4 ms·

OK, try this one: Lt Cdr Worf is testing the USS Defiant's impulse engines after a refit. He is currently coasting along in a straight line at a constant 0.6c,

by dghf 5y ago

OK, try this one: Lt Cdr Worf is testing the USS Defiant's impulse engines after a refit. He is currently coasting along in a straight line at a constant 0.6c, and passes Deep Space Nine. We'll call time on board the defiant t and time on board DS9 t', and say that the Defiant flies by DS9 at t = t' = 0. At t = 10 minutes, Worf decides to reward his efforts with a cup of bahgol, only to discover the replicator is on the blink. After about another 10 minutes of pressing various buttons, he gives up and logs a ticket with the DS9 help desk over the subspace network. Because the Defiant is travelling in a straight line at a constant speed of reference, it is in an inertial frame reference, and it is just as valid to see DS9 as moving away from the Defiant at 0.6c as the other way round, and this in fact is what we must do to work out what time on DS9 corresponds to "now" on the Defiant. At 0.6c, the Lorentz factor is 1.25: so for every 1.25 minutes that passes on the Defiant, a single minute passes on DS9 -- or put another way, for every minute that passes on the Defiant, only 0.8 minutes pass on DS9. So when Worf submits his ticket at t = 20 minutes, on DS9 it's t' = 16 minutes. Subspace comms are instantaneous, or so close to it as makes no difference, so O'Brien picks up the ticket very soon after t' = 16 minutes. He replies straight away -- "Have you tried turning it off and on again?" -- and sends the response back over the subspace network. This is where relativity of simultaneity comes in. DS9 is also in an inertial frame of reference, and in that frame it is the Defiant that is moving away at 0.6c, that has a Lorentz factor of 1.25, and where only 0.8 minutes pass for every minute on DS9. So for O'Brien, t' = 16 minutes is simultaneous with t = 12.8 minutes (not t = 20 minutes): allowing for time for O'Brien to read the ticket and write his response, Worf will receive it somewhere around t = 15 minutes -- while he's still tinkering with the replicator. Somewhat surprised, he tries the solution, it works, and he goes off to enjoy his cuppa, never sending the ticket he's just received a response to. This is why FTL risks messing with causality.

Andrew_nenakhov 5y ago
Thank you for this elaborate answer, but this does not seem right. I am not very well versed in the StarTrek lore, but they use warp drives, which are alcubierre drives, so they expand and fold space to move, thus never actually achieving an FTL speed themselves. If we don't move at relativistic speeds, there would be no time dilation effects, so we'll always have t == t'. Next off, I feel that this backwards inertial frame of reference is not right. But I'm too lazy to get into actual math so let's put this matter to rest until we get means of FTL travel or information transfer.

by dghf 5y ago

Andrew_nenakhov 5y ago

Thank you for this elaborate answer, but this does not seem right. I am not very well versed in the StarTrek lore, but they use warp drives, which are alcubierre drives, so they expand and fold space to move, thus never actually achieving an FTL speed themselves. If we don't move at relativistic speeds, there would be no time dilation effects, so we'll always have t == t'. Next off, I feel that this backwards inertial frame of reference is not right. But I'm too lazy to get into actual math so let's put this matter to rest until we get means of FTL travel or information transfer.