Length contraction from two inertial frames

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Discussion Overview

The discussion focuses on the concept of length contraction in special relativity as observed from two different inertial frames. Participants explore the implications of measuring proper length and Lorentz contracted length, and the properties that allow these measurements to hold true when switching reference frames.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants describe the relationship between proper length and Lorentz contracted length, emphasizing that both observers measure different lengths depending on their relative motion.
  • One participant suggests that the postulate of special relativity, which states that all inertial frames are equivalent, underlies the observed phenomena.
  • There is a question about how to define the same proper length when the rod is measured in different reference frames, highlighting the complexity of the concept.
  • Some participants propose that the term "reciprocity" may describe the relationship between the two observers, while others prefer the term "symmetry" to describe the situation.
  • One participant expresses hesitation in using "reciprocity," suggesting that it may imply a mathematical relationship rather than a physical symmetry.
  • Another participant connects the discussion to the "Golden Rule" as an example of reciprocity in relationships.

Areas of Agreement / Disagreement

Participants express differing views on the terminology used to describe the relationship between observers, with some favoring "reciprocity" and others preferring "symmetry." The discussion remains unresolved regarding the most appropriate term to use.

Contextual Notes

Participants note the challenge of defining proper length consistently across different frames, indicating a potential limitation in the discussion regarding assumptions about length measurements.

bernhard.rothenstein
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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
 
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The postulate from special relativity, that any two reference frames moving with constant relative velocity are equivalent?
 
bernhard.rothenstein said:
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'?
 
bernhard.rothenstein said:
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.
 
length contraction

HallsofIvy said:
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"?
 
bernhard.rothenstein said:
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.:smile:
 
Personally, I hesitate to use "reciprocity" or "reciprocal"... preferring instead "symmetry" of the inertial observers, followed up by an explicit statement of the symmetry.
 
Yes, when I see the word "reciprocal", I think of 1/x.
 

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