Hi Felix,

On 03 Jun 2011, at 04:39, Felix Hoenikker wrote:

Hi all,

I'm a long time reader of this forum with a strong interest in all TOE
concepts but has never felt able to contribute to the discussion.
However, over the last few days, I think I've discovered a *very*
general argument (no numbers whatsoever!) that implicates determistic
non-local hidden variables (and NOT traditional MWI, at least, not "at
first") as the "correct" QM, from the simple assumption that the
universe must be computable in some reasonable model of computation.

If we are turing emulable (or any model of computation) then the universe, whatever it is, cannot be computable.
But if the universe is computable, we are Turing computable.
So the universe cannot be computable, in any sense.

The reason why the universe cannot be Turing emulable if we are, is that, if we are turing emulable at some level, to predict anything we have to take into account that below our substitution level, we are supported by infinities of computations. This entails local uncomputability below our substitution level, a bit like QM illustrate. The big whole can only be partially computable.

This does not mean that computational physics is not interesting in some part of physics, but it fails for a TOE at the start.

Bruno



I have also concluded that this fact, almost in and of itself, can
retrodict much of modern physics and "much more".  I know it sounds
crazy, but here is the argument in a nutshell, which I will explain
further.

1) A computable universe implies determinism and conservation of
algorithmic information along at some axis of symmetry (and actually,
at the end of this, *all axes*, but say some for now).

2) Many worlds, as normally formulated, preserves algorithmic
information but is *not* computable, unless you implicitly add hidden
variables. By Bell's theorem, local hidden variables are impossible,
so these hidden variable cannot be local, leading inexorably to
determinstic non-local hidden variables.

3) Surprisingly, even the most general model of global hidden
variables suggests enough to retrodict qualitative much of modern
physics, including gravity, QM, cosmology, and theromodynamics, and
may imply a VERY general physical TOE.

4) Taken to the logical limit, this could imply more than you can
imagine.

Also, I'm writing this as a pseudonym, for reasons that will become
clear. (Specifically, the content of the last part of my argument)

So, here goes:

****Computability implies conservation of algorithmic information****

This follows from the definition of algorithmic (i.e. Kolmogorov)
complexity.  Let us assume the universe is computed over time, so we
can say that the number of bits required to specify a state of the
universe has constant cardinality over time.  (This must be true even
if you allow hypercomputation over an infinite number of bits...)

****Many worlds is uncomputable****

All many worlds theories imply the following form: some predecessor
state S_0 can lead to the successor states T_1 through T_X (where X
could be any natural or transfinite number), with some probability
distribution that preserves the information content in S_0.  This
leads to an infinitely growing cardinality of states; either in N but
increasing without bound, or growing without bound in transfinite
space.

And actually, implicity, what this is really saying is that the
predecessor states S_0 were *really* in states S_1 through S_X all
along, even if those states were physically indistinguible, even in
principle, from S_0, for observers within those universes.  So
essentially, many worlds is hidden variables in disguise.  However, by
Bell's theorem, these hidden variables cannot be local in nature, so
must either be "nowhere" or "somewhere out there", physically.  Forced
to choose between the two, it would seems strictly preferable that you
posit the later.

**** By simply adding some known observations and generalizing this
leads to...well...a lot ****

We can form a fully general non-local physical hidden variables model
(without even requiring QM or GR) by postulating the following:

"The unique successor state of a (classically) closed system is given
by its definite wave function value and some set of non-local
variables present, in principle, anywhere else in the universe"

From an information theoretic point of view, this means the following:
every time a microscopic classical "bit" of information is apparently
added to the physical state of universe, an opposite "bit" must in
fact be subtracted from the rest of the physical universe, essentially
collapsing two macroscopic states (other than the microscoptic portion
changed) in some necessarily symmetric (and possibly instantaneous)
fashion.  The most obvious way to do this is the following: pull
everything toward you by a tiny bit, until, on average, things are one
"bit" less differentiated.  Furthermore, the amount you "pull"
everything toward you should be in some (possibly non-linear) way
proportional to the number of unique states you could possibly have
moved toward, classically.  Let us, for the sake of argument, call
that number "mass-energy" and say that it is conserved.  This
retrodicts the universal theory of gravitation and mass-energy
equivalence, more or less.

