Time Dilation Explained: Muon Decay & Reaching Earth

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Discussion Overview

The discussion revolves around the phenomenon of time dilation as it relates to muon decay and their detection on Earth. Participants explore the implications of muon half-life, the effects of speed on their decay, and the experimental evidence supporting or challenging these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant notes that muons have a half-life of 2.2 microseconds and questions whether a billion muons are needed to confirm their presence on Earth, given that only about 70 would arrive due to decay.
  • Another participant argues that assuming a 2.2μs half-life in our frame leads to predictions about muon numbers at different altitudes, which can be experimentally tested, but notes that decay rates measured in our frame do not support this half-life.
  • A later reply expresses interest in the experimental tests conducted at different altitudes and requests specific references for these tests, indicating a desire for more concrete evidence regarding time dilation predictions.
  • One participant provides a link to an FAQ that contains formal references and discussions related to experimental evidence, but does not elaborate on the content of those references.

Areas of Agreement / Disagreement

Participants express differing views on the implications of muon decay rates and the validity of the 2.2μs half-life in the context of time dilation. There is no consensus on the interpretation of experimental results or the necessity of a specific number of muons for detection.

Contextual Notes

Some limitations include the dependence on the assumptions about muon production rates and decay in different frames, as well as the unresolved nature of the experimental results regarding the half-life measurement.

Quandry
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As I understand it muons have a half life of 2.2 microseconds, thus, at the speed of light cannot get to the earth. But based on exponential decay, of every billion muons which head or way, about 70 will actually get here. Using time dilation the full billion will get here.
Do we need a billion to say we have muons, or is 70 enough?
 
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You are correct that the simple arrival of muons at the Earth's surface doesn't tell you anything. However, if you assume that their half life is 2.2μs in our frame then you are making predictions about the numbers you would expect to see at different altitudes (and their production rate in the upper atmosphere, which would need a very good explanation), which can be tested. We have done tests at different altitudes (see the experimental basis for SR sticky thread at the top of this forum) and the decay rates don't support a 2.2μs half life when measured in our frame.
 
Ibix said:
You are correct that the simple arrival of muons at the Earth's surface doesn't tell you anything. However, if you assume that their half life is 2.2μs in our frame then you are making predictions about the numbers you would expect to see at different altitudes (and their production rate in the upper atmosphere, which would need a very good explanation), which can be tested. We have done tests at different altitudes (see the experimental basis for SR sticky thread at the top of this forum) and the decay rates don't support a 2.2μs half life when measured in our frame.
Many thanks. Your reference to test at altitude would be of great interest. I have found predictions based on time dilation but so far have not found actual tests. If you had a more specific reference for me that would be appreciated.
 
The experimental evidence thread is a single post with a link to an FAQ which is a list of formal references with some discussion.
 

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