The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity.
This should not be called a thought experiment. The ladder experiment should be a description of an experiment including what should be observed i.e. the outcome. In principle there could be two outcomes then both should be mentioned which an explenation which is wrong.
It involves a ladder, parallel to the ground, travelling horizontally and therefore undergoing a Lorentz length contraction.
Correct.
As a result, the ladder fits inside a garage which would normally be too small to contain it.
Wrong reasoning. What should be observed is that the ladder fits in the garage which is called Lorentz length contraction.
This is true assuming length contraction is a physical effect.
On the other hand, from the point of view of an observer moving with the ladder, it is the garage that is moving, so it is the garage which will be contracted to an even smaller size, thus being unable to contain the ladder.
That means of this experiment there are two possible conflicting outcomes.
In relativity, simultaneity is relative to each observer, and so the question of whether the ladder fits inside the garage is relative to each observer, and the paradox is resolved.
That simultaneity is "relative" to each observer be true, but that does not answer the question if the ladder fits in the garage when I perform this experiment
1. Paradox
Because of its high velocity, the ladder undergoes the relativistic effect of length contraction, and becomes significantly shorter.
Like before it is the other way around. First the ladder becomes shorter and second length contraction as an explanation.
We could, if we liked, simultaneously close both doors for a brief time, to demonstrate that the ladder fits.
The emphasis is on the word simultaneously.
As an observer moving with the ladder is travelling at constant velocity in the inertial reference frame of the garage, this observer also occupies an inertial frame, where, by the principle of relativity, the same laws of physics apply.
You should explain what means that the same laws of physics apply.
What should be true that the outcome should be indepent of the two observers.
From this perspective, it is the ladder which is now stationary, and the garage which is moving with high velocity.
Including the whole environment.
It is therefore the garage which is length contracted, and we now conclude that it is far too small to have ever fully contained the ladder as it passed through: the ladder does not fit, and we can't close both doors on either side of the ladder without hitting it.
The missing word is simultameously. We can't close both doors simultaneously.
Part of the problem is that simultaneous for both observers mean something physical different.
You have to perform this experiment in reality to decide whose opinion is wrong and maybe both.
2. Resolution
3. Shutting the ladder in the garage
4. Ladder paradox and transmission of force
5. Man falling into grate variation
7. See also
Following is a list with "Comments in Wikipedia" about related subjects
Train 1 is at rest. This train has the rest length L0
Train 2 has a speed v > 0. This train is smaller than Train 1 and is under going Length contraction
An observer at rest perpendicular to point "X" will observe both trains.
This example becomes interesting considering observers on each train
An observer on Train 1 will first see the Front of the train and then the Back of the train.
When he has a clock he can measure the length of the Train 2.
The result will be that there is length contraction.
The problem comes with an Observer on Train 2. In his view Train 1 is moving but also the entire landscape.
He can select two approaches: Clocks in the rest frame and moving clocks on Train 2.
When he uses clocks in the rest frame he will realise that it will take longer to travel along Train 1 (using a fixed point on Train 2 and Front and Back of Train 1) than to travel along Train 2( using a fixed point on Train 1 and Front and Back of Train 2)
When using clocks on Train 2 the obeserver should understand that these clocks run slower.
This raises a serious question how symetrically Length contraction really is.
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Created: 31 January 2015
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