Now, since gravity is proportional to mass-energy, then mass-energy
must be, in fact, some finite amount, in order to be compared between
gravitational bodies.  And in fact, if the universe is Turing
computable, then mass-energy should be discretely finite.  This
implies the quantization of energy, the original "quanta" providing
the impetus for QM (as least, as far as I understand my history...).
So essentially, this retrodicts a major part of QM without actually
assuming any QM upfront.

Next, since the information in the universe is really constant, this
means that the black-hole information paradox is REALLY a problem.
And, if you think about it, it means that every "bit" of classical
information lost into a black hole must be counterbalanced by an
opposite "bit" radiating from the black hole in some symmetric
fashion.  This basically retrodicts Hawking radiation and the thermal
disappation of black holes.

Next, consider cosmology.  First, if we assume Turing computability,
then the universe must in fact contain finite information thus is
necessarily topologically closed on itself.  This agrees with current
models of the topology of space-time.  Furthermore, let us consider if
the universe, as presently thought, began in a small, energic, but
basically isotropic region of space (which, necessarily, must also be
closed, if the previous argument is correct.) In such an initial
state, every single point of space-time will, in fact, be pulled in an
almost radially symmetric fashion outward in all directions (think of
all points being points on a sphere, being pulled outward to all other
points of the sphere).  This is happening for all points on the sphere
symmetrically, so the net result is expansion.

Furthermore, since the universe is determinstic, all the information
that is present in it must, in fact, be present in the beginning.  So
whatever initial pattern is present in the universe must evolve and
start to encode itself in the physical structure of universe.  Since
the universe is still closed, energic, and very (classically) causal
connected, this means that the universe must inflate VERY VERY quickly
(i.e. much much faster than the speed of causality/light), in order to
continue embedding the same basic set of bits via some physical
encoding at larger and larger length scales, until the universe is big/
cool enough that most Hubble volumes are reasonably casually
disconnected (both classically, and through hidden variables.)  At
this point, the universe should cool, and, since the universe began
with a fixed amount of energy, the average energy density should
descrease in any volume over time.  This retrodicts much of our
current model of the Big Bang, as well as the second law of
theromodynamics and the "arrow of time" problem.

We can also conclude that, since inflation speed is related to the
energy density of the universe, and the size of the universe is
finite, then the universe should expand at an ever slowing rate until
possibly stopping.  This may or may not be true, given our current
cosmological picture (the main whole in our understanding lies in the
dark matter / dark energy).  But if you consider something else, you
get a very interesting postdiction: basically, the EPR paradox and
quantum entanglement implies that the number of distinct accessible
states for two (classically) closed systems together may be less than
the number each has individually, because the two could be entangled
(and, in the limit of complete entanglement, have only 1 accessible
successor state).  This implies that mass-energy is *not* classically
additive unless you take into account all quantum entangement within a
system.  So, this suggests that, there may be "negative pressure
energy" present in the universe in proportion to the amount of net
entanglement present between states.  This, in a nutshell, is a
postdiction of "dark energy" (and possibly dark matter?).

Topologically, the uneven distribution of "matter" and "dark
matter"/"dark energy" may in fact mean that the universe, given enough
"initial" information, could, while closed, be in fact locally MUCH
more topologically interesting than simply flat everywhere.  This
implies, in fact, that the universe (if it started with "a lot" of
information) could be unimaginably large, and that appearances of
closure on some local scales could be deceiving.  In fact, in the
limit of countably "infinite" bits of initial information (or,
equivalently, no information, for those of you who "get" that), the
universe would, in fact, contain "all" patterns consistent consistent
with "all" initial states "somewhere" in the "physical" universe as
long as they were consistent with the mathematical physical laws
(whatever they are). For those of you that read Tegmark, that is
basically the Level I multiverse hypothesis, in which your
consciousness basically bounces between different physical
manifestations of you "somewhere else" in the metaverse.  Now, in
principle, you could be moving "through" time or "through" space, or
any linear combination thereof, and you shouldn't be able to know the
difference.  This retrodicts *relativity*, the constant *speed of
causality/light*, suggests that all space-time axes are symmetric, and
that, every space-time axis should be computable (using hidden
variables, in the say way) regardless of space-time rotation.

