Aharanov Bohm - Wholesale Beyond Retail
Wheeler refers to the Aharanov-Bohm effect as an example of It From Bit and he appears to be making a very purposeful step here. I will try but I do not feel I can do this effect justice so for a better explanation please refer to this video. It’s been a while since my E&M or my Multivariable Calculus.
The setup for the Aharanov-Bohm effect is as follows:
A screen with two slits for electron beams to enter the space from.
A space for them to traverse through.
A screen on the other side of the space to register the effects of the electron beams.
A shielded magnetic field inside the space (the field region). The magnetic field B outside the shielded region is 0, whether or not the field inside is 0.
Electrons are fired through the slits, the beams fan out and interfere. They then cause an interference pattern on the screen.
The magnetic field is turned off.
Despite the fact the magnetic field B in the space has not changed, the interference pattern shifts. (!)
The explanation for this, more eloquently put in the video, can be put:
Gauss’s Law for magnetism states Div(B) = 0.
We know from vector calculus that the divergence of the curl of any vector field A is zero: Div(Curl(A)) = 0.
We therefore invent the concept of a magnetic potential field A such that B = Curl(A).
We solve for A outside the field region and find that while A is zero inside and outside the field region when B is switched off, A cannot be zero even outside the field region when B is on, despite the fact that B is zero outside the field region. This is due to Stoke’s law which allows tells us the integral around a closed path of the field A must be equal to the integral of the curl of A over the enclosed area, effectively: Int(Dot(A, dcurve)) = Int(Int(Dot(Curl(A), dArea))).
From the definition of A, Curl(A) is just B. But B is nonzero at some points within the enclosed area so A cannot be zero everywhere in the space.
When plugged into the wave equation for the electron non-zero A has an effect.
Wheeler’s previous example was that of registration of a single photon - one bit. Here there is a one bit decision in terms of whether the interference pattern is shifted one way or the other. However, there are also the interference pattern and the magnetic field strength themselves which appear to be more than just a bit. Wheeler argues of the interference pattern that it is simply a statistical distribution of yes-no decisions, and makes a similar argument for the strength of the magnetic field based on a magnetometer. Here he says we are dealing with “bits wholesale” rather than “bits retail”. He appears to be making the point that even complicated phenomena that do not appear binary ultimately reduce to a collection of binary registrations (or observations).
