# Time dialation in different parts of a fast moving rocket

1. Jul 29, 2012

### fawk3s

I have no idea if Im picturing this whole scenario wrong, so please hear me out and try to point me in the right direction.

Anyways, say we have a fast moving rocket with a person in it. Lightning strikes a side of it. So the light travelling from the bolt to the person/observer is travelling perpendicular to the direction that the rocket is moving in. (In the picture, light travels from A to B. So when the rocket is moving, it ends up travelling from A to B' to an outside observer.)

http://img6.imageshack.us/img6/4254/abrod.png [Broken]

As for the outside observer, the light travels a longer distance (from A to B') with the speed c, so it takes longer time. In the rocket, however, it travels a shorter distance with the speed c, and therefore takes less time to reach its destination than for the outside observer. So it seems to the outside observer that things have slowed down in the rocket. Makes sense to me so far.

It also makes sense to me when the lightning hits the rear end of the rocket. Then light has to travel a longer distance (as the outside observer sees it, because the rocket is moving in the same direction as light from the bolt) and therefore takes more to reach its destination and it still seems as if time has slowed down in the rocket.

But where I get confused is here: when light hits the front end of the rocket (rocket is moving toward that direction), the outside observer sees that light from the bolt has to travel a shorter distance to the inside observer. And because the speed of light is the same for both observers, that would mean that it takes less time for the outside observer to see the light reach its destination. But that would mean that time has sped up in the rocket.

This really confuses me because that way it seems like at the back of the rocket time has slowed down, but in the front it has sped up. But obviously its supposed to be slowed down all the way.

Where do I go wrong?

Thanks in advance, and I hope my text wasnt too confusing all the way and you understood what I was talking about.

Last edited by a moderator: May 6, 2017
2. Jul 29, 2012

### Staff: Mentor

You neglected the important effect of the relativity of simultaneity. Imagine that there are clocks at the front and rear of the ship which are synchronized in the frame of the ship. According to the outside observer, those clocks are not synchronized: the clock in the rear shows a time ahead of the clock in the front. Regardless of where the lightning strikes, the outside observer will always see the clocks in the moving ship operating slowly compared to his own. That outside observer will say: As the light flash traveled from front to rear (or vice versa) an amount of time ΔT elapsed on the ship's clocks; during that time an amount of time ΔT*gamma elapsed on the observer's clocks. Moving clocks run slow in all cases. (Note that the ship observers will claim a different travel time for the light than ΔT.)

3. Jul 29, 2012

### Bill_K

The outside observer does not interpret this as time dilation. He realizes, as you say, that the light has a shorter distance to travel. The same thing applies even when the velocity is nonrelativistic.

To see the effect of time dilation you have to use a forward-and-backward round trip, like Michelson and Morely did.

4. Jul 29, 2012

### Staff: Mentor

If you use a round trip, then you don't have to worry about clock synchronization since the ship measures the travel time on a single clock. Much easier!

5. Jul 29, 2012

### fawk3s

That actually confuses me even more. I found this link:

Its a pretty close scenario to what we are talking about here. But as Sarah sees it, the last spaceship receives the light before the first one, so it takes less time for the light to reach the last spaceship, because both lights were fired simultaneously. For example, say, from the observer's point of view who is on the ship, it takes 5 seconds for both ships to receive it. But Sarah sees the last ship receives it with 3 seconds, while the first one receives it with 7, for example.

So it would appear as time had slowed down for the first ship, and sped up for the last.

And what exactly causes the clocks in front and back of the ship show different time?

Thanks in advance, and sorry if Im being stupid here but Im really stuck.

6. Jul 29, 2012

### ghwellsjr

There are a lot of issues going on here. You are attempting to analyze what's going on physically at the lowest levels, which is good but you are overlooking a fundamental issue. You seem to think that the two observers can actually watch the propagation of light, correct? How do they do that? If you think about it, since they are tracking the progress of the light, they really can't know instantly where the light is. All they can do is wait for the light to bounce off of something and measure how long it takes for the reflected light to propagate to their eyes. Then they have the impossible situation of determining when in that "round" trip of light the reflection actually occurred. Think about this issue before you jump to any conclusions about what actually happens.

