Nick Boström have been trying to calculate the probability that
we live in a computer simulation. His answer to how you go about
this (below) if we live in an infinite universe with infinite simulations
seems to fit how one could do probabilities in a multiverse with an
infinite number of universes as well.
Lennart Nilsson
"To deal with these infinite cases, we need to do something like thinking in
terms of densities rather than total populations. A suitable density-measure
can be finite even if the total population is infinite. It is important to
note that we to use some kind of density-measure of observation types quite
independently of the simulation argument. In a “Big World” cosmology, all
possible human observations are in fact made by somebody somewhere. (Our
world is may well be a big world, so this is not a farfetched possibility.).
To be able to derive any observational consequences from our scientific
theories in a Big World, we need to be able to say that certain types of
observations are more typical than others. (See my paper “Self-Locating
Belief in Big Worlds” for more details on this.)
The most straightforward way of making this notion precise in an infinite
universe is via the idea of limit density. Start by picking an arbitrary
spacetime point. Then consider a hypersphere centered on that point with
radius R. Let f(A) be the fraction of all observations that are of kind A
that takes place within this hypersphere. Then expand the sphere. Let the
typicality of type-A observations be the limit of f(A) as R--->infinity."
-----Ursprungligt meddelande-----
Från: everything-list.domain.name.hidden
[mailto:everything-list.domain.name.hidden] För Brent Meeker
Skickat: den 6 april 2006 18:21
Till: everything-list.domain.name.hidden
Ämne: Re: Do prime numbers have free will?
Stathis Papaioannou wrote:
> Tom Caylor writes:
>
>
>>1) The reductionist definition that something is determined by the
>>sum of atomic parts and rules.
>
>
> So how about this: EITHER something is determined by the sum of atomic
parts
> and rules OR it is truly random.
>
> There are two mechanisms which make events seem random in ordinary life.
One
> is the difficulty of actually making the required measurements, finding
the
> appropriate rules and then doing the calculations. Classical chaos may
make
> this practically impossible, but we still understand that the event (such
as
> a coin toss) is fundamentally deterministic, and the randomness is only
> apparent.
>
> The other mechanism is quantum randomness, for example in the case of
> radioctive decay. In a single world interpretation of QM this is, as far
as
> I am aware, true randomness.
Unfortunately there is no way to distinguish "true randomness" from just
"unpredictable" randomness. So there are theories of QM in which the
randomness
is just unpredictable, like Bohm's - and here's a recent paper on that theme
you
may find interesting:
quant-ph/0604008
From: Gerard Hooft 't [view email]
Date: Mon, 3 Apr 2006 18:17:08 GMT (23kb)
The mathematical basis for deterministic quantum mechanics
Authors: Gerard 't Hooft
Comments: 15 pages, 3 figures
Report-no: ITP-UU-06/14, SPIN-06/12
If there exists a classical, i.e. deterministic theory underlying
quantum
mechanics, an explanation must be found of the fact that the Hamiltonian,
which
is defined to be the operator that generates evolution in time, is bounded
from
below. The mechanism that can produce exactly such a constraint is
identified in
this paper. It is the fact that not all classical data are registered in the
quantum description. Large sets of values of these data are assumed to be
indistinguishable, forming equivalence classes. It is argued that this
should be
attributed to information loss, such as what one might suspect to happen
during
the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it
follows
from the positivity of the Hamiltonian. Our world is assumed to consist of a
very large number of subsystems that may be regarded as approximately
independent, or weakly interacting with one another. As long as two (or
more)
sectors of our world are treated as being independent, they all must be
demanded
to be restricted to positive energy states only. What follows from these
considerations is a unique definition of energy in the quantum system in
terms
of the periodicity of the limit cycles of the deterministic model.
>In a no-collapse/ many worlds interpretation
> there is no true randomness because all outcomes occur deterministically
> according to the SWE. However, there is apparent randomness due to what
> Bruno calls the first person indeterminacy: the observer does not know
which
> world he will end up in from a first person viewpoint, even though he
knows
> that from a third person viewpoint he will end up in all of them.
>
> I find the randomness resulting from first person indeterminacy in the MWI
> difficult to get my mind around. In the case of the chaotic coin toss one
> can imagine God being able to do the calculations and predict the outcome,
> but even God would not be able to tell me which world I will find myself
in
> when a quantum event induces splitting. And yet, I am stuck thinking of
> quantum events in the MWI as fundamentally non-random.
It's also unclear as to what "probability" means in the MWI. Omnes' points
out
that "probability" means some things happen and some don't.
Brent Meeker
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Received on Thu Apr 06 2006 - 12:52:22 PDT