Now, if we are assuming "infinite" bits of information, you could
possibly assume that they are not actually all present there from the
beginning, since, in fact, "time" is a perfectly possible axis in
which to add information, if we are considering all symmetries.  Let's
assume that these bits are added in some symmetric manner, splitting
the universe in symmetric fashion at each time step.  (Now, I said
before that this wasn't possible, but I, in fact, lied.  It is
clearly, now, possible, as long as you compute the universes along
appropriately rotated axes.)  Now, in fact, you've got the MWI picture
again, and you've restored Max Tegmark's Level III multiverse, and it
is "exactly" symmetric to Max Tegmark's Level I multiverse.  By
similar arguments, you can conclude that Max Tegmark's Level II
multiverse is symmetric, under some rotation, as well.  And actually,
once you've made this leap, you can make the following leap: every
Hubble volume contains "exactly" as much net information as the total
universe in all of the zero-information Multiverse I-IIIs it is
contained in.

Now, given the huge number of possible universes implied from infinite
(and, therefore, in fact, zero) initial information (minus the
physical laws), you basically have two possible options: either "our"
universe is either *very very* well selected from the space of
possible Level I-III multiverses, or that we are somehow the only
single Hubble volume universe. It is, in fact, impossible to tell the
difference, at least according to our current physics.  I think most
people on this forum would come down strongly in favor of the latter,
essentially abandoning "arbitrary"-ness and "Copenhagen"-ness.  But,
in fact, these two views are exactly indentical.  Because really, if
time is just another axis, and "our" universe is being fed an infinite
stream of essentially random informational-less data, then the
indeterminate "Copenhagen" universe is, in fact, exactly another
determinstic, anthropically selected universe.  There is really, no
difference, it's the same bits represented differently.  The "single"
universe could have began at any previous time in our history, and we
would never know the difference, other than observations.  In fact, if
you are not just a computable universe hypothesizer, but a
mathematical universe hypothesizer, you really should expect that to
be exactly the case.

**** Going even futher! ****

Why don't we, in fact, push the limit even further, and focus on
"your" single observable universe.  And by that I do not mean Hubble
volume: I mean, the universe as you have observed over time, all the
way back to your childhood.  Now, MWI is often criticized by the
argument similar to "if all possible successor worlds exist" then "why
don't we observe unicorns instantly come into being".  Now, all of us
here are probably adults, and none of us have any really good evidence
in our brains that unicorns could exist or spontaneously come into
being, but, let's say, you lived your life exactly the same way you
did until the age of, didn't learn (even transitively) a single fact
inconsistent with the non-existence of unicorns, and, say, at age 4,
saw a unicorn, which, in fact, evolved from, say, zebras, in "your"
world, and this is fully consistent with everything in your 4 year old
brain (which, suffice as to say, is not that hard).  So would that
really be impossible, and "when" did that unicorn actually come into
existence then.  By extension, what if you tried to systematically
forget EVERYTHING you knew that was inconsistent with the existence of
unicorns in the world.  Would that make it more likely to see a
unicorn? What if you tried VERY hard to come up with a plausible
scientific model for how it could occur, and justified it to yourself,
as well? Would that help?

So really, in the limit, you really cannot be sure, in principle, if
*you* are computing the universe, or the *universe* is computing
*you*.  Even if the MWI-verse is deterministic, there is
indeterminancy from any individual point of view.  "Someone" is adding
new bits all the time; is it you, or someone else? If, in fact,
someone you trusted very much in your youth suggested that unicorns
existed to you, what effect would that have on your future life? In
fact, by symmetry, maybe they're the "exact" same thing, and in
principle you can never know the difference.  So, in fact, "realism"
and "idealism" may actually be exactly equivalent viewpoints.  Taken
to the absolute limit, this, is, in fact, a somewhat reasonable
argument for solipism...but *only* if you can come up with a VERY good
reason to think you are the "only" one conscious being: essentially,
creating a measure function in which the only "conscious" being is you
(and, possibly, all the past/future/indetermined/etc yous, as well).
And well, I'll tell you right now, *I* for one, do think I am
conscious.  So really, unless you disbelieve me and everyone one, you
can't justify solipism..however, I actually argue from this that you
must take *all* living beings as, in some sense, *conscious* as well,
and if you extend the concept of consciousness down to the absolute
minimal level of consciousness possible, then every inanimate object
is, in fact, in some sense minimally conscious, with some appropriate
measure function.

