# Length contraction and interstellar travel

1. Jan 18, 2010

### Referos

Interstellar travel is always a problem in science fiction: you can't have the hero hibernate for millions of years whenever he or she wants to travel to another star, but it's annoying when spaceships just magically move faster than light.

However, wouldn't length contraction from special relativity partially solve this? Imagine that a ship is travelling at 0.999999c. Maybe we will never reach this speed, but, still, it's not a physical impossibility. Now, at this speed, $$\gamma = 707$$. The distance from Earth to, say, Alpha Centauri is $$4.153 * 10^{16} m$$ (4.39 light years), but the passengers in the ship would observe this length to be contracted to $$5.87*10^{13} m$$. At 0.999999c, this distance can be covered in 195 934 s, which converts to roughly 2.26 days.

Sure, when returning to Earth, they would realize that years have passed due to time dilation.
Still, from the passenger's perspective, they can reach other stars in a somewhat small amount of time.

Now, the fact that I can't remember a science fiction novel or film that used this idea instead of faster-than-light travel must mean that I've got something wrong, but I'm not sure.

2. Jan 18, 2010

### jacksonwalter

The energy required to get to that speed is enormous. I can't see a ship weighing less than 1000kg with enough resources, probably at least 104kg really. In order to get to gamma=707, that's 6 x 1023 J, or at least 7 x 106 kg of anti-matter at 100% efficiency. Good luck.

3. Jan 18, 2010

### dacruick

Correct me if im wrong, but if the ship is travelling almost at the speed of light, doesn't that mean the length of the ship is very small, not the distance it is going.

Or are you also assuming that using relativity you can say that the ship moving from star A to star B is the same as the whole universe traveling in the opposite direction?

4. Jan 18, 2010

### Naty1

Try this for more than you wanted to know....

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

You can also search here on physics forums for things like time travel, space travel, twin paradox and so forth...this has been discussed hundreds of times...

Last edited by a moderator: May 4, 2017
5. Jan 18, 2010

### bcrowell

Staff Emeritus
Referos, your analysis seems right, although I haven't checked the numbers.

Right. In the galaxy's frame, the ship is shortened. In the ship's frame, the galaxy is shortened.

With constant acceleration and deceleration at one gee, I believe the round-trip clock time from earth to the center of the galaxy works out to be on the order of a century (which would correspond to tens of thousands of years on earth).

Re jacksonwalter's point about practical issues -- another problem is that you'd be burned up by frictional heating from the interstellar medium.

6. Jan 18, 2010

### jambaugh

You can't speak of "the length" without qualifying "as seen by...". The ship as seen by itself is unchanged. The distance between stars as seen by the ship is contracted. The ship as seen by people moving with the stars is contracted. The distance between stars as seen by people moving with the stars is unchanged.

To see why this seemingly paradoxical two way contraction is not so paradoxical, consider a somewhat analogous situation.

Imagine a very little planet and two astronauts standing some distance apart looking at each other from atop hills. Suppose the planet is so small that from where they stand the angles of each man's vertical direction is 60deg from the others. Each see's the other's vertical distance as 1/2 their actual height because each sees the other as leaning relative to their own vertical.

Right! It's all relative.

7. Jan 18, 2010

### Nabeshin

General comment: This is the whole reason going fast is so beneficial for futuristic space flights. Sure, in the framework of Newtonian mechanics, extra speed means you get there a bit quicker, but the relativistic effects are the real key.

Two novels which pop into my head which make a big to-do about the time dilation effects of relativistic space travel: Forever War and the Ender's Game series. Oh, and Tau Zero by Paul Anderson, but that one's not as well known. Within any decent hard SF book, these effects are given due consideration.

Cheers!

8. Jan 18, 2010

### Janus

Staff Emeritus
Larry Niven built a whole novel around this idea in A World Out of Time, and Heinlein's Time for the Stars also relies on it. The main reason that it doesn't get used more often is that so much time passes for both Earth and the destination. Sure, the Hero can get to 20 Leonis Minoris in 25 days of his own time, but it will do little good if the situation he set off to resolve transpired 48 yrs ago by planet time when he arrives. (And that's just taking into account his own travel time. If we are restricted to light speed signals, he won't even find out about it for 48 yrs.)

