Re: Do prime numbers have free will?

From: Brent Meeker <>
Date: Thu, 06 Apr 2006 09:20:50 -0700

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:


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 - 12:21:52 PDT

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