travelling close to the speed of light

kbaumen

I'm sure this has been asked a million times but a quick search didn't give me quite definitive answers so here it goes:

Imagine a spaceship travelling away from the Earth at 0.99c. For argument's sake, lets ignore the acceleration and deceleration stages of the ship (is that valid?). Simply the ship starts travelling at 0.99c. Now the ship stops and according to the ship's clock, they have travelled for a day which on Earth is a year or so (or whatever the difference works out to be). How far is the ship from the Earth? Surely if it has been a year, then it has travelled almost a lightyear within a day (according to ship's clock) which can't be true. So where and why is it?

P.S. This is not homework, merely a question that came to mind when watching this.

ghwellsjr

At 0.99c, one day on the ship is one week on Earth so the spaceship will be one lightweek away from Earth when it stops. For it to be one year, the ship would have to be traveling at greater than 0.999996c. Aside from that minor detail, everything else you described is correct.

kbaumen

Ok, yes, I admit, that year was a shot in the dark with the main thing being that different times have elapsed.

So you're saying that the ship is then a lightweek away from the Earth when it stops. But the ship's clock says that is has travelled for only a day. Does that mean that the people on the ship experienced travelling faster than the speed of light?

ghwellsjr

Actually, after I posted, I looked at the video and it says that at 99% of the speed of light, a single day onboard is a full year of Earth time (4 minutes into the video). This is wrong which makes me wonder how many other their other numbers are wrong.
No, they still measure their speed at 0.99c, however, in the Frame of Reference in which they are at rest during the trip, everything around them is length contracted and traveling past them and the Earth only has to travel behind them by about a lightday while their destination was only a lightday away at the beginning of the trip.

dydxforsn

Space Lorentz contracts towards you if you are in the spaceship. It's the same way with the cosmic ray muon that can only live for a very short while, not long enough to travel from the upper atmosphere to the surface of the earth (even at the insane speeds they travel), yet we still measure them a large number of muons at sea level. The muon essentially sees earth "Lorentz contract" up towards itself so that it is able to make the journey from upper atmosphere to sea level within its very short lifetime.

You can travel across the galaxy if you want in your lifetime (200,000 light years across about). Assuming you travel at like 0.9999c and are comfortable with the rest of earth getting like 2,000,000 years older while you complete the journey..

ghwellsjr

At 0.9999c, the ratio of Earth time to ship time is only 70. You have to go way faster than that to get 2 million years to pass on Earth. As I said earlier, even 0.999996c is less than a ratio of one Earth year to one ship day.

kbaumen

Ok, cheers guys, that explains it.