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===The uncertainty principle===

===The uncertainty principle===

As a result of the wave nature of a particle, certain paired physical properties such as position and [[momentum]] cannot both be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and visa 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, 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 visa 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> Dx \times Dp \ge \frac{h}{4\pi}</math>

* The "hidden variable" interpretation<ref>http://www.reasons.org/resources/non-staff-papers/the-metaphysics-of-quantum-mechanics</ref> says that there is actually a [[determinism|deterministic]] way to predict where the wavefunction will collapse; we simply have not discovered it.  [[Von Neumann]] attempted to prove that there is no such way; however, [[John Stuart Bell]] pointed out an error in his proof.

* The "hidden variable" interpretation<ref>http://www.reasons.org/resources/non-staff-papers/the-metaphysics-of-quantum-mechanics</ref> says that there is actually a [[determinism|deterministic]] way to predict where the wavefunction will collapse; we simply have not discovered it.  [[Von Neumann]] attempted to prove that there is no such way; however, [[John Stuart Bell]] pointed out an error in his proof.

* The many-worlds interpretation says that each particle does show up at every possible location on its wavefunction; it simply does so in alternate universes.  Thus, myriads of alternate universes are invisibly branching off of our universe every moment.

* The many-worlds interpretation says that each particle does show up at every possible location on its wavefunction; it simply does so in alternate universes.  Thus, myriads of alternate universes are invisibly branching off of our universe every moment.

* The currently prevailing interpretation, the Copenhagen interpretation, states that the wavefunctions do ''not'' collapse until someone observes the particle at a certain location; until someone observes it, it exists in a quantum indeterminate state of simultaneously being everywhere in the universe.  However, [[Schrodinger]], with [[Schrodinger's cat|his famous cat experiment]], raised the obvious question: who, or what, constitutes an observer? What distinguishes an observer from the system being observed? In essence, the Copenhagen Interpretation requires consciousness to distinguish observers from inanimate matter.

* The currently prevailing interpretation, the Copenhagen interpretation, states that the wavefunctions do ''not'' collapse until someone observes the particle at a certain location; until someone observes it, it exists in a quantum indeterminate state of simultaneously being everywhere in the universe.  However, [[Schrodinger]], with [[Schrodinger's cat|his famous cat experiment]], raised the obvious question: who, or what, constitutes an observer? What distinguishes an observer from the system being observed? In essence, the Copenhagen Interpretation requires a [[soul]] or something else to distinguish observers from inanimate matter.

==Applications==

==Applications==