Time dilation of Muons and a Paradox

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In the discussion about the time dilation of muons in a linear accelerator, participants explore how different inertial frames perceive the number of muons detected at the end of the accelerator. While it is initially suggested that varying speeds and directions should result in different observed counts of muons, it is clarified that all observers will agree on the total number of muons detected, despite differences in time measurements due to relativistic effects. The conversation highlights the importance of considering both time dilation and length contraction in understanding these phenomena. Ultimately, the consensus is that while observers may disagree on the timing and duration of events, the actual number of muons reaching the detector remains constant across all frames. This reinforces the principles of special relativity and the consistency of physical laws across different reference frames.
  • #61
DaleSpam said:
Actually, it is the approaching speed which is important.

Are you talking about the approaching speed of Muons w.r.t the other End ?

Is it different from the relative velocity of Muons w.r.t the the other End ?

And how important exactly !
 
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  • #62
Samshorn said:
I assume you've been told many times that that's completely false,
Since you are assuming what have happened so far, can I safely assume that you did not read the previous discussions.

Samshorn said:
...Historically, length contraction was introduced by Fitzgerald and Lorentz in order to account for the results of the Michelson-Morley experiment, long before anyone ever dreamed of muons or even special relativity.
I agree, that Fitzgerald introduced/coined the term Length contraction to explain the results of MMX. But again, we are not discussing when was it first proposed.

Samshorn said:
And of course the MM experiment along with all other failed attempts to measure absolute velocity and all the experimental demonstrations of the invariance of light speed, and indeed the Lorentz invariance of all physical phenomena in terms of standard inertial coordinates, collectively are irrefutable experimental evidence of both length contraction and time dilation.
MMX was about the light and its properties, whereas, Time Dilation of Muons has nothing to do with Light and it's properties because if it does, there are contradictions of Logic. Again for the later part you need to read the previous posts.

Samshorn said:
Also, length contraction emerges from Lorentz's theorem of corresponding states based on the already-known laws of electrodynamics, and of course Lorentz always stressed the physical reality of (and necessity of) this contraction for active transformations.

Why don't then you just give me a real example of this physical reality, it will end all the conflicts.
Samshorn said:
You need to distinguish between intrinsic and extrinsic state variables, and between passive and active transformations.

Unfortunately, I don't know what all this mean. I suggest you read the previous discussions, if you think, there is an obvious mistake somewhere.
 
  • #63
This thread is going around in circles. Enough.
 

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