Aging when travelling near the speed of light

[Cyran]

Hi!

If you started a 50 light-year journey at the age of 20, traveling at 99.9% of the speed of light, would you look like 70+ years old when you arrived at the destiantion? How much would you have aged? And how would you experience the time on the spaceship? Would it feel like 50 slow years passing on Earth or would it feel like just a day or two has passed?

Thanks for reading and I hope your answers will make me wiser :)

 

[Nugatory]

Do you mean 50 light-years according to you on the spaceship? You are sitting in your spaceship watching the entire universe rushing past you at 99.9% of the speed of light, and there's something 50 light-years away... It will take 50 years for that something to reach you, and of course you will age by 50 years while you wait (What else could possibly happen while you're waiting for 50 years?).

Or do you mean 50 light-years according to someone on Earth watching you zoom away at 99.9% of the speed of light?

 

[ghwellsjr]

Hi!

If you started a 50 light-year journey at the age of 20, traveling at 99.9% of the speed of light, would you look like 70+ years old when you arrived at the destiantion? How much would you have aged? And how would you experience the time on the spaceship? Would it feel like 50 slow years passing on Earth or would it feel like just a day or two has passed?

Thanks for reading and I hope your answers will make me wiser :)

If before you started, you decided to travel to a destination that was 50 light-years away and you took off at 99.9% of the speed of light, it would take just over 50 years to get there according to the Earth's rest frame. However, time for you would be dilated by a factor of 22.366 so you would age by only 50/22.366 which is 2.24 years so you would not look 70+ years but rather 22.24 years and it would feel like a 2.24 year journey. You would only have to bring 2.24 years worth of supplies, assuming that you could re-supply at your destination.

 

[Ibix]

As Nugatory noted, you have to be a bit more careful about specifying problems in relativity than you were. The reason is that anybody who is not accelerating can consider themselves at rest. That means that for the guy on the spaceship, the planets are rushing along at 99.99% of light speed and both the planets and the distance between them are length contracted. If he says it's 50ly between them, people on the planet will say it is rather more than that. If people on the planet say it's 50ly between them, he'll say it's rather less.

Ghwellsjr has already worked out the problem I suspect that you mean, so I won't bother repeating it. However, if you want to learn relativity the easiest way to avoid confusing yourself is to remember never to specify a velocity, position, distance or time without specifying who measured it, and always to remember that two people in relative motion won't agree on any of it.

 

[ghwellsjr]

Come on guys, the OP said he was traveling at 99.9%c which can't apply to his own rest frame, can it? It's obvious he was referring to the Earth's rest frame. Besides, if he started the journey, that means he accelerated and so we would have to consider a non-inertial rest frame for the traveler and it would be very difficult for him to actually measure the distance during the journey. Let's keep the problem and the answer simple.

 

[Orodruin]

Come on guys, the OP said he was traveling at 99.9%c which can't apply to his own rest frame, can it?

Which is exactly why I think it is important to make a point out of this. I have seen examples of university teachers messing up terminology with respect to this and I generally spend a lot of time in my SR class to have the students unlearn misconceptions they got from earlier courses briefly touching SR. Questions that boil down to something like "how far will the electron have to travel in its rest frame to reach the plate?" (with intended non-zero answers - the correct answer of course being "zero, in the electron rest frame the plate is travelling") are not uncommon. Therefore, stressing that more precise terminology is needed is important in my book - many students are of the impression that you really can say that you are traveling at 0.999c (as an absolute), when all that is implied is that this is the relative velocity between you and the background.

 

[Cyran]

Do you mean 50 light-years according to you on the spaceship? You are sitting in your spaceship watching the entire universe rushing past you at 99.9% of the speed of light, and there's something 50 light-years away... It will take 50 years for that something to reach you, and of course you will age by 50 years while you wait (What else could possibly happen while you're waiting for 50 years?).

Or do you mean 50 light-years according to someone on Earth watching you zoom away at 99.9% of the speed of light?

Sorry if I was unclear before its hard to formulate the question right when I know next to nothing aboyt physics and relativity. I meant a journey to a star that's 50 light-years away from earth.

If before you started, you decided to travel to a destination that was 50 light-years away and you took off at 99.9% of the speed of light, it would take just over 50 years to get there according to the Earth's rest frame. However, time for you would be dilated by a factor of 22.366 so you would age by only 50/22.366 which is 2.24 years so you would not look 70+ years but rather 22.24 years and it would feel like a 2.24 year journey. You would only have to bring 2.24 years worth of supplies, assuming that you could re-supply at your destination.

Wow that was exactly the kind of answer I was after. Really amazing information...This question is something that's been occupying my mind for a long time because I love to think about space travel. And I've always wondered how the spaceship crew would age when traveling to distant stars/planets.

 

[PeterDonis]

I meant a journey to a star that's 50 light-years away from earth.

