Previously, i made a suggestion where choice was in fact not only resultant from a wave function collapse, but could itself be a function or a part of what we call the wave function itself. Thinking about it with some detail, we might even start to think of a particular wave function ψ for the human being or better said, the observer denoted as α. From here, it seemed to be quite simple to formulate actual wave function collapses where we describe the observer and the observed under the same system 1).

(1) αψ'(βψ,k)=|(αβ)ψ|^2

Those familiar with statistical mechanics and quantum field theory will know the in's and out's of the technicalities of the mathematics, which are generally-classed here as not too difficult. In equation 1, we find the description of two states, state α and state β, which both resemble seemingly independant values, that is, until the seperabiity of the two are naturally tended to in quantum mechanics. These are the systems of the observer and the observed.

In quantum mechanics, we often deal with observables; quantum eigenstates of a system arise when a sufficient measurement has taken place. In this arguement, the observer and her state vector (of wave description) are often forgotten, in lets say a random physical state of A, we would find that in this description A|ψ>=λ|ψ> we would find λ being an eigenstate of A, however, where is the observer in all this? The random appearance of observables are often unpredictable, for we do not know how quantum system appear to chose the eigenstates it has, and what would appear non-deterministically from a wave function of possibilities.

I cannot answer this paradox, but i can suffice some kind of description for the observers role, and how her wave function may be entangled as the same description of the external system (the observed). In equation 1, the observer α and the observed β have a closed connection upon the square of the wave function, which means information in α and β described by their wave fields ψ have collapsed.

More important relations arise. Our experience of observation occurs in real linear time. In fact, we may describe this in a form using the usual notation of A^n+1=Δt, and never has a negative value because of real-time effects caused by observation. Having the left hand-side of equation 1 being a function of a change in time gives us the integral of the the time lapse with the boundary given as ω and let D=αβ;

∫|DΨ|^2=((αβ)ψ,k)Δt (2)

ω

The usage of k in equation 1 and equation 2 measure the field-strength in which ψ' (the so-called outgoing field)

and ψ (the incoming field) interact.

Because the observer experiences real time, the unobserved object cannot be experienced in real time until the collapse of the wave forms ψ' and ψ. This means that they exist in probability given:

ξ(α,β)=∫Vψ'Vψ^(e^i ∫dt_n(α,ψ')+(β,ψ)k) (3)

The part denoted as Vψ'Vψ is what's called a vertex. The vertex crosses over the fields to each other, so that field ψ' interacts with field ψ. The V is actually for the representation of a linear change with the two states.

Here we calculate the change in which would occur

∞

∏ dψ(α_n,β_n)=dψ'(α1,β1)dψ(α2,β2) (4)

i=1

In this instance, i have arbitrarily-chosen to use a feyman path integral, but representing it for the abstractual use of explaining the parameter's of the observers wave function αψ'. But then, mathematics is an abstractual tool anyhow, so it doesn't really matter. All which matters is that it represents the linear changes of states α and β from α_1β_1 to α_2β_2. The shift can be construded as a sucession of time (between the interacted states of α and β) under the statistical description of |(αβ)ψ|^2, given that the observation must result in a real time scenario, and the amplitude gives a positive value of 1 thus that |x_n|^2=1.

In equation 3 we also find the use of the symbol k, which is also found scattered in the previous equations. k is the field-strength, as you might remember, and such a coupling might occur as:

k=(t_1-t_2)(t_2+t_1)/∫ α,β dt

But how such a coupling happens is pretty trivial. So, should the observer have her own wave descriptions, and have such descriptions have a mathematical meaning within the equations of phyics?

1) The observer and the observed have been often described by physicists as having ''a profound relationship.'' Whilst i do not agree consciousness in general has a massive effect on the outside world, the idea has however given rise the interconnectivity of the fundamental world (a hype i don't share in the same light)

http://www.starstuffs.com/physcon2/index.html.