Space Travel: Time Dilation at Near Light Speed Explained

[magi]

Space travel again :)

Ciao.

Time slows down when traveling close to light speed.

So my question is.

I travel out in space to a distant star, accelerating close to light speed.
When i have traveled for 10 years, my time and on Earth 300 years have past.

Have I traveled nearly 10 light years out in space from Earth or have I traveled nearly 300 light years out in space?

 

[pervect]

Ciao.

Time slows down when traveling close to light speed.

So my question is.

I travel out in space to a distant star, accelerating close to light speed.
When i have traveled for 10 years, my time and on Earth 300 years have past.

Have I traveled nearly 10 light years out in space from Earth or have I traveled nearly 300 light years out in space?

In the Earth's frame of reference, you are at a point 300 LY away from Earth.

In your frame of reference, the Earth is 10 light years away from you - assuming you are still moving at nearly light speed, that is.

Time dilates, distances contract, and relativity is simultaneous. If you accelerate up to near-lightspeed, reach your destination, and slow down again after 10 years by your clocks, the Earth will appear to be 300 LY away.

 

[magi]

Ok.
So after accelerating for 10 years(300 Earth years) and slowing down after another 10 years(300 Earth years) i have traveled 20 years my time but traveled nearly 600 light years out in space. :)

Is there any chance to reach speeds near light, to be able to reach distant stars in a human life time in the future?

 

[russ_watters]

It is unlikely that technology will enable humans to even reach 1% of the speed of light in our lifetimes.

 

[pervect]

The energy requirements to reach any sort of relativistic velocity are enormous.

To reach a 2:1 time dilation factor you will have to supply at 100% efficiency (and nothing is 100%) an amount of energy equal to the rest energy (mc^2) of your payload.

I believe that the technology to extend one's lifespan will likely arrive long before the technology to achieve control over such large energies, and to solve other problems (like dealing with the problem of the interstellar media at such high velocities).

 

[DaveC426913]

Is there any chance to reach speeds near light, to be able to reach distant stars in a life time?

I think you are asking if it can be done in the lifetime of the pilot not within our lifetime.

Yes. You can even do it comfortably at 1G and get fairly far.

Anyone care to put some numbers to this?

Let's set up some parameters:
Let's say he is driving a Bussard ramjet, so he doesn't have to worry about running out of fuel.
He accelerates for 20 years at 1G, then turns his ship around and decelerates at 1G for 20 years.
That leaves him half of his life left over to raise his family on the new distant planet.

How far has he travelled?
How much time has passed for him/Earth?

 

[dicerandom]

There's a table of such things here: http://musr.physics.ubc.ca/~jess/p200/str/str13.html

The chart stops around 28 years total ship time, but he would have traveled close to half a billion lightyears (twice the "fly by" 10 year figure).

 

[DaveC426913]

According to that table, our pilot can make it - not merely to distant stars - he can make it to the next galaxy (2MLy) - and he can do it in less than 30 years.

 

[magi]

It is unlikely that technology will enable humans to even reach 1% of the speed of light in our lifetimes.

What about in the future.

Will we be able to reach speeds close to light so we can reach the stars?

 

[russ_watters]

Well, the rest of my lifetime is the future, but beyond that...? Who knows. I don't think it's likely given how far short of that we currently are, but ehhh - maybe.

 

[Jorrie]

According to that table, our pilot can make it - not merely to distant stars - he can make it to the next galaxy (2MLy) - and he can do it in less than 30 years.

Yes, Andromeda galaxy (2Mly) reached in about 29y total ship time. It's very easy to calculate for 1g acceleration/deceleration, which is about 1 ly per y^2. The equation then approximates to: ship time = 2 ln(distance).
Earth time would advance by about 2 My, since average speed is very close to speed of light. [Thorne: Black Holes and Time Warps (notes)]

 

[pervect]

There's a table of such things here: http://musr.physics.ubc.ca/~jess/p200/str/str13.html

The chart stops around 28 years total ship time, but he would have traveled close to half a billion lightyears (twice the "fly by" 10 year figure).

There is similar information in

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

However, note the fuel requirements for such a rocket, which is discussed a bit in the above FAQ;

You are already at a 10:1 mass ratio burning pure matter/antimatter for even a short trip. A trip to Andromeda requires a 4100:1 mass ratio.

Let's look more closely at the 10:1 mass ratio. That's 1 ton of payload, 5 tons of matter, and 5 tons of antimatter for fuel!

I do not personally expect to see antimatter available in ton quantities in my lifetime, or in the lifetime of any poster here.

And that's not all. Even if we had ton-quantities of antimatter available, is very unlikley that one will be able to accelerate continuously at 1G with, for instance, an antimatter-beam-core rocket.

For more info on the beam core concept, see for instance.

http://ffden-2.phys.uaf.edu/213.web.stuff/Scott Kircher/beamedcore.html

Like all high ISP designs, the high ISP comes at the cost of lower acceleration (given reasonable-tech limits on heat dissipation and energy handling capacity). Burning pounds of antimatter in a second without vaporizing yourself is not an easy task. ANd mere pounds/ second would not be enough for some (actually many) of the scenarios being discussed here.

