What is the status of Everett's Thought Equation? Here is Hugh Everett's PhD Thesis:
http://philosophyfaculty.ucsd.edu/faculty/wuthrich/PhilPhys/EverettHugh1957PhDThesis_BarrettComments.pdf
On page 9 he says:

"We have the task of making deductions about the appearance of
  phenomena to observers which are considered as purely physical systems
  and are treated within the theory."

If I got this straight, Everett proposed something kind of like a thought experiment. But it wasn't exactly an experiment you did with thoughts. It was an equation you made with thoughts. A thought equation.
With quantum mechanics, you can write a wave equation to describe a particle. Or perhaps a group of particles. The more particles you describe, the more complex the equation gets. Everett proposed something bold. A wave equation that contains all the particles of object to be measured. But he didn't stop there. If you're going to measure the object with a particle detector, or a ruler, or a clock, those things are made out of particles themselves, and in the equation they go. Now you've got an object made of particles as well as measuring tools made of particles all in the wave equation. But that's not all. An observer, like you or me, is also made of particles. In the equation we go. Or at least something like us: "an automatically functioning machine" with senses and memory.
This idea of Everett's is now that the entire wave equation can be set in motion as a purely physical system. The wave never needs to collapse, as it does in other versions of quantum mechanics, because as the object and the observer interact, the observer's memory will contain the outcome of its measurements. Everett called the measurements encoded in the modeled observer's memory "relative state". 
The wave equation itself, the "universal wave function" as he put called it, would presumably be the absolute state.
Everett's thought equation could, in theory, be turned it into real mathematics. But a wave function describing all the particles needed to make an object, and measuring tools, and an observer would take an unreasonable amount of paper and time to write down.
My question is...
Aren't those limitations gone in the information age?
Shouldn't we be able to turn Everett's wave equation that contains an observer into a computer model?
I know there is a Human Brain project working on simulating the human brain for medical purposes.
What's the status on physicists modeling an observer?
Example of what I'm asking about
We have lots of models of reality. But not one like Everett's thought equation. When we want to make a model of the solar system, we make a model of the solar system. When we want to make a model of a particle of light, we make a model of the particle of light. What we don't do is make a model of an observer made of particles interacting with the particle of light performing a measurement. And that is precisely what is happening in Everett's thought equation.
So, if we are to implement Everett's idea with software, the primary requirement is:


*

*Make a model of an observer performing a measurement


We have plenty of models of things we measure, but we don't have any models of the measurement actually being made by an observer. Now there are some stipulations on how this can be achieved. Everett stresses repeatedly that the observer is a purely physical system, interacting with the object being measured in a purely physical way.
This can be translated into the following software requirements:


*

*There are no special rules that give an object in the model the power of observation or measurement. The only rules of the model govern the mechanical interactions of the objects within it.

*Through the mechanical interactions of the objects in the model, the objects arrange into compounds that act similarly to atoms and molecules.

*The simulated atoms and molecules form the necessary components for an automatically functioning machine with senses (such as cameras or eyeballs) and a memory (such as a computer or a brain)

*The simulated machine with the sensor and memory interacts mechanically with the object and the measuring tools, and a measurement is recorded in the memory of the observer
Why I'm asking
Software that fulfills these requirements would present two different sets of information to anyone examining it.
First, the algorithm and its variables and their values. This could be exposed to the researcher explicitly, or accessed through a debugger. This is how the program looks to the programmer as it's running. This is the program's absolute state.
The second set of information in the software cannot be found in the variables of the model directly. Some of the variables in the model form an observer with a memory. You have to look at that memory to find the second set of information. An abstract set of relational data. This is how the program looks to something that exists inside in it. This is the program's relative state.
The relative states are the unique feature of software that meets these requirements. With other models, you only have one set of states. By simulating measurement within the model, we have two states, absolute and relative. The idea is to then take the relative states of the model, which are the observations made by a simulated observer, and compare them to our observations of reality. This leads to some very interesting questions and answers.
For example, let's ask the simulated observer to measure the position and momentum of a particle simultaneously. How will the observer do? The observer's first measurement will disturb the particle being measured and affect the second measurement.
Other models don't have a measurement happening as a mechanical process inside it. So they need to comply with the uncertainty principle in other ways. But the absolute/relative model has a measurement actually occurring inside it, and it seems intuitive the model is going to implicitly produce measurements in accordance with the uncertainty principle.
Just as Einstein had to remind us that the space and time we measure and discuss in physics are relative, here is Everett telling us that the matter we measure is also a relative state of reality.
Perhaps the absolute states of the program are indeed compliant with the uncertainty principle. But they don't have to be. If the predictions of the model come from the relative states, only the relative states have to be consistent with empirical reality. Nothing in the software requirements dictates anything about the true nature of absolute matter, except that they form an observer whose measurements are consistent with ours.
Hopefully that is somewhat clear.
Are there research programs trying to implement Everett's Thought Equation?
How far along are they?
 A: This question contains a lot of misunderstandings regarding quantum theory. As for your question, "Are there research programs trying to implement Everett's Thought Equation?", the answer is that nobody is working on what you described.
A: OK - here's the complex answer to what I think you are asking.
David Deutsch on AI and the MWI of QM I will quote the extended piece:

