Wavefunction Collapse
Quantum particles are actually waves with complex amplitude spread out
in space and evolving according to deterministic laws, except when a measurement
occurs. During a measurement, the wavefunction instantaneously changes
into a state consistent with one of the possible measurement outcomes.
The probability of any given outcome is dependent on the amplitude of the
wave. In most cases, this means that the wavefunction becomes suddenly
localized in space, when before it was widely distributed.
Pros
It is easy to visualize how waves propagate because we have experience
with sound waves, water waves, etc.
Cons
The collapse of the wavefunction is a mysterious thing. Several ideas have
been put forward as to what causes it. Some think there is something special
about the human mind that is able to collapse wavefunctions, and that the
world is a blur of waves until a human observes it. Some think that the
wavefunction collapses every so often all by itself, so that things never
go for more than a tiny fraction of a second in a blurred state.
The collapse violates time symmetry, because it never happens that a
wavefunction de-collapses.
In whose reference frame is the collpase instantaneous? Since one never
detects the same particle in two different detectors at space-like separation,
this would lead me to believe that the wavefunction collapses within the
past light cone of the measurement. This results in difficulties in defining
the equation for wave propagation between measurements, but it does restore
time symmetry. The wavefunction must now depend on both the future and
the past constraints.
The wavefunction of two entangled particles cannot be represented as
two waves in a three dimensional space, but as a single wave in a six dimensional
space. This gets ridiculously complex for large numbers of particles.
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