area and how all the energy of the signal is spread out across the whole sphere but the receiving dish gets less and less of that energy the farther away you are. Seems like at some point no matter how good your receiver is, unless that receiver takes the form of an arc several hundred thousand light years wide you’re just not going to be able to do much with it. It’s similar to the thing about the Hubble telescope and the galaxies 12 or 13 billion light years away/old – you can add magnification and improve resolution to an extent but eventually you’re up against the fact that you can only magnify what’s there in the first place, and most of the light from those suckers went in other directions. An infinitely powerful telescope sitting where Hubble is would not be able to make out individual stars in those galaxies unless they shone fiercely enough for the law of averages to land some of their spread-out dissipated photons on the telescope’s collectors, and for anything short of a supernova that chance would be awfully low unless the telescope remained aimed at that section for a very very long period of time.
I also don’t know the limits of our signal-sending technology so even if my ken of spatial geometry was up to snuff and I could lay out the formula for what’s available at what distance, I could not put in the figures for what our best reasonable effort would be.
According to this page, the detection limit of the SETI survey using the Arecibo radio telescope was 8E-27 W m[sup]-2[/sup], capable of detecting a 9E+12 W EIRP (Equivalent Isotropic Power) transmitter 1000 light-years away. Arecibo itself, when used as a transmitter, has a 1E+13 W EIRP, so the maximum distance for a pair of them to communicate is just over 1000 light years.
However the threshold quoted above is for a survey where the telescope scans over the entire sky. I believe the dwell time for each section of the sky is only tens of seconds. If you know the target location and you can train your telescope on that target for many hours, you can do at least one order of magnitude better the above numbers.