Recommended Readings
A lot of Nick Herbert’s book this week with some of Edward Harrison’s “Cosmology” thrown in there.
Von Neuman
In the course of searching for a proper interpretation of Quantum Theory some tried to assume that quantum objects were actually ordinary particles or everyday objects that we just didn’t have all the information on. Von Neuman went the opposite route, assuming everything was a quantum process. This lead him (and Heisenberg to some extent) to require two processes: Type one processes where an object expands into its possibilities, and type two processes where some actuality is decided. Those who’ve read the CTMU should find this familiar. The issue becomes: where to locate a type two process? Mathematically the “von Neumann chain” can be broken at any point and only one point seems particularly privileged in the whole sequence of events - that of the interface between mind and brain. What that means, no one knows.
EPR Experiment
Einstein did not believe in the sort of indeterminacy, or other weirdness, quantum theory seems to imply. With a couple other scientists he proposed the Einstein-Podolsky-Rosen experiment to show that a quantum object - a photon in our example - must have definite properties. Take a light source that emits entangled photons in opposite directions, directing them each at a calcite detector to measure the polarization at some angle. Individually each of the beams (we will over the course of our experiment emit more than one photon after all) are unpolarized, 50/50 chance of a hit on the detectors. Taken together however, their paired polarization is determined, they must always take the same value. Now take one of the detectors and move it closer to the source than the other. Say we somehow, using our free choice of what we measure, have that closer detector take some measurement. Then the polarization of the first measured photon means the second photon must be in the corresponding state. The photons are moving away from each other at the speed of light, however, so it would seem no information transfer between the two is possible. Einstein argued this experiment shows that Quantum Theory is therefore a complete theory of phenomena only, and not a theory of reality. He argued that the photon must have a defined polarization value for each angle. Einstein was assuming locality though. Herbert points to three possible conclusions:
The photons really do have defined polarization and Quantum Theory is incomplete.
The photons communicate “telepathically” to one another, returning us to non-locality or spooky action at a distance.
Denying the independence of spatially separated systems.
Bell’s Theorem
John Bell comes on the scene and takes up the EPR “paradox”. Using some (comparatively simple) mathematics he takes the following steps:
Assume locality in an EPR like experiment.
Show that a certain inequality must be satisfied.
Note that this inequality is not satisfied in the EPR experiments.
Conclude that reality must be non-local.
Personally, at this stage, I’m a fan of the third conclusion above; not that the photons somehow communicate with each other by senseless, medium-less magic, nor that each one is just a table of polarization values waiting to be queried, but instead that they are in a sense united.
