Estimating Mass Uncertainty of Mesons Using the Uncertainty Principle

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Discussion Overview

The discussion revolves around estimating the mass uncertainty of mesons using Heisenberg's Uncertainty Principle. Participants explore the relationship between the lifetime of mesons and their mass-energy uncertainty, focusing on theoretical implications and calculations related to unstable particles produced in high-energy collisions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant introduces the uncertainty relation ΔE x ΔT > h-bar/2, suggesting that the lifetime of the meson can be interpreted as the uncertainty in time.
  • Another participant mentions the uncertainty equation Δx x Δp ≥ h/2 and questions how it relates to energy, indicating a need for clarification on the role of energy in this context.
  • A participant explains that the uncertainty in the mass-energy of the meson is related to its lifetime, proposing that the relationship involves the transition rate from a quantum state to the state of the meson, which is influenced by the uncertainty in energy.
  • It is noted that ΔE can be interpreted as the uncertainty in the meson's mass expressed in MeV.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretation of the uncertainty principles, with no consensus reached on the specific calculations or implications. The discussion remains open-ended with multiple viewpoints presented.

Contextual Notes

Participants reference different uncertainty relations and their applications, but there are unresolved questions regarding the integration of these concepts into a cohesive calculation for mass uncertainty.

Who May Find This Useful

This discussion may be useful for first-year physics students or individuals interested in quantum mechanics, particularly those exploring the implications of the uncertainty principle in particle physics.

Arieniel
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Hello, I am in first year physics and I was wondering if anyone could help me out with a question. Its dealing with Heisenberg's Uncertainty prinicple:

A meson is an unstable particle produced in high-energy paritcle collisions. Its rest energy is about 135 MeV and it exisits for an average lifetime of only 8.70 x 10^-17 s before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty delta m/m in its mass determination.
thankyou ahead of time for the help !
Arieniel
 
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One of the uncertainty relations is ΔE x ΔT > h-bar/2. (You can interpret the lifetime as the "uncertainty" in time.) Does that help?

And welcome to the Physics Forums, by the way! :smile:
 
Last edited:
Further Question

Thanks for welcoming me to board,
i know that there is an uncertainity equation of delta x delta p is >/ h/2
does this come into play and where does the energy come into play, because i found delta E
 
The uncertainty in the mass energy of this meson (mc^2) is related to the lifetime of the particle via:
{uncertainty in mc^(2)}*t ~ h-bar.

The reason this works is more subtle than your course goes into, but it has to do with the "cross section" that the particles see as they collide to create this short-lived particle. One can calculate the transition rate from the quantum state {collection of some particles} to the state where you have a meson, and this will depend on the range of energies for which this transition can happen (ie, the uncertainty in the energy to create the meson). The inverse of this transition rate is the lifetime of the meson. So you can see at least where the inverse relationship between the uncertainty in mass-energy of the meson and its lifetime.
 
The ΔE can be interpreted as the uncertainty in the meson's mass (rest energy). Express it in units of MeV.

Note: I was just struggling with a more complete answer, when I noticed that Javier beat me to it.
 
I sincerely thank you both! You have saved me from burning the midnight oil! I appreciate this greatly!

Cheers
Arieniel
 

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