1. Dec 29, 2005

### Jir

Recently I started reading about relativity and found this flaw like thingy. I asked a friend of mine who studied physics and he came with the unsatisfying answer: 'at speeds like that everything kind of blurrs so the spearman wont crash into the door'.

Is the following correct and a paradox or not?

There is a spearman, with a spear of 7 meters long, who is running at 0.9c. He wants to run trough a room which is also 7 meters long. In the room is a man who has 2 buttons: one to open the first door and one to open the second door. However that man wants to keep out the draft and only wants to open 1 door. Will the spearman crash into the door or not?

The Doorman will see the spearman contracted to 3.05 meters so according to him the spearman will fit perfectly.

However the spearman will see the room contracted to 3.05 Meters so it wont fit according to him.

Who is right? And why? I'm kind of confuzzled by this.

Thanks in advance for anybody helping me.

2. Dec 29, 2005

This is a common missconception. In relativity becuase the idea of simultaniousness is lost the spear man will see the front door open then the back door open, next the front door will close once he is through it and finally the back door will close. This is what the spear man sees. The person controlling the door will still see just what you discribed. I know this sounds odd but it is the way relativity works. =)

3. Dec 29, 2005

### Staff: Mentor

The Barn and the Pole

This is a standard "puzzler" in special relativity called the "The Barn and the Pole" paradox. Its resolution rests on understanding that the two observers will disagree on whether both doors were closed at the same time. (Not sure what you mean by only opening one door. You'd better open the second door pretty quick or the spear will just smack into it. No need for relativity to understand that!)

http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/polebarn.html

4. Dec 29, 2005

### Jir

Thanks for the very clear explenations. Helped me allot :)

5. Dec 29, 2005

### Tom Mattson

Staff Emeritus
As others have explained this isn't a flaw. But you're right, that is a very unsatisfying answer!

6. Dec 30, 2005

### O Great One

I have a question. What if the spearman stops running once he gets inside the room and the second door isn't opened? The doorman sees the room at 7 meters long and the spear at 3.05 meters long, so no collision with the second door. The spearman sees the room at 3.05 meters and the spear at 7 meters so he smacks into the second door. So how can both situations be true?

7. Dec 30, 2005

### JesseM

If the spearman stops, then he changes velocity, and the length of the spear relative to the barn will change--the doorman will see the spear expand, the spearman will see the barn expand, and once he has come to rest they will be in the same rest frame, so they'll agree that both the spear and the barn are 7 meters long. Whether or not the spear bumps either door depends on the exact details of how quickly the spearman decelerates, how the spear is positioned when it comes to rest relative to the barn, and so on.

8. Jan 3, 2006

9. Jan 3, 2006

### Staff: Mentor

It's not a real paradox, but only an apparent paradox. There is no problem with the theory, if you understand it.

10. Jan 3, 2006

### JesseM

11. Jan 3, 2006

### George Jones

Staff Emeritus
Most dictionaries include 2 definitions of paradox that are contradictory. The standard paradoxes of special relativity are paradoxes acoording to defintion 2a of http://www.m-w.com/dictionary/paradox" [Broken], but not according to definition 2b.

This is the best way to look at the situation.

Regards,
George

Last edited by a moderator: May 2, 2017