Is Faster-Than-Light Travel or Communication Possible? (1997)

Thanks for not turning it into a fight! (And I apologize for my contentious tone; I was inappropriately gearing up for battle there.)

I thought you might be thinking of Bruno, the scientist who really was burned at the stake; it's a good thing for everyone that this wasn't for his science. (Of course, it would've been better if people weren't burned at the stake in general. Certain modern elements have reminded us of how painful a death that was...)

I also learned a few things about Galileo from Biography Base's article on him; thanks for that link!

The more I learn about that case, the less it sounds like Religion versus Science and the more it sounds like a conventional miscarriage of justice. A frail, sick, stubborn old man should never have been treated like that, even though he did call the Pope a simpleton. The Pope is the Pope, and has certain standards to maintain; it doesn't reflect well on Christ when His Vicar abuses the courts to make trouble for people who insult him.

It seems implausible that all of the aliens would agree to ignore us, even less so for them to consistently arrive at that conclusion in an independent manner. Then again, Earth might be exceptionally boring and consistently uninteresting to spacefaring aliens. Who knows? Maybe life is really rare.

Ah, good observation! But what you're describing isn't relativistic time dilation. It is called "the (non-Relativistic) Doppler effect", and can be commonly experienced when a race car, an ambulance, or a train passes you: When it's approaching, the noise will have a higher pitch than when it's passed. This is because the frequency of things that move towards us appear higher than they are, and that of things that move away from us appear lower. It's also why stars that move away from us appear more red than they are (they are said to be "red-shifted").

Imagine the same scenario you described (there's actually no need to use faster-than-c speeds for it), but your friend has planted clocks all along the path that you're traveling. Once he's back at his starting position, he synchronizes them all (there are techniques to achieve this - Einstein famously proposed one). Now when you pass him and keep moving away from him, every second you take a picture of your own clock next to the clock planted on the path. In a non-relativistic world, the pictures will show that your clock is always synchronized with all of your friend's clocks. Making the observation this way rids us of the Doppler effect.

But a non-relativistic world isn't the real world! In reality, if you go fast enough (close enough to c), the pictures will show e.g. your clock marking 12:00:01 when the clock in the path marks 12:00:02. And your clock marking 12:00:02 when you encountered the next clock in the path marking 12:00:04. In other words, your friend (and everything that's stationary with respect to him) will measure your time passing more slowly. Using these example numbers, in what for them is the pass of 2 seconds, you (and everything moving at your same speed - like your clock) have only aged 1 second. This is relativistic time dilation. It's shocking, but it's a fact that's been established for 110 years (and its mathematical consequences help explain even the microelectronics you and me are using). Now this happens no matter what speed you move with respect to your friend. But for everyday speeds it's so small as to be imperceptible - it only becomes noticeable at speeds like that of GPS satellites.

An immediate question is:

> Wait, if I move away from my friend, from my point of view my friend is moving away from me. So I should measure his clocks advancing more slowly than mine.

And that is correct, and is exactly what would happen!

> But the pictures I took show the opposite?

No! They show your clock compared to different clocks. And these clocks on the path, that your friend synchronized, by your measurements they all started at different times. I.e. for you, none of these clocks are synchronized. For your friend, they all marked 12:00:00 simultaneously. For you, they all marked 12:00:00 at different moments. In non-relativistic physics, simultaneity was an absolute concept: If two things happened at the same time, they happened at the same time for everybody. In reality, if I'm moving with respect to you, what happens at the same time in different locations for me, doesn't happen at the same time for you.

Which is negative when it comes to FTL...