The red dots shown below, are RF transmitters.
Clocks are located nearby each of these RF transmitters.
All spaceships are identical and thus have identical rocket engines.


Assume that all 4 spaceships were originally close together and during this time they synchronized their clocks. Next, they moved the spaceships apart such that each spaceships RF transmitter, the red dot, is positioned 300,000 km horizontally and vertically from two other spaceships. Crisscross distances between A and D, and, B and C, therefore become 424,264 km each.

Once in these positions, they send RF pulses to each other at preplanned times. As expected, the spaceships positioned 300,000 km apart receive the RF pulse 1 second after the preplanned pulse release time. From A to D, and B to C, they measure 1.4142 seconds pass to receive the pulse, just as expected. So all the clocks seem to be synchronized, and the spatial distances seem to be verified.

Next, at another preplanned time, all spaceships fire their identical rocket engines and maintain a preplanned acceleration G-force until reaching 260,000 km/s. At this speed, the engines are shut down and thus the velocity of 260,000 km/s is maintained.

Question: Will everything seem the same, meaning from their point of view, will pulses sent from ship to ship give the same results as before, meaning the 1 second and 1.4142 second results ?

  • 1
    $\begingroup$ This is Bell's spaceship paradox. During acceleration spaceships C and D will recede from A and B respectively and when they shut engines off they will be further from each other than before acceleration. Also, clocks C and D will be out of sync with clocks A and B. researchgate.net/publication/… $\endgroup$
    – user139020
    Commented Feb 9, 2017 at 9:09

1 Answer 1


After the engines are shut off, they will still be at rest relative to each other, so it will look exactly the same as before. Even before they fired their engines, they were traveling at great speed relative to other galaxies and this is no different. Stuff that is at rest relative to each other and not too distant from each other will always look Newtonian. (Too distant is hand wavy, but one light second should fine.)


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