How does the length contraction work for proper length?

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Discussion Overview

The discussion revolves around the concept of proper length and its relationship to length contraction in the context of special relativity. Participants explore the definitions of proper length, the implications of measuring lengths from different inertial frames, and the nature of events in spacetime.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant defines proper length as the minimum distance between two events in any frame and questions how length contraction applies when measured from another inertial frame.
  • Another participant asserts that proper length is the longest length and not defined between two events, suggesting a misunderstanding of the concept.
  • A participant seeks clarification on why proper length is not defined between two events, emphasizing that length is the distance between two simultaneous measurement events.
  • One participant elaborates that while measuring the length of an object, different observers may choose different simultaneous events, leading to varying measurements due to length contraction.
  • Another participant questions the definition of proper length as the minimum spatial separation, suggesting either a misreading or an error in the source material.
  • A participant discusses spacetime diagrams, noting that events with a spacelike interval do not have a causal relationship and that the concept of proper length may not apply in the same way as in other contexts.
  • One participant clarifies that the distance between two events is not equivalent to measuring the length of an object, emphasizing the role of time-like and space-like intervals in determining measurements.

Areas of Agreement / Disagreement

Participants express differing views on the definition of proper length and its application in measuring lengths across different inertial frames. There is no consensus on the correct interpretation of proper length or the relationship between events and measurements.

Contextual Notes

Participants reference definitions and concepts that may depend on specific interpretations of spacetime and relativistic measurements, leading to potential misunderstandings or differing perspectives on proper length and length contraction.

Ashuron
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Well..

Proper length ,from my understanding, is the minimum distance between 2 events in any frame.
Then, how does the length contraction work? suppose someone from other inertial frame try to measure the length..
The length will be contracted to L/gamma..shorter than proper length..

Some arguments from physicsforums seems try to tell that the events measured from another frame are completely different events..
 
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So your understanding is wrong.
It is patent that proper length is the longest. And it is not between two events.
 
thx a lot..
btw why not between 2 events?
 
Ashuron said:
thx a lot..
btw why not between 2 events?

Length is the distance between two simultaneous measurement events at two point.
 
Ashuron said:
Well..

Proper length ,from my understanding, is the minimum distance between 2 events in any frame.
Then, how does the length contraction work? suppose someone from other inertial frame try to measure the length..
The length will be contracted to L/gamma..shorter than proper length..

Some arguments from physicsforums seems try to tell that the events measured from another frame are completely different events..

Two events in one frame are the same events in any other frame. I think what they meant was that an object is composed of many events. When you measure the length of an object, you will not choose the same two events as somebody else who is moving with respect to you. You choose what you think are two simultaneous events (an event at one end of the object and the other end of the object). Somebody else measuring that object will not choose the same events when making their measurement.
 
then why my text defined proper length as the minimum spatial separation possible..?
 
Ashuron said:
then why my text defined proper length as the minimum spatial separation possible..?

Either you read it wrong, or they are in error. The proper length of an object is the length of the object at rest with respect to you when you measure it. Anything else is Lorentz contracted.
 
like in spacetime diagram..let one event is on the origin..and another event at the region of space like interval..
such both event have no causality relationship since their spacetime interval is space like..
there is no situation where the second event is in the region of time-like interval
 
Again, the distance between two events is not the same as measuring the length of an object. If you have two events with a time-like interval between them, then the minimum distance you will ever measure between them is if they happen in the same place, and it will be zero. If the interval is space-like, then there is a world line in which the distance is minimized.
 

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