starship-design: Re: Even less Fun with Spacetime

[TLG.van.der.Linden@tip.nl (Timothy van der Linden)]

Lee,

>Never mind the fact that I don't believe this BUT, try this from the internet:

OK, ignoring that you sent this letter to Ken first ;)

<Some text removed>

>Thought Experiment #1: You're on Earth, and I fly by in my rocket as before. 
>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 falls. 

Hmm, try comparing it with a magnifying glass. When I look trough the glass
at you, you look bigger. However when you look at me through the magnifier,
I look bigger.
I measure your thumb by my thumb and conclude your thumb is two of my
thumbs. You however conclude that my thumb is twice as big as yours.
CONTRADICTION! Yet it happens. You just can't communicate through a symmetry
and then compare the results as if you used linear translation.

Relativity does not only create a lens for spatial directions, but also for
time. Like many have written before me, most of us are not used to seeing
time as a "normal" dimension, therefore the implications sound so strange.

>So, as you probably suspected, here is the 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. 

Just like Ken told you, *this* isn't a measurement problem, even if you
magically could read the other person's watch as if it was at your own
wrist, you'd see that it runs slow.


>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 A
>stro 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? 

Yes, just like I wrote in the letter "increasingly less fun with spacetime":

The stationary twin thinks his brother lived slower or equal all the time.
But the moving twin thinks his brother first lived slower, than started
living hyperfast, and finally slower again. However his brother lived
hyperfast more than he lived slower, so the net result is that his brother
lived faster.

BTW. Astro does have multiple reference frames, it just makes things a
little bit harder, but not impossible.

>[I think the author's point here is 1) time is not a constant, and 2) all 
>frames of reference are identical just as Zenon said. Unfortunately, the 
>frames part is very hard to grasp, so much so that I still have a hard 
>time accepting this after 30 years.

Good explained examples can do miracles in teaching. I hope that some of
what I wrote you and the group may at least start some candles burning.

Timothy