Distance traveled by pi mesons in special relativity

In summary, the 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 it will travel a maximum distance of 0.1c before decaying. Additionally, anything in it's own rest frame has a velocity of 0.
  • #1
jaejoon89
195
0

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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  • #2
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?
 
  • #3
So the time it travels before decaying wrt the rest frame of the meson is just the L value (not L_0)?
 
  • #4
On the other hand... How far does anything move in its own "rest frame?" Isn't that 0?
 
  • #5
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 ..
 
  • #6
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?
 
  • #7
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:

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein in 1905 to describe the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers regardless of their relative motion.

2. What is the difference between special relativity and general relativity?

Special relativity deals with the laws of physics in inertial frames of reference, while general relativity extends this to include accelerated frames of reference and the effects of gravity on space and time.

3. What are the key principles of special relativity?

The key principles of special relativity include the constancy of the speed of light, the relativity of simultaneity, and time dilation and length contraction at high speeds.

4. How does special relativity affect our understanding of time and space?

Special relativity shows that time and space are not absolute, but are relative to the observer's frame of reference. It also introduces the concept of spacetime, where time and space are intertwined and cannot be separated.

5. What are some real-world applications of special relativity?

Special relativity has many practical applications, such as GPS technology, which relies on precise time measurements and takes into account the effects of time dilation due to the satellites' high speeds. It also plays a role in particle accelerators and nuclear reactors, as well as in the development of technologies such as nuclear power and nuclear weapons.

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