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So I'm calculating how long it will take for half of some muons to decay for in a stationary observers frame of reference. They have a half life of 2.2 * 10^-6 and are moving at a speed of .98c towards earth. I've calculated the gamma factor to be 5.02519. I know that T = Gammafactor * To I've rearanged the equation. Othe people i know are getting different answers from me so I just need to know whether or not i am right since i am unsure at this stage.

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closed as off-topic by ACuriousMind, yuggib, Kyle Kanos, Martin, Qmechanic May 28 '15 at 23:45

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  • $\begingroup$ See scivee.tv/node/2415 for an extended explanation from the past in glowing black and white... $\endgroup$ – DJohnM May 28 '15 at 12:05
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    $\begingroup$ By "stationary observer" can we assume you mean one stationary relative to the Earth, not stationary relative to the muons? Also, to see if you're using the equation correctly, are you treating the figure of 2.2 * 10^-6 as being "T" or "To"? $\endgroup$ – Hypnosifl May 28 '15 at 12:30
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I always get confused when I have to think about time dilation and length contraction. For that purpose I have a couple of rules of thumb:

  • Distance you measure contracts when you move
  • Times between events decrease (for you) when you move
  • Your lifetime increases (for others) when you move

You have correctly computed the $\gamma$-factor to be $\gamma=1/\sqrt{1-{0.92}^2}=5.021$

We can now use the third rule of thumb above, so the measured lifetime of the muons (as seen from earth) should be higher than the lifetime in their own frame of reference.

Therefore the lifetime should be $T=\gamma\times T_0=1.105\times10^{-5}$ seconds

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