Question about Lorentz Contraction

[Johnny5]

Does Lorentz contraction apply only to the length of bodies, only to distances traveled in space, or both? The formula I am asking about is:

 

[math] L = L_0 \sqrt{1-v^2/c^2} [/math]

 

Thank you

[J.C.MacSwell]

Does Lorentz contraction apply only to the length of bodies' date=' only to distances traveled in space, or both? The formula I am asking about is:

 

[math'] L = L_0 \sqrt{1-v^2/c^2} [/math]

 

Thank you

 

Both

[Johnny5]

Both

 

Can you explain why you claim both?

 

Thank you

[Tom Mattson]

It's both because the manner in which it was derived does not depend on whether the space between two points is filled with matter. If you think about it some, you will see that it wouldn't make any sense if the answer were not "both". Take two planets, separated by a distance L₀ in their mutual rest frame. Then Buck Rogers goes zipping by in his starship with speed v in a direction parallel to the line joining the centers of the planets. How far apart are the planets in Buck's frame? Well, if the answer to your question were not "both", then the answer to my question would depend on whether or not there is a giant ruler between the two planets, which is absurd.

[Johnny5]

It's both because the manner in which it was derived does not depend on whether the space between two points is filled with matter. If you think about it some, you will see that it wouldn't make any sense if the answer were not "both". Take two planets, separated by a distance L_{0[/sub'] in their mutual rest frame. Then Buck Rogers goes zipping by in his starship with speed v in a direction parallel to the line joining the centers of the planets. How far apart are the planets in Buck's frame? Well, if the answer to your question were not "both", then the answer to my question would depend on whether or not there is a giant ruler between the two planets, which is absurd.}

 

_{Perfectly answered Tom, thank you.}