# (length contraction)the distance travel or the object length shorter?

1. Sep 13, 2014

### benting180

Consider the following case:
First frame S, which is earth.
Second frame S', which is rest relative to rocket.
Rocket are moving in speed of v relative to earth.

Problem:
Due to time dilation, from frame of S, the clock in rocket is running slower.
Likewise, due to time dilation, from frame of S', the clock in earth is running slower.

Then, from frame of S', it can be said that the earth is moving in speed of v relative to rocket.
Since the time in earth is passing slower, so we can say the distance the earth travels must be shorter(c=d/t).
Like wise, from frame of S, it can be said that the rocket is moving in speed of v relative to earth.
Since the time in rocket is passing slower also, so we can say the distance the rocket travels must be shorter also(c=d/t).

My problem is that if from the frame of S, will we see the length of rocket shorter?

2. Sep 13, 2014

### Luca_Mantani

Sure, if the Rocket has lenght L at rest, when you measure its lenght with relative velocity of v, you will see a contraction in the direction of motion.

3. Sep 14, 2014

### benting180

Statement1: From frame of S, we will see the distance the rocket shorter
I can't understand that how from the frame of S, we will see the length of rocket shorter if statement1 is correct.
The distance and the length of rocket shorter at the same time?

4. Sep 14, 2014

### HallsofIvy

Staff Emeritus
That's the whole point of "relativity"- the answer is relative to the frame of reference. From the frame of reference, S, in which the earth is stationary and the rocket is moving, it is the rocket that is shorter. From the frame of reference, S', in which the rocket is stationary and the earth is moving, it is the distance to the earth that is shorter.

That has nothing to do with the time dilation of either object.

5. Sep 17, 2014

### benting180

But, since velocity is relative. Can the following paragraph be true?

From the frame of reference, S, in which the earth is stationary and the rocket is moving, it is the distance to the rocket that is shorter. From the frame of reference, S', in which the rocket is stationary and the earth is moving, it is the earth that is shorter.

If not, why is wrong?

6. Sep 17, 2014

### A.T.

Shorter than what? When you measure distances, you have to decide in which frame your ruler is at rest.

7. Sep 17, 2014

### jartsa

Well let's see ... If the rocket is moving, it's shortened. If the earth is moving, it's shortened. This is very clear.

If the distance between the earth and the rocket is moving, is the distance shortened? This is very unclear.

Usually observers think that distances between the observer and other objects are non-moving distances.

Let's say the rocket and the earth both think the usual way.

At the moment when the rocket passes asteroid X, the rocket thinks the distance between the rocket and the earth is 3 ly, for example.

At the moment when the earth sees the rocket passing the asteroid X, the earth thinks the distance between the rocket and the earth is more than 3 ly.

So yes, it seems to be kind of unsymmetric.

8. Sep 17, 2014

### A.T.

When you introduce a third object (asteroid X) and use it for distance measuremnts, you make it asymmetric. How is the asteroid X moving relative to Earth and rocket?

9. Sep 17, 2014

### jartsa

How would I make it symmetric then?

Let's give the rocket and the earth alarm clocks, synchronized when the rocket launches, and let's tell them to measure the distance when the clock rings.

The earth and the rocket agree about the relative speed, and then there's the symmetric time dilation. So this seems to work, they measure the same distance.

The earth says the rocket measured too late, and the rocket says the earth measured too late.

10. Sep 17, 2014

### benting180

New thought

I have a new thought now, please check whether I am correct
Base on the principle that moving object relative to some reference frame would be shorter from that frame of reference.

Take the same example,
First frame S, which is earth.
Second frame S', which is rest relative to rocket.
Rocket are moving in speed of v relative to earth.

since the rocket is the only thing moving relative to earth, so the only length of rocket will be contracted from earth's perspective.
But earth are not the only thing moving relative to earth. From rocket's perspective, all he see including the scene( may be some stars or rock that rocket may pass by ) and earth except the rocket itself is moving . Therefore, from rocket's perspective, it will see earth is shorter and the distance it travel is shorter also(since the length of stars and rock ,space between stars and rock are also contracted)

Am I right?

11. Sep 18, 2014

### jartsa

No you are not right.

When you are in the rocket, the universe moves past you. It's a flattened universe because it moves, and the universe being flattened has no effect at all on the motion of the universe.

Time dilation has no effect on the motion either. Or alternatively we just do not ask questions like: "if an object has velocity v, then how much is that velocity changed by the time dilation caused by the velocity".

12. Sep 19, 2014

### benting180

Would you mind pointing out where I am wrong since I can't do so even though I understand your first paragraph. And I can't see the link between your second paragraph and my statement, would you mind pointing that out also?

13. Sep 19, 2014

### jartsa

Let's see.

You:
Therefore, from rocket's perspective, it will see earth is shorter and the distance it travel is shorter also(since the length of stars and rock ,space between stars and rock are also contracted)

Me:
When you are in the rocket, the universe moves past you. It's a flattened universe because it moves, and the universe being flattened has no effect at all on the motion of the universe.

So I was agreeing that universe is shortened, and then I said that is no reason for the universe, including the earth, to move slower.

While you were saying that all distances in the universe are shorter, and that is why the earth moves slower.

... Except that you didn't say that. Oops. Well the earth does not travel slower, so the distance traveled by the earth is not shorter. You said the distance traveled is shorter. There's an error, right?

And then the other error. From post #1:
Since the time in earth is passing slower, so we can say the distance the earth travels must be shorter(c=d/t).

The distance the earth travels is not shorter, so you must be wrong there, right? Time dilation has no effect on that distance.

Last edited: Sep 19, 2014