An observation about relativistic space travel...

1. Jul 2, 2015

litup

I suppose I am not the first to notice this, but if you are going at say, 0.999c you will have shrunk by a factor of about 20 and everything else on the craft.

Suppose the spacecraft is 2000 meters long, at 0.999c it will shrink to about 100 meters long.

So suppose a person 2 meters tall, 2000 mm, standing up, is now 100 mm high.

So suppose you have a 2 meter ruler. If you hold the ruler upright (aiming in the direction of travel) it is now 100 mm long. BUT if you now move it 90 degrees, now aiming at the sides of the spacecraft, it will now have grown back to it's full 2000 mm.

That suggests you can make a speedometer by just having 2 rulers at 90 degrees off, one pointing in the direction of travel and one pointed sideways. You would be able to see the sideways ruler is still 2000 mm long but you would also see the up and down pointed ruler at 100 mm. So having a chart, you could figure out your velocity by seeing the difference between the two rulers!

Is there something wrong with this scenario?

2. Jul 2, 2015

georgir

If your rulers are moving along with you (in other words, not moving relative to you) then they will appear completely normal to you.
If they are moving relative to you they will indeed appear squished to you in their direction of travel, and you could use that squishing to determine their velocity. But you can determine their velocity in more obvious ways too.

3. Jul 2, 2015

litup

It seems to me that since in the vertical position, you and the ruler aimed in the direction of travel, you would think the ruler to be exactly your height, 2 meters.
But moving it sideways, pointed to the sides of the spacecraft, from the travelers POV, the ruler would grow to be about 40 meters long!

4. Jul 2, 2015

Ibix

Length contraction is an effect that you can measure in objects that are moving relative to you. It isn't something you ever see in yourself.

If I went past you at constant velocity in a relativistic rocket, you would look normal to you and I would look length contracted to you. On the other hand, I can argue that I'm stationary and you're moving, so to me I look normal and you look length contracted. (I'm using "look" slightly sloppily here - what you actually see is more complex because we need to factor in the changing light speed delay.)

Basically your own speed is always zero relative to yourself, so your speedometer always measures zero. And there are simpler ways to measure someone else's velocity relative to you than the method you are proposing, like Doppler radar.

5. Jul 2, 2015

georgir

Nope, you can't compare different dimensions like that. To compare them you rotate them and they seem equal.

6. Jul 2, 2015

phinds

But you ARE going at .999c, right now as you read this. Motion is relative. Period. Choose a frame of reference and in that frame of reference you can, depending on your choice of FOR, be going anything from 0 to .999999+c

7. Jul 2, 2015

harrylin

Think a little more: how would you measure its length?
- you could put it next to another meter stick. What will you measure?
- or you could lie down next to it. what would you see?

The meaning of "relativistic" is that you will see nothing different from what you would expect to see in rest.

8. Jul 2, 2015

Staff: Mentor

You are moving at .999c right now, relative to someone somewhere in the universe. Can you use your speedometer to measure this speed?

9. Jul 2, 2015

litup

I was thinking since the whole ship and everything in it compresses but only in one dimension you would be able to see the fact that there is no lateral compression. Why would you see everything the same if the up and down dimension squishes but the left and right doesn't?

10. Jul 2, 2015

Staff: Mentor

You are misunderstanding something important here - length contraction is something that you observe in things that are moving relative to you. You aren't moving relative to yourself, so you never observe yourself or the stuff at rest relative to you being length contracted.

Suppose that there are three spaceships: Lefty, Righty, and you. Lefty is flying away from you to the left at .5c, and Righty is flying away from you at .5c in the opposite direction, to the right. All three of you are carrying your crossed meter-stick devices.

You will observe (this is trickier than it sounds because light from different parts of the meter sticks will reach your eyes at different times so you can't just go with what you'd see watching them through a telescope) that your own meter sticks are the same length, while Lefty's and Righty's mismatch because of length contraction consistent with moving at .5c relative to you.

Lefty and Righty will both observe that their own meter sticks are the same length, and because you are at moving at .5c relative to them, they will observe that your two sticks mismatch because of length contraction consistent with a relative velocity of .5c. Lefty will also observe that Righty is moving at .8c (yes, .8c! not .5c+.5c=c) relative to him, so will observe that Righty's meter sticks are mismatched by even more; and likewise for Righty's observation of Lefty's meter sticks.

11. Jul 2, 2015

rootone

What is your speed relative to yourself?
Obviously it can only be zero.
Thus the traveller does not experience relativistic effects at all, everything in the ship looks the same.
The apparent 'squishing' is what will be observed from the point of view (reference frame) of an external observer when the traveller's speed relative to them approaches light speed.

Last edited: Jul 2, 2015
12. Jul 3, 2015

harrylin

It's just the opposite: why would you see everything the same if there was no length contraction? And what would you expect to see?
Perhaps you don't know that the speed of light is independent of the motion of the ship. Without length contraction you would be able to see an effect of motion in the moving ship, because light rays bouncing off a mirror in one direction would take longer than light rays bouncing off a mirror in another direction.
- https://en.wikipedia.org/wiki/Michelsonâ€“Morley_experiment#Light_path_analysis_and_consequences

13. Jul 3, 2015

litup

Thanks everyone for helping me see the way things work in relativity. I thought I was onto something there, you guys straightened me out:)