FTL Travel: The Matryoshka Paradox

[Sirius_Prime]

TL;DR Summary

If the energy needed to accelerate is always the same for a resting object, can ships stacked into each other reach FTL speeds by considering their carrier a resting position?

Okay, so, I hope you all have patience with me. I didn't study physics but enjoy reading and theorizing, so I'm familiar with many concepts but not with the formulas.

The thought occurred to me when I was considering that when traveling along with an object you only need to expend enough energy to accelerate *relative* to the object. So if you are on a moving train, on a moving planet, in a moving solar system, in a moving galaxy, you are still exerting as much force to move to move as you would have if nothing of the above mentioned was moving. If I recall correctly, this was due to inertia.

So, let's say we have a bunch of ships that are carriers for carriers for carriers to the Nth degree. Just like the famous Russian Matryoshka doll. The biggest ship with all the other ones inside starts from the planet's orbit and accelerates to 10% of the speed of light relative to its starting position. Then, once it reaches it, the 2nd biggest ship launches. Now, it moves at 10% of the speed of light but should not affected by it, just like we on Earth aren't affected by our solar system's movements while on the train. It also accelerates to 10% and launches the next ship. So on and so on and so on.

Now, they all only move at 10% of the speed of light relative to their starting, resting position, which should be possible. However, eventually they would be moving away at >100% of the speed of light relative to the planet all these ships started from.Ignoring the debris and particles and assuming they would be moving in a perfect vacuum (or have some shielding to neutralize / ignore the particles they hit), what would be preventing them from achieving what is effectively FTL travel?I asked similar questions in other places and usually the responses circled around some mysterious observer. But the actual distance traveled should not be reliant on the lack or presence of an observer once they arrive at their destination and stop relative to the initial starting position, right?In any case - thank you for your time and reading this. I'm sure it sounds silly to people who studied the subject for years or even decades, but it just has been bugging me as I never found an actual explanation.

 

[PeterDonis]

eventually they would be moving away at >100% of the speed of light relative to the planet all these ships started from.

No, they wouldn't, because velocities do not add linearly in relativity. You have to use the relativistic velocity addition formula:

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

If you check the math, you will see that, relative to the planet all the ships started from, the speeds of the ships will approach the speed of light more and more closely the more ships you have, but will never reach it.

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[sophiecentaur]

Summary:: If the energy needed to accelerate is always the same for a resting object, can ships stacked into each other reach FTL speeds by considering their carrier a resting position?

you only need to expend enough energy to accelerate *relative* to the object.

You have to leave your intuition behind for this. It's only been about a hundred years since this started to be understood and our 'intuition' is based on the experience of thousands of years.

When the guy on the final ship in your chain measures the speed of light on board he will get exactly the same answer as he did when he started this Russian doll exercise. This will be the same in whichever direction he does his measurement.

Obvs, when the people on the launch pad observe and measure his speed, he will be going pretty damn fast (depending on how much money they spent) and there may even be a bit of Red Shift. This would assume that the process didn't take many Earth generations i.e. the time to reach that final speed (plus the light years for the signal to get back). Any longer and the Taliban (or equivalent) could well have taken over and destroyed the Earth station. (It's my personal opinion that Science may not, in fact be immortal so there has to be a limit on any predictions of possible advances in knowledge.)

 

[Sirius_Prime]

No, they wouldn't, because velocities do not add linearly in relativity. You have to use the relativistic velocity addition formula:

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

If you check the math, you will see that, relative to the planet all the ships started from, the speeds of the ships will approach the speed of light more and more closely the more ships you have, but will never reach it.

Alright, so does that mean that since the Milky Way is moving at ~580,000 m/s we would have it marginally easier accelerating in the opposite direction?

When the guy on the final ship in your chain measures the speed of light on board he will get exactly the same answer as he did when he started this Russian doll exercise. This will be the same in whichever direction he does his measurement.

Sooo all the ships he started from would be basically still floating next to him since he couldn't accelerate past 10%?

 

[sophiecentaur]

Sooo all the ships he started from would be basically still floating next to him since he couldn't accelerate past 10%?

How do you come to that conclusion? He's still leaving the other ships behind and their apparent speeds, relative to him, are greater for the first ships in the chain. Like I / we have said, relativistic life is not like low speed life. You have to 'follow the rules' and not try to come to your own conclusions on the basis of the limited amount you have learned or accepted about this.

 

[PeterDonis]

does that mean that since the Milky Way is moving at ~580,000 m/s we would have it marginally easier accelerating in the opposite direction?

No. Speed is relative. The Milky Way is moving at that speed relative to some particular thing, but how hard it is to accelerate an object has nothing to do with how fast it is moving relative to some particular thing.

Sooo all the ships he started from would be basically still floating next to him since he couldn't accelerate past 10%?

No. Each ship sees the ship before him moving, relative to him, at the same speed, 10% of the speed of light. But ship number 100, for example, will not see ship number 1 moving relative to him at 10 times the speed of light (10% times 100). He will see ship number 1 moving relative to him at a speed very, very close to the speed of light.