Relativity - Did I break it relatively bad? (pun intended)

[KvickFlygarn87]

OK, imagine a stick 30cm long, a hole 20cm deep, and a hatch above the hole.

The stick is falling towards the hole near c. In any ref system other than the stick's, the stick is, say, 15cm. The istant the stick enters the hole, the hatch closes, and the stick is instantly decelerated completely, extending the stick to 30cm.

What happens, or am I wrong on some point

From the brain of an 8th grader, surely incorrect somehow.

[BeefTenderloin]

You've missed a hugely fundamental part of relativity, called the relativity of simultaneity. Things that are simultaneous in one reference frame are not simultaneous in another reference frame.

The hole observer sees the stick enter the hole, decelerate, then the lid close, being wedged open by the stick.

The stick sees itself enter the hole, then the lid immediately shutting on it.

[ZetaX]

Being decelerated, while sounding like a trivial and intuitive notion, should also be defined carefully; you can also create a lot of paradoxes otherwise. Wikipedia had a short list of such and length-contraction related paradoxes I think.

In general, there essentially can be no contradictions in special relativity:

Its axioms are consistent, i.e. can not cause a contradiction by themselves, if one assumes that the so-called axioms of ZFC (Zermelo-Fraenkel & choice) are consistent. The latter has survived many much harder beatings by mathematician so far (but the consistency is provably impossible to prove, see Gödel's incompleteness theorem). This obviously only implies that pure thought experiments cannot contradict it and says nothing about its applicability to real life.

[K^2]

It's called Ladder Paradox. The linked wiki article covers it pretty well.

[kahlzun]

By the time the hole snapped shut, the bottom of the hole would be a -lot- deeper.

[KvickFlygarn87]

Oh, so I was sorta wrong. This couldn't happen.

Also kahlzun, I meant that the very instant the stick is completely in, the hatch closes instantly. This a theoretical experiment, not a practical one.

[vexx32]

Okay, you're missing another part of relativity (or just general physics, not sure), as I see it. There is no such thing as "instant". It must take time for the hatch to close, or else it hasn't moved.

[ZetaX]

The "instant" (a.k.a.: much faster than the other processes involved) closing is no problem at all.

[K^2]

Oh, so I was sorta wrong. This couldn't happen.

Not sure what you mean. Scenario you described is perfectly reasonable. What wouldn't happen is stick getting longer when it stops. After looking through it, Ladder Paradox page doesn't cover acceleration too well. (It only briefly mentions it in relation to another paradox.) I'll prepare some graphs to show what would happen when the object decelerates "almost" instantly from light speed. I'll use the ladder instead of the stick, just like in paradox, because spacing between rungs gives a really good picture of how it deforms.