What is the relationship between energy and half life in special relativity?

QuantumJG
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Homework Statement



A particle has a rest mass of m0 and a half life of t0. An observer measures the half life of the particle, which has a total energy of E and a momentum of p.

Find an algebraic expression for the half life the observer measures for the particles, using only the symbols defined above.

I really don't know how to start this problem!
 
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Hi QuantumJG! :smile

With questions like this, be logical …

start by writing out all the relevant equations you know (in this case, including the decay-rate equation) …

what do you have? :smile:​
 
Really all that I have is:

E^2 = (pc)^2 + (mc^2)^2

t = γt_0
 
And the equations for the decay?
 
Hi Joel. :)

This problem becomes very simple when you recognize that

\gamma = \frac{E_{total}}{E_{rest}}
 

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