Changes

This means that we can never measure both the position and momentum of a particle simultaneously with arbitrary [[precision]]. The more precisely we wish to measure one observable, the less precisely we can measure the other at that time.

This means that we can never measure both the position and momentum of a particle simultaneously with arbitrary [[precision]]. The more precisely we wish to measure one observable, the less precisely we can measure the other at that time.

Contrary to popular belief, this is ''not'' merely a measurement issue. While it is often stated that it is not possible to know the precise position and momentum of a particle at the same time, this is misleading; it implies that the particle has precisely defined position and momentum, but that information is unavailable to us. In fact, the Uncertainty Principle tells us that a particle cannot have precisely defined position and momentum simultaneously.

Contrary to popular belief, this is ''not'' merely a measurement issue. While it is often stated that it is not possible to know the precise position and momentum of a particle at the same time, this is misleading; this statement implies that the particle has precisely defined position and momentum, but that information is unavailable to us. In fact, the Uncertainty Principle tells us that a particle cannot have precisely defined position or momentum.

A similar example is [[time]] and [[energy]], the product of which also has a lower limit. Quantum fluctuations are a result of this, where for short time, there is enough energy in "empty space" to create a pair of particle and antiparticle, such as electron and positron. Although this appears to be a strange or extreme process, it is the only one to explain some properties of black holes. Laser physics with ultrashort [[laser]] pulses is another field, where the limit in the product of time and energy plays an important role.

A similar example is [[time]] and [[energy]], the product of which also has a lower limit. Quantum fluctuations are a result of this, where for short time, there is enough energy in "empty space" to create a pair of particle and antiparticle, such as electron and positron. Although this appears to be a strange or extreme process, it is the only one to explain some properties of black holes. Laser physics with ultrashort [[laser]] pulses is another field, where the limit in the product of time and energy plays an important role.