[QUOTE=kriesel;539076]NASA uses some pretty hefty high gain antennas and knows where to point them to pick up the faint signals from our interplanetary probes, which are still very close compared to Alpha Centauri.[/QUOTE]True, but ...

The following analysis ignores factors of two or so.

The interplanetary probes have ~1m antennae and powers of ~10W. The ground-based antennae are ~100m aperture and use ~100kW power.

Now make the antennae 1km in diameter (SKA sized) and use a 1GW transmitter at each end.

The remote end now has 10[SUP]6[/SUP] times the sensitivity and is receiving 10[SUP]4[/SUP] the power per unit area. This is a factor 10[SUP]10[/SUP] larger, so the probe could be 10[SUP]5[/SUP] further away for the same bit rate.

At the other end, the receivers are 10[SUP]2[/SUP] times larger and receive 10[SUP]8[/SUP] times the power to unit area. The gain is again 10[SUP]10[/SUP], so everything is consistent.

The probes are ~100AU away. A parsec is 10[SUP]5[/SUP] AU (actually, it is 206265 AU but I'm ignoring factors of 2.06), so the probes are presently 10[SUP]-3[/SUP] parsecs from us. Multiplying by 10[SUP]5[/SUP] and we obtain a distance of 10[SUP]2[/SUP] parsecs.

But we are ignoring something important: bandwidth. The data rate used to the most distant probes is somewhat greater than 10[SUP]3[/SUP] bits per second. There are 10[SUP]7[/SUP] seconds per annum and let us assume we wish to send 10[SUP]6[/SUP] bits per annum. That is a bit rate of 10[SUP]-1[/SUP]bits per second, or a factor of 10[SUP]4[/SUP] times slower.

Our range has now increased to 10[SUP]2+4[/SUP] parsecs. A megaparsec comfortably covers the entire Local Group of galaxies, in line with the claim made in my previous post.

Added in edit: the detectors on the probes are very likely less sensitive than those on the DSN, given that they are built with 1970's technology. Any gains from this source will help compensate for any adverse rounding errors implicit in the above analysis.

[QUOTE=xilman;539081][QUOTE=retina;539075]And the equipment required for both the receiver and transmitter still hasn't been invented here.[/QUOTE]Not true.

<snip technical details>[/QUOTE][QUOTE=xilman;539082]<snip>

Our range has now increased to 10[SUP]2+4[/SUP] parsecs. A megaparsec comfortably covers the entire Local Group of galaxies, in line with the claim made in my previous post.[/QUOTE]I don't disagree with your technical analysis. Actually I haven't really examined it closely, but I'm happy to assume it is perfectly fine and valid. Okay, so let's assume from a technical POV that we can communicate.

But this question wasn't about the technical aspects:[QUOTE=retina;539075]Would we even have the patience to last it out over the many millennia that would take?[/QUOTE]This is a problem of longevity and/or boredom and/or societal things and/or evolutionary aspects. We can't communicate with anyone over distances on the scale of 10[sup]6[/sup] MLY simply because we don't have FTL communications equipment or life preserving/extending methods to let us live long enough.

What projects have humans ever had that have endured over many generations? Anything that doesn't produce results in the near future (i.e. 10s to maybe 100 years) just isn't going to last.

Voyager-1's distance from earth is about 2.22*10[sup]13[/sup] m. One light year is 9.46073*10[sup]15[/sup] m.

IIRC Voyager-1's transmitter is about 20 watts. Cheerfully ignoring any directionality in the transmitter, and any redundancy and error correction in the transmissions, for a transmitter at 1 light year just to match the signal strength of Voyager-1 at the receiver, the inverse square law says the signal would have to be over 181,000 times as strong, or over 3.6 MW. That's getting up there. The most powerful radio transmitter I found reference to is a 2 MW transmitter in Hungary. The most powerful EM transmitters of any kind I found any reference to were radar installations. The Duga woodpecker was around 10 MW. [url=https://www.globalsecurity.org/space/library/report/1999/nssrm/initiatives/cobradan.htm]Cobra Dane[/url] can hit a peak of 15.4 MW, and averages 0.92 MW. The Jim Creek VLF transmitter (callsign NLK) can manage 1.2 MW.

