# Length contraction, train along a line, and a detector

1. May 14, 2015

### Nick666

I was reading a closed thread here about the length contraction being real or not. The best I could understand my self is that space is the one that contracts, the final post by an experienced forum member saying something like its the space-time that changes, it rotates.

But I still have to ask this. So we have a train that is 299.792.458 meters long, travelling along a line. We setup a timer on that line such that it begins to record when the train touches it, and stops recording when the train stops touching it. The faster the train moves the shorter the time recorded. But at the train speed of 299.792.000 m/s, will the timer record more or less than a second ?

Last edited: May 14, 2015
2. May 14, 2015

### A.T.

In which frame?

3. May 14, 2015

### Nick666

Its a train on a railroad line. Just that its a long train.

4. May 14, 2015

### PeroK

I guess you meant that the this was the rest length of the train.

It's easier to see what's happening in the train's frame. The faster the timer moves towards to train, the less time it will take to pass. If the timer gets close to the speed of light it will be just over 1 second in the train's frame.

But the timer will be running very slow in the trains frame. So, the timer will record only a fraction of a second.

All observers will agree on what the timer records.

5. May 14, 2015

### DrGreg

A.T. is asking you who made the measurement of 299792458 metres: someone on the train or someone on the line?

6. May 15, 2015

### Nick666

I think the measurement is what perok said...at rest.

Ok, so from the stationary railroad line's point of view, the train's length contraction is real.

7. May 15, 2015

### Mentz114

In the stationary railroad coordinates the train is still the same length. Everyone agrees on the reading on the timer clock for its passage of the train.

One might say that for the timer the train appeared much shorter than it does for the train observer.

8. May 15, 2015

### Nick666

Ok. So how about this ? if we have a timer, on a railroad line, that records for how long it doesnt detect sunlight photons, and a 299792458 meters long train moving at almost c, the timer will record for a fraction of a second ?

9. May 15, 2015

### Ibix

Yes, the timer will record some fraction of a second of shadow. You can get this from the LT. The train is stationary in the primed frame, the front at x'=0 and the back at x'=-1 (measuring in light seconds). The front of the train is at the origin of the non-primed frame at t=0. The back of the train is at the origin when
$$\begin{eqnarray} x'&=&\gamma(x-vt)\\ -1&=&-\gamma vt \end{eqnarray}$$You can see that t is a very small number.

This is rather different from what you would see if you looked at the whole train, which is what the Terrell rotation thread you have also posted on, is talking about. Here you are focussing on one point at a time, and arranging not to have to worry about lightspeed delay. If you factor both of those things in, life gets more complex. It's like the difference between trying to work out what a map would look like if you moved the origin (easy, just move the gridlines) and what a photo would like if you moved the camera (a very different problem).

10. May 15, 2015

### Mentz114

Is that not the same as the original setup ? I do not wish to change my statement. No one disputes the timer will register much less than a second. How does this impact on the length of the train ?

11. May 15, 2015

### ghwellsjr

Length contraction is a coordinate effect. That's because length is a coordinate effect. It's not enough to say that from the stationary observer's point of view the length of the train is contracted just because his clock reads a fraction of a second. That observer must also measure the speed of the train and then calculate the length of the train based on the time it took to pass.

And in order for the stationary observer to measure the speed of the train, he must make two measurements of, say, the leading edge of the train at two different times, at least one of which must be a remote measurement. That remote measurement requires him to make an arbitrary assumption about the one-way speed of light (something that he cannot independently measure). Depending on that arbitrary assumption, he can get a wide range of speeds for the train and therefore a wide range of lengths for the train. None of these lengths can be considered any more real that any of the others, not even the one that he gets when he assumes that light takes the same amount of time to go from him to the leading edge of the train as it does for the reflection to get back to him.