Distance traveled by pi mesons in special relativity

[jaejoon89]

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.

 

[thebigstar25]

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?

 

[jaejoon89]

So the time it travels before decaying wrt the rest frame of the meson is just the L value (not L_0)?

 

[jaejoon89]

On the other hand... How far does anything move in its own "rest frame?" Isn't that 0?

 

[thebigstar25]

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 ..

 

[Redbelly98]

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.

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?

 

[thebigstar25]

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 ..