## Uncertainty and Virtual Particles

#### The Heisenberg Uncertainty Principle:

In 1927, Heisenberg formulated a fundamental property of quantum mechanics which said that it is impossible to measure both a particle's position AND its momentum exactly. The more precisely we determine one, the less we know about the other. This is called the Heisenberg Uncertainty Principle. The mathematical relation is:
This means that the uncertainty in the position (x) times the uncertainty in the momentum (p) is greater than or equal to a constant (h-bar divided by two.)

This principle can also be written in terms of energy and time:

This means that the uncertainty in the energy of a particle multiplied by the uncertainty of time is greater than or equal to a constant (h-bar / 2). So for a very short time the uncertainty in the energy can be large. This leads into the idea of...

#### Virtual Particles

In many decays and annihilations, a particle decays into a very high-energy force-carrier particle, which almost immediately decays into low-energy particle. These high-energy, short-lived particles are virtual particles.

The conservation of energy seems to be violated by the apparent existence of these very energetic particles for a very short time. However, according to the above principle, if the time of a process is exceedingly short, then the uncertainty in energy can be very large. Thus, due to the Heisenberg Uncertainty principle, these high-energy force-carrier particles may exist if they are short lived. In a sense, they escape reality's notice.

The bottom line is that energy is conserved. The energy of the initial decaying particle and the final decay products is equal. The virtual particles exist for such a short time that they can never be observed.

Most processes among fundamental particles are mediated by virtual-carrier particles. For example see neutron beta decay, the production of charm particles, or the decay of an eta-c particle.