The first experimental test used to falsify the collapse approach was
suggested by British physicist David Deutsch in 1985. However, it is
still not practical to implement, as it requires artificial
intelligence (AI) and reversible nano-electronics.
In Deutsch's thought experiment, an atom, which has a determinate spin
state in one axis, 'left' for example, is passed through a
Stern-Gerlach apparatus that has the possibility of measuring it in
another axis, as either spin 'up' or spin 'down' in this case. This
means that the atom is then in a superposition of 'up' and 'down'
states from the perspective of an observer who has not yet become
entangled with it. This superposition travels to an AI's artificial
'sense organ'. Here it is provided with two options: it may be
detected as either spin 'up' or spin 'down'. The AI's conscious mind
then records the result.
The collapse approach predicts that this will cause the atom to
collapse into one determinate state, with either a determinate 'up' or
'down' (but not 'left' or 'right') spin. The Everett approach predicts
that the mind will branch into two, one mind will record up and one
down (but neither will record 'left' or 'right').
The whole process is then reversed so that the atom emerges from the
entrance to the Stern-Gerlach apparatus and the mind forgets which
result it recorded. This process does not erase any of the AI's other
memories however, including the memory that they did record the atom
to be in a definite state.
If a 'left-right' detector was placed at the entrance of the
Stern-Gerlach apparatus then the collapse approach predicts that it
will be detected as being in either a 'left' or 'right' state with
equal probability. If the Everett approach is correct then the atom
will be in the same state that it was in before the measurement, it
will still have a 'left' spin.
Deutsch argued that: "this experiment allows the observer to 'feel'
himself split into two branches: The interference phenomenon seen by
our observer at the end of the experiment requires the presence of
both spin values, though he accurately remembers having known at a
previous time that only one of them was present. He must infer that
there was more than one copy of himself (and the atom) in existence at
that time, and that these copies merged to form his present self".

So, all you need is an artificial intelligence running on a quantum computer. Neither of which we have at present.
A: You seem to imagine that simulations of an observer would consist of simulating each atom or molecule. For a single observer, the number of atoms or molecules is more than $10^{23}$. I doubt that any computer currently existing is up to the task of simulating $10^{23}$ classical systems never mind $10^{23}$ quantum systems.
The knowledge required to construct an Artificial Intelligence does not currently exist, and there is no particular reason to expect that to change any time soon. So we're not going to have computer simulations of thought any time soon.
There are simpler models of observers. A person is a large relatively warm system in contact with an environment. As such, anything a person knows about a quantum system is going to be spread among many other systems in his environment long before he has given much thought to what he has observed. Some models explain what will happen when information from a quantum system is spread redundantly among many other systems. Such models explain some features of relative states, such as the orthogonality of vectors describing measurement results.
Your question also includes an error:

Perhaps the absolute states of the program are indeed compliant with
  the uncertainty principle. But they don't have to be. If the
  predictions of the model come from the relative states, only the
  relative states have to be consistent with empirical reality. Nothing
  in the software requirements dictates anything about the true nature
  of absolute matter, except that they form an observer whose
  measurements are consistent with ours.

All quantum states are consistent with the uncertainty principle. Any quantum state is an eigenvector of some observable, and this imposes limitations on how sharp other observables can be in that state.
