MadSci Network: Physics |
Dear Sanam, One of the rules of Quantum Mechanics, called the Heisenberg Uncertainty Principle, states that it is impossible to know precisely the energy of a state of a system and simultaneously the lifetime of the state. Mathematically, the Principle looks like dE * dt >= hbar/2 where dE is the uncertainty in the energy, dt is the uncertainty in the time, and hbar is Planck's constant divided by (2 pi). The maximum range for a virtual gauge boson (force carrying particle), or any exchanged particle, can be estimated as the speed of light multiplied by the uncertainty in the time Range = c * dt Using the Uncertainty Principle above, and the minimum energy uncertainty m*c^2 for a particle of mass m, the maximum range is on the order of Range = hbar / (2 m * c) Now you can solve for the mass of the exchanged particle in terms of the range. For a more rigorous derivation of the relationship between exchanged particle mass and range of the force, look in any Quantum Mechanics text for "Yukawa potential". Japanese physicist Hideki Yukawa estimated the mass of the pion as 100 MeV/c^2 given a typical nuclear size of about one femtometer. You should also be aware that there are much more accurate ways of determining the W and Z masses than working backwards from their estimated ranges. --Dr. Randall J. Scalise http://www.phys.psu.edu/~scalise/
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