Consider the wavefunction formalism of quantum mechanics, where a
function Phi maps tuples of the form to
complex numbers. t is usually interpreted as time and x1, x2, ...
(which are themselves 3-tuples) as positions of particles. Suppose
then, this wavefunction represents an infinite set of physical
systems for every possible t, where each system is
three-dimensional and have no extent in time. There is no
transtemporal identity for these systems, meaning one cannot say
that one system at time t "is" another system at time t’. (Therefore
no causal structure is possible.) Every system contains n
particles, and the measure of the subset of systems at time t with
particles at positions x1, x2, ..., xn is |Phi(t, x1, x2, ...,
xn)|^2. If the wavefunction takes other parameters such as spin
states, these are summed over (i.e. Sum_over_all_y |Phi(t, y, x1,
x2, ..., xn)|^2).
All possible structures that can be encoded in the positions of no
more than n particles, including presumably human beings if n is
large enough, appear in these infinite sets of systems. But some
structures appear “more often” or have larger measures than
others, and from this we can understand the probabilistic
predictions of quantum mechanics. For example, consider a
wavefunction that represents an experiment in which the
experimenter measures the z-spin of a particle in the state
(|up>+|down>)/Sqrt(2). At t=0, all systems include an experimenter
who is about to measure the z-spin of the particle. At t=2, half
of the systems include an experimenter who remembers observing
spin-up and half of them include an experimenter who remembers
observing spin-down.