Understanding the Length Contraction Paradox in Special Relativity

Click For Summary

Discussion Overview

The discussion revolves around the "length contraction paradox" in special relativity, specifically involving a scenario with a spearman and a room of equal length. Participants explore the implications of relativistic effects on measurements of length and simultaneity, addressing whether the spearman will collide with a door based on differing perspectives of observers.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant presents a scenario where a spearman running at 0.9c believes he will collide with a door, while a doorman perceives the spearman as contracted and fitting through the door.
  • Another participant argues that simultaneity is lost in relativity, suggesting that the spearman will see the doors open sequentially, which may prevent a collision.
  • A participant introduces the "Barn and the Pole" paradox, emphasizing that observers disagree on the simultaneity of events, which is crucial for understanding the scenario.
  • One participant questions the situation where the spearman stops running, noting that the doorman sees the spear contracted while the spearman sees the room contracted, leading to confusion about potential collisions.
  • Another response suggests that if the spearman decelerates, both observers will eventually agree on the lengths of the spear and room, but the specifics of the deceleration could affect whether a collision occurs.
  • Several participants discuss the nature of the paradox, with some stating it is only apparent and not a real paradox, contingent on understanding the principles of relativity.
  • One participant mentions the "bug/rivet paradox" as another example of apparent paradoxes in relativity, highlighting the role of spacelike separation and the limitations of rigid body assumptions in relativistic contexts.

Areas of Agreement / Disagreement

Participants express differing views on whether the scenario constitutes a real paradox or merely an apparent one. There is no consensus on the implications of the spearman's actions or the resolution of the paradox, as multiple interpretations and models are presented.

Contextual Notes

Limitations include the dependence on definitions of simultaneity and the assumptions regarding the behavior of objects at relativistic speeds. The discussion does not resolve the mathematical details or the exact conditions under which the scenarios unfold.

Jir
Messages
7
Reaction score
0
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.
 
Physics news on Phys.org
This is a common missconception. In relativity because 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. =)
 
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
 
Thanks for the very clear explenations. Helped me allot :)
 
Jir said:
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! :biggrin:
 
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?
 
O Great One said:
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.
 
It's not a real paradox, but only an apparent paradox. There is no problem with the theory, if you understand it.
 
  • #10
Doc Al said:
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.
 
  • #11
Doc Al said:
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 definition 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
 
Last edited by a moderator:

Similar threads

Undergrad Solving Paradox: Man Running with Pole Reaches Door Before Button is Pressed
  • · Replies 27 ·
Replies
27
Views
3K
High School The Paradox of Relativity Length Contraction
  • · Replies 166 ·
6
Replies
166
Views
15K
Undergrad Is the Killer Crate Paradox Resolved?
  • · Replies 60 ·
3
Replies
60
Views
6K
Undergrad Accelerated Triangle and Length Contraction
  • · Replies 40 ·
2
Replies
40
Views
5K
High School Any plausible explanation for dynamical length contraction?
  • · Replies 83 ·
3
Replies
83
Views
6K
Undergrad Pole-Barn Paradox: Is My Understanding Correct?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Special Relativity in Rotating Reference frame
  • · Replies 20 ·
Replies
20
Views
2K
Graduate What Causes the Twins Paradox and Length Contraction in Relativity?
  • · Replies 79 ·
3
Replies
79
Views
7K
Graduate Closing speed and length contraction paradoxes
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad Paradox: Rocket ship moving in a circle
  • · Replies 12 ·
Replies
12
Views
2K