W/Z Bosons & energy conservation

[smulc]

I recall watching a documentary a while ago that explained the production of different force carriers. A bit that stuck in my head was that (if I remember correctly) W and Z bosons were able to violate the law of energy conservation. The energy to create these particles was apparently 'borrowed'. It explained that the more energy is borrowed, the less time the particle can survive which is why these bosons have such a small range. A large amount of energy is required due to their large mass so the energy can only be 'borrowed' for a very small amount of time compared to other force carriers.

Is this correct? I'm not able to find any more information about it. I don't know the the information was wrong or if it was just dumbed down so much that it became very inaccurate.

Thanks.

 

[Mark M]

That's a misconception that is often used in popular science, that particles can violate the conservation of energy 'if they do it quick enough!'. Energy is always conserved in quantum mechanics. See this entry from Wikipedia in 'Conservation of Energy':

"In quantum mechanics, energy of a quantum system is described by a self-adjoint (Hermite) operator called Hamiltonian, which acts on the Hilbert space (or a space of wave functions ) of the system. If the Hamiltonian is a time independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Note that due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position momentum uncertainty principle, and merely holds in specific cases (See Uncertainty principle). Energy at each fixed time can be precisely measured in principle without any problem caused by the time energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics."

 

[mfb]

Virtual particles violate their energy-momentum relation, which can lead to "wrong" masses. In the case of nuclear decays, for example, the virtual W has a mass smaller than its regular rest mass. This is nothing special about the W/Z, all other particles can do this, too.