We are not alone?

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If we go by our own civilisation, there are a number of explanations as to why we neither see nor hear of aliens:

Radio Signals:
Our TV/radio signals have been emitting for about 100 years. However, what you need to realise is that we only actually emitted signals to space for a few decades. Todays communications systems are much more efficient than in the days of the first Sky At Night episodes, and so our little green men (assuming they have kit advanced enough to piece together a very weakened signal), will see things like I Love Lucy, early Coronation St, Sky At Night when Mr Moore was a young man, and of course Hitler. But today, TV companies do not broadcast adverts for the latest Sky package to ET, as they are unlikely to take it up. And digital TV renders the signal encrypted, so they probably wouldn't even see it, even if it was strong enough. They could maybe detect some later episodes into the 70s, but only Sky At Night would make it worth while, and by then you had some awful TV, so it probably put them off.

There were efforts in the 1960s as part of the Cold War to detect Russian planes etc, by bouncing signals off our atmosphere. These were powerful enough to emit to space, and again, were a short term signal.

And of course, the Arecibo Radio Telescope in Puerto Rico sent signals out to space in 1974. This was the first intended signal, and was about as powerful as we could do at the time, but again, a short term signal in the big scheme of things.

Also, they would not detect many of our radio signals, as they are encrypted. What ET might be using is neutrinos, as they are better at travelling those sort of distances. We will probably do this in time ourselves.

Intersteller Travel
We don't actually see aliens turning up to say hello, why?
Space travel is tricky. Actually no, space travel is really difficult. It takes a lot of energy to get up there, and once you're there, you have to protect against all sorts of nasty things like radiation, loss of breathable air, you have to maintain your biosphere of a space ship, you have to prevent yourself from going mad (there's only so many episodes of I Love Lucy you can watch), and when you're half way out of your own star system, you'll be asking yourself why the smeg are you going anyway? Why wouldn't you just send a robot, and save a heap of resources?
If you're thinking that ET might want to explore/expand their civilisation, you might want to answer why? Looking at our own situation, our own population looks set to stablise at about 12billio(ish). We should be able to feed that many people, and it may even reduce over time. The reason this is happening is birth control.
Birth Control is easier and cheaper than going into space to colonise other worlds (this seems a bit of an understatement, but you'd probably get bored if I wrote "very very very ......... very much easier").
They could send probes of course, and robots. And given, as you say, that a civilisation probably existed billions of years ago (although more like millions), they probably missed us.
Looking for possible alien civilisations in our own little corner of this galaxy, we wouldn't look at the nearest stars, as they are mostly Red Dwarfs (not ideal). There are however, some stars in a group a bit further away, that are like ours, which suggests that our system got flung out of that group. So there may be (or have been , or will be) an alien civilisation there.
Also, aliens in other galaxies probably exist. The current thinking is to look at old galaxies, so (as you said), they would be well advanced.
But they are unlikely to make it over here, owing to the huge distances.

Physical signs of Aliens
There are other ways of detecting alien societies, such as heat and light. With the mass deployment of LED bulbs, the Earth is getting brighter at night. The way things are going, we will be detectable by aliens in the not too distant future, just by our lights. And that doesn't include heat. Even if we stop the Global Warming thing from the greenhouse effect, if our economy continues to grow, we will heat the Earth from direct waste heat, owing to the huge amount of energy we would consume. This is because of the relationship between the economy and energy consumption.

Its thought that in about 200 years(ish), we will see a detectable rise of a few degrees from this effect globally. We see it currently as urban heat islands, but this will only increase as we develop. If we continue to grow economically at current rates, the oceans will boil in 400 years time (this won't happen in reality of course, but serves to illustrate the issue).

So when we are sufficiently developed, aliens could detect both our heat and light from many light years away. They can also have a rough idea of what organisms are in our atmosphere, and the basic composition of gases. But won't see us unless we find a way of sending signals for a long time in the right way that they can detect.

If our aliens feel the need to grow economically beyond what their planet can support (which would be silly), they may feel the need to build a Dyson Sphere. This would be easy to detect (although very difficult to build), as again, it would emit waste heat, but at a scale that could be detected from a huge distance. But remember the comment about space travel and birth control.

So assuming our aliens have comparable gravity wells, and the ability to do the whole birth control thing, and the likelihood that they will have some equivalent of I Love Lucy, going by our own experience, we can assume that they sent signals, but basic radio signals would only have lasted for a short time (relatively speaking). Any signals that they do send would probably be something other than basic radio signals, such as neutrinos, or some kind of gravity wave, or other system we hadn't considered. These would have to be emitted for a huge amount of time for us to pick them up, otherwise we would miss them

This also applies for robots/probes. They could send out a million probes, but its unlikely we would come across one, as there are so many systems they could send them to. We could look for signs of energy emissions for ships, or asteroid mining etc, but these would be close by systems.

Of course I do hope we will one day see some evidence of aliens, but we must remain sceptical (if for nothing else, our sanity).
So, I can eat all the biscuits myself, then. :)
 
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