starship-design: More fun with Bright and Dwight

["L. Parker" <lparker@cacaphony.net>]

This came from the web...

When you have a paradox that won't go away easily, you design a thought experiment to look at that paradox as closely as possible. Then either the paradox goes away, or you have a good disproof of the theory. So let's look more closely at this both-of-us-see-each-other's-clocks-going-slow business.


Thought Experiment #1: You're on Earth, and I fly by in a rocket. Right as we pass each other, we both start our stopwatches. When your stopwatch says that one minute has passed, you check my stopwatch. Because I'm in a different frame, my watch is running slow: it only says thirty seconds. 

Now let's play that exact situation back from my frame. You looked at me after only thirty seconds; but your clock was running slow, so it said only fifteen seconds. CONTRADICTION! We agree that when you looked at me, my watch said thirty seconds: but did your watch say fifteen seconds (as I thought), or sixty (as you thought)? So we have taken what we intuitively felt made no sense, and exploited that to come up with a paradox that will test relativity: if there isn't a way out of that paradox, Relativity fails. 

So, as you probably suspected, there is a way out of the paradox. The problem, as with most of modern Physics, comes in making the measurement. Suppose that when I passed you the first time, and we synchronized our watches, we were right next to each other. That means that sixty seconds later (your frame), when you checked my watch, I was a long way away. How do you look at my watch a long way away? Your eyes take in light that bounced off it; your ears take in sound coming from it; whatever you do, you're using something that travelled from me to you. And it took time to do it. 

The point is, you can't say "I'm looking at his watch now." You have to say "I'm looking at light that came from his watch a while ago," and I have to say the same thing when I look at you. So when you and I are in different places, whatever we see about each other is old news. And we have to take that into account when we say "This is what I'm seeing on his watch," admitting that this is simply what his watch used to say. When we take that into account, we can plug through the math of Einstein's equations and we wind up without a paradox. 

Well, that was a sneaky way out. Looks like we can't disprove Relativity unless we can make measurements from the same place, at the same time, twice! Which we clearly can't do if one of us is moving, right? 

Well ?

[L Parker] I think this is one of the reasons that Einstein disliked QED, IT CAN provide a method for instantaneous, simultaneous measurement at a distance, and I'm sure he suspected it...back to the story:

Thought Experiment #2: The Paradox of the Twin. When paradoxes have their own names, they tend to be pretty simple. So it is with this one; the Paradox of the Twin is actually simpler than the experiment I discussed above, although you will see how it comes in response to that one. 

Two twin brothers, Astro and Clay, bid a tearful farewell as Astro journeys into space. Astro is gone for twenty earth years, but because he is moving so incredibly fast, his clock is running very slowly and only a year passes in his own frame. When he returns, Clay is gray-haired and wrinkly, while Astro is still young and healthy. Based on Relativity, it makes perfect sense to say that less time passed for Astro because his clock was running slow. But then you can ask, what happened from Astro's perspective? He wasn't moving, and Earth was; so Clay's clock was moving slowly; so shouldn't Clay be the young one? CONTRADICTION. Think about that for a while. Does Einstein have a way to wriggle out of this one? 

As before, yes, he does; and yes, it's sneaky and weird. Astro doesn't have a reference frame. You can't look at things from his perspective, because he turned around in mid-flight. I mentioned earlier that an inertial frame means one which keeps on travelling at a constant speed. When Astro turned around; when he lost his stomach because the rocket was suddenly stopping and starting up again in the other direction; he should have realized that he was now in a different inertial reference frame from the one he started in. So all bets are off, as far as Special Relativity is concerned. Clay's perspective tells the true story, and for Astro to calculate his brother's age, he has to take his reference-frame-change into account in his calculations. When he does, he will get the same result Clay got: young Astro, old Clay.

[L Parker] This is the flaw with Ken arguement as Timothy points out. The theory depends on an inertial frame and does not hold up for non-inertial frames...

Lee Parker

"This double nature of radiation (and of material corpuscles) is a major property of reality, which has been interpreted by quantum-mechanics in an ingenious and amazingly successful fashion. This interpretation, which is looked upon as essentially final by almost all contemporary physicists, appears to me as only a temporary way out."

Albert Einstein