Why does length contraction occur in Lorentz transformations?

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SUMMARY

Length contraction occurs in Lorentz transformations due to the relativistic effects of time dilation and simultaneity. When an observer measures the length of a rod moving at a velocity close to the speed of light, they perceive the ends of the rod as not being simultaneous in time. This discrepancy leads to the conclusion that one end of the rod has traveled further than the other, resulting in a contracted length from the observer's inertial frame of reference.

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  • Understanding of Lorentz transformations
  • Familiarity with the concept of simultaneity in special relativity
  • Basic knowledge of time dilation effects
  • Ability to apply relativistic equations for length contraction
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  • Study the derivation of Lorentz transformations in detail
  • Learn about time dilation and its mathematical implications
  • Explore practical examples of length contraction in high-velocity scenarios
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lincs_b
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Hi, This isn't actually a coursework question but rather a part of my course which I'm struggling to get my head round.
I can use formula to calculate the amount that an object contracts but I can't seem to get my head around why this happens.
I've been trying to imagine a rod traveling past me(my frame of reference is inertial and not moving) with a constant velocity, close to the speed of light, but I don't understand why the rod is contracted from my frame of reference.
Thanks for any help in advance.
 
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Hi lincs_b! :smile:

Why? Because it does … because that's what the equations tell you. :wink:

Roughly speaking, it's because when you measure its length, you do so at what you think are simultaneous times at each end,

but it thinks that those times are not simultaneous, and so one end has had time to travel a little further than the other! :biggrin:
 
tiny-tim said:
Hi lincs_b! :smile:

Why? Because it does … because that's what the equations tell you. :wink:

Roughly speaking, it's because when you measure its length, you do so at what you think are simultaneous times at each end,

but it thinks that those times are not simultaneous, and so one end has had time to travel a little further than the other! :biggrin:

Thank you very much!
 

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