Two Slit Experiment
In the two slit experiment, a photon is shot at a barrier that has two
vertical slits in it, very close together. There is a screen behind
the barrier. One looks at the pattern formed on the screen by a great
number of photons hitting it (perhaps it is a piece of film). The
photons are sent through one at a time to make sure they cannot interfere
with one another. If both slits are open, a pattern emerges with
a set of vertical bands. If only one slit is open, a diffuse pattern
appears, much wider than any of the bands. So, opening the second
slit somehow prevents the photon from reaching the areas between the bands.
If photons are waves as in classical theory, this is easy to explain.
Part of the photon goes through one slit and part through the other and
the waves from the two parts interfere. This is exactly what happens
to sound waves and water waves. However, each photon hits the screen
and darkens one little tiny spot of film, which seems to imply that it
is a particle. If we put detectors behind each slit and look, we
either see the whole photon go through the left slit, or the whole photon
go through the right slit. We never see both detectors go off, each
with a photon of half the energy of the original.
Copenhagen
The photon is neither a particle nor a wave, it is a mysterious quantum
entity that has neither property until it is measured. The mathematics
of quantum mechanics correctly predicts the results we see, and these are
the laws for these mysterious entities that make up the world. It
is an unanswerable question to ask what happens before the photon hits
the screen.
State Reflects Observer's Knowledge
Our knowledge of the particle before it hits the slits looks like a plane
wave. After it goes through, it is two interfering wavefronts.
We don't know where the particle will land, but we do know it is unlikely
to land in one of the dark areas. After it hits the film, we know
exactly where the particle hit.
Wavefunction Collapse
The photon really is an amplitude wave, and quantum mechanics predicts
how it will evolve. However, there is a mysterious process called
“measurement” that causes the wavefunction to instantaneously collapse
back down to a single point, with probabilities determined by the amplitude
of the wave. Whenever the photon hits the film or a photon detector,
it collapses, but when it passes through the slits, it does not.
Pilot Wave
The photon consists of both a particle and a guide wave. The wave
goes through both slits and interferes to produce the band structure.
The particle is pushed by the guide wave to the bright spots on the film
and away from the dark spots. The particle causes the film to react
where it impacts. If you are sneaky in your setup, you will see that
the guide wave has to adjust itself before you make some change
to the slits.
Transactional
Each spot on the film competes to complete the transaction with the emitter.
Each area on the film has two possible transactions that it can complete,
one where the photon goes through the right slit and one where it goes
through the left slit. For the dark areas, these two transactions
cancel one another out, making it unlikely that they will complete.
For the bright areas, the transactions reinforce one another and are much
more likely to complete.
Many Worlds
There are two sets of universes, each containing a version of our photon,
one set in which the photon passes through the left slit and one set in
which it passes through the right. (Actually there are an even
greater number of universes in which the experiment is never carried out
in the first place, but we are ignoring those.) The photons are particles
that carry a property called “quantum phase” which oscillates as they travel.
Two universes which are identical except for the photon arriving at a certain
point on the film with opposite phases, cancel each other out. Neither
one is “real”. Maybe it is more correct to say that the multiverse
cannot contain two such contradictory universes in the first place, rather
than to imagine them existing, and then meeting and going “poof”.
Correspondence Between Interpretations
As I said, the mathematics makes the same predictions, regardless of which
interpretation we choose. The sum of the quantum phases over all
the universes at a particular point of spacetime is proportional to the
amplitude to find the photon at that place. Similarly, the guide
wave is effectively the sum of all universes, except for the one they call
“real”.
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