Nugatory's point is that "50 light-years away from earth" is an incomplete specification. To be complete, you would have to say "50 light-years away from Earth according to the Earth's rest frame" or something similar. ghwellsjr's answer assumed that that was what you meant, but without that extra clause in italics, what you said does not unambiguously convey what ghwellsjr assumed you meant. Distance is frame-dependent in relativity, so a scenario in which the star is 50 light-years away in Earth's rest frame is very different from a scenario in which the star is 50 light-years away in the rest frame of the rocket traveling at 99.9% of the speed of light relative to Earth. (In the latter scenario, the star would be 50 * 22.366 or about 1118 light-years away according to Earth's rest frame.)

 

[PeterDonis]

the OP said he was traveling at 99.9%c which can't apply to his own rest frame, can it?

But he also said the star was 50 light-years away, which could apply to either frame (the Earth frame or the rocket frame). And, as Orodruin pointed out, many people don't really understand that velocity, like distance, is relative.

 

[Cyran]

Nugatory's point is that "50 light-years away from earth" is an incomplete specification. To be complete, you would have to say "50 light-years away from Earth according to the Earth's rest frame" or something similar. ghwellsjr's answer assumed that that was what you meant, but without that extra clause in italics, what you said does not unambiguously convey what ghwellsjr assumed you meant. Distance is frame-dependent in relativity, so a scenario in which the star is 50 light-years away in Earth's rest frame is very different from a scenario in which the star is 50 light-years away in the rest frame of the rocket traveling at 99.9% of the speed of light relative to Earth. (In the latter scenario, the star would be 50 * 22.366 or about 1118 light-years away according to Earth's rest frame.)

Ah I get it now :) Thanks for clarifying!

 

[Cyran]

By the way I read on Wikipedia a moment ago about Interstellar travel, and something boggled my mind. I'm not sure I understood it correctly but they said that it would take roughly the same amount of energy to accelerate an object of 1 ton to 1/10 of light-speed as the whole world's energy consumption in one year (2008). That’s just insane, can’t wrap my head around that. And 1 ton is nothing if we talk spaceships with a whole crew and cargo.And that's just the acceleration, right? What about all the energy it would require to keep the spaceship going in that velocity for a very long time.

 

[Orodruin]

By the way I read on Wikipedia a moment ago about Interstellar travel, and something boggled my mind. I'm not sure I understood it correctly but they said that it would take roughly the same amount of energy to accelerate an object of 1 ton to 1/10 of light-speed as the whole world's energy consumption in one year (2008). That’s just insane, can’t wrap my head around that. And 1 ton is nothing if we talk spaceships with a whole crew and cargo.And that's just the acceleration, right? What about all the energy it would require to keep the spaceship going in that velocity for a very long time.

It is indeed a very large amount of energy. However, neglecting collisions with interstellar dust and radiation, once the velocity is reached, there is no energy requirement to keep it going. After all, the ship is at rest in its own rest frame. Now, matching velocity with the target destination is another issue that will require additional energy.

 

[PeterDonis]

I read on Wikipedia a moment ago

Can you give a link to the specific article?

they said that it would take roughly the same amount of energy to accelerate an object of 1 ton to 1/10 of light-speed as the whole world's energy consumption in one year (2008).

"Roughly" is quite an understatement. The relativistic formula for the energy required to accelerate an object from rest to speed $v$ (where "speed" here is relative to the starting point) is $E = m c^2 \left[ \left( 1 / \sqrt{1 - v^2 / c^2} \right) - 1 \right]$. If we plug in m = 1000 kg, v/c = 1/10, and c = 299,792,458, we get E = 4.5 x 10^17 Joules. That's about 126 Terawatt-hours, and according to Wikipedia, world energy consumption in 2008 was about 144,000 Terawatt-hours, or about 1000 times as much as the energy we just calculated. To use up 144,000 Terawatt-hours in accelerating a 1-ton mass, you would have to accelerate it to about 98% of the speed of light.

What about all the energy it would require to keep the spaceship going in that velocity for a very long time.

As Orodruin pointed out, it takes no energy (if we neglect collisions with interstellar matter and radiation) for the spaceship to go at a constant speed. When we sent astronauts to the Moon, or when we send space probes to other planets, they only need rocket power if they need to change speed or direction; the rest of the time they just coast.

 

[Cyran]

Can you give a link to the specific article?

"Roughly" is quite an understatement. The relativistic formula for the energy required to accelerate an object from rest to speed $v$ (where "speed" here is relative to the starting point) is $E = m c^2 \left[ \left( 1 / \sqrt{1 - v^2 / c^2} \right) - 1 \right]$. If we plug in m = 1000 kg, v/c = 1/10, and c = 299,792,458, we get E = 4.5 x 10^17 Joules. That's about 126 Terawatt-hours, and according to Wikipedia, world energy consumption in 2008 was about 144,000 Terawatt-hours, or about 1000 times as much as the energy we just calculated. To use up 144,000 Terawatt-hours in accelerating a 1-ton mass, you would have to accelerate it to about 98% of the speed of light.

