[ExI] QT and SR

[Lee Corbin]

John Clark writes

> You're not screwed. I think you would agree that if relativity is
> consistent and the string breaks in one point of view it must break in
> them all.

Yes, but that does not address the heart of the mystery.
I need to go dig out that excellent paragraph you wrote which I
vividly remember as a complete explanation (much better than
my own earlier and longer one).

> So let's forget about the string for the moment and just imagine
> observing 2 distant spaceships at rest relative to you in the night sky
> 90 degrees apart. Suddenly at the same instant (from your point of
> view) both start accelerating to the same very high speed in the
> same direction. The apparent distance between spaceships does not
> change, but imagine if it did; 90 degrees of the night sky would start
> to contract to a point even though neither you nor any of the trillions
> of stars in that part of the sky changed their motion one bit.
> 
> Obviously it's crazy that now we can only see 270 degrees of the
> universe because of what two distant spaceships did.

Sorry, but I find all this quite baffling. I don't know what some
imaginary decrease in that geometry you describe has to do
with anything. First you say that they're 90 degrees apart in
my field of vision, then they take off in the same direction
(presumably away from me). The apparent distance between
them *does* decrease;  I think you must mean the *measured*
distance (which corrects for distance, relative velocities, light
signal delay, and so on).

> Now forget the spaceships and just observe a string moving very
> fast, it will contract in the direction of motion just like spaceships;
> put these two things together and you can only have a broken string.

Yes, but some readers may wonder why the spaceships don't
break and the strings do. For example, your argument might
be applied to the front end and the back end of a spaceship, thus
suggesting that perhaps spaceships should break too. And the
answer is *not* that it's merely that spaceships are built of
sterner stuff. No, the answer is that the spaceships are independently
powered.  If all the spaceships were on a Union Pacific train each
tied down to its own flat car, the entire train would contract, 
and the strings between the spaceships would not break.

> Although it can be a useful approximation if things don't become too
> extreme there really is no such thing as an "accelerating frame of
> reference".

Right. When people attempt to see what's really going on in
this paradox and they begin to use this phrase, it's a sign that
they should stop right there and see if they can't express
their thoughts in other language.

> For example, an observer on the lead ship will know
> with certainty that he is accelerating and know the direction it is
> occurring, he will note that the following spaceship is keeping up
> with him so it must be accelerating too.

Well, no, that's not correct. According to his *measurements*
(beyond mere observations) the trailing spaceship is not keeping
up with him.

See Part Four of a dialog I just wrote and will post next.
It's how Galileo himself might have understood Bell's
Spaceship paradox, and my entire goal in writing the
essay was to demonstrate on an intuitive level (allowing
not even one equation) why logic dictates that the string
must break.

Lee