Changes

===The uncertainty principle===

===The uncertainty principle===

As a result of the wave nature of a particle, neither position nor [[momentum]] of a particle can never be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and vice versa.  Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]]:<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>

As a result of the wave nature of a particle, certain quantities cannot be known to an arbitrary precision simultaneously. An example is position and [[momentum (physics)|momentum]].  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and vice versa.  Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]]:<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>

:<math> Dx \times Dp \ge \frac{h}{4\pi}</math>

:<math> \sigma_x \sigma_p \ge \frac{\hbar}{2}</math>

where:

where:

* Dx = uncertainty in position

* <math>\sigma_x</math>is the [[standard deviation]] (uncertainty) of position

* Dp = uncertainty in momentum

* <math>\sigma_p</math> is the [[standard deviation]] of momentum

* h = [[Planck's Constant]]

* <math>\hbar</math> is the [[Planck's Constant|reduced Planck's constant]]

==Interpretations==

==Interpretations==