Placeholder Image

Subtitles section Play video

  • 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,

  • this video's sponsor.

  • Brilliant is based off the principle that active problem solving is the fastest path

  • towards mastery of a new concept or skill - and now they've taken it to the next level

  • with tons of visual interactivity across their math and science courses.

  • You can interact with the math of gears and pulleys and computer programming and the pythagorean

  • theorem!

  • To gain a deeper understanding of science and mathematics and to sign up for free, go

  • to

  • The first 200 people will get 20% off an annual Premium subscription with full access to all

  • of Brilliant's courses and puzzles.

  • Again, that's - and thanks to Brilliant for their support.

uppose there are two spacecraft attached by a very long thin string.

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

B1 spacecraft string contraction length object brilliant

The Rocket & String Paradox

  • 14 1
    Summer posted on 2021/08/18
Video vocabulary