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starship-design: Even less Fun with Spacetime
Never mind the fact that I don't believe this BUT, try this from the internet:
You're standing on Earth as I go by in my rocket. When you look at my clock,
you notice that it's running slowly because time runs slowly in my reference
frame. When I look at your clock, what do I see? Is your clock running slow,
fast, or right on time?
Score yourself a "good try" point if you said that I see your clock running
fast. But don't get too excited, because the actual answer is: I see your
clock running slow. Just like you see my clock running slow.
That's right, it was something of a trick question. It's the most natural
thing in the world to think that if you see my clock running slow, I should
see your clock running fast. But then you have to ask the question: when I
flew by, who decided that you should be fast and I should be slow? Why not
the other way around? After all, my frame (in which I'm not moving but you
are) is just as valid as your frame (in which the Earth isn't moving but the
rocket is). So, by symmetry, we must see the same thing! If you see my clock
running slow, I have to see your clock running slow!
Which proves I'm right; but it doesn't get us out of the paradox. It still
doesn't make sense for us both to see each other's clocks moving slowly: if
you're still with me, [I am] this should seriously bother you. (If you're
not still with me, take a break and come back. Long paper, complicated
subject.) [I took the break anyway] 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-
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.
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
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?
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
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?
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.
The rest of relativity is a lot like those last two thought experiments,
usually done with enough math to rigorously prove the results that I
"hand-waived" my way through. You can come up with - and explain - more
and more time-dilation paradoxes. Some of your explanations lead to other
bizarre relatavistic phenomena. You can show that length is different in
different reference frames, destroying the classical concept of space;
that mass is different in different reference frames, destroying the
classical concept of matter; and that mass and energy are the same thing,
destroying the classical concept of a winnable war. And Einstein did all
of this, in the first decade of this century. His theory explained what
happens when things go astonishingly fast, just as Quantum Mechanics was
explaining what happens when things get amazingly small. (And Einstein
went on to form the General Theory of Relativity, which explains what
happens when things get incredibly big.) All of this is the wonder of
modern Physics, the lure that drew me and so many others into the field:
concepts which are as far out as any of science fiction or fantasy, are
real, and can be analyzed and discussed intelligently rather than kind
of mumbled about. And now that you have made it all the way through this
paper, you can talk more intelligently about them than most. And maybe -
hopefully - you're starting to wonder what else you can say about them.
[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.