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

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Homework Help Overview

The discussion revolves around the relationship between energy and half-life in the context of special relativity, specifically focusing on a particle with a defined rest mass and half-life as observed by an external observer.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss relevant equations, including the decay-rate equation and the energy-momentum relation. There is an emphasis on identifying the correct relationships and variables involved in the problem.

Discussion Status

Participants are actively sharing equations and attempting to clarify the relationships between the variables. Some guidance has been offered regarding the use of the Lorentz factor and the decay-rate equation, but no consensus or complete solution has emerged yet.

Contextual Notes

There is a mention of needing to derive an expression based on the defined symbols, indicating that the problem may have constraints related to the use of specific variables and equations.

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

[itex]\gamma = \frac{E_{total}}{E_{rest}}[/itex]
 

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