In this context, the method followed by the Matrix to "collapse the wavefunction" is not bound by any fundamental necessity of respecting the relativistic invariance. There is no theoretical obstacle in conceiving its operations as based on some "universal time" that admits a relation of "absolute simultaneity" between conscious events, as long as this simultaneity relation remains compatible with the physical relation of causal independence in space-time.

Such a simultaneity structure, if it is needed, still has a major advantage over the simultaneity structure needed in some other interpretations of quantum physics (such as hidden variables and some Spontaneous collapse interpretations), because it is a non-physical structure :

- It does not suffer from the impossibility to specify a mathematical determination of how this simultaneity relation itself evolves in space-time in the face of the space-time curvature described by General Relativity;
- It does not need to exist between all physical space-time points, but only needs to exist between individual minds, to order their conscious events of physical perceptions;
- We do not need to search for any new mathematical
reconstruction of Quantum Field Theory relatively to this
simultaneity structure so as to formulate new non-local physical
causality laws for collapse (or any kind of world selection)
there.

Now let us consider this latter hypothesis and see where it goes.

Consider an EPR experiment where both measurement events A and B (conscious perceptions) are separated by a space-like interval, so that the question of which one happens first, is not a relativistic invariant.

In one viewpoint, A happens first, so that it "chooses" its result, only bound by the constraint of compatibility with the quantum probability law as it comes in the absence of the measurement B. Then B happens, but facing a different context: its "choice" is bound by the fact that A happened first, which modified the quantum probability that B faces, in comparison with the case if A did not happen. Moreover, in the extreme case that both measurements are done along the exact same axis, B does not have anymore choice at all.

In the other viewpoint, the time order between A and B is reversed, so that the same story can be said, but exchanging the roles of A and B.

Now the question is : can we reconcile both viewpoints, by adding up their necessities, and telling the story in a way that keeps the symmetry between A and B ?

Note that if A comes first but both measures happened to be made in the same direction, then B's result cannot be chosen at all, but is determined by A's result. But this should remain true if reinterpreted saying that B comes first. In this case the question whether B has any choice or not, cannot depend anymore on whether the directions of measures are the same or not, since A's direction cannot be claimed to have been chosen yet. Therefore we should conclude that, anyway B's result is not chosen at all, disregarding what A does.

Note that this conclusion simply coincides with the way things naturally appear : when we are observing something, we do not have the feeling that we are making any choice on the result of our observation. It all looks like, this result is given to us from the outside. However, it cannot come from a physical outside, since... there is no such a thing as a physical reality, and the measurement result did not really exist before it was perceived.

Instead, what exists outside the individual minds, and that provides the perception results, is the Matrix. And the Matrix provides to each individual mind his perception results, every time immediately in reaction to this mind being about to have that perception (thus after decoherence). And in order for this behavior of the Matrix to keep a relativistic invariance, it has to strictly operate, in its way of "choosing" the data, a randomness in conformity with the quantum probability laws, in a non-local, holistic manner.

Now what if experiments do not confirm this, but on the contrary, display an effect deviating results from chance even when there are several observers (and with even higher amplitude) ? Maybe, because this cannot anyway constitute a faster-than-light communication, since the different observers are quite close to each other and they have a perception delay of, maybe 0.1s, that is much slower than the time needed by the light to cross the distance between them; so that it is not "who observes first depends on the space-time coordinates system" but "all observers are equally first observers anyway".

From this, follows an idea of answer about how the situation inside the brain differs, so as to open the possibility for the mind to exert free will inside the brain by deviating the perception results from a randomness complying with quantum probabilities : that, when a quantum random process occurs inside a brain, there is only one mind that will clearly be the first observer of that process, with no ambiguity from a relativistic invariant perspective.

The interest of this idea, is that it might be experimentally tested, by setting a quantum randomness generator whose output would be carefully confined for having a clearly well-defined first observer, and checking if that observer's will can influence the output of this generator. The most obvious way would involve a device like Google Glass to directly project such random light signals onto the retina. However I am not sure if such confinement methods would suffice. If it fails, it might be because of insufficient confinement. Maybe, a effective success would require some way of inserting a random generator directly into the brain. Such an experiment might be tried on animals too, though it would be much harder to explain to them to "try to influence the result by will"...

Specifications for a Mind Makes Collapse interpretation of quantum physics

A mind/mathematics dualistic foundation of physical reality

Introduction to quantum physics (notions of states and measurements)

Main page of arguments on quantum physics interpretations

On materialism and its pathological pseudo-arguments far from science

my reply on quantum idealism and science