# Special Relativity, Time Dilation and Speed Changes

This is from someone relatively clueless, so please forgive any stupidity in the question...but.

The Twin Paradox indicates that for the person who is travelling near the speed of light, speed and distance are dilated/compressed.

To the people in the ship, they would - from their perspective - be moving significantly faster than their actual speed, as they are completing a 2-year journey in 18 months.

My question is in regard to their fuel and how they'd change their velocity.

If you were to fire a thruster to produce 9.8m/s of deceleration (from the crews perspective) when the ship is at maximum speed (for example, where time dilation is at a 2:1 ratio), what would be the effect relative to an observer at the origin or destination of the journey?

Would a 1 second burn at 9.8m/s from the crews perspective equate to a 2s burn at 4.9m/s from the perspective of someone at the origin?

So all of your timings for acceleration/deceleration would need to compensate for time-compression (ie. if you could accelerate for the first half of a trip and decelerate for the second half of a journey that is 2 years from the origin/1.5 years for the crew, your 'flip' would be timed 9 months into the trip, as it would be performed on-board)?

And of course the fuel requirements for the course corrections would have to adjust for the effective mass of the ship, which will become higher as you approach the speed of light.

So from the perspective of someone at the origin or destination, the acceleration of the incoming ship would appear non-linear when at extremely high (near light-)speeds, even though it would be linear from the perspective of the crew.

• Your 3rd paragraph has a basic misconception. The people on the ship would perceive their speed to be the same as that measured by those observing them (apart, perhaps, for a minus sign). In the standard 2-frame S and S' configuration the relative speed must be the same for both frames, by symmetry. The time they measure is shorter by a factor $\gamma$ but the distance between start and finish is also shorter by a factor $\gamma$ Commented Jun 8, 2022 at 13:37
• This question should help you understand how to think of acceleration in the twin paradox (especially John Rennie's appendix). physics.stackexchange.com/questions/242043/… Commented Jun 8, 2022 at 17:36

To the people in the ship, they would - from their perspective - be moving significantly faster than their actual speed, as they are completing a 2-year journey in 18 months.

Laypeople in the ship would see milestones passing by at high rate, which would cause them to say: "We are moving fast".

Physicists in the ship say: "Milestones are moving at speed close to c, and distances between consecutive milestones are short, this means that the destination arrives here soon".

If you were to fire a thruster to produce 9.8m/s of deceleration (from the crews perspective) when the ship is at maximum speed (for example, where time dilation is at a 2:1 ratio), what would be the effect relative to an observer at the origin or destination of the journey?

Would a 1 second burn at 9.8m/s from the crews perspective equate to a 2s burn at 4.9m/s from the perspective of someone at the origin?

According to such observers inertia of rocket is eight times larger than inertia of same rocket at rest. So they observe deceleration 1.225 m/s^2.

So all of your timings for acceleration/deceleration would need to compensate for time-compression (ie. if you could accelerate for the first half of a trip and decelerate for the second half of a journey that is 2 years from the origin/1.5 years for the crew, your 'flip' would be timed 9 months into the trip, as it would be performed on-board)?

Yes.

And of course the fuel requirements for the course corrections would have to adjust for the effective mass of the ship, which will become higher as you approach the speed of light.

According to rocket crew rocket motor needs to run 18 months at normal fuel consumption rate.

According to launchpad crew rocket motor needs to run 24 months at abnormally slow fuel consumption rate.

So from the perspective of someone at the origin or destination, the acceleration of the incoming ship would appear non-linear when at extremely high (near light-)speeds, even though it would be linear from the perspective of the crew.

Yes. According to someone at the origin or destination inertia of the accelerating rocket changes. Thrust of rocket stays unchanged according to everyone.