Understanding the Length Contraction Paradox in Special Relativity

[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 won't 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 won't fit according to him.

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

Thanks in advance for anybody helping me.

 

[Wizardsblade]

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. =)

 

[Doc Al]

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!)

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

 

[Jir]

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

 

[quantumdude]

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 won't crash into the door'.

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

 

[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?

 

[JesseM]

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?

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.

 

[Jir]

A few days after new year, so Happy new year everybody :).

I found this in the link Doc Al posted:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/bugrivet.html#c1

I understand most what is written there, but what I don't understand is why its still a paradox. A good Theory should have no paradoxes right?

 

[Doc Al]

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

 

[JesseM]

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

Jir may be asking about the specific scenario in the link, the "bug/rivet paradox"--the link doesn't explain the resolution to the paradox. The paradox in that scenario would disappear if you imagined the bottom of the rivet and the head of the rivet were two separate objects, so there would just be a disagreement about whether the head of the rivet hits the wall before or after the bottom of the rivet hits the bottom of the hole. But if there can be disagreement about the order, this means these two events would have a spacelike separation, which means the event of the the head hitting the wall could have no causal influence on the bottom of the rivet before it reaches the bottom of the hole. So in the bug's frame of reference, the rivet would become stretched as the head was instantaneously decelerated as it hit the wall while the bottom continued on at the same velocity--basically the apparent paradox comes from imagining the rivet as a perfectly rigid object, so decelerating one part of it would instantly decelerate every other part by the same amount, but perfectly rigid objects are forbidden in relativity, accelerating one part of an object can only affect other parts of the object when a density wave traveling at the speed of sound in the material (always less than the speed of light) has had time to travel between the two parts.

 

[George Jones]

It's not a real paradox, but only an apparent paradox.

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" , but not according to definition 2b.

There is no problem with the theory, if you understand it.

This is the best way to look at the situation.

Regards,
George