Harry Turtledove actually takes this idea for his “Worldwar” series, where aliens show up with what is essentially circa 2000 AD technology (they’re *very[./i] conservative, so even though they have interstellar ships, their weapons technology isn’t more advanced than it needs to be) in a WWII world. Human scientists know that these bits of silicon are doing the same things as their vacuum tubes, but they can’t figure out how.
But the mere existence of such things gives them enough information to keep plugging.
There is a lot of difference between keeping the goal of the Manhattan Project secret for a few years and keeping secret since 1945, or whenever it was, the existance of alien beings flying around or the secret of super-duper US flying machines.
In the former case the likelyhood of the beans not being spilled is vanishingly small and in the second case such machines would have been under develpment for 60 years with no operational machines as output.
Keeping a secret is inversely proportional to the amount of people keeping that secret.
Do I think the government can keep a secret?
Depends on what you define as “the government”.
Do I think 4 government officials can keep a secret among themselves? Sure.
Do I think dozens and dozens of military officials, armed guards, and politicians can keep a secret for over 45 years just because they are sworn to secrecy and threatened with their lives? Hell no. It’s just way too easy for someone to leak anonamously or leave some info for others to find when they pass.
People seem to forget the “the govenment” is made up of actual U.S. citizens. Not a bunch of mystery men who are out to get the public and hide secret stuff from them.
You’re forgetting something. All technology is rapidly developing it’s own version of Moore’s Law. The rate of change varies between technologies, and the amount of resources being devoted to the improvements, but we’re rapidly doubling our knowledge on everything, so FTL may not be a million years out, it may only be a thousand or less.
Since we’ve got no idea of what form an FTL drive might take, it’s difficult to make an accurate guess as to how long it would take for us to puzzle it out. However, just knowing that it can be done would be a big boost for us. Additionally, the laws of physics, as far as we know, work the same everywhere. So we’d be able to puzzle out a great deal about the technology, even with our limited knowledge. Once we’ve got that mastered, will be able to sort out the rest of it eventually.
The first thing we’d do, I’d wager, is puzzle out their computer technology. Because their systems would no doubt be faster and more powerful than anything we’ve got. Once we had that cracked, and were able to program it with a language we understand, then we could work out the rest of their technology in no time.