Since energy is uncertain, it can be "borrowed" for short periods of time. It takes about 1Mev of energy to create a positron and an electron. How long can this amount of energy by "borrowed" before it must be paid back by having the positron and electron anihilate each other?

Use Planck's constant h = 4×10^-15 eV·s to calculate

The vacuum is not empty! It is filled with particle-pairs appearing and disappearing on "borrowed energy".

In a sufficiently strong electric field, a positron-electron pair will separate and gain enough energy from the field during their 6×10^-22 seconds of life to pay back its debt without annihilating. The pair then become permanent citizens of the universe, created from nothing!

Many elementary particles are unstable and live only a short time. Their mass-energy cannot have a precise value and varies over a range given by the energy-time uncertainty relation. For example, a particle that lives for just 6×10^-22 seconds will have a mass-energy that is uncertain by at least 1 Mev.

Examples --- What this is an example of

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