Physics Help Forum Strange question on length contraction

 Special and General Relativity Special and General Relativity Physics Help Forum

Jul 30th 2009, 08:42 PM   #1
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,573
Strange question on length contraction

I'm reading a book on relativity and working through the exercises so I don't get too rusty. The following question is rather odd.
 The measuring rod employed by S will appear from S' to be shortened by a factor $\displaystyle (1-u^2/c^2)^{1/2}$. Hence, when S measures the length of the bar fixed in S' he might be expected to obtain the result $\displaystyle l = l'/(1-u^2/c^2)^{1/2}$ This contradicts equation (6.3). Resolve the contradiction (Hint: It will be observed from S' that S fixes the position of the forward end of the bar first and the position of the rear end a time $\displaystyle ul'/c^2$ later.)
where 6.3 is the normal length contraction relation. I don't see why he might be expected to obtain $\displaystyle l = l'/(1-u^2/c^2)^{1/2}$.

Jul 30th 2009, 08:55 PM   #2
Physics Team

Join Date: Jul 2009
Posts: 310
 S will appear from S' to be shortened by a factor (1-u^2/c^2)^{1/2}
$\displaystyle S \sqrt {1 - \frac{u^2}{c^2}} = S'$

$\displaystyle S = \frac{S'}{\sqrt {1 - \frac {u^2}{c^2}}}$

???

I'm not understanding how this is a contradiction?

I haven't taken relativity yet, know some background knowledge, but I don't see any difference between the equation derived and:

Length contraction - Wikipedia, the free encyclopedia
__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Jul 30th 2009, 10:09 PM   #3
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,573
 Originally Posted by Deco I'm not understanding how this is a contradiction?
It isn't. I think the author of the book is suggesting a way someone may misinterpret Lorentz contraction. I don't follow what he's saying though. Perhaps because I know relativity.
 Originally Posted by Deco I haven't taken relativity yet, know some background knowledge, but I don't see any difference between the equation derived and: Length contraction - Wikipedia, the free encyclopedia
When talking about Lorentz contraction you have to be very careful to specify in what frame the object is at rest and in what frame the object is moving. I guess the problem is inquiring about a particular misinterpretation.

If you're interested in the relativity I've created my own tutorials on these derivations. You might enjoy working through them.

Try following the proof of the expression for time dilation here
Light Clock

After you have the expression for time dilation worked out you can follow the proof for Lorentz contraction. There are two that you might want to follow.
Lorentz Contraction
Lorentz Contraction – Version 2

I'm always looking for feedback on my web pages so if you read them let me know what you think. Thanks.

Pete

Jul 30th 2009, 10:15 PM   #4
Physics Team

Join Date: Jul 2009
Posts: 310
 When talking about Lorentz contraction you have to be very careful to specify in what frame the object is at rest and in what frame the object is moving.
That was my solution to the contradiction before I re-evaluated it.

 If you're interested in the relativity I've created my own tutorials on these derivations. You might enjoy working through them. Try following the proof of the expression for time dilation here Light Clock After you have the expression for time dilation worked out you can follow the proof for Lorentz contraction. There are two that you might want to follow. Lorentz Contraction Lorentz Contraction – Version 2 I'm always looking for feedback on my web pages so if you read them let me know what you think. Thanks.
I've read a derivation of Lorentz Contraction in a textbook I was look at recently.

So far, it has shown me the simplest (I think) derivation. These websites seem alright though.
__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Jul 30th 2009, 10:26 PM   #5
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,573
 Originally Posted by Deco So far, it has shown me the simplest (I think) derivation.
Interesting. What was the approach used? I'm always looking for new approaches.

 Jul 30th 2009, 10:35 PM #6 Physics Team     Join Date: Jul 2009 Posts: 310 McGraw-Hill Ryerson Canada - School - Physics 12 That's the book that contains (what I think to be) a simple proof. Bad overall textbook though. __________________ "Dissent is the highest form of patriotism." - Thomas Jefferson. "Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild I study Mathematical Physics at the University of Waterloo. -DC

 Tags contraction, length, question, strange

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post fredreload Special and General Relativity 5 Dec 8th 2015 08:44 AM ILoveGeeks Light and Optics 1 Feb 6th 2012 04:13 AM savior_self Special and General Relativity 0 Nov 8th 2011 12:34 PM werehk Special and General Relativity 4 May 15th 2009 03:11 PM kkh814 Special and General Relativity 1 Feb 28th 2009 08:03 AM