Oh my bad! I got it wrong because here in Sweden our decimal comma is your decimal mark hehe. Your calculation is the same as the one in the article but a lot more detailed :)EDIT: Missed your last sentence. That’s great and fitting to know since my original post was about that speed. Great stuff for conversations about this subject.

As Orodruin pointed out, it takes no energy (if we neglect collisions with interstellar matter and radiation) for the spaceship to go at a constant speed. When we sent astronauts to the Moon, or when we send space probes to other planets, they only need rocket power if they need to change speed or direction; the rest of the time they just coast.

Amazing didnt know that!

 

[Cyran]

It is indeed a very large amount of energy. However, neglecting collisions with interstellar dust and radiation, once the velocity is reached, there is no energy requirement to keep it going. After all, the ship is at rest in its own rest frame. Now, matching velocity with the target destination is another issue that will require additional energy.

But wait that's what I meant, after the velocity is reached I want the spaceship to travel at matching velocity to the target destination e.g. 1/10 of light-speed. Does that not require any energy at all if you avoid collisions? Or did I misunderstand what you meant with matching velocity?

 

[Orodruin]

Assuming the destination has the same rest frame as the origin of the trip, you will be traveling at a velocity relative to the destination. The velocity matching occurs in the end, i.e., when you slow down in the destination rest frame.

 

[Cyran]

Assuming the destination has the same rest frame as the origin of the trip, you will be traveling at a velocity relative to the destination. The velocity matching occurs in the end, i.e., when you slow down in the destination rest frame.

Sorry but I don’t understand what you mean with rest frame. To make it simple for me. I know the amount of energy it takes now to accelerate a ship to 1/10 of light-speed, but if I want that ship to continue traveling at 1/10 of light-speed for a long time I don’t need any further energy? The engines can be shut down and it will just cruise at that speed once it’s achieved? I just want that cleared out and I’ll stop bothering you guys with simple questions hehe. I'll have to come up with a harder question next time J

 

[Orodruin]

If you shut the engines off, you will continue moving at the same speed you were moving before. This is just Newton's first law.

In relativity (and classical mechanics too ) velocity is not something absolute. It is not sufficient to say that something is moving at 0.1c, you need to specify relative to what it moves with 0.1c. There is always a frame where the rocket is not moving and the destination is moving towards the rocket, this is the rocket rest frame.

 

[DaveC426913]

The reason is that anybody who is not accelerating can consider themselves at rest. That means that for the guy on the spaceship, the planets are rushing along at 99.99% of light speed and both the planets and the distance between them are length contracted.

In reality, a guy in a spaceship can easily conclude that he is moving relative to the stars, since he will easily detect a huge compression of distance between stars along one axis. Moreso, every object - the stars and planets themselves - will be massively compressed to a disc along that same axis.

 

[PeterDonis]

if I want that ship to continue traveling at 1/10 of light-speed for a long time I don’t need any further energy? The engines can be shut down and it will just cruise at that speed once it’s achieved?

As long as "speed" means "speed relative to the starting point", yes, this is correct. As we have been saying, "speed" is relative, but once you've fixed what you are measuring speed relative to (in this case, the rocket's starting point), then yes, you don't need any energy if you don't change speed.

 

[RandyD123]

I think this is where things break down for that average person. When someone says 50 light years away, they usually mean from earth. Meaning if the Moon were 50 light years away it would take a beam of light 50 years to get there. Me standing on Earth shining a beam of light at the moon, I would age 50 years by the time it got there.

However, if I were traveling in a ship and side by side with that beam of light, it would take ME a whole lot less time for me to get there.

Is that right? And if so, would I "feel" time dilation?

 

[PeterDonis]

Is that right?

Strictly speaking, you couldn't travel alongside the beam of light the whole way, since an object with nonzero rest mass can't travel at the speed of light. But you could travel fast enough to be only a little bit behind the light when it arrived.

if so, would I "feel" time dilation?

No. You would feel perfectly normal. You would just have aged a lot less than 50 years when you arrived.

 

[collinsmark]

Is that right? And if so, would I "feel" time dilation?

Like PeterDonis said. You would not "feel" time pass any differently.

The kicker here is that if your destination is 50 light years in Earth's rest frame, then once you qucikly accelerated to 99.9% the speed of light (with respect to Earth's rest frame, and assuming you survived that incredible acceleration somehow) the distance to your destination is only $\left( 50 \mathrm{\ light \ years} \right) \left( \sqrt{1 - \left( 0.999 \right)^2} \right)$.

This goes along with the earlier posts about distances being frame dependent. What was once a vast distance has become a mere hop, skip, and jump.