What is the essence of the ladder paradox in relativity?

[L Drago]

TL;DR

See in ladder paradox the ladder is moving in very high speeds. So from the perspective of an observer outside or barn's frame, it will appear to contract and fit. But from the ladder's frame the barn will contract and the ladder will not fit.

According to relativity of simultaneity, events may not always be simultaneous from both frames of reference. The scenario described above happens due to lorentz length contraction and relativity of simultaneity.

Please help me understand where I am getting this concept wrong.

 

[anuttarasammyak]

There is an expanation of ladder pradox https://en.wikipedia.org/wiki/Ladder_paradox .
Do you find anything unclear or wrong there ?

 

[Dale]

The relativity of simultaneity is the most difficult concept for students to learn.

The thing that helped me was to realize that nature doesn’t care about simultaneity. She cares that causes come before effects. But two events that are simultaneous cannot possibly have a cause and effect relationship. So nature simply doesn’t care which comes first.

 

[Halc]

Please help me understand where I am getting this concept wrong.

You don't seem to have any of it wrong. Yes, it is essentially due to relativity of simultaneity.

There are only two important events:
F The front of the ladder passes through the rear door to exit the barn
R The rear of the ladder passes through the front door to enter the barn

In the barn frame, event R occurs before event F, and so the ladder is contained within the barn in the duration between those events.
In the ladder frame, event F occurs before event R., and so the ladder sticks out of both sides of the barn in the duration between those events.
That's a simple illustration of relativity of simultaneity. It is nothing but a coordinate difference in the respective assignment of a time coordinate to each of those two events.

 

[PeroK]

The thought experiment that helped me understand this is to consider a train moving past a station platform. On the platform we have two clocks - one at each end. The clock at the far end of the platform records the time the front of the train passes this point (event A). And, the clock at the near end of the platform records the time the rear of the train passes this point (event B). These clocks are at rest relative to each other and we assume they have been synchronized, so represent a measure of the time coordinate at those points in the platform frame.

Let's assume that, in the platform frame, the moving train is the same length as the platform. This means that the front of the train is at the far end of the platform at the same time as the rear of the train is at the near end of the platform. So, the two clocks record the same time for events A and B. As an aside, that experiment defines a good, operational definition of the length of an object that is moving in the frame of reference in which its length is measured.

Now, if we imagine that the train returns to the platfoms and stops, then we find that the rest length of the train is longer than the platform. Note that we are imagining a relativistic train in this case, so that the length contraction is significant.

So far, so good. We have a simple case of length contraction.

But, now, we consider the events A and B in the frame of the train. We can imagine two more clocks at either end of the train - they are at rest relative to each other and, if synchronized, represent a measure of the time coordinate at those points in the train frame. The platform is not only shorter than the train, but is also length contracted in the train frame (as the platform moves past the train). In any case, event A happens first in the train frame (the front of the train passes the far end of the platform). At this time (in the train frame), the near end of the platform is somewhere along the train. Then, event B happens. At this time (in the train frame), the front of the train has already moved well past the far end of the platform.

We see that events A and B are not simultaneous in the train frame. So, simultaneity (i.e. two events having the same time coordinate in a given frame of reference) depends on the frame of reference.

PS in this case, we derived the relativity of simultaneity from length contraction. It's also possible to derive the relativity of simultaneity directly from the two postulates of SR.

 

[Herman Trivilino]

TL;DR Summary: See in ladder paradox the ladder is moving in very high speeds. So from the perspective of an observer outside or barn's frame, it will appear to contract and fit. But from the ladder's frame the barn will contract and the ladder will not fit.

The ladder is moving at a very high speed relative to the barn. In the rest frame of the barn the ladder is contracted and will fit. In the rest frame of the ladder the barn is contracted and the ladder will not fit.

Note the differences in the way I phrased it. In particular note that your observer is in the rest frame of the barn, but also in the rest frame of the ladder. It's just that he's at rest relative to barn but he's in motion relative to the ladder. Also note that the barn is in motion relative to ladder.

According to relativity of simultaneity, events may not always be simultaneous from both frames of reference. The scenario described above happens due to lorentz length contraction and relativity of simultaneity.

Please help me understand where I am getting this concept wrong.

You are glossing over the details of the role of the relativity of simultaneity. You're not wrong, you're just incomplete. Can you explain how the relativity of simultaneity makes it possible for the length contraction to be symmetrical? That is what you are missing. Fill in that detail and your understanding will be complete.

 

[L Drago]

The ladder is moving at a very high speed relative to the barn. In the rest frame of the barn the ladder is contracted and will fit. In the rest frame of the ladder the barn is contracted and the ladder will not fit.

Note the differences in the way I phrased it. In particular note that your observer is in the rest frame of the barn, but also in the rest frame of the ladder. It's just that he's at rest relative to barn but he's in motion relative to the ladder. Also note that the barn is in motion relative to ladder.

You are glossing over the details of the role of the relativity of simultaneity. You're not wrong, you're just incomplete. Can you explain how the relativity of simultaneity makes it possible for the length contraction to be symmetrical? That is what you are missing. Fill in that detail and your understanding will be complete.

Suppose the barn is at rest and ladder in very high speeds if a person is sitting on a ladder, from his perspective the barn will appear to contract and the ladder will not fit.

But from the barn's perspective the ladder will appear to contract and fit in the barn.

From a person's perspective standing observing the ladder and barn the ladder should contract and fit inside the barn.


These are all perspectives given that the barn is at rest. Relativity of simultaneity basically means that two events don't need to occur in the same way in two or more frames of references for example my first and second perspective.