To get comparable signal strength at the receiver from a transmitter [i]ten[/i] light years away, it would need to be broadcasting its signal at 360 MW. I'd say being able to build a transmitter that powerful -- and have it work for any length of time -- would be proof enough of a sophisticated technology.

A high amount of directionality in the transmission, and foreknowledge of what kind of signal to look for, could significantly increase the range.

Since EM energy is quantized, I suppose it's possible to work out how far away a transmitter at a given frequency and power (say 1 kW) can get before there's a significant chance that not even a single photon from it would hit the receiver per second. Alas, I'm too lazy to work out the details.

There's also the problem that, as I heard in a lecture on the problems of getting data from the Voyager probes, "the receiver is not at absolute zero."

[QUOTE=retina;539085]What projects have humans ever had that have endured over many generations? Anything that doesn't produce results in the near future (i.e. 10s to maybe 100 years) just isn't going to last.[/QUOTE][LIST][*]Egyptian pyramids.[*]A number of religions.[*]al-Qarawiyyin, Bologna, Paris, Oxford, Cambridge, ... universities.[*]European cathedrals.[/LIST]To name but a few.

[QUOTE=xilman;539088][LIST][*]Egyptian pyramids.[*]A number of religions.[*]al-Qarawiyyin, Bologna, Paris, Oxford, Cambridge, ... universities.[*]European cathedrals.[/LIST]To name but a few.[/QUOTE]All of those produced results in the near term.

[QUOTE=Dr Sardonicus;539087]Since EM energy is quantized, I suppose it's possible to work out how far away a transmitter at a given frequency and power (say 1 kW) can get before there's a significant chance that not even a single photon from it would hit the receiver per second. Alas, I'm too lazy to work out the details.[/QUOTE]Let us assume that the photons are of visible light.

The frequency 4×10[SUP]14[/SUP] Hz is that of red light, 8×10[SUP]14[/SUP] Hz is violet light, so let's take the mean of 6×10[SUP]14[/SUP] Hz for our working wavelength, which is yellowy-green.

Planck's constant h is 6.62607015×10[SUP]−34[/SUP] Js by definition.

Remembering that E = hν, the energy of a single photon is thus 4×10[SUP]-19[/SUP]J. The receipt of one photon per second corresponds to a power of 4×10[SUP]-19[/SUP]W or, equivalently, 1kW is 2.5×10[SUP]21[/SUP] photons per second.

A ground-based optical laser has a divergence of around 10[SUP]-5[/SUP] (2 arcsec) radians if limited by atmospheric turbulence. Active optics on a 10m telescope (or a regular 4m orbiting telescope) can reduce that by two orders of magnitude. Assume a 10m receiving telescope. This subtends an angle of10[SUP]-7[/SUP] radians at a distance of 10[SUP]8[/SUP] metres and will receive the full 2.5×10[SUP]21[/SUP] photons per second. It is now just a matter of applying the inverse square law: √2.5×10[SUP]21[/SUP] = 5×10[SUP]10[/SUP]. Accordingly, a 10m aperture telescope at a distance of 5×10[SUP]18[/SUP]m will receive 1 photon per second. In more convenient units this is 162 parsec.

The above assumes negligible losses through absorption and at the detector. Detectors are already 80% efficient so that assumption holds. The average absorption for 6×10[SUP]14[/SUP] Hz light is about a factor of 2 for each kiloparsec in the solar neighborhood. 2 [SUP]0.162[/SUP] = 1.11 so the assumption holds here too.

TL;DR around 100 parsec.

Of course, 1kW is a rather low power but 1 photon per second is reasonable for transmitting a megabit message per annum, given that the background from the transmitting star is very low within the bandwidth of even a half-way decent laser. Push the power up to 10kW and you could reach a kiloparsec.

Incidentally, this answers my question about 30m-class telescopes. They have a range 3 times further than a 10m telescope and my guess of at least a kiloparsec was pretty accurate. Thanks for prompting me to perform the calculation.

