# Why does length contraction solve this? (2 Lightclocks)

1. Dec 28, 2015

### kablion

Hey,
I'm currently working on an explanation of the special Relativity. Now I'm at the point of explaining length contraction, but I don't understand why the following example is a reason for length contraction to exist:

Imagine we have two Lightclocks in a fast moving Rocket. Lightclock 1 points in the direction of movement and lightclock 2 is perpendicular to that.

In the inertial frame of the rocket both lichtclocks run synchronously. But from another inertial frame they would run asynchronously, because the way, that the light in lightclock 1 has to travel is longer than the way in lightclock 2. That can't be, because the lightclock has to run synchronously. So one thinks of the lenght contraction as solution.

But the lightclock 2 has two lightways with the same lenght, whereas lightclock has one longer way, when the light has to travel in the same direction as the rocket. That means through lenght contraction, the total way is equal, but it still runs asynchronously because the time both lightclocks need to complete one of the to ways isn't equal. So why is lenght contraction the solution to this, althought it only solves the total distance.

To make it more visible to you I've found a video, that shows my problem. The only thing: It's german. But the things that are said don't matter if you read my post:

I hope you understand what I mean and can help me.

Kablion

2. Dec 28, 2015

### Staff: Mentor

This doesn't make sense. If the total distance (which is what I assume you mean by "way") the light has to travel is the same, and the speed of the light is the same, then the time it takes the light to travel must be the same.

3. Dec 28, 2015

### kablion

Ok I guess you didn't understand me right.
The total way the light has to travel is divided in two ways (I think you know what a lightclock is?!): the way the light has to travel from the first mirror to the second mirror and the light has to travel back again to the first mirror.
So the lightclock, which points in the direction of movement, has a longer first way than the second way.
But the lightclock which is perpendicular has both ways with the same length.
So due to length contraction the total length (way1 + way2) of both lightclocks is equal,
but the lengths of the way1 of both lightclocks is not equal (same to way2)

Ok way easier to understand is the question:
At the end of the Video after the length contraction happens, all photons arrive at the sun at the same moment,
but the photons arrive at the outer circle at different moments. Why does this difference of the arrival time not matter? For the observer in this inertial frame all photons arrive at the same moment on the outer circle.
I think this problem isn't solved with length contraction.

4. Dec 28, 2015

### Mister T

They arrive at the same time in the rest frame; but not at the same time in the moving frame, because they are spatially separated along the line of motion.

5. Dec 28, 2015

### Vitro

@kablion it's only the total distance which matters, total time is the total distance divided by c and it is the same for both clocks.

By the way, that video is slightly wrong at 2:49 and 2:52, the four pulses would not arrive at the inner circle simultaneously in the shuttle frame.

6. Dec 28, 2015

### kablion

Ok I think I understand now what my real problem here is:
Why or How can 2 events occur at the same moment in one frame, but in another frame they occur at different moments?
Has this scenario or theory a name?

7. Dec 28, 2015

### Staff: Mentor

Yes. This is the relativity of simultaneity. It is the single most challenging concept to learn.

All frames agree if two co-located events occur at the same time, but for events that are spatially separated, different frames will disagree about whether or not they are simultaneous.

8. Dec 28, 2015

### PeroK

That video is misleading because the light source is of significant size. You really need to redo the problem with a point source of negligible size.

Note that if events are simultaneous at the same point in space in one frame, they must be simultaneous and at the same point in space in another frame.

But if events are simultaneous and at different points in one frame, then they will not in general be simultaneous in another frame.

In the video this happens noticeably when the light rays going left and right get reflected. In the moving frame these events are simultaneous: Both rays get reflected at the same time. But, in the rest frame, the ray on the left gets reflected before the ray on the right gets reflected. In the rest frame these are not, therefore, simultaneous events.

9. Dec 28, 2015

### Staff: Mentor

This is true. So what? A "tick" of the clock is a round trip; the fact that the two legs of the round trip have unequal lengths for one of the light clocks is irrelevant, as long as the round trip time is the same for both, which it is.

10. Dec 28, 2015

### kablion

Ok to all of you: You helped me a lot! Thank You!
That relativity of simultaneity was the one thing I missed on understanding special Relativity.