Distance traveled by pi mesons in special relativity

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Homework Help Overview

The discussion revolves around the distance traveled by pi mesons, which have a proper average lifetime of 2.6*10^-8 s, while moving at a speed of 0.9c. Participants are exploring the implications of special relativity on the decay of these particles in relation to their rest frame.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the interpretation of distance traveled in the rest frame of the pi meson, with some suggesting the need to consider time dilation. There are discussions about whether the distance should be zero in its own rest frame and how to approach the calculation of distance using the average lifetime provided.

Discussion Status

There is an ongoing exploration of the concepts involved, with participants offering hints and clarifications regarding the relationship between proper time and the distance calculation. Multiple interpretations are being discussed, particularly concerning the frames of reference involved.

Contextual Notes

Participants are navigating the complexities of special relativity, particularly the definitions of rest frames and how they relate to the motion of the pi mesons. The original poster's teacher has indicated that the problem may be a trick question, adding to the uncertainty in the discussion.

jaejoon89
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Homework Statement



The proper average lifetime of pi mesons is 2.6*10^-8 s. If a beam of these pi mesons is moving with a speed of 0.9c, then

with respect to rest frame of the pi meson, how far does it travel before it decays?

Homework Equations



L=L_0 sqrt(1-(v/c)^2)
T=T_0 sqrt(1-(v/c)^2)

The Attempt at a Solution



I thought it was 0 because it's not moving with respect to itself. My teacher says this is a trick question... so I was wondering if zero is not the case even though it seemed at first simple enough.
 
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why it should be zero?? .. well, I`ll give you a hint:

you are give the average lifetime of the pi meson (which represents the proper time) , can you first find the time dilation then go on from there to find the distance of travel?
 
So the time it travels before decaying wrt the rest frame of the meson is just the L value (not L_0)?
 
On the other hand... How far does anything move in its own "rest frame?" Isn't that 0?
 
hmmm , i don't get what you are pointing to .. but as i told you , since you are given the average lifetime(proper time) and the speed of the pi meson you can first get the time needed to calculate the distance you are asked to get .. and why you have to do so?

it is simply because you are now in a rest frame of the pi meson (say i.e this frame is the earth) and from that frame you have to calculate the distance which the pi mesons tranvels .. so what do you need ? you need to find the time with respect to the new frame .. does what i say makes sense now? .. try once again and tell me if you still have any questions ..
 
jaejoon89 said:
On the other hand... How far does anything move in its own "rest frame?" Isn't that 0?
I agree with you. And your teacher did say it's a trick question.

thebigstar25 said:
it is simply because you are now in a rest frame of the pi meson (say i.e this frame is the earth)
No, the pi meson is moving with respect to the Earth, at 0.9c. The pi meson rest frame is not the Earth frame.

What is the velocity of anything, by definition, in it's own rest frame?
 
Redbelly98 said:
I agree with you. And your teacher did say it's a trick question.


No, the pi meson is moving with respect to the Earth, at 0.9c. The pi meson rest frame is not the Earth frame.

What is the velocity of anything, by definition, in it's own rest frame?

I apologize for confusion, and thanks Redbelly98 for clarifying this question ..
 
Last edited:

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