If you don't know why, here's a riddle for you: you are the first space colonist who reaches our closest star, Proxima Centauri. How do you send a message back, such as "We arrived" , plus maybe a photo of a planet you intend to colonize? Piece of cake, you say. Point your parabolic antenna back towards Earth and beam the message. Voyager is doing just that, but from closer to home. Only 20 light-hours away from Earth. Voyager is using a transmitter of about 20 W and an antenna of about 2 meters in diameter. You are about 2000 times farther away. Since radio waves lose power with the square of the distance, you have a problem 4 million times harder to solve than Voyager. Actually, your problem is much, much harder than this: your friends on Earth pointing their antennas towards you are blinded by the star that practically touches your spaceship. You are separated from that star by an angle measured in seconds of arc. You need to shout very loud to be heard over the tremendous noise made by your fiery neighbor. But you can do that, you presumably have a portable nuclear reactor with you and can use gigawatts to solve this essential problem.
But now, imagine you are an alien chatting merrily over radio waves with a friend in the same planetary system around Proxima Centauri. If you don't take a humongous antenna, point it in the absolute exact direction of Earth, and use a few Gigawatts of power to beam a message, how are we, Terrans, supposed to hear you? How is SETI supposed to discover aliens who are not purposely beaming waves straight at us?
The assumption of SETI has been that an advanced civilization is broadcasting a narrow-band (in the 'water hole' and possibly modulated) omni-directional signal using a large amount of energy. We can see stars across the galaxy (and, indeed, in other galaxies), so by using some large fraction of a star's energy this should be possible.
We're not far from having the telescope technology that enables us to spectrally sample the atmospheres of extrasolar planets to detect gases that are associated with life (as we know it) and even of technological civilizations (e.g. chlorofluorocarbons). This is a form of SETI too. Using such technology, an alien civilization could beam signals to selected planets that show such signs and save the energy of broadcasting omnidirectionally.
The purpose of SETI is not necessarily to confirm such possibilities (my opinion is that civilizations like us are really rare at this stage of the Universe's evolution - maybe less than one per galaxy). But at least to rule them out.
I don't think you really understand the problem domain. There are 3 main independent parameters you can tweak to improve maximum transmission range: transmit power (100,000x more power has been done commercially), antenna size (we now have a dish antenna over 250x larger), and you can increase the transmission frequency to substantially improve collimation by many orders of magnitude (e.g. use a laser instead of sub-GHz).
> your friends on Earth pointing their antennas towards you are blinded by the star that practically touches your spaceship
A star puts out a lot of power, but it's spread pretty evenly across a blackbody spectrum. You can certainly overpower it within a very narrow frequency range. Your bandwidth/power ratio might be quite abysmal compared to wifi, but it's workable.
> How is SETI supposed to discover aliens who are not purposely beaming waves straight at us
I think the idea is that perhaps they would be beaming waves straight at various stars. This is something I can easily imagine humans doing in the near future.
I bet you can build an antenna on / near Earth large enough to pick up the Voyager's signal at 4 light years. I don't think that a star emits much radio waves at the same frequently range you choose for your radio transmission, and especially has the same modulation side bands.
That said, MW-class radio transmittets are not heavy, their cooling systems are. You also don't need to transmit continuously, you can send bursts as long as your thermal budget allows. For energy, you have unlimited sunlight.
Could the sun be used as a gravity lens for radio waves? I know people are thinking about doing it for building a telescope, so I assume longer wavelengths work, too.
If you don't know why, here's a riddle for you: you are the first space colonist who reaches our closest star, Proxima Centauri. How do you send a message back, such as "We arrived" , plus maybe a photo of a planet you intend to colonize? Piece of cake, you say. Point your parabolic antenna back towards Earth and beam the message. Voyager is doing just that, but from closer to home. Only 20 light-hours away from Earth. Voyager is using a transmitter of about 20 W and an antenna of about 2 meters in diameter. You are about 2000 times farther away. Since radio waves lose power with the square of the distance, you have a problem 4 million times harder to solve than Voyager. Actually, your problem is much, much harder than this: your friends on Earth pointing their antennas towards you are blinded by the star that practically touches your spaceship. You are separated from that star by an angle measured in seconds of arc. You need to shout very loud to be heard over the tremendous noise made by your fiery neighbor. But you can do that, you presumably have a portable nuclear reactor with you and can use gigawatts to solve this essential problem.
But now, imagine you are an alien chatting merrily over radio waves with a friend in the same planetary system around Proxima Centauri. If you don't take a humongous antenna, point it in the absolute exact direction of Earth, and use a few Gigawatts of power to beam a message, how are we, Terrans, supposed to hear you? How is SETI supposed to discover aliens who are not purposely beaming waves straight at us?