Does the Pole-Barn Paradox Challenge Einstein's Theory of Relativity?

[Michio Cuckoo]

I'm sure many of you are familiar with the "Pole-Barn" paradox.

It demonstrates the concept (or lack of) simultaneity from two different inertial reference frames. (basically whether 2 events happen at the same time depends on the relative speed of the observer)


My paradox concerns a heated pole that cools down.

From Barn's reference frame (perspective):

-As soon as the pole is fully inside the barn, both door's shut at the same time.
-At this point in time, both ends of the pole are yellow-hot.

-As soon as the front end of the pole reaches the back door, both doors open at the same time.
-At this point in time both ends of the pole are red-hot.



From Pole's reference frame:

-Both doors do not shut and open at the same time.
-Even though the pole can't fit into the barn, it passes through smoothly.

And the most surprising of all:
The pole is red-hot at one end and yellow-hot at the other!


How can this be?!

The Relativity Postulate: The laws of physics are the same in all inertial reference frames.

So if the laws of physics are the same, how come from the Pole's perspective, it does not cool uniformly, but has different temperatures at both ends?

 

[PAllen]

As a general rule, you will find that adding complications to a learning scenario (like barn pole) rarely helps you learn. Instead, it is more useful to think harder about the basic scenario.

In your case, there is nothing more mysterious than more of the same - relativity of simultaneity. In the pole frame, the doors don't open at the same time; the poles ends didn't start cooling from yellow hot at the same time; so obviously, they don't reach red hot at the same time either.

The laws are the same. The description of initial conditions at the same time per each observer can be very different.

[edit: You can clarify by stating the moment you describe as yellow heat really means the moment the ends were 'instantly' heated to yellow from whence they were allowed to cool. Then, in the pole frame, the heating was not simultaneous, so why on Earth should the cooling produce red at the same time?]

 

[San K]

I'm sure many of you are familiar with the "Pole-Barn" paradox.

It demonstrates the concept (or lack of) simultaneity from two different inertial reference frames. (basically whether 2 events happen at the same time depends on the relative speed of the observer)My paradox concerns a heated pole that cools down.

From Barn's reference frame (perspective):

-As soon as the pole is fully inside the barn, both door's shut at the same time.
-At this point in time, both ends of the pole are yellow-hot.

-As soon as the front end of the pole reaches the back door, both doors open at the same time.
-At this point in time both ends of the pole are red-hot.
From Pole's reference frame:

-Both doors do not shut and open at the same time.
-Even though the pole can't fit into the barn, it passes through smoothly.

And the most surprising of all:
The pole is red-hot at one end and yellow-hot at the other!How can this be?!

The Relativity Postulate: The laws of physics are the same in all inertial reference frames.

So if the laws of physics are the same, how come from the Pole's perspective, it does not cool uniformly, but has different temperatures at both ends?

There are no unresolved paradoxes in relativity. As PAllen has pointed out, the transmission of heat (motion, momentum etc) cannot happen faster than the speed of light.

Einstein is right, as far as relativity (special and general) is concerned, however it's possible that his understanding of, some areas of, Quantum Mechanics was incorrect.

 

[Michio Cuckoo]

In your case, there is nothing more mysterious than more of the same - relativity of simultaneity. In the pole frame, the poles ends didn't start cooling from yellow hot at the same time; so obviously, they don't reach red hot at the same time either.

The ends were 'instantly' heated to yellow from whence they were allowed to cool. Then, in the pole frame, the heating was not simultaneous, so why on Earth should the cooling produce red at the same time?]

In my example the ends were not instantly heated. The pole was already uniformly yellow- hot as it was rushing toward the barn.

You said that in the Pole's frame, both ends didn't start cooling from yellow-hot at the same time. But doesn't a uniformly heated bar cool evenly?

If Einstein said that the laws of physics are the same in all inertial reference frames, that would apply to thermodynamics.

In this case, the pole could be red-hot at one end and yellow-cool at the other. Which wouldn't be the case if the pole cooled evenly. Unless you're telling me that is not a violation of thermodynamic principles.

 

[Ich]

You said that in the Pole's frame, both ends didn't start cooling from yellow-hot at the same time. But doesn't a uniformly heated bar cool evenly?

You said that the pole is not uniformly heated. You said that it is (in every instant) uniformly heated in the barn frame, so its temperature cannot be possibly uniform in its own rest frame.

Also, there is no law of thermodynamics that says that a nonstatic spatial temperature distribution must be the same in all reference frames.

 

[Michio Cuckoo]

You said that the pole is not uniformly heated. You said that it is (in every instant) uniformly heated in the barn frame, so its temperature cannot be possibly uniform in its own rest frame.

Also, there is no law of thermodynamics that says that a nonstatic spatial temperature distribution must be the same in all reference frames.

Now you've led me to come up with this question. A Pole is at rest w.r.t. to a Barn. While still at rest, the Pole is uniformly heated until it glows yellow-hot; then it is accelerated towards the Barn.

According to S.R., it is not possible for the Pole to cool uniformly in both reference frames. <<< As said by Science Advisor Ich

So, in which frame does it not cool uniformly?

In its own frame, in the Barn's frame, or both?

 

[HallsofIvy]

The way you have that set up, it does not cool uniformly in either frame.