On 24/06/2017 5:23 pm, Russell Standish wrote:
On Sat, Jun 24, 2017 at 03:59:56PM +1000, Bruce Kellett wrote:
Well, I have just taken a quick look. What strikes me is that the
first paragraph of Appendix D defines "Observer moments psi(t) are
sets of possibilities consistent with what is known at that point in
time, providing variation upon which anthropic selection acts. ...
We wish to determine the probability of outcome a being observed."
So you assume a probabilistic model from the outcome. Why would you
do that? Why not a deterministic model?
I do spend over a hundred pages prior to the chapter on QM going into
the reasons! But to try to signpost this, and maybe save you the
effort of reading my book, the basic reason is that our 1p view must
be the result of evolution - not biological evolution, per se, but
anthropic evolution - the result of variation of possible futures, and
anthropic selection from those possible futures to the actual result
seen. Along with heredity (which in QM gives rise to unitarity), we
have the three pillars of evolution as espoused by Lewontin.
Consequently, the probabilistic model needs to be there right from the
start to provide the variation on which anthropic selection acts.
OK, it was possibly the case that you gave arguments earlier in the
book. But I was going on the basis of the Appendix "Derivation of
Quantum postulates".
But the problems only begin with the assumption of a probabilistic
model. Psi(t) is the set of possibilities consistent with what is known
at time t. But how do you limit this set? At the moment, I could go to
the pub for a drink, could open a bottle of wine at home, stroke the
cat, turn on the telly, talk to my wife, etc, etc,..... The
possibilities consistent with what is known at this time is not a well
defined set, or limited in any way.
Because you then go on to define projection operators in terms of a sum
over the members of this set of possible outcomes. That is meaningless
unless you are already assuming the the outcomes are just possible
results for a well-defined measurement, and that this measurement
process can be defined in a linear vector space.
Another problem occurs further down when you seem to have complex
numbers of observers observing an observer moment. Why you should have
more than one observer for any observer moment is a mystery yet to be
solved. But then you go on, in eq. B8 to define the inner product in
terms of the probability function. But you have merely multiplied
together two expansions in terms of projections over possible outcomes
-- assuming that there is a linear span over the space in the process.
This gives the Born rule, sure, because you have built it into your
derivation of the inner product.
So you know about QM from the start, and devise a strategy to get
you there. One of the problems that many-worlders face in their
attempts to derive the Born rule from within MWI is that they cannot
independently justify a probabilistic model.
Yes, but I don't start with the MWI (namely, I don't start with a
Hilbert space and unitary equation of motion - ie Schroedinger's
equation). I start with evolution in a generic multiverse.
Why a multiverse? You no doubt argue for it elsewhere, but that is not
apparent in your quantum derivation.
And I do not understand why the most general equation for computing psi
as a function of time is a first order differential equation. The
equation could clearly be non-linear in psi -- such things have been
postulated after all, as in general relativity and GRW for instance.
Besides, you do not show that the operator H is the Hamiltonian and the
energy operator. You do not derive the basic commutation relations
between position and momentum operators -- a relation that is central to
the whole of QM.
If you have a
probabilistic model in 3 or more dimensions, Gleason's theorem tells
you that the Born rule is the only consistent model for
probabilities.
My arguments go through in fewer than 3 dimensions as well, AFAIK,
although that would a relatively uninteresting world - very black and
white :). Which is why I suspect it is independent of Gleason.
But you have to say why you want a probabilistic
interpretation in the first place. Deutsch's attempts founder on the
fact that he has to assume that small amplitudes have small
probabilities, even to get started, so his argument is manifestly
circular.
Yes - I think the problem with those approaches is that they start
with a Hilbert space and unitary equation of motion (ie a classic
MWI), and then fail to generate the Born rule because there is no
observer in their mechanics.
As I said, you build a probabilistic model in at the start, so
Gleason's theorem is going to get you the Born rule automatically.
Or if you don't assume Gleason, you have an equivalent result by
another route. Assuming a probabilistic model is a very powerful
starting point......
Sure - but it is necessary. If evolution did not work the way it did,
we could only ever be Boltzmann brains, isolated observers existing
fleetingly, barely having time to consider what to have for lunch, let
alone figuring out the meaning of the universe. Fortunately for us,
evolution does work to generate complex worlds from simple beginnings,
meaning an evolved world is overwhelming more likely to occur in the
Multiverse of Everything than Boltzmann brain existences.
Why do you have to have evolution? It seems to me that you are allowing
enough empirical science to creep into your deliberations to give you
the results you want. I don't think Boltzmann brains are the only
alternative to evolution. Evolution could work in all sorts of different
ways -- such as Lamarkianism, etc. The only reasons we rule these out
are empirical. Similarly, the only reason for going to quantum mechanics
is solidly empirical -- classical physics just does not work all the way
down. So one will never be able to derive quantum mechanics from
general, non-empirical considerations. It is just too weird for that!
Bruce
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