Kindly react positively and kindly tell which part have I not understood completely.

 

[L Drago]

The thought experiment that helped me understand this is to consider a train moving past a station platform. On the platform we have two clocks - one at each end. The clock at the far end of the platform records the time the front of the train passes this point (event A). And, the clock at the near end of the platform records the time the rear of the train passes this point (event B). These clocks are at rest relative to each other and we assume they have been synchronized, so represent a measure of the time coordinate at those points in the platform frame.

Let's assume that, in the platform frame, the moving train is the same length as the platform. This means that the front of the train is at the far end of the platform at the same time as the rear of the train is at the near end of the platform. So, the two clocks record the same time for events A and B. As an aside, that experiment defines a good, operational definition of the length of an object that is moving in the frame of reference in which its length is measured.

Now, if we imagine that the train returns to the platfoms and stops, then we find that the rest length of the train is longer than the platform. Note that we are imagining a relativistic train in this case, so that the length contraction is significant.

So far, so good. We have a simple case of length contraction.

But, now, we consider the events A and B in the frame of the train. We can imagine two more clocks at either end of the train - they are at rest relative to each other and, if synchronized, represent a measure of the time coordinate at those points in the train frame. The platform is not only shorter than the train, but is also length contracted in the train frame (as the platform moves past the train). In any case, event A happens first in the train frame (the front of the train passes the far end of the platform). At this time (in the train frame), the near end of the platform is somewhere along the train. Then, event B happens. At this time (in the train frame), the front of the train has already moved well past the far end of the platform.

We see that events A and B are not simultaneous in the train frame. So, simultaneity (i.e. two events having the same time coordinate in a given frame of reference) depends on the frame of reference.

PS in this case, we derived the relativity of simultaneity from length contraction. It's also possible to derive the relativity of simultaneity directly from the two postulates of SR.

Suppose the barn is at rest and ladder in very high speeds if a person is sitting on a ladder, from his perspective the barn will appear to contract and the ladder will not fit.



But from the barn's perspective the ladder will appear to contract and fit in the barn.



From a person's perspective standing observing the ladder and barn the ladder should contract and fit inside the barn.





These are all perspectives given that the barn is at rest. Relativity of simultaneity basically means that two events don't need to occur in the same way in two or more frames of references for example my first and second perspective.

Kindly explain which perspective I am getting wrong. Kindly react positively and help me understand where I am wrong.

 

[PeroK]

I'm not sure what you think you are getting wrong.

 

[L Drago]

I'm not sure what you think you are getting wrong.

I thought I must be getting something wrong but thanks for clarification now I know the information is authentic and accurate.

 

[PeroK]

I thought I must be getting something wrong but thanks for clarification now I know the information is authentic and accurate.

If you want to learn SR, you need a good source. The first chapter of Morin's book is free online here. If you like his style, you can buy the rest of the book:

https://davidmorin.physics.fas.harvard.edu/books/special-relativity/

 

[L Drago]

If you want to learn SR, you need a good source. The first chapter of Morin's book is free online here. If you like his style, you can buy the rest of the book:

https://davidmorin.physics.fas.harvard.edu/books/special-relativity/

Thanks a lot @PeroK. Now I have realized instead of just reading random articles from internet, I must follow a reliable source of information like a book. This random reading of articles of SR from internet was the reason of my misunderstanding in time travel thread.

 

[jbriggs444]

Kindly explain which perspective I am getting wrong. Kindly react positively and help me understand where I am wrong.

You understand that both interpretations of the scenario are consistent with a single physical reality? That there is no conflict between the two?

Putting doors on the barn that are (or are not) closed "simultaneously" with the ladder completely inside is often used to emphasize the dependence on the relativity of simultaneity.

Alternately, one might place flags on the ends of the ladder that are (or are not) raised simultaneously when the ends are outside the barn.

 

[PeterDonis]

There are only two important events:
F The front of the ladder passes through the rear door to exit the barn
R The rear of the ladder passes through the front door to enter the barn

But in the frame in which the ladder is at rest, the phrasing you use is not natural. A more natural phrasing would be:

F: The rear door of the barn passes over the front of the ladder, so part of the ladder is now outside that door.
R: The front door of the barn passes over the rear of the ladder, so no part of the ladder is now outside that door.

Phrasing it that way might make it somewhat easier to see what is going on.

 

[Herman Trivilino]

These are all perspectives given that the barn is at rest.

No, the only thing you can claim is that the barn is at rest relative to the ground underneath it. There is no such thing as an absolute state of rest. That is the point of the first postulate.

 

[Herman Trivilino]

Suppose the barn is at rest and ladder in very high speeds if a person is sitting on a ladder, from his perspective the barn will appear to contract and the ladder will not fit.

But from the barn's perspective the ladder will appear to contract and fit in the barn.

From a person's perspective standing observing the ladder and barn the ladder should contract and fit inside the barn.

I'm not sure why you repeated all that. I summarized it all in the first paragraph of the post you replied to!

 

[L Drago]

No, the only thing you can claim is that the barn is at rest relative to the ground underneath it. There is no such thing as an absolute state of rest. That is the point of the first postulate.

So I should write barn is in rest with respect to the ground and thank you for correcting my mistake

 

[Herman Trivilino]

So I should write barn is in rest with respect to the ground and thank you for correcting my mistake

It makes no difference for the purposes of the barn-ladder paradox. All that matters is that the barn and the ladder are in relative motion. You might as well claim that the ladder is at rest relative to a rocket ship flying past. The point is that it makes no difference.