Relativistic Effects on Muons' Probability to Reach Earth Surface

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SUMMARY

The discussion centers on the relativistic effects impacting the probability of muons reaching the Earth's surface. It concludes that length contraction of the distance to Earth is the primary factor increasing this probability, rather than time dilation of the muon's mean life. The confusion arises from the relationship between the muon's frame of reference and the observer's frame, emphasizing that only one effect is relevant in this context.

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with muon decay and mean life
  • Knowledge of length contraction and time dilation principles
  • Basic grasp of reference frames in physics
NEXT STEPS
  • Study the implications of length contraction in special relativity
  • Explore time dilation effects on particle lifetimes
  • Investigate the role of reference frames in relativistic physics
  • Learn about experimental evidence of muon behavior in Earth's atmosphere
USEFUL FOR

Students and educators in physics, particularly those focusing on special relativity and particle physics, will benefit from this discussion.

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Homework Statement


Within the system of the muon, which relavisitic effect increases the probability for the muon to reach the Earth surface?
Length contraction of the distance to Earth.
Time dilation of its mean-life.
Both of the above.
None the above, the probability is lower in the system of the muon.


Homework Equations


Its conceptual


The Attempt at a Solution


I thought it was both, but the online homework system says that length is correct. am i wrong and why?
 
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Since the muon is the "clock" (its lifetime is a natural clock), what frame will see that clock slow down?
 
Time dilation in one frame is the same as length contraction in another frame, but not in both. Think about it. Which frame are they asking the question in?
 
Last edited:

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