[ExI] spaceship string theory

[Lee Corbin]

Jef writes

> I just realized that while Damien and Stefano appeared to agree with
> my intuitive model, they apparently reached the opposite conclusion
> from my own.  I thought initially that they were both being ironic.
> 
> My point was that we have NO evidence of such disintegrative effects
> (or their cousins) at any fraction of c, despite many experiments,
> albeit with objects much less massive than spaceships.  My conclusion
> was that the string would quite obviously NOT break, despite
> observation from a different inertial frame showing the distance
> increasing.

You're quite wrong, though I don't blame you for not understanding
the rather awful (IMO)
http://grenouille-bouillie.blogspot.com/2007/10/how-to-teach-special-relativity.html

> It seems to me as simple as pointing out that the multiple spacecraft
> and their strings form a single system within a single inertial frame of
> reference.

True enough, and I commend your courage in going up against all
those web references. It's also unsatisfying to be told the bald
truth:  when you draw the hyperbolas for constant acceleration
on a space time diagram, and the new x'  (x prime) axis
(representing a line of simultaneity) is at an angle to the old one,
the intervals along x' where the hyperbolas cross are more separated.

But the only way to compute that for sure that I know about is
to compute the spacetime interval along the new x' axis.
(This spacetime interval is however---since that x' axis is a line
of simultaneity for the spaceships once they've reached a
constant velocity (which is easiest to think about)---at that
point the same as distance so far as they're concerned).

But that hardly helps the intuition.  Here is what I wrote to an
offline correspondent concerning this:

My friend asked:

> [Say there is] a single ship 210m long, with engines a bit over halfway 
> along at the 110m point, and engines at the back. You seem
> to claim  that at some point the ship's hull will be ripped apart.

And I replied:

[Yes, that's correct, the ship's hull will be ripped apart.]
The key point, all right---you've put your finger exactly on it!

> What??? I can see that if it's dragged forward by a massive gravity
> field, and tidal effects pull more fiercely on the bow than the stern.
> But not when the ship is in deep space. And if it does happen that
> way, why only get torn apart in the middle, rather than at numerous
> places along its length? Thus my intuition can't cope.

And so I concluded my explanation to him with this:

The last part is easy:  the powerful engines are mounted only at the
back and at the half-way point.... [though babbling about spacetime
diagrams and hyperbolas of constant acceleration] doesn't help
the intuition one bit.

But I think this does help:

First, though, mount a ceiling clock in your living room, and
suppose that it's incredibly accurate, just as your wristwatch is.
Presently, the ceiling clock appears to you to be running fast.
There are two reasons for that. The first (less satisfying one)
is that it's further out of the Earth's gravitation field, and clocks
run faster there. Being stuck in a gravitational well causes
clocks to run more slowly. 

The more satisfying explanation of the clocks is to use the Equivalence
Principle, and to assert that you, your wristwatch, and the ceiling clock
are perhaps aboard a spaceship accelerating at one gee. Einstein's
great [General Relativity] breakthrough was to assume that no experiment
you can perform locally can tell the difference.

Now one grants that the ceiling clock certainly *appears* to be running
fast. That's because when it emits photons you move towards them
at an accelerated speed and catch up to them faster than if you were
merely traveling at the same speed as they were when they left the
clock. So as the minute hand strikes 12, there is a delay while its
photons come down to you, but after you do the measurement (which
takes that into account) you have to reach the conclusion that that
clock is running fast. (Naturally, this does not mean that you measure
the velocity of the photons as faster than c---no, because you are now
traveling faster in the forward direction than the ceiling clock was
emitting them, and so you're suffering a bit of time dilation with the
consequence that you measure the photons going only at c.)

But this goes on hour after hour, and in your *measurements* as 
well as *observations* that ceiling clock simply *is* running faster.
The ceiling clock is indeed objectively running faster, just as clocks
in space actually run faster than they do here on Earth.

So I'll be a bit fanciful with the language now for my own amusement.
Let's suppose that these ships are all ships of the Linebarger, and you
are the stop-captain [people familiar with the works of Cordwainer
Smith may appreciate SF references, but it has no bearing on the
logic here] who has been drafted for unusual duty: you are
to manage the rear engine, while the go-captain is in the forward
compartment managing the mid-point engine. At any short moment
when you study the two clocks, you must conclude "The idiot go-
captain's clock has been running fast (and forgetting that you guys
accelerated together according to the original orders and original
logs) from what you see now---even though let's say you've reached
constant velocity---he must have jumped the gun when he took off!
He must have, since his silly clock is running fast. Just looking at his
clock (which must show the same time as your ceiling clock),
affirms this. Since the atomic engines are so very powerful, his
premature departure must be what ruptured the vessel, and he's
further away from you than he's supposed to be.

(Not only that, but since the space-buoys that you pass seem
closer together than they're supposed to be (because of the
contraction of things moving relative to you) even from that
perspective he's too far along. He's passing space-buoy #96
instead of space-buoy #92 as he should be, further indication
that he jumped the gun.  I don't know whether this parenthesized
paragraph really adds to the explanation or not, I admit, but there
might be some potential here. I'll think about that.)

So the go-captain and his top half of the space ship are separated
from you, more or less proportionally to the speed you've obtained
relative to the solar system and space buoys that are passing by
(although from your laboratory measurements, it's they which
are moving, not you and the other captain).

What puzzles me is that I don't know if your ceiling should appear
closer to you than the ship's architecture designs specify. It probably
does---or at least did while the spaceship was accelerating. And
the explanation is mechanical: the thrust affects you before it gets
transmitted along the beams of the ship to the ceiling, and the
beams are under compression. Since signals can only go as fast
as light, if you move your end of a steel rod here, the far end
only moves later. But here appearance is reality: I believe that
you measure the distance to your ceiling as a little short. But
won't that mess with the measurement of the ceiling clock's
retardation?  So this paragraph too may be a bit suspect.

Of course you *remember* that the go-captain took off exactly
when you did, and then gradually the stress along the ships
beams increased, and then there was the rupture. But your
relief captain who slept through the whole acceleration phase
now finds (a) the ceiling clock is running ahead  (b) the
go-captain's clock in the separated front half of the ship
is even more in advance. 

I think that this helps explain it, and perhaps "explains" why the
hyperbolas (of constant acceleration) on a spacetime diagram
are further apart when you look at them along a new space
axis that's inclined to the old one.

Lee