Pole in the Barn Paradox: Exploring Relativity of Simultaneity

[RH111]

Hi all,

I've been exploring the concept of the Relativity of Simultaneity. However, I cannot grasp the Pole in the Barn Paradox. Here is the video to the version of this paradox I am referring to: https://worldscienceu.com/lessons/11-3-the-pole-in-the-barn-paradox/

In this situation, the runner carrying a pole (traveling near the speed of light) sees the barn through a Lorentz contraction and determines that the barn is too small for his pole to fit in the barn at any given time.
An observer, on the other hand, sees the pole through a Lorentz contraction and determines that it can fit in the barn at some given moment. Apparently, based on the relativity of simultaneity it is valid for both of their perspectives to be correct, and apparently, they both occur from each of their perspectives (maybe I am misinterpreting this).

I'm still not convinced that this is true. For instance, if the pole were rotated 90 degrees and the runner approached the barn such that the pole's length was parallel to the entrance of the barn, from his perspective it wouldn't fit. Wouldn't this mean he would crash into the barn? Alternatively, to the observer, he should pass through because the pole's length is shorter than the barn's entrance in her perspective. How could both of these be true? I understand that simultaneity is relative; however, how could two different realities result in two completely separate paths through time (one where the runner passes through and the barn is left without a scratch, and another where the entrance of the barn is severely damaged by the pole) and both be valid?

Any explanation would be appreciated as I can't bring myself to sleep over this XD.

Thanks.

 

[mfb]

Length contraction only occurs in the direction of motion. A pole orthogonal to the motion doesn't get length contracted, and the pole will crash into the sides of the barn. There is also no relativity of simultaneity to consider here as the whole pole is at the same place in running direction.

 

[RH111]

Length contraction only occurs in the direction of motion. A pole orthogonal to the motion doesn't get length contracted, and the pole will crash into the sides of the barn. There is also no relativity of simultaneity to consider here as the whole pole is at the same place in running direction.

I completely overlooked the basis of Lorentz contractions. This makes sense to me now. Thank you.

 

[RH111]

I completely overlooked the basis of Lorentz contractions. This makes sense to me now. Thank you.

I am once again questioning the Pole in the Barn Paradox.
My previous doubt was based on an incorrect understanding of Lorentz contractions. However, I now have a new scenario in mind.

Let's say there are two sensors: one at the entrance and another at the exit of the barn. The barn is set to explode if both sensors detect the pole at the same instance. Now, what will happen?
From the observer's perspective, the pole cannot possibly be in the entrance and exit of the barn simultaneously because its length is Lorentz contracted to be shorter than the barn's length in the observer's perspective. From this perspective, the barn will not explode.
The runner, however, sees the barn through a Lorentz contraction and determines that the pole will, without a doubt, be in the entrance and exit simultaneously (as it appears longer than the barn), thus causing the barn to explode.

What happens?
Do the sensors' perspectives matter here? They are identical to the observer's, so does that mean the observer is correct and the runner is wrong? How can both be correct in this situation?

Is my conceptual basis at flaw here again?
Thanks again.

 

[Ibix]

The barn is set to explode if both sensors detect the pole at the same instance.

How will you determine that they detect the pole at the same time? When you work through any answer to that question you will find that your system only detects simultaneity in the barn frame. (Edit: or one particular frame anyway, not necessarily the barn frame.)

 

[robphy]

What happens?
Do the sensors' perspectives matter here? They are identical to the observer's, so does that mean the observer is correct and the runner is wrong? How can both be correct in this situation?

Is my conceptual basis at flaw here again?
Thanks again.

A spacetime diagram is worth a thousand words.
Try to draw one.

 

[Vanadium 50]

Is my conceptual basis at flaw here again?

simultaneously

How exactly does that work?

 

[anuttarasammyak]

What happens?
Do the sensors' perspectives matter here? They are identical to the observer's, so does that mean the observer is correct and the runner is wrong? How can both be correct in this situation?

I prepare detailed setting for investigation.

The signals from sensors of "a part of him is here" at the entrance and at the exit of Barn come to PC in the middle of Barn with light speed. If they match simultaneous Barn PC explodes.

The signals from sensors of "a part of him is here" at the head and at the tail of Pole come to small PC in the middle of Pole inside with light speed. If they match simultaneous Pole PC explodes.