Another issue is that you are trying to "harmonize" your scenario from two different points of view at the same time. You need to analyze everything from just one point of view, say, first when the rocket is moving and the outside observer is stationary and second when the rocket is stationary and the outside observer is moving.

A third issue is that you are thinking that the "slow down" of the rocket's clock is caused by the increase in light propagation time as the rocket moves farther away. Think about a similar scenario where the rocket starts out far away and is approaching the outside observer. If you analyze it correctly, you will conclude that still the rocket clock is ticking away slower than the stationary clock, even though it looks like it's ticking faster.

A fourth issue that you need to consider is that when the rocket man observes the outside observer's clock, he determines that it is ticking slower than his own. The clock slow down issue is symmetrical, they each determine that the other ones clock is ticking more slowly than their own. And it doesn't matter whether the rocket is receding away from the outside observer or approaching it. And it doesn't matter if you analyze either of those two situations from the point of view of the outside observer treating the rocket as in motion or from the point of view of the rocket man treating the outside observer as in motion.

Last edited by a moderator: May 6, 2017
7. Jul 29, 2012

### Staff: Mentor

8. Jul 29, 2012

### fawk3s

That is a nice analyzation of my post. I like honest and brutal truth and I actually do have something to learn from this post. You are indeed correct that I tend to solve problems trying to understand what is "physically going on at the lowest levels." But the foremost and the most bugging issue for me here is the thrid one. I cant seem to put my finger on what makes that clock tick slower although it seems to tick faster in the scenario where the rocket is approaching an outside observer. I cant visually realize what is causing it.

I guess you could say that Im chasing the answer for the question "What causes time dilation?" here, but not exactly hoping for the answer to be that "c is same for all observers, and therefore time and space are relative in order to adjust to that", but looking for more of a visual explanation/scenario which I fail to see myself.

9. Jul 29, 2012

### Bill_K

fawk3s, I'll say it again.. the reason you're having trouble seeing time dilation in this example is, the time difference does not result from time dilation. It's purely a Newtonian effect.

Suppose for convenience the length of the rocket is 2L. With a little high school algebra you can find that when light travels forward to the inside observer, it takes time t1 = L/(c - v). Similarly a backward trip takes time t2 = L/(c + v). Nothing relativistic about this. The exact same result would hold for small v, or for sound waves, etc. And there is no mention at all of clocks running slow or fast.

Now consider a round trip from the center to one end and back again. It takes tA = t1 + t2 = 2Lc/(c2 - v2). Ok.

A round trip along the sideways path takes time tB = 2L/√(c2 - v2). Relativity comes in when you try to compare these two results. Why are they different?

a) The sideways trip is where you get time dilation. Viewed from the rocket, the sideways round trip must take time 2L/c. The fact that tB is greater than this can only be explained by time dilation: the ground observer says that time on the rocket is running slower, by a factor of c/√(c2 - v2).

b) Now why is tA greater than tB? The ground observer explains this by saying that the distances are unequal. He observed the length of the rocket to be 2L, but is forced to conclude that the actual length was greater than 2L by another factor of c/√(c2 - v2). So from his viewpoint, 2L was the contracted length.

So you need round trips, you need to compare lateral and longitudinal motion, and you need to assume that on the rocket the velocity of light is c no matter what.

10. Jul 29, 2012

### jartsa

Let's consider two identical sprinters, facing opposite directions, at the middle of a fast moving rocket.

When these sprinters start off, the velocity changes are different. We know this, because we know that these people, whose brains must be running at different speeds, will say that the velocity changes are the same.

A stationary observers sees that the rear facing runner reaches the rear wall faster than the front facing runner reaches the front wall.

Now let's consider a fast moving rocket, where at the middle of the rocket some light is inside a piece of transparent material with extremely high refractive index. (so that we can say that the light inside this material moves at the same speed as the rocket)

When light moving towards the front of the rocket leaves the transparent material, the new speed of the light will be c, and the speed change of the light is c - speed of rocket.

When light moving towards the rear of the rocket leaves the transparent material, the new speed of the light will be c, and the speed change of the light is c + speed of rocket.

The light with the larger speed change reaches the rocket wall first.

Last edited by a moderator: May 6, 2017