It seems to me that COMP should lead to MWI plus a preferred basis where
the latter derives from well defined computational states. Many of the
problems with the MWI should not arise here, they are an artifact of the
theory never defining what an observation is, appealing to ad hoc
intuitive notions that are never formulated from within the theory
itself.
The notion that the environment plays a fundamental role should be
rejected on physical grounds, it just explains the effective physics we
observe just like air resistance explains why Newton's laws were not all
that obvious to people who lived many centuries ago.
The only way you can explain Newton's law to students is by letting them
contemplate a perfect vacuum. It doesn't matter here how physically
unrealistic that perfect vacuum is or isn't. The same is true for
quantum mechanics. You'll never make process if you always invoke the
environment and environment induced decoherence to try to define
fundamental concepts, because Nature cannot possibly work that way on
the fundamental level.
Instead, within quantum mechanics (i.e. if we forget about the desire to
derive QM from COMP or some other deeper theory) defining observers as
computations, means that they should be represented as operators of the
form:
sum over input of |output><input|
which leads to a preferred basis when you introduce an environment.
Saibal
On 11-09-2015 17:07, Bruno Marchal wrote:
On 11 Sep 2015, at 03:10, Bruce Kellett wrote:
On 11/09/2015 5:00 am, Bruno Marchal wrote:
On 10 Sep 2015, at 01:20, Bruce Kellett wrote:
On 10/09/2015 7:42 am, Brent Meeker wrote:
On 9/9/2015 10:27 AM, Bruno Marchal wrote:
On 09 Sep 2015, at 07:55, Quentin Anciaux wrote:
As for Bruce, could you then be honest, and simply say you don't
believe in the many world interpretation and don't want to
explore it... yes we're talking mostly metaphysics on this list,
if you dislike it, I wonder what you're doing here.
Indeed the point is notably that we can reason about this, that
is doing science, so that we never disagree except about the
choice of the assumptions.
Now, I disagree with Bruce, and I guess many philosophers and
scientists, except Deutsch (on this), but I do think that QM
(without collapse) is a theory of many worlds (in a perhaps
admittedly more abstract than usual notion of world).
If we define a physical world by a set of events close for
interaction,
But can computationalism give a coherent account of this? Doesn't
the UD imply at every set of events will have many (countably
many?) causal histories and infinitely many causal futures.
then the "many-world" is a consequence of the linearity of the
wave evolution together with the linearity of the tensor product.
But they are only "many" FAPP. Decoherence suppresses cross terms
in the density matrix, but it doesn't make them zero - and I don't
think it's even provable that there is a unique basis in which it
diagonalized FAPP. And of course we have no theory of quantum
spacetime. QM assumes a continuous spacetime, so QM is not the
last word and if computationalism only reproduces QM it will fail
when QM fails.
I think it is clear that Bruno does not understand either QM or the
MWI. MWI is not a consequence of the linearity of the wave
function.
It is when you define a world by the maximal consistent extension
close for the local observable interactions.
That is not a consequence of linearity. Linearity gives
superpositions. You only escape from the superpositions to distinct
non-interacting worlds by imposing some non-linearity somewhere. In
MWI this is hidden in the trace over environmental states. But this
is just as much a non-linear collapse as in any other collapse model.
On the contrary, linearity of the tensor product gives the
superposition, and linearity of the wave evolution assures that the
terms of the superposition behaves like we see pure states, when in
fact we are ourself superposed. It assures also the non interaction of
the terms, but it does not imply the lack of interference. Then
decoherence explains the *hardness* (and the need of amnesia) of
realizing the interference of the branches in which we "belong".
Superposition is the consequence of linearity,
OK. And if the computations done can interfere, they have an
equivalent physical reality, and determined alternate accessible
realities, but if entangling oneself with them, we loss or make very
hard the ability to see the interference.
Just because you can't see it it does not follow that it is not there.
Yes. That's my point.
and superposition implies interactions between outcomes.
?
I would say interference between the outcomes.
Many-worlds requires decoherence in a preferred basis,
I would say that classical macroscopic brain or universal machine
requires a classical-enough base, which benefits of that
decoherence, although with quantum computing we can exploit the
ignorance by changing the base (which is still rather mysterious
from the comp pov).
There is no such thing as a "classical" basis for Hilbert space.
Quantum computing is irrelevant here.
?
All linear space have bases (if you are OK with the axiom of choice).
A basis is a classical notion. All basis are classical.
with actual zeroing of the off-diagonal terms in the density
matrix. Indeed, this latter step is just the standard "collapse"
postulate in a different guise. So, far from eliminating
"collapse", MWI relies on it as much as any other interpretation of
QM.
Not at all. There is no physical collapse, just an epistemological
differentiation when one get entangled in the other's business.
You appear to be referring to Everett's original 'relative state'
interpretation,
I refer (here) to any theory which assumes that the SWE apply to both
the particles and the observers.
Well, to tell you the truth, I believe that just computationalism
implies the "many-dreams" in arithmetic. No need to know quantum
mechanics. I do not assume quantum mechanics at all once we assume
computationalism. I just say that the SWE (or MWI, which is logically
equivalent) confirms the many-dreams theory (arithmetic "seen from
inside") up to now.
in which there was only ever one world --
... or zero world. "world" are never really defined.
the other parts of the wave function played no role. But this was
soon realized to be unworkable. You really should read up on modern
versions of MWI. I recommend Shlosshauer, Rev. Mod. Phys. 76 (2004)
1267. Or
http://arxiv.org/abs/quant-ph/0312059
or his book on the subject.
I have no problem with that paper. It looks it confirms what I said.
Maybe you can elaborate, as I am not sure why you refer to it. I read
most of Griffith papers, and Omnes' books. I agree with a lot in them,
except that they lost me very often in the philosophical
conclusion(s) where they lack rigor, and seems to believe in some
primary universe, which is useless, and contradicted (my job) by
computationalism (which is my starting hypothesis).
Bruno
Bruce
The real difference between interpretations is whether this
"collapse" is a physical process or merely an epistemological one.
In the MWI, actually in Everett theory, there is only the SWE.
Sating "there is no collapse", means, for a logician, that we don't
add the collapse postulate (unlike many textbook). So the collapse
is necessarily an epistemological, even indexical, and relative,
notion.
In MWI, which reifies the wave function
Which is indeed an error, at least with the mind-body problem in
mind, but physicists do this very often.
and the elements of the superposition, the collapse is definitely
physical.
?
So it is, after all, no different in this respect from the von
Neumann Copenhagen interpretation.
I have a problem. In Everett theory there is no postulation of
collapse. The collapse is explained by the postluation of universal
machine, or at least good approximation of universal machine.
Copenhague:
- SWE
- Collapse
- Dualist theory of mind and matter
Everett:
- SWE
- COMP
And what I try to explain is that COMP ->. [](COMP -> SWE) &
(COMP -> SWE), so "my" theory is just
- COMP
Formally it is just any theory which is Turing universal, and
observation is defined by the logic of self-reference (of rcher
entities living there) and the intensional variants.
This is not supposed to compete with physics, but to supply the
qualia, and the range of non communicable, but true, realities.
Bruno
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