Which is the case happening :
A The both PCs explode.
B The both PCs do not explode.
C Barn PC explodes but Pole PC does not.
D Pole PC explodes but Barn PC does not.

I think the answer is B. What is your answer ?

 

[pervect]

I am once again questioning the Pole in the Barn Paradox.
My previous doubt was based on an incorrect understanding of Lorentz contractions. However, I now have a new scenario in mind.

Let's say there are two sensors: one at the entrance and another at the exit of the barn. The barn is set to explode if both sensors detect the pole at the same instance.

As many others have pointed out already, the key here is the phrase "the same instant". In another post you write:

Apparently, based on the relativity of simultaneity it is valid for both of their perspectives to be correct,

In the context that simultaneity is relative (which you seem to be at least somewhat aquainted with), what does "the same instant" _mean_?

 

[PeroK]

I am once again questioning the Pole in the Barn Paradox.

There are only two things that matter: the set of events under consideration; and, their coordinates in each reference frame. If you stick to that you can't go wrong.

The way to go wrong is to introduce a new complexity, such as sensors, and lazily forget to specify the relevant sensor events and their coordinates in each reference frame.

 

[PAllen]

If you have sensors attached to the barn doors, synchronized with simultaneity in the barn frame, there will be no explosion. If you have sensors attached to the rod (detecting e.g. the barn door boundary), synchronized with simultaneity per the rod frame, then there will be an explosion. Whether or not there is an explosion is not sensitive to which frame you observe or calculate in. Instead, it depends on how you synchronize 'simultaneous' for your sensors.

 

[anuttarasammyak]

If you have sensors attached to the rod (detecting e.g. the barn door boundary), synchronized with simultaneity per the rod frame, then there will be an explosion.

In post #8 I find no moment that two sensors at ends of rods are ON simultaneously in rod IFR.

 

[PAllen]

In post #8 I find no moment that two sensors at ends of rods are ON simultaneously in rod IFR.

The sensors attached to the rod would not be at the ends of the rod. They would be at a separation of the apparent width of the barn in the rod frame, anywhere along the rod. In the rod frame, it makes no sense for the sensors to be at the ends of the rod

 

[Grasshopper]

It is a hard thing to exorcise the Newtonian concept of simultaneity from your mind.

 

[Ibix]

It is a hard thing to exorcise the Newtonian concept of simultaneity from your mind.

@pervect often quotes a piece of teaching research which suggests it's the hardest thing about relativity.

I find it easiest to sketch a Minkowski diagram for any scenario. Then sketch the other frame's axes and you can mentally scissor them to Euclidean perpendicularity and see roughly what happens to the diagram. If you learn that events trace out hyperbolae as they are boosted then you can do it more accurately.

Don't try to answer the question until you've done that. Then you'll have a qualitative picture in your head (or on a piece of paper) in any relevant frame and you can talk about them without tripping over Newtonian intuitions. And you can do the formal Lorentz transforms if you need quantitative answers.

 

[vanhees71]

Yes, but here the problem is that you have to forget to think about the plane you draw you Minkowski diagram on in terms of Euclidean geometry, and that's at least as hard as to forget about the Newtonian spacetime paradigm. If you draw Minkowski diagrams you have to make yourself always clear that the coordinate grid must be constructed with the hyperbolae in the Minkowskian plane rather than circles in the Euclidean plane.

 

[Grasshopper]

@pervect often quotes a piece of teaching research which suggests it's the hardest thing about relativity.

I find it easiest to sketch a Minkowski diagram for any scenario. Then sketch the other frame's axes and you can mentally scissor them to Euclidean perpendicularity and see roughly what happens to the diagram. If you learn that events trace out hyperbolae as they are boosted then you can do it more accurately.

Don't try to answer the question until you've done that. Then you'll have a qualitative picture in your head (or on a piece of paper) in any relevant frame and you can talk about them without tripping over Newtonian intuitions. And you can do the formal Lorentz transforms if you need quantitative answers.

I think I got it on an intuitive level when I was taught that the second term in the Lorentz time transformation equation is related to clock synchronization. Since it's always there if x is non-zero, then any measurement of something moving in the x direction presumably will to have to deal with the relativity of simultaneity (Hopefully that's correct, because it's the crutch I've used to try to understand the concept, lol).