Filters, Superpositions and Entanglements


 Superpositions are not necessarily entanglements.
 A superposition is what happens at a beam splitter.
 An entanglement is what happens in a non-linear crystal.

 Zeilinger et al[1], don't use beamsplitters to make entangled
 particle pairs. Superpositions and entanglements are different.
 Wavefunction collapse can be alot like tapping a computer
 programmer on the shoulder while s/he is in deep superposition
 of many associated concepts; destoying their concentration.

 Decoherence is a loss of the ability to  make meaningful 
 distinguishments, or the loss of the ability
 to maintain a record of a past event (entanglement) and
 this diffusion or dispersion does not destroy all record
 of the past event but makes it increasingly unrecoverable
 in a theromdynamic sense, which itself can probably be modelled
 as a damping in an impulse-response (Green's functions) sense,
 like a pair of bells having clanged against each other
 and that correlated ringings of each bell, fading like a memory of
 the past as the energy of the event disperses within the bell.

 Single-moded spatio-temporal solitons (light-bullets)
 are recognized for their ability to resist such dispersion
 and are proposed for this reason as candidates for qubits
 which resist decoherence. Other possibilities for
 decoherence resistent qubits might be BE condensates,
 superconductors, and superfluids, and extremely stabilized
 laser-light (non-interaction experiments); all of which
 effectively seem to homogenize their component units to the
 point where they act in extreme unison (coherence).
 Pure coherence, unadulterated, is apparently not possible
 in any finitely bounded system. But we none-the-less have
 computers, which function almost completely as if this
 idealism of both continuity and closure were attainable in a
 finite system.

 The Zen master will tap the meditating student on the shoulder
 to remind him that closures are indeed just as much a part of
 life as coherence. Decisions have to be made.

 An electric battery represents distinguishment. Its potential
 energy is meaningless without continuity (a circuit).
 But shorting out the terminals of the battery and explosively
 releasing all its energy is also meaningless.

 We build an electric circuit with resistance (decoherence) and
 yet it can still have meaning, but that meaning is generally 
 derived from outside the energy economy of that circuit.

 The battery's energy is eventually depleted and it fails
 to serve its purpose to make some form of distinguishment.

 In order for its purpose to survive, the energy must
 be replenished from the outside, but not with excessive
 greed (we live off the land and should respect the Time
 it takes to feed us and itself).
 Decoherence is not without distinguishment.

 We use circuits with large resistances as "space heaters"
 and from this we derive a distinguishment or contrast of
 heat and cold on those cold winter nights, but as with
 anything else, the 'burning of space'
 (or land like the rainforests) is not without its consequences.

 Contrast is as important as brightness, but these two
 should not be confused with each other.

 I like the idea of portraying this in terms of ideal mirrors,
 which reflect all the colors in a specific direction, as opposed
 to white paper which also reflects all the colors equally, though
 not with specific direction (diffuse). Is the mirror, when
 crushed into many pieces, the same as the white paper ?

 The mirror appears gray because it is really black in the
 regions where light is not reflected. And black and white
 and grey are merely distinguished by relative brightness.

 "Superpositions" are distinguished from "filters" by their
 ability to add as well as subtract. Filters only subtract.

 When two systems are superposed and then separated, their
 former superposition becomes an entanglement.

 A filter can exist without a superposition; as in the 
 spatial filters in holography.

 A superposition cannot exist without the concept of a filter
 (in terms of destructive interference); as in non-spatial filters 
 in holography (thick holographic filters using Bragg selectivity,
 filtering in the time-like domain using convolution instead 
 of multiplication of the impulse response and signal in the 
 space-like domain) 

 Entanglement cannot exist without superpositions and filters; 
 as in the more recent quadrature mirror "filters" or wavelet 
 analysis, .... (Indeed it should be called
 "analysis" as it is very similar to what a psychoanalyst
 does in terms of a patient's _subjective_ spatio-temporal
 memories. The analyst essentially unravels the [en]tangled
 threads of space-time in a patient's memories (historical
 threads) and reweaves them into a more "flat" or "euclidean"
 road map. Similarly, the entangled space-time histories
 are unravelled in a _physical_ signal by multi-resolution
 analysis of both it's static (deterministic) and dynamic
 (non-deterministic) content.)

 It should be understood here that the distinction of "spatial"
 and "temporal" in the above cases are in terms of space-like
 and time-like functional domains. The different definitions
 of "time" that can arise and the many further implications 
 are developed elsewhere.

 The chinese-box-like hierarchy is derivable from analogous 
 systems in other fields like linguistics, politics, economics, 
 etc., where the same hierarchy is more evident. 

 The overall model is suggestive that a generalized communication 
 theory abstracting the communicated units and associatively derived
 information, as well as the inherent uncertainties, can work
 across the normal boundaries of soft and hard sciences.

[1] Anton Zeilinger et al, Quantum Teleportation, Quantum Non-demolition,...