### 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. Examples include
neutron beta decay,
the production of charm particles, and the
decay of an eta-c particle, all of which we will explore in depth soon.