What does Judaism say about the Discovery of Aliens?

Congratulations. One of the best responses given on any site here on Chabad.Org.

The danger that I see is that we are easily distracted from worshiping G-d as evidenced by the technology and the celebrity status of some here on Earth, could you imagine if we actually made contact with E.T.s? There's so much idolatry as it is. Remember there are terrestrial beings in the spirit realm that would have us break the 1st through 5th commandments.

Who knows? Maybe. If so, I'd like to meet one! I would ask questions about spirit, their lives, their belief system and why there came here, etc.
Let's assume that if they are advanced enough to make it across time and space to come here, then they are also evolved enough to let us evolve in our own way, as well..
Personally, I'd go to their home planet incognito and just watch them!

Archic information - after all, there was little or nothing of Quantum Physics at that date.
Try some more up-to-date papers - there's plenty to choose from in the "reputable" scientific world.
Also note "THEORY" or Relativity, NOT "LAW" of Relativity.

to all other inhabited planets. I didn't know that was in our scriptures. AWESOME!!! Cool!!!

Please, please, please study the actual works of Einstein rather than other people's take on what they THINK he said. (or what they want you to believe he said).
After all, the issue of rotation (it is impossible to prove which body is revolving around which) is correct if, and only if, there are two and not more than two objects in existence. The addition of a third (assuming a 3 dimensional universe) makes mapping possible and by the application of simple scientific and astronomical rules, it becomes simple in the extreme to ascertain what rotates about what.
This stems from the fact that science teaching in most schools doesn't go far enough for people to understand Einstein's theories themselves. People are reliant on others - often with their own agenda - providing disservice and deliberate misinformation to the public.

I don't understand why there should be aproblem at all for 2 reasons 1. science only makes hypotheses ,and 2. with Einsteins theory of relativity it is impossible to prove which body is revolving around which.
p.s. Why the extreme conviction in disproving the Bible!

"Fear before him, all the earth: the world also shall be stable, that it be not moved."

All this passage is telling me is that the earth is to last for a long time; it is not "to move" - go away or be destroyed.
when I think of something stable I think of something that doesn't change much with the passing of time. Life itself can be stable; one can stay in one place (not change, not develop). That doesn't mean that time doesn't go by and life doesn't expire.
So, we go back to what I just stated: The Bible is full of symbolism which can be interpreted to ones interest.
It is obvious that I don't read the same verse the way Stephen does, and that's fine, as long as we don't poke one-another's eyes out!

I am fascinated with the idea of life on other planets. The very same vastness of the Universe which makes foreign life so likely also makes contact with it unlikely because of the distances between stars. I would imagine that if there are beings who are designed or who have evolved with big enough brains like ours, that they might have religion, too. Who's to say we're the smartest anyway? There might be beings who are smart enough to be far more pious than we are.