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Old Oct 8th 2009, 05:22 PM   #1
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A variant of the Pole-Barn Paradox

I'm having some trouble explaining the reasoning behind calling something a proper length. Here's the problem:

Bill is driving in a car, which he measures to have a length of 6m. Using his knowledge of special relativity, Bill is going to attempt an amazing stunt - he will park his car (temporarily, at least!) in a garage that is only 4m deep! To prove that he has successfully completed his stunt, Ted, who is standing by the garage, will carefully watch as Bill enters the garage, and close the front door of the garage when Bill's car is fully inside (the back door of the garage is closed already). Let Ted's reference frame be S and Bill's reference frame be S'.

a) Bill measures his car to have a length of 6m. Is this a proper length? Why or why not?

b) Ted measures the length of the garage to be 4m. Is this a proper length? Why or why not?

I know that they both are (probably), but I can not explain why. I know that Ted measured the length of the garage in a frame at rest, so it is a proper length, I'm having the most trouble with the car.
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Old Oct 9th 2009, 12:32 AM   #2
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From what i understand, both will be proper lengths as there is no relative motion between the observer and object observed.
Bill in the car finds that he does not move with respect to it.
The same for Ted and the garage.
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Old Oct 9th 2009, 06:39 PM   #3
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Originally Posted by Aryth View Post
a) Bill measures his car to have a length of 6m. Is this a proper length? Why or why not?
6m is the proper length of the car.
Originally Posted by Aryth View Post
b) Ted measures the length of the garage to be 4m. Is this a proper length? Why or why not?
4m is the proper length of the barn.
Originally Posted by Aryth View Post
I know that they both are (probably), but I can not explain why. I know that Ted measured the length of the garage in a frame at rest, so it is a proper length, I'm having the most trouble with the car.
When speaking of proper length it's important to specify what object it is that you're referring to.
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Old Oct 13th 2009, 02:05 PM   #4
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I did a bit of thinking and I understand it now. Thanks for the help.
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Old Oct 21st 2009, 07:40 AM   #5
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Originally Posted by Aryth View Post
I'm having some trouble explaining the reasoning behind calling something a proper length.
Simply put, something is referred to proper when it is unique to an object. Hence the rest mass is often referred to as proper mass since there can be only one unique value to it.
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