If just .001% of 10 billion Earth-like planets orbiting sun-like stars in the Milky Way have harbored advanced, intelligent life, shouldn’t we have seen some kind of evidence of their past existence, since this would equal 100,000 civilizations?

Great question! Complicated answer. Let’s start by looking Earthward at ourselves, then we’ll compare that looking spaceward toward the stars.

As you know, homosapiens are the advanced, intelligent life form on Earth which is now technologically advanced and space faring.

Now by some estimates, humans have been on this planet only for the last 200,000 years, or one fifth of one million years. There are a thousand million years in a billion years, and the Earth is about 4.54 billion years old. So, humans have been on Earth for only a tiny fraction of Earth’s existence. Here’s a graphic to illustrate that point and more to follow below.

This image illustrates what it would look like on a 24 hour clock comparing the age of Earth to the presence of humans. In fact, life itself has existed on Earth for less of half the lifespan of the planet, what to speak of humans.

So you can see, even though we have a planet in the goldilocks orbital region around our sun, someone looking at Earth many light years away would not see humans even though humans are here, because the light or radio waves haven’t reached them. They would assume this a dead planet. Humans have existed on this planet, in terms of a 24 hour clock, 1 minute and 17 seconds. In terms of exploring space, for less than 1 second.

You see, just because humans have been on Earth about 200,000 years doesn’t mean humans have been emitting radio waves and exploring space for all that time. In fact, we only began exploring space 60 years ago and emitting radio waves for a couple of hundred years. In the history of Earth, we have explored space (in terms of a 24 hour clock) for only a flash of a portion of a second.

That’s us. Now let’s look at the stars.

Let’s say there are 100,000 planets with advanced life like humans on them right now.

However, since the galaxy is 200,000 light years across, someone on a planet on the other side of the galaxy from us would not be visible to us. We’d see that as a planet with no human-like people because it would take light and radio waves 200,000 years to reach us. Now take into consideration that of the 100,000 planets with human-like people on them (as you suggest in your question), it took us 200,000 years to get to the point of emitting radio waves and exploring space. Hence, we’re looking for a very narrow window in a planet’s lifespan that intelligent life might be detected. Not only a tiny fraction of the planet’s existence has it had intelligent life, but only a tiny fraction of the time the intelligent life existed there were they able to emit radio waves and explore space, even if all conditions were favorable for that planet to eventually develop intelligent life.

Furthermore, the sky is very big. Looking for exoplanets, we have explored less than 3% of the total sky so far.

Put all of that together and the chance we would have detected other intelligent life is almost nil to date, even though it might still be out there somewhere. The guy below might be the exception.

What are the chances of two planets from the same solar system having sentient species that reach space exploration around the same time?

This is a great question, but unfortunately no one will be able to give a definitive answer as to the chances.

This is simply because we do not yet know if life exists anywhere other than Earth. It is still within the realm of possibility that Earth is the only place where any kind of life, what to speak sentient life, exists.

Finding such life would be an affront to many religions that contend that God created life on Earth only, and therefore finding even a fossil of a microbe on another celestial body would be the holy grail of science and have reverberating effects throughout human society. The theory of evolution would be proven.

It is believed to be highly likely that life does exist elsewhere in the universe simply by the laws of probability, but that being said, we have found no evidence to support this theory.

So now we can come back to your original question: “What are the chances of two planets from the same solar system having sentient species that reach space exploration around the same time?” Based on the fact that life has not been discovered anywhere, the chances to sentient life forms existing in the same solar system is practically nil (but not impossible).

Here’s how scientists are going to detect alien life from millions of miles away

http://bit.ly/2DNAmdR

Do you think aliens have received our communications and chose not to respond?

Do you think aliens have received our communications and chose not to respond? Well, who knows, but…. radio waves travel at the speed of light. We’ve been emitting radio waves for maybe a hundred years. A hundred light years radius around our solar system doesn’t encompass a lot of stars. So the answer to your question is “probably not.”

Does anyone believe in extraterrestrial life? If yes, why? If no, why not?

Pretty much all of science and scientists in the world believe in extraterrestrial life, even though no evidence of extraterrestrial life has ever been found to date. Why do scientists believe in extraterrestrial life? Simply because there are billions of stars in the Milky Way galaxy and billions of galaxies in the universe. Somewhere it is highly likely that extraterrestrial life exists. It is even possible that extraterrestrial life of some form or another exists on Titan, within our own solar system!

Will an alien invasion by secular and militaristic extraterrestrials solve a lot of problems on Earth?

An alien invasion by secular and militaristic extraterrestrials would solve one of the biggest problems we have here on Earth. That problem being: does life exist on other planets? Finally we would have an answer!

How can we believe in God, but not in alien/extraterrestrial life or vice versa? This seems like a paradox to me.

I don’t see either as being dependent on the other. In other words, you can believe in God and not in extraterrestrial life. Many religious people do in fact hold that view. On the other hand, you can believe in extraterrestrial life and not believe in God. I know many people who hold that view.

So I don’t see a paradox at all. According to the Google dictionary, a paradox is “a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.” I fail to see a contradiction that two different people can hold either view. It’s all theory.

In reality, we do not know for sure that life exists anywhere other than Earth because we have never found any evidence of life, although we continue the search. We have yet to find even a fossil of a microbe from space. However, the laws of mathematical probability suggest that with billions of planets in this galaxy and billions of other galaxies, it is likely that there is at least microbial life somewhere, if not something more advanced. We just haven’t the proof yet.

Similarly, except for subjective experiences, there is no proof that God exists either, although people believe that God exists. Maybe both exist. Maybe neither exists. I suppose it’s a question of faith in either view.

Do aliens come on Earth or Mars and we sometimes see them and sometimes not?

No alien that we know of has ever come to Earth.
As far as not seeing aliens, some aliens are microbes. Probably most are microbes. It’s hard to see microbes without a microscope.

Using our current technology, how close to us would an alien spacecraft have to be before it could detect Life on Earth?

During Earth’s night you can see the lights of major cities from the moon. So this would imply that further out from the moon one could detect light. Then there are the radio and television waves. They go out infinitely into space, but they become four times weaker every time the distance doubles. In any case, we pick up radio signals from Voyager I and II even though they have left the solar system, so I would suppose people could pick up our radio signals quite far away.

If aliens in our galaxy are exponentially super advanced, why have they not completely colonized the entire Milky Way by now?

Well, let’s not put the cart before the horse. Right now we don’t know for sure that any life exists anywhere other than Earth. We suppose it does by mathematical calculations, but we haven’t even found a fossil of a microbe from space.

Secondly, suppose there is some super advanced civilization (your use of “exponentially” doesn’t seem to make any sense), the reason they probably haven’t completely colonized the entire Milky Way Galaxy is that for them, as for us, the laws of physics make it pretty much impossible to achieve interstellar travel because of the vast distances involved. And even if they could colonize some surrounding systems by now, it would take light and radio waves 100,000 years to reach us from the other side of the galaxy.