Go Back   Physics Help Forum > College/University Physics Help > Special and General Relativity

Special and General Relativity Special and General Relativity Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Jul 30th 2009, 07:42 PM   #1
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,551
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 $\displaystyle l = l'/(1-u^2/c^2)^{1/2}$.
Pmb is offline   Reply With Quote
Old Jul 30th 2009, 07:55 PM   #2
Physics Team
 
Deco's Avatar
 
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' $

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

???

This contradicts equation (6.3). Resolve the contradiction
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
Deco is offline   Reply With Quote
Old Jul 30th 2009, 09:09 PM   #3
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,551
Originally Posted by Deco View Post
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 View Post
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
Pmb is offline   Reply With Quote
Old Jul 30th 2009, 09:15 PM   #4
Physics Team
 
Deco's Avatar
 
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
Deco is offline   Reply With Quote
Old Jul 30th 2009, 09:26 PM   #5
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,551
Originally Posted by Deco View Post
So far, it has shown me the simplest (I think) derivation.
Interesting. What was the approach used? I'm always looking for new approaches.
Pmb is offline   Reply With Quote
Old Jul 30th 2009, 09:35 PM   #6
Physics Team
 
Deco's Avatar
 
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
Deco is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Special and General Relativity

Tags
contraction, length, question, strange



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Question about length contraction fredreload Special and General Relativity 5 Dec 8th 2015 07:44 AM
Could any smart cookie help me with this optics/focal length question? ILoveGeeks Light and Optics 1 Feb 6th 2012 03:13 AM
Length Contraction problem savior_self Special and General Relativity 0 Nov 8th 2011 11:34 AM
Length contraction werehk Special and General Relativity 4 May 15th 2009 02:11 PM
Length Contraction kkh814 Special and General Relativity 1 Feb 28th 2009 07:03 AM


Facebook Twitter Google+ RSS Feed