The perfect relativistic quantum particles simulation

[Jeronimus]

How would a physicists expect a perfect relativist quantum particles simulation to look like?

Can anyone give a description of its functionality?

Let's say for example, someone would program a simulation, composed of a 4D space-time diagram. Within this simulation are a large amount of quantum particles "floating around". At any given spacetime point or volume within this simulation, the simulation would give you the exact probability of detecting a given particle or the strength of the particle field.
Here i must ask, when QM physicists are talking about the probability of detecting a particles within a given volume of space, do they mean 3D space or 4D-space(spacetime)? The above description is just an about how i would imagine it to give you a picture of what kind of answer i am expecting.

What kind of properties/functionality would an expert demand of such a simulation, to consider it perfect? What kind of information would he have to be able to extract out of this simulation to consider it complete as in being powered by a TOE?

Assume we have access to arbitrary fast computers with arbitrary large amount of memory.
Such a simulation, with enough particles simulation, would under the right conditions form molecules, proteins, bacteria, insects and higher life eventually (ignoring philosophical considerations).

 

[pervect]

I'm afraid I can only give a rather vague answer. One replaces particles with a wavefunction, $\Psi$. The best model is quantum field theory, which isn't a relativistic theory of particles but a relativistic theory of the field given by the wavefunction.

There's a rule that turns the value of the wavefunction (which is a complex number) into a probability of detecting a particle.

And there's other rules that describe the evolution of the wavefunction.

 

[Jeronimus]

I'm afraid I can only give a rather vague answer. One replaces particles with a wavefunction, $\Psi$. The best model is quantum field theory, which isn't a relativistic theory of particles but a relativistic theory of the field given by the wavefunction.

There's a rule that turns the value of the wavefunction (which is a complex number) into a probability of detecting a particle.

And there's other rules that describe the evolution of the wavefunction.

A little bit more specific would be nice.

Let's say a physicist is sitting in front of the screen running the simulation. He has no idea which model was used to create the perfect simulation. How would he determine if the simulation was perfect?

For example, let's say he would draw a cube or some other geometrical object within the simulation, and then he would get the detection probabilities for all particles involved within that volume.
Which other information would a physicist have to be able to extract from a "world"-simulation, to consider it perfect?