[QUOTE=retina;539089]All of those produced results in the near term.[/QUOTE]You don't know how such institutions think.

I know that Oxford colleges regularly plan on century-long time scales. An example is the planting of hardwood forests for future construction requirements.

European cathedrals were also known to their designers and builders that it would take well over a century before the job would be done.

[QUOTE=xilman;539093]You don't know how such institutions think.[/QUOTE]

Sony has a 400-year business plan.

[QUOTE=xilman;539092]Let us assume that the photons are of visible light.

The frequency 4×10[SUP]14[/SUP] Hz is that of red light, 8×10[SUP]14[/SUP] Hz is violet light, so let's take the mean of 6×10[SUP]14[/SUP] Hz for our working wavelength, which is yellowy-green.
<snip>
Of course, 1kW is a rather low power but 1 photon per second is reasonable for transmitting a megabit message per annum, given that the background from the transmitting star is very low within the bandwidth of even a half-way decent laser. Push the power up to 10kW and you could reach a kiloparsec.
<snip>[/QUOTE]
Thanks for the example calculation.

I wonder -- is aiming a highly directional signal so it hits the target thousands of years later a problem?

I also note that there is no shortage of naturally-occurring EM radiation of the yellow-green frequency you mention. It is, for example, pretty nearly the frequency emitted most intensely by Mr. Sun.

[QUOTE=xilman;539093]You don't know how such institutions think.

I know that Oxford colleges regularly plan on century-long time scales. An example is the planting of hardwood forests for future construction requirements.

European cathedrals were also known to their designers and builders that it would take well over a century before the job would be done.[/QUOTE][QUOTE=chalsall;539097]Sony has a 400-year business plan.[/QUOTE]So not even close to a millennium. Forget about 1e6 years. That's what I thought.

[QUOTE=Dr Sardonicus;539100]Thanks for the example calculation.

I wonder -- is aiming a highly directional signal so it hits the target thousands of years later a problem?

I also note that there is no shortage of naturally-occurring EM radiation of the yellow-green frequency you mention. It is, for example, pretty nearly the frequency emitted most intensely by Mr. Sun.[/QUOTE]Aiming is not really a problem.

Exercise: compute the width of a 10[SUP]-7[/SUP] radian beam at a distance of 100 parsecs. I've already told you that 1 parsec is 2×10[SUP]5[/SUP] astronomical units. Long before we will be targeting a specific exoplanet we will know its orbit around its star, and the latter's proper motion. If they open communication, even with a one-bit transmission (i.e. a continuous wave beacon) , observing its Doppler shift will yield orbital and rotational parameters. We already have data from Gaia which is easily good enough (nanoradian) for the stellar motions.

In fact, there isn't much background radiation from the star. IIRC (meaning I haven't checked my facts) about a million visible light photons per square metre of collectiing area per second are received from a magnitude zero star. The sun's absolute magnitude is 4.83, which is what its apparent magnitude would be at a distance of 10 parsecs. It would be 9.83 at a distance of 100 parsecs. Let's round that up to 10 for convenience. A 10-magnitude difference corresponds to a 10[SUP]-4[/SUP] difference in intensity. A 10m telescope 100 parsecs away would receive around 10[SUP]6-4+2[/SUP] = 10[SUP]4[/SUP] visible photons per second from the Sun. The visible spectrum covers a range of around 400nm. Here is a quote from [url]https://en.wikipedia.org/wiki/Laser_linewidth[/url]

[I]An optimized multiple-prism grating laser oscillator can deliver pulse emission in the kW regime at single-longitudinal-mode linewidths of Δ ν ≈ 350 MHz (equivalent to Δ λ ≈ 0.0004 nm at a laser wavelength of 590 nm).[/I]

Assuming an appropriately tuned detector, this is a Q-factor of 10[SUP]6[/SUP] and the telescope will detect one background photon per 100 seconds.

Incidentally, I met a solar astronomer on La Palma at the end of last year. I was surprised to learn that their 1m telescope is actually photon-limited because of the large image scale and the narrowness of their bandpass filters. That is for a G2V star at a distance of 5×10[SUP]-6[/SUP] parsecs.