Fitzgerald-Forentz contraction problem

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Two individuals on a fast train attempt to demonstrate Fitzgerald-Lorentz contraction by dropping bags of flour from the front and back of the train. Despite being in the same inertial frame, they will measure a distance greater than 500m when they return to the ground, indicating that contraction has occurred. The discussion clarifies that while they are in the same frame during the drop, their measurements correspond to the ground frame, where relativistic effects apply. The Lorentz-Fitzgerald equations can be used to derive the expected measurement. This scenario effectively illustrates the principles of relativistic length contraction.
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Dear All, Have a small problem:

Two chaps attempt to demonstrate the phenomenon of Fitzgerald-Lorentz contraction. The two meet at the centre of a fast train which is L = 500m long and traveling at a speech of u = 0.7c to synchronize their watches.

One sits at the front of the train while the other sits at the back. At a previously agreed time, both drop a bag of flour from the train so that it marks the ground beneath. When the train has stopped, they drive back to where they dropped the bags and measure the distance between the two marks. What distance do they measure? Have they actually demonstrated the Fitzgerald Lorentz contraction?*CONFUSED* Surely as they are in the same train, they are in the same inertial frame of reference? And hence, relativistic effects will not be relavent?
 
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same as each other? same as the ground?
or same as they will be when they measure on the ground?

Do you think they'll measure 500m? And NOT demonstrate contraction?
 
capslock said:
Dear All, Have a small problem:

Two chaps attempt to demonstrate the phenomenon of Fitzgerald-Lorentz contraction. The two meet at the centre of a fast train which is L = 500m long and traveling at a speech of u = 0.7c to synchronize their watches.

One sits at the front of the train while the other sits at the back. At a previously agreed time, both drop a bag of flour from the train so that it marks the ground beneath. When the train has stopped, they drive back to where they dropped the bags and measure the distance between the two marks. What distance do they measure? Have they actually demonstrated the Fitzgerald Lorentz contraction?


*CONFUSED* Surely as they are in the same train, they are in the same inertial frame of reference? And hence, relativistic effects will not be relavent?

yes, they will have demonstrated the LF contraction. When they go measure the distances on the ground, it will be larger than 500 m.
If you call the train the S` frame, this is a measurement corresponding to delta t'=0 and delta x'= 500 m. Plug that in the LF equations and find Delta x. That will be the value they will measure on the ground.
 
nrqed said:
yes, they will have demonstrated the LF contraction. When they go measure the distances on the ground, it will be larger than 500 m.
If you call the train the S` frame, this is a measurement corresponding to delta t'=0 and delta x'= 500 m. Plug that in the LF equations and find Delta x. That will be the value they will measure on the ground.
LF equations? I'm working from the Lorentz equations. How do I derive them?

Best Regards, James
 
capslock said:
LF equations? I'm working from the Lorentz equations. How do I derive them?

Best Regards, James

Same equations.. LF= Lorentz-Fitzgerald, which is what you call Lorentz equations. Sorry.

Btw, you are right that they are in the same frame, but they are effectively making a length measurement in the frame of the ground, so relativistic effects are relevant.

Pat
 
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