[SEQ RERUN] On Being Decoherent

MinibearRex

Today's post, On Being Decoherent was originally published on 27 April 2008. A summary (taken from the LW wiki):

When a sensor measures a particle whose amplitude distribution stretches over space - perhaps seeing if the particle is to the left or right of some dividing line - then the standard laws of quantum mechanics call for the sensor+particle system to evolve into a state of (particle left, sensor measures LEFT) + (particle right, sensor measures RIGHT). But when we humans look at the sensor, it only seems to say "LEFT" or "RIGHT", never a mixture like "LIGFT". This, of course, is because we ourselves are made of particles, and subject to the standard quantum laws that imply decoherence. Under standard quantum laws, the final state is (particle left, sensor measures LEFT, human sees "LEFT") + (particle right, sensor measures RIGHT, human sees "RIGHT").

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This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Where Experience Confuses Physicists, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.

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Today's post, On Being Decoherent was originally published on 27 April 2008. A summary (taken from the LW wiki):

When a sensor measures a particle whose amplitude distribution stretches over space - perhaps seeing if the particle is to the left or right of some dividing line - then the standard laws of quantum mechanics call for the sensor+particle system to evolve into a state of (particle left, sensor measures LEFT) + (particle right, sensor measures RIGHT). But when we humans look at the sensor, it only seems to say "LEFT" or "RIGHT", never a mixture like "LIGFT". This, of course, is because we ourselves are made of particles, and subject to the standard quantum laws that imply decoherence. Under standard quantum laws, the final state is (particle left, sensor measures LEFT, human sees "LEFT") + (particle right, sensor measures RIGHT, human sees "RIGHT").

For all these types of experiments, how do they "aim" the particle so it hits its target from far away? It would seem that the experimenters would know pretty much where the particle is when it shoots out of the gun (or whatever), so would not the velocity be all over the place?

Only if they make the departing aperture small. A wider aperture allows the departing wave to be tight.

Does the polarization vector change as the photon moves along?

It depends which basis you look at it in. It is conventional to consider a photon's 'polarization' to be ploarization subspace that contains all of its time dependence. The phase then indicates the rest of its state. However, you can look at it other ways. A circularly polarized photon moving +z can be considered as a rapid shift between various orientations of +x and +y polarization... but it's simpler to just let it be in a circular polarization state and let the phase vary. A photon's state in this sense IS its 'main' wavefunction as you call it. There is no distinction. People usually shorthand think of a photon to have perfectly-defined momentum, but of course that would mean the photon extends through all of space. Real photons have multiple momentum components, and form a wavepacket or a static state. In particular, and very relevantly, you can construct electromagnetic field states (photons) that are inverse square laws - the static electrical field from a charge - and these have a very broad momentum distribution.

why can we put in the minus sign in the eqation that you say "we will need" later, instead of a + sign?

I can't find any minus signs in this post, but to take a stab in the dark at whatever it is you're referring to, subtraction is the special case of addition after one of a particular set of phase shifts.