uppose there are two spacecraft attached by a very long thin string.
If both craft suddenly accelerate the same amount at the same time, they should stay
the same distance apart.
Except, now they’re moving... and in our universe moving objects undergo length contraction
and get shorter in the direction of motion.
The spacecraft and string should each have their lengths contracted, and be shorter.
So do the spacecraft and string as a whole contract, with the two spacecraft closer to
each other?
Or do the spacecraft individually contract but stay separated the same amount, while
the string shortens & risks snapping?
Assuming the string has no significant strength, the spacecraft shouldn’t move any differently
than if there were no string at all - and since they both underwent the same acceleration,
they should stay separated the same as when they started.
Which means when the string shortens, it must snap.
But how?
Is length contraction a real, physical, force?
Yes, yes it is - from a certain point of view.
The electromagnetic forces which hold the string together undergo length contractions,
too, and so the very atoms and intermolecular separations within the string are contracted,
literally pulling the string shorter - or tearing it apart if its ends are tied to,
I dunno, two heavy spacecraft.
So length contraction makes the string tear itself apart.
But...from another point of view, the string breaks for a different reason.
Because, from the perspective of a moving object, events that used to be simultaneous
no longer are - in this case, from a perspective moving along with the spacecraft's final speeds,
the front spacecraft actually accelerates first, and so for a while is moving away from
the back spacecraft - by the time the back one catches up, the rockets are farther apart
than when they started!
All this is much more easy to keep track of if you use spacetime diagrams to correctly
describe the whole situation (rather than just trying to think about length contraction
on its own, or relativity simultaneity on its own, or whatever).
But the point is, from a moving perspective, it's the spacecraft that snap the string.
OK, so then why don’t the spacecraft tear themselves apart when they accelerate?
If the string snaps, why don't ALL objects explode whenever they move?
Well, that can only happen if different pieces of the object independently accelerate, like
how the two spacecraft each have their own propulsion.
Normal objects aren’t like that; instead, one part is pushed or pulled, and then the
intermolecular forces in the object transmit that acceleration to the other bits of the
object.
And when those intermolecular forces experience length contraction, the object as a whole
simply contracts instead of being torn apart.
But any time there are multiple sources of acceleration on multiple parts of an object...
in principle it could get torn apart by length contraction.
Or you might say perhaps it gets torn apart because those different parts start accelerating
at different times.
It depends on your point of view - literally.
In our universe, it’s not just space and time that are relative - in some cases, it’s
also whether you’re torn apart, or tear yourself apart.
In putting together this video, it was really helpful for me to work out the spacetime diagram
for bell's spaceship paradox myself - and that's exactly the idea behind Brilliant,
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