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Comment by palish | Hacker News Reader

Question:

In the year 2200, if a 10 year old child were to travel to the planet at a speed of 0.9999c, then were to immediately turn around and travel back to Earth, they would be approximately 50 years old. However, what year would they arrive back on Earth?

Assumptions:

- no acceleration or deceleration time.

- the planet is exactly 20 light years away.

- the velocity of the ship remains exactly 0.9999c while in transport.

(The answer is not 2240. It's much greater. My question is, how much greater?)

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Your problem statement is wrong.

The child is traveling 40 light years at 0.9999c, which takes about 40 years + 35 hours. However the child won't arrive back 50, the child will not yet be 11. See http://www.wolframalpha.com/input/?i=time+dilation+traveling... for the exact age.

See http://en.wikipedia.org/wiki/Twin_paradox for more on this, including an explanation of why your belief about the age of the traveler is wrong.

How can this be?

If the child were moving at 0.9999c (which is less than 1.0000c) and the planet is 20 light-years away, then how could it take less than 20 years for the child to reach it? Let alone ~0.5 years?

EDIT: Here's an explanation from a friend:

  light always travels at c even if you're already moving close to c
  but it's impossible for anything to travel faster than c
  so if you're traveling at .9999c
  the passage of time must be scaled for the traveler
  to make light on the ship appear to move at c
  even though it's only moving at 1-.9999c

That's... awesome.

  If the planet is 20 light years away, you're saying we 
  could reach it in less than a year if we attain a velocity
  of 0.9999c?

Yes. In the reference frame of the traveler, very little time passes. However, when he returns, people on earth will have aged more than 40 years.

This is also why particles traveling at c cannot possibly decay: no time passes for them. A photon is everywhere at once, from its own point if view.

Amazing. I hope to some day wake up and have a deep conceptual understanding of the relationship between velocity and time in relation to the various bodies at play.

I also hope to have an understanding of what it means for a photon to be everywhere at once, from its own point of view.

In the end, I guess I just want to understand the universe just a bit more than I do.

Special relativity is actually quite accessible and really interesting - find a good book or set of lectures on iTunes U or something. (General relativity, the generalised version including acceleration and gravity, is what makes people think relativity is hard).

  This is also why particles traveling at c cannot possibly
  decay: no time passes for them. A photon is everywhere at
  once, from its own point if view.

That's a really great explanation. For the first time, I've been able to visualize how light can be both a particle and a wave. Thank you.

Time dilation (special relativity) has nothing to do with wave-particle duality (quantum physics). The infinite time dilation of photons is due to their velocity, not their wave-like nature.

Furthermore, all particles (electrons, protons, quarks, etc.) have wave-particle duality just as much as photons do.

Wave-particle duality is even observable with larger molecules: http://link.aps.org/doi/10.1103/PhysRevLett.88.100404

Thanks for the correction. s/wave/continuous beam/.

According to the traveler you're traveling as fast as you think the traveler is traveling. The only way to make that work out is that to the traveler the destination is much closer than it is for you. This is called length contraction.

And rounding it out, different observers disagree on which events are simultaneous. In particular until the traveler turns around, the traveler thinks that the Earth was left recently. After the traveler turns around, in the new reference frame the traveler left the Earth close to 40 years prior.

Relativistic travel would be one-way essentially. It would allow one to travel the visible universe within a current human lifespan (of course, with ridiculous power requirements). Anything left behind would have experienced thousands of millions of years of time.

Sci-fi dealing with this topic: Forever War, Ender's series, a few stories from Niven's Known Space universe.

See also the anime Gunbuster, which has teenagers piloting giant robots (so far no surprise) into deep space at measurable percentages of c. Getting back after saving the world they find their school friends have grown up and had kids.

Right. Time/space dilation effectively makes the trip shorter for the person traveling near c.

Here's a really mind-blowing thing: If you were able to accelerate at a fairly reasonable rate indefinitely - say - using an interstellar ramjet, you could conceivably circumnavigate the entire universe within a human lifetime (in your own frame of reference, of course)

Of course, interstellar ramjets might not actually work in practice... but still, the concept of time/space dilation holds.

Last I heard from the hard science fiction people, such ramjets have an upper speed limit imposed by some sort of drag. Can't remember for certain... maybe Atomic Rockets has something on them... yeah, http://www.projectrho.com/rocket/slowerlight.php#Bussard_Ram... . They say 0.12c is the best speed for ramjets.

I think you've got it reversed. From Earth's perspective, it would take exactly 40 years, but the child would age very little.

http://www.wolframalpha.com/input/?i=time+dilation+traveling...

2828 years + 2200 = 5028 A.D. says wolfram alpha

Fascinating.

  40 years at 0.90000c =   91.76 years
  40 years at 0.99000c =  283.55 years
  40 years at 0.99900c =  894.65 years
  40 years at 0.99990c = 2828.00 years
  40 years at 0.99999c = 8944.00 years

With the caveat that nobody will be traveling at 0.99999c for 40 years. You'd be really really far away by then.

Well, you'd still be less than 10,000 light-years away. That's still well within the galaxy.

5028

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