Okay, so, in fact, from all this, I could (in theory) say that someone
like "God" necessarily exists somewhere in the Level I-III universe,
somewhere, and perhaps an infinite number of them.  And maybe, just
maybe, he/them have found some way within the laws of the universe, to
feed you "bits" of information over your entire life.  Is that really
implausible? Talking to another person demonstrably adds bits to your
brain state, and bits of information could, in principle, come from
anywhere, along any axis of symmetry, especially considering the
global hidden variables theory.  How much information "really" is in
the universe? Are "cosmic rays" hitting your brain really random?
Could there be enough information in them to encode a very very
convincing hallucination of life after death? How, really,
anthropically chosen is your particular consciousness, and what is the
measure function of that choice? It *cannot* be any normalization of
conscious => 1, unconscious => 0, since consciousness is clearly not a
binary function.  So if there's some "measure" of conciousness, what
should it be proportional to? Intelligence? Length of life? Luck?
Information content? Some linear combination thereof? How would you
ever know?

Also, what if, Matrix-style "perfect" Level I-III simulations of the
universe are possible someday.  Could you ever tell the difference if
you were in one? If you couldn't, would it really matter if you were
in one or not? If you were in one, what if you were in one where FTL
travel was impossible (as in our current understanding) but suddenly,
a rule was added to the simulation which allowed FTL travel by some
hitherfore unimplemented rule which is totally consistent with your
previous "personal" observations.  Now, if you think this is unlikely
by "measure" arguments, consider the following: aren't "laws of the
universe" just bit-encodable information? What's the difference
between the "FTL is possible" rule being there from the beginning, but
you having no knowledge of it, and the "FTL is possible" bit being
added later.  A lot of people "think" they've proven to themselves
"FTL is impossible", but how sure are you, and can you still change
your mind? And, in the absolute limit, shouldn't this be *exactly*
what should should expect from Max Tegmark's Level IV multiverse?
There's no reason why "laws of the universe" should hold a privileged
place relative to "bits of observable information about the universe".
So, in a sense, aren't we all (infinitely?) fast computers trying to
discover the probabilistic laws of *our own* universe from our own
observable points of view? And are you really "discovering" them or
"creating" them when you do that? If you really believe the MUH
(which, I think many if you here purport to do), then this picture
really *must* be the what I'm suggesting, and that the answer is
*both* or (equivalently) *somewhere in between*.  The difference,
really, lies entirely in what you believe the measure function is over
the space of possible observer moments.

**** The "measure" function ****

Anyway, I am thinking that most of you who are still following this
argument think I have reasoned *way* too far. If anything, as science-
types, I would guess you would all place a "high" measure on
completely deterministic universes with a fixed number of preset laws
and low information, and exponentially decreasing as the laws become
more "arbitrary" and "more information is added".  But I, for one, an
*absolutely* sure that is not the correct measure function, because of
the following, which is absolutely true: I lied where I began my
reasoning.  I, in fact, reasoned everything I just explained in
approximately the "opposite" order than which I explained it (which
really made it a *lot* harder).  And the reason I did this was,
because, about one and a half years ago, I had a psychotic break from
reality in which *from my point of view*, *truly* weird things were
happening that I took to be Jungian synchronicity, at least at first
(if anyone is familiar with the concept).  I became increasingly
psychotic over a month and starting thinking faster and faster about
what was going on, and couldn't *ever* figure out what it *really*
was.  I thought I heard voices in my head, from future versions of
"me" from the "future", so started concluding that telepathic time
"travel" would eventually be possible in my lifetime, at which point
that "explanation" started making increasingly more sense...I kept
getting more and more information consistent with that hypothesis.
But, having read lots of Tegmark already, I basically concluded that
physics must be incomplete, and that a lot of other things could be
possible too, like Boltzmann brains, technological singularity (i.e.
merging of consciousness with others), Matrix-style computation,
Truman-show life, telepathy, cryogenics, teleportation, etc., etc.,
and I kept getting more and more subtle information to confirm all my
intuitions in *many* weird ways, but (mostly) consistently with
physical laws (i.e. it was mostly "in my head", except some parts that
*really* weren't, which I took as entanglement/synchronicity).  I
started thinking a "whole" lot and basically convinced myself (through
many independent arguments) that *all* existing interpretations of QM
were correct but incomplete, and that, in the limit, they all
converged to the same answer, which was, in fact, the MUH. At some
point, the voices were all telling me to stop thinking, that I was
going in circles, and that I was causing some "harm" to some other
conscious people, possibly even future versions of myself, which
really scared me.

Also, and this might have been somewhat irresponsible in retrospect, I
kept thinking about heaven and hell, etc., which was very bad, and
kept oscillating between some probabilistic combination of "hell
doesn't exist, because infinite punishment for