Length contraction from two inertial frames

1. Jul 10, 2007

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

2. Jul 10, 2007

CompuChip

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

3. Jul 10, 2007

HallsofIvy

Staff Emeritus

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

4. Jul 10, 2007

country boy

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.

5. Jul 10, 2007

bernhard.rothenstein

length contraction

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

6. Jul 10, 2007

country boy

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.

7. Jul 10, 2007

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.

8. Jul 10, 2007

Staff: Mentor

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