9. Jan 18, 2010

### gpslavov

But very interestingly, in the event that the Earth is about to be destroyed, it wouldn't matter that 50 years have passed between departure and arrival. Humanity can reach another star, hopefully with habitable planets, well within the lifespan of one generation, which is awesome! =)

10. Jan 18, 2010

### Matterwave

Theoretically, this could work. Sadly, 4.36 years would have passed on Earth in your 2.26 day journey, so, everyone you know back home has just aged by 4.36 years. For a trip to the center of the galaxy, everyone you know back home has died.

Communication is also a problem. If you ever wanted to talk with your friends back on Earth, expect a 8.72 year delay in response time...

11. Jan 19, 2010

### devronious

This is interesting, I ran a length contraction / time dilation experiment using sub atomic motion to create relativistic effects of length contraction and what I found is that the space-time surrounding the event was contracted, not just the particle involved. The distance to the next object becomes shorter, but it can also be perceived by outside and seperate frames of reference. This is of course a new experiment, you can find it at wintschlabs.com, its fairly easy to create and if your interested in observing first hand length contraction its worth the time to build.

The interesting thing here is, how is the space surrounding the particle contracted, should just the object in motion which has velocity be the contracted object? It seemed to me that it may have suggested that space was moving with the particles and that the space was the item contracted, not the particle itself. How can a moving object contract something that is separate from it, if velocity is the cause of contraction and the main component wouldn't anything contracted have to have velocity? Including the space-time which clearly the experiment shows is contracted.

The idea lead me to the theory that space-time originates from each and every particle, and that it moves with particles as they travel. If this is the case then relativity makes much more sense and relative motion and everything about it becomes clear why and how they happen. Each particle is its own frame of reference because of this.

You have to remember that both length contraction and time dilation occur for the ship, these offset eachother so that observers don't see it travelling at faster than its actually moving. Imagine if just space's length was contracted, wouldn't its velocity be much greater than it actually was, velocity = d/t and if d is much shorter to the destination its velocity would be massive. But t or time slows counteracting this change. They compliment eachother so as to not create a velocity that does not truely reflect the velocity before relativistic affects. But there is something that does change and that is the passage of time. This is why the muon ages so little and its decay is allowed to pass so far into the earth, see the muon experiment. So I think your people on the ship would age very little and time to them would seem to barely pass by, they wouldn't need cryo sleep would they? The muon didn't, perhaps thats the evidence you need.

-Devin Wintch

Last edited: Jan 19, 2010
12. Jan 21, 2010

### GRDixon

You've got the right idea. During his trip the measuring rods of earth's rest frame are zipping by at .999999c. How can more than 4E16 meters of these rods pass by in only 2.26 days of shipboard time? Because they are LENGTH CONTRACTED. Why Gene Roddenberry (the creator of Star Trek) never played this card is a mystery and a disappointment. Warp 5??? C'mon.

13. Jan 21, 2010

### pervect

Staff Emeritus
1) You've got it right as near as I can tell.
2) Try Gregory Benford's Galactic Center Novels ("In the Ocean of Night, etc).

Of course, even if Benford, a physicist, hadn't written the novels, the science wouldn't change. Also, the fact that Benford is a physicist doesn't make his novels non-fiction - while some elements of the story are inspired by actual physics, other story elements aren't, and it may be hard to distinguish which are which without specialized knowledge.

14. Jan 21, 2010

### DocZaius

The first thing that popped out at me regarding why science fiction novels wouldn't use this, is the acceleration. I'm surprised it's not been brought up in this thread, which makes me think that I'm missing something. The kind of acceleration humans could survive would limit their average speed. The speeds mentioned here would be attained only during a portion of the flight (middle point if the flight is half acceleration half decceleration). The stress on the body is also a consideration if you want a healthy population on the other side of the journey so you might want to limit the acceleration more than merely enough for "survivable."

15. Jan 22, 2010

### jacksonwalter

Nah, if you keep a constant 10 $$\frac{m}{s^{2}}$$ you only have to accelerate for about a year (c/a, convert to years). See https://www.physicsforums.com/showthread.php?t=370572" thread.

Last edited by a moderator: Apr 24, 2017
16. Jan 22, 2010

### Nabeshin

As the poster above me points out, this isn't the reason it's seldom used in science fiction. The reason is, according to observers not aboard the ship, it will take the ship at least the distance the ship is traveling (in light years) years to get there. So when the Enterprise-D gets called to the Neutral zone 1100 ly away on an urgent mission, it would take at least 1100 years for it to arrive, even if those on board only experience hours or minutes! Sort of slows the pace of things, don't you think?