Length contraction from two inertial frames

[bernhard.rothenstein]

R' is an observer from I'. A rod is in a state of rest relative to him. He measures its proper length L(0). An observer R from I measures its Lorentz contracted length L related by
L=L(0)sqrt(1-vv/cc) (1). If we reverse the situation, R measuring the proper length of the rod R' measuring its Lorentz contracted length. Please tell me what is the name of the property that makes that (1) holds in that case as well.
Thanks

 

[CompuChip]

The postulate from special relativity, that any two reference frames moving with constant relative velocity are equivalent?

 

[HallsofIvy]

R' is an observer from I'. A rod is in a state of rest relative to him. He measures its proper length L(0). An observer R from I measures its Lorentz contracted length L related by
L=L(0)sqrt(1-vv/cc) (1). If we reverse the situation, R measuring the proper length of the rod R' measuring its Lorentz contracted length. Please tell me what is the name of the property that makes that (1) holds in that case as well.
Thanks

By "reverse the situation" do you mean that the rod is now moving with speed v relative to R instead of R'?

 

[country boy]

Please tell me what is the name of the property that makes that (1) holds in that case as well.
Thanks

It's the same property, of course. Relativity works both ways. But the problem is how to define the same proper length when when the rod is measured in the two reference frames. When the rod goes from being at rest in one frame to being at rest in the other, how do we know it has the same length? Relativity gives a way to define this.

For an interesting related question, see the forum topic titled "special relativity puzzle," which deals with the problem of hopping from one frame to another.

 

[bernhard.rothenstein]

length contraction

By "reverse the situation" do you mean that the rod is now moving with speed v relative to R instead of R'?

Thanks. Yes. Has the situation something om common with "reciprocity"?

 

[country boy]

Thanks. Yes. Has the situation something om common with "reciprocity"?

Sorry Bernhard, we weren't answering your question. If you are looking for a general term then, yes, reciprocity describes this type of relationship. Another example of such a relationship is the Golden Rule.

 

[robphy]

Personally, I hesitate to use "reciprocity" or "reciprocal"... preferring instead "symmetry" of the inertial observers, followed up by an explicit statement of the symmetry.

 

[jtbell]

Yes, when I see the word "reciprocal", I think of 1/x.