# Verification of the Lorentz contraction of the space

1. Sep 9, 2007

### cheffo

question for the Lorentz's space contraction

I imagin this thought experiment: a train which travels with the speed of light is trying to enter a tunel which has absolutely the same form and dimmension like the train's shape, as if the the train goes slowly with his regular speed it will enter with no problem. If we put 3 observers one on the train, one staying on the top of the tunel waiting to see the train passing below him, and one staying near by watching the train's passage through the tunel? If the movement is relative and a fast traveling object (with c) contracts for a staying observer what phenomena will all the observers see? For the first one it's the tunel who comes, for the second it's the train as for the third who is hardly needed I am interested to know what will he see because I am picturing my self as him and I don't want to take the place of the others. With the time dilatation the things are more clear. As Brian Greene describes it : if two travellers in the open space are moving face to face with a fictional digital clock on their heads and if the are moving with the speed of ligft every one of them will consider the clock of the other ticking slower than the one they own. However it's explicable, my question does not argues with the theories, but there is this thing that I don't understand.

Last edited: Sep 9, 2007
2. Sep 9, 2007

### Staff: Mentor

Seems to me that your second and third observers are both at rest with respect to the tunnel, so they are in the same reference frame--thus they "see" (measure & deduce) the same thing.

The tunnel observers see the train as contracted; the train observers see the tunnel as contracted. Do you have a question about this situation?

Note that it's perfectly OK to have a thought experiment in which the train moves at a high speed, but that speed can never equal or exceed the speed of light.

3. Sep 9, 2007

### cheffo

Re:Lorentz space contraction

Thank you for the fast answer! I think, that even if the train does not achieve or exceed c the space contraction will take effect and I realy think that this will create different realities for the observer in the train and the one on the top of the tunel. The experiment could be made with a tunel which is normaly a little bit smaller than the train. Then if the train is fast enough it will pass through the tunel if not it will crash. I want in my thought experiments the trains people, cars ... etc to have the ability to travel with c. Einstein's thought experiments are full with light speed trains and stuff.

4. Sep 9, 2007

### Staff: Mentor

Why would it crash? I hope the tunnel is open at both ends!

A better example of what you are probably concerned with is the famous "barn and pole" problem. A fast runner carrying a pole that has a rest length exactly equal to the length of the barn runs through the barn. From the barn's viewpoint, the pole is smaller than the barn, thus both doors can be shut while the barn is inside. But from the runner's viewpoint, the barn is too small to contain the pole and thus the doors cannot be shut with the pole completely inside. They are both "right". To understand this, you need to consider the relativity of simultaneity as well as length contraction.

Well, you're out of luck--relativity forbids it. But all relativistic effects can be plainly seen at sub-lightspeeds, like 0.9c.

No. Einstein's trains go fast, but not that fast!

5. Sep 9, 2007

### cheffo

I am sorry but I think I am still missunderstood. let's say we have a train or something else moving with 80% of the speed of light, just enough for the space contraction to take effect. I am pretty sure I am facing a paradox here. In the first question i mensioned a detailed experiment described in The Elegant Universe where a boy and a girl George and Grasy can achieve 99,5% from the speed of light. It doesn't matter the exact speed of moving. 80% or 99,5% from c is enough to obtain the contraction. That i what I am trying to explaine to myself. One of Einstein's experiments consists: what shall I obseve if I am in a train and there s a mirror located on the front wall of the wagon? What shall I observe if the train moves with the speed of light? will the mirror be black? He asks himself this question before he creates his theory. Before he posts his principle of the constant speed of light. The main idea is that he wants to prove that the Newton laws of adding the velocities don't match there. If it is not a train which can gos with c let put this particular train into my experience.

6. Sep 9, 2007

### cheffo

I just red your last replay. I wasn't aware of tha barn - pole paradoxe I think this is the same situation? thank you after all. And sorry for the inadequat replies. hope I can count for your opinion in the future.

7. Sep 9, 2007

### cheffo

I understood what they mean with this paradox. I saw that there is a difference between my case and the bug-rivet or pole-barn paradoxes. They speak about long pole and a long barne. What if we turn the pole across and it's a 20m pole and the barn has a gate which is 19m wide will the pole pass through if it's fast enough (0,9c) or not? This resume all the questions with the trains. Thank you again.

8. Sep 9, 2007

### Staff: Mentor

OK, I see what you're saying. Yes, Einstein used such thought experiments to show that Galilean addition of velocities just won't work with lightspeeds. As long as you realize that a consequence of relativity is that massive objects (like trains and people) cannot achieve lightspeed.

Realize that moving objects only contract along their direction of motion. If you turn the pole sideways, its length won't contract (it will just be thinner). So a 20m pole turned sideways will not make it through a 19m wide door. (Both sets of observers see the pole as 20m long and the door as 19m wide.)

I'm not sure what this has to do with your original example with the train through the tunnel, since the train isn't turned sideways. If you still have a question about that scenario, perhaps you can restate it.