An aside, concerning what actually requires simulation / arithmetic
explanation.
The algorithm of the collapse dynamics itself operates in a domain meta
to the physical, and in this regard there is a reversal of causality
with respect to the physical and the arithmetic. But I don't think this
is what Bruno'spaper The Origin of Physical Laws and Sensations is
driving at. The process of the collapse dynamics is deeply interwoven
with the physical time evolution of quantum systems in the linear
dynamics, and even if we agree that the collapse dynamics is primarily
arithmetical, and even prior to the physical, this does not say anything
about the nature of the linear dynamics.
As Everett explains, the functional identity of the observer is the
record of observations. It is this definition which resolves the
fundamental difficulties in the interpretation of quantum theory. It is
only this identity to which there is the appearance of collapse. The
collapse dynamics is the change to the linear dynamics, and is therefore
of different logical type. It is to the linear dynamics as acceleration
is to velocity.
As Everett explains, the algorithm of the linear dynamics runs as time
passes, and the perceptual point of view / frame of reference passes
along the linear time dimension of space-time. That is the algorithm of
the body-mind that produces the contents of the sensorium. At the point
in time along the linear time dimension of space-time, at which the new
observation is formulated in the sensorium, and thus added to the record
of observations, the functional identity of the observer, the functional
identity of the observer changes. This new version of the observer
exists in a different version of the four dimensional space-time
universe, defined by a different quantum state.
I would point out that these two different algorithms are being
implemented at different levels of logical type, and this too has to be
inherent simulation. Time passes as the simulation exercises a specific
linear dynamics, a specific time evolution of the position and state of
matter and energy in the virtual environment observed by the observer. A
new observation is formulated as part of this process. But upon the
making of each observation, the algorithm itself changes. This is what
experiments show, so this has to be formulated in arithmetic. Thus the
arithmetic requires two different levels of logical type, just as a
physical reality must if it is to account for the observed phenomena.
All this is what has to be simulated in a simulation, all of which is
perfectly feasible. I have written the dual algorithmic form of the
computation in C Language which I append here in case anyone is interested.
But just because it can all be simulated, this does not in my view imply
'the reversal between physics and arithmetic'.
But I am entirely open about this.
Andrew
Appendix
Here the logical form of the standard von Neumann-Dirac formulation of
quantum mechanics operational for the functional identity of the
observer as defined by Everett is presented as pseudocode in C language.
If variables ?, observation, and observables[], and function
get_sensorium_contents() were instantiated in suitably coherent memory
of a quantum computer, such a program would produce the subjective
realities of all possible functional identities of an observer, in the
form of Everett's branching tree of memory configurations.
So the running of this algorithm, and ? the unitary quantum state,is all
we have to explain in order to explain our experience of physical
reality. As Russell points out in Theory of Nothing page 5 " There is a
mathematical equivalence between the Everything, as represented by this
collection of all possible descriptions and Nothing, a state of no
information.". Since Nothing is equivalent to Everything, ?, which
explains the existence of the algorithm, there is nothing to explain
except the running of the algorithm!
void transtemporal_reality () {
/* Initialisation */
Boolean new_observation = true;
Observation observation = LIGHT;
Functional_Identity observer = 1;
World world_hologram = NO_OBSERVATIONS;
Correlations_Record observables[];
Quantum_State ?;
Elapsed_Time t = 0;
int c = 0;
while (observer != 0) {
/* Process 1 -- Quantum time -- The exercise of the collapse dynamics -
Change of quantum mechanical frame of reference */
if ( new_observation ) {
world_hologram = world_hologram + observation;
display (world_hologram);
observer = observer + observation;
observables[c++] = observation;
? = quantum_state_defined_by (observables)
new_observation = false;
}
/* Process 2 -- Space-time time -- The exercise of the linear dynamics -
Change of inertial frame of reference */
else {
t = t + PLANCK_TIME
new_observation = compute_neural_state (?, t);
if ( new_observation)
observation = get_sensorium_contents();
break;
}
}
}
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