Muons Decaying on Mt Washington: Expert Answers

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Discussion Overview

The discussion revolves around the concept of length contraction and time dilation in the context of muons decaying as they travel towards the Earth's surface. Participants explore the implications of Special Relativity, particularly how these effects are perceived from different reference frames, specifically the muon's frame versus the Earth's frame.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how the distance to the Earth's surface can be contracted from the muon's perspective, questioning the reality of physical space between the muon and the surface.
  • Another participant asserts that in the muon rest frame, the decay time is fixed at 2.2 µs, and discusses the relationship between decay distance and length contraction, suggesting that the time dilation factor corresponds to the length contraction factor in the muon frame.
  • A participant challenges the notion that physical space cannot be manipulated, stating that if this were true, Special Relativity would not hold, implying a need to reconsider preconceptions about space.
  • Another participant emphasizes that spacetime is the "real thing," and how it is divided into space and time is subjective, depending on the observer's reference frame.
  • One participant notes the confusion arising from the term "observer" being used interchangeably with "reference frame" in discussions of Special Relativity.
  • A later reply suggests that one can consider an observer at rest in the muon's reference frame to clarify the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of space and time in relation to Special Relativity, with no consensus reached on the interpretation of length contraction and its implications for the muon's perspective.

Contextual Notes

Participants reference the complexities of relative motion and the definitions of space and time, indicating that misunderstandings may arise from the terminology used in the context of Special Relativity.

bugatti79
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TL;DR
Length contraction from Muons perspective
Dear Experts,
Currently I am reading up on Special Relativity.
I struggle to understand how from the perspective of the Muon that the distance to the surface of the Earth is contracted and thus more Muons arrive at the surface based detector.
How can this be? To me the physical space is real between the muon and the surface and thus cannot be manipulated. How can this space be „contracted“ so that the muons arrive faster?
I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...
Any clarity is appreciated! Thanks
 
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It is one and the same thing: in the muon rest frame, the decay time is 2.2 ##\mu##s. So, even at close to the speed of light the length decay distance would only be 660 m (in the Earth frame) without length contraction. In the Earth frame the time dilation factor is the dame as the length contraction factor in the muon frame. It's nicely described on the first pagehttp://www.pas.rochester.edu/~advlab/reports/pelcher_rapach_muon.pdf.
 
bugatti79 said:
To me the physical space is real between the muon and the surface and thus cannot be manipulated.

This is a conceptual hurdle to get over. If what you say were true, then there would be no SR. But, as there is SR, your preconceptions must be misplaced.
 
The "real thing" is spacetime. How you divide that into space and time is a matter of choice, although there's an obvious way to do it for each observer.

Two reference frames in relative motion have different natural choices, so they measure different things and call them both "distance through space". So no-one is manipulating space - the two frames just mean different things when they talk about space.
 
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bugatti79 said:
I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...
"Observer" is often used as a synonym for "reference frame" in the context of SR, which leads to a lot of confusion.
 
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bugatti79 said:
I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...

Just have the observer be at rest in the rest frame of the muon.
 

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