A problem with the solution to the ladder paradox

[student34]

TL;DR

A problem with the solution to the ladder paradox

Imagine that there is a very tight string connected to the bottom of each barn door. Each barn door opens and closes vertically. If the string breaks the barn blows up. The doors have to close at the same time for the string not to break. If the doors open one at a time, the extra distance separating the the two doors will surely break the string. Now the ladder goes through at very high speeds. Does the barn explode or not?

It seems as though one of the observers is having an illusion

 

[Vanadium 50]

The doors have to close at the same time

1. Please describe mechanism that enforces "at the same time".
2. How does this mechanism work after boost?

 

[student34]

1. Please describe mechanism that enforces "at the same time".
2. How does this mechanism work after boost?

I did describe it. The string must be perpendicular to the doors' motion or the barn blows up.

 

[hutchphd]

Summary:: A problem with the solution to the ladder paradox

Now the ladder goes through at very high speeds. Does the barn explode or not?

What ladder? Is this the ladder experiment or a string experiment? You are making this more complicated for no reason. Which do you want to discuss?

 

[Nugatory]

The doors have to close at the same time for the string not to break. If the doors open one at a time, the extra distance separating the the two doors will surely break the string.

Short answer: The ends of a piece of string won’t work to enforce simultaneity.

Long answer: you have constructed an interesting variant of the rigid rod fallacy; read this insights article and also Google for and understand the “bug-rivet” paradox.

The string will not remain straight in any frame because the ends must start moving before the middle (even classically, there’s no transverse force on the middle segment until after the ends have been displaced by the motion of the doors). It will stretch into a curved shape and whether it breaks or not will depend on the details of its modulus of elasticity, yield strength, and linear density.

To analyze this problem correctly and completely we would have to calculate the tension at every point along the string as a function of time. It will be easiest to do this in the barn frame, but it’s still going to be rather hairy. Once we’ve done this, we can transform the tension:time function to the ladder frame (there are some subtleties here) and we’ll get the same break or not result as in the barn frame (or any other frame for that matter).

 

[Nugatory]

What ladder? Is this the ladder experiment or a string experiment? You are making this more complicated for no reason. Which do you want to discuss?

We start with the classic pole-barn paradox, which is sometimes written using a ladder instead of a pole. The doors slide vertically and are connected by a string that will break instead of stretching. If the two doors do not move in unison the distance between the attachment points will increase; the hope is that this physically unrealizable string can be used to detect absolute simultaneity.

 

[hutchphd]

FYI: The link to "this insights article" did not work for me.
How is this version of the ladder done? The doors slam shut and open (in the barn frame) very fast?? Why go down this road?

Edit: we were in fact simultaneous. But my question still holds: why comingle these arguments?

 

[hutchphd]

For the OP (in the previous thread IMO prematurely truncated) it seems to me the issue here is how to unambiguously specify the size of an object. The size of a rigid object should be that which is measured in the usual way with a ruler in the rest frame of the object. By fiat. The length of the object is then frame dependent.
This seems to me equivalent to not using relativistic mass as a concept and for the same good reasons. Semantics do matter. Problem solved or does this fall apart?

 

[jartsa]

I did describe it. The string must be perpendicular to the doors' motion or the barn blows up.

Okay so we want the string to stay horizontal while being lifted up. That's an impossible task for two lifters.

Many lifter along the string can do it without any problem.

 

[mitochan]

Summary:: A problem with the solution to the ladder paradox

Imagine that there is a very tight string connected to the bottom of each barn door. Each barn door opens and closes vertically. If the string breaks the barn blows up. The doors have to close at the same time for the string not to break. If the doors open one at a time, the extra distance separating the the two doors will surely break the string. Now the ladder goes through at very high speeds. Does the barn explode or not?

May I interpret you as one of the sketches attached ?

The string will not be broken when the doors move in a synchronized way, i.e. the two door operators do the same procedure watching their clocks one at the front wall and the other on the back wall of the barn. Of course the two clocks should be well synchronized on the ground the detail of which Einstein described in his first SR paper. We can substitute that string constraint to the above operation by watching the clocks as above said.

 

[phinds]

May I interpret you as the sketch attached ?

Clearly not since he specifically said the doors open vertically and you've drawn doors that open horizontally. Read the thread over again. Other posts clearly recognize what he said.

 

[PeroK]

Eugene Khutoryansky has a video on this:

 

[jartsa]

Okay so we want the string to stay horizontal while being lifted up. That's an impossible task for two lifters.

Many lifter along the string can do it without any problem.

When those many lifters lift, simultaneously in the barn frame, non-simultaneously the ladder frame, the string stays horizontal in the barn frame, tilts in the ladder frame.

The string ends should stay next to the barn doors in all frames, which means that the sting should get longer in the ladder frame. Luckily the string's tilting away from the direction of its motion in the ladder frame has the effect of string becoming less length-contracted in the ladder frame.

Thanks to length contraction the string can suddenly increase its length in one frame while keeping the same length in another frame, all without breaking or becoming stretched.

 

[mitochan]

May I interpret you as one of the sketches attached ?

One more as attached.

 

[MikeLizzi]

When those many lifters lift, simultaneously in the barn frame, non-simultaneously the ladder frame, the string stays horizontal in the barn frame, tilts in the ladder frame.

The string ends should stay next to the barn doors in all frames, which means that the sting should get longer in the ladder frame. Luckily the string's tilting away from the direction of its motion in the ladder frame has the effect of string becoming less length-contracted in the ladder frame.

Thanks to length contraction the string can suddenly increase its length in one frame while keeping the same length in another frame, all without breaking or becoming stretched.

I get the same results. Non-intuitive to say the least.

 

[student34]

When those many lifters lift, simultaneously in the barn frame, non-simultaneously the ladder frame, the string stays horizontal in the barn frame, tilts in the ladder frame.

The string ends should stay next to the barn doors in all frames, which means that the sting should get longer in the ladder frame. Luckily the string's tilting away from the direction of its motion in the ladder frame has the effect of string becoming less length-contracted in the ladder frame.

Thanks to length contraction the string can suddenly increase its length in one frame while keeping the same length in another frame, all without breaking or becoming stretched.

Thanks, this seems correct, but I am still thinking about it.