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Pi meson travel before decay - special relativity?
The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10^-8 s. It moves at a speed of 0.95c and I found the lifetime from an Earth observer to be 8.33x10^-8.
The next question asks for the distance it travels before decaying, as measured by an observer on Earth. I got 24.97 and my online homework says I'm within 10% of the correct value but I don't know what I need to do to get the completely correct answer.
The third part confuses me completely because I don't have part 2, even though I have a hunch that it's the easiest part. It asks how far it would travel if time dilation did not occur.
Help! Thanks!
3 Answers
- husoskiLv 71 decade agoFavorite Answer
In the earth frame, the meson is traveling at 0.95c, for a time of 8.33E-8 s. How do you get 24.97 in this frame? I get 0.95 * 2.997E8 m/s * 8.33E-8 s = 23.72 m. Aha! I get it....you forgot to multiply by 0.95, I'll wager.
The third part is just 0.95c times the proper time. As you can see from the given numbers, that will be around 8 m or about a third of the relativistic distance.
- troutfisherLv 51 decade ago
the distance traveled is just .95 c t = .95 x 2.998x10^8 x 8.33x10^-8 = 23.72m
I think you left out the .95.
Without time dilation the time of travel would be 2.6 x 10^-8 and the distance would be calculated the same way with this new time value.
Source(s): Wikipedia fundamental constants to get c