"Light sail" designs become very attractive in that one does not have to carry along the fuel required, but like other high ISP approaches it is hard to imagine a 1-g light sail driver. Also, the issue of "how to stop" needs to be addressed with light-sail designs.

And if we somehow manages to beat all these difficulties, we have to avoid (somehow) of being fried by the interstellar media, which will appear to be an ultra-relativistic beam of radiation. As the FAQ mentions, even the CMB background radiation will be blue-shifted into a lethal beam of radiation, hot enough to melt any known material.

So let me go back to my original point. We are making great strides in biology, and it makes a lot more sense to simply be more patient. Interstellar travel will probably always take a long time, but if we can live for 1000 years, a 50 year journey may no longer be an insurmmountable obstacle. Certainly ultra-efficient recylcling will be required for 50 year journeys, but the issue of supplying enough energy to keep a human being going for 50 years, and even the problem of dealing with atmosphere loss through a hermetically sealed hull over that time will be a lot less than the "tons of antimatter" required for a brute-force physics approach of trying to achieve ultra-relativistic velocities.

Other far-out ideas (but still more plausible than brute-force relativistic velocities IMO) include building mechanical bodies, or "uploading" minds from the human brain into software on advanced computers.

 

[DaveC426913]

What about in the future.

Will we be able to reach speeds close to light so we can reach the stars?

As noted, we can reach relativistic speeds in principle, merely by continuing to accelerate indefinitely. The rate-limiting factor is in creating an engine efficient enough that we don't need a lot of fuel.

 

[magi]

There's a table of such things here: http://musr.physics.ubc.ca/~jess/p200/str/str13.html

The chart stops around 28 years total ship time, but he would have traveled close to half a billion lightyears (twice the "fly by" 10 year figure).

I guess you could learn to live in a 2 g gravety.
Wonder how the table would look like if you accelerate 2g instead?
Or what about 2-3 g when you sleep to reach the stars faster?

:)

 

[nrqed]

There is similar information in

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

However, note the fuel requirements for such a rocket, which is discussed a bit in the above FAQ;

You are already at a 10:1 mass ratio burning pure matter/antimatter for even a short trip. A trip to Andromeda requires a 4100:1 mass ratio.

Let's look more closely at the 10:1 mass ratio. That's 1 ton of payload, 5 tons of matter, and 5 tons of antimatter for fuel!

I do not personally expect to see antimatter available in ton quantities in my lifetime, or in the lifetime of any poster here.

And that's not all. Even if we had ton-quantities of antimatter available, is very unlikley that one will be able to accelerate continuously at 1G with, for instance, an antimatter-beam-core rocket.

For more info on the beam core concept, see for instance.

http://ffden-2.phys.uaf.edu/213.web.stuff/Scott Kircher/beamedcore.html

Like all high ISP designs, the high ISP comes at the cost of lower acceleration (given reasonable-tech limits on heat dissipation and energy handling capacity). Burning pounds of antimatter in a second without vaporizing yourself is not an easy task. ANd mere pounds/ second would not be enough for some (actually many) of the scenarios being discussed here.

"Light sail" designs become very attractive in that one does not have to carry along the fuel required, but like other high ISP approaches it is hard to imagine a 1-g light sail driver. Also, the issue of "how to stop" needs to be addressed with light-sail designs.

And if we somehow manages to beat all these difficulties, we have to avoid (somehow) of being fried by the interstellar media, which will appear to be an ultra-relativistic beam of radiation. As the FAQ mentions, even the CMB background radiation will be blue-shifted into a lethal beam of radiation, hot enough to melt any known material.

So let me go back to my original point. We are making great strides in biology, and it makes a lot more sense to simply be more patient. Interstellar travel will probably always take a long time, but if we can live for 1000 years, a 50 year journey may no longer be an insurmmountable obstacle. Certainly ultra-efficient recylcling will be required for 50 year journeys, but the issue of supplying enough energy to keep a human being going for 50 years, and even the problem of dealing with atmosphere loss through a hermetically sealed hull over that time will be a lot less than the "tons of antimatter" required for a brute-force physics approach of trying to achieve ultra-relativistic velocities.

Other far-out ideas (but still more plausible than brute-force relativistic velocities IMO) include building mechanical bodies, or "uploading" minds from the human brain into software on advanced computers.

I just wanted to thank you for the very very interesting post!

Patrick

 

[Jorrie]

I guess you could learn to live in a 2 g gravety.
Wonder how the table would look like if you accelerate 2g instead?
Or what about 2-3 g when you sleep to reach the stars faster?

:)

Have not seen a table for this, but for long time of constant +acc/-acc, the approximate equation is:
t_ship = 2ln(ax)/a, where a is acc. in g (or ly/y^2) and x distance in ly. For 2g, the time is slightly more than half of that for 1g. The 'sleep' scenario is much more complex. Have to use the full equation:
x = [exp(a t_ship)+exp(-a t_ship)-2]/(2a) and integrate numerically with changing a over time :-)