How does the length contraction work for proper length?

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SUMMARY

Length contraction is a fundamental concept in special relativity, where the proper length of an object is defined as the length measured in the object's rest frame. When measured from another inertial frame, the length appears contracted to L/gamma, where gamma is the Lorentz factor. Proper length is the longest measurable distance between two simultaneous events at either end of an object, while measurements from different frames involve different sets of events, leading to variations in perceived length. The distinction between proper length and contracted length is crucial for understanding relativistic effects in spacetime.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with Lorentz transformations and the Lorentz factor (gamma)
  • Knowledge of spacetime diagrams and event intervals
  • Concept of simultaneity in different inertial frames
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  • Study the derivation and implications of Lorentz transformations
  • Explore the concept of simultaneity in different inertial frames
  • Learn about spacetime diagrams and their applications in special relativity
  • Investigate the relationship between time dilation and length contraction
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Students and professionals in physics, particularly those studying special relativity, as well as educators looking to clarify concepts related to length contraction and proper length measurements.

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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