Why a silk thread snaps when two ships move in perfect sync
In short: If two rockets accelerate identically in the same direction, they should stay the same distance apart. Yet, a thread connecting them will eventually snap. This paradox reveals that physical objects cannot maintain fixed dimensions when forced into specific paths, as relativistic effects create stresses that exceed their material limits.
In 1959, E. Dewan and M. Beran first described a thought experiment where two rockets start at rest in an inertial frame S. They accelerate simultaneously and equally as measured in S. Because their velocities are always equal in this frame, the distance between them remains constant. At first glance, it seems the thread connecting them should remain intact.
However, the physics of special relativity dictates otherwise. In the rest frame of the rockets (S'), the accelerations are not simultaneous due to the relativity of simultaneity. Since the thread is a physical object held by electrostatic forces, it maintains its rest length and cannot stretch to accommodate this growing gap.
From the perspective of the original frame S, the situation is viewed through length contraction. While the distance between the ships is fixed, the thread itself must contract as it gains velocity. Because the thread is prevented from contracting by its connection to the ships, it experiences intolerable stress and eventually reaches its elastic limit. This demonstrates that objects constrained to move with fixed dimensions relative to an inertial frame will experience relativistic stresses.
The paradox remains a subject of nuance. While most agree the string breaks, some physicists, like Petkov and Franklin (2009), argue the stress isn't caused by length contraction (which they view as a mathematical rotation in four-dimensional space) but is purely an effect of relativistic acceleration. Regardless of the interpretation, the paradox highlights how electromagnetic fields and the relativity of simultaneity create real physical consequences for moving matter.
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Sources
- Summary by Intellect · source: Bell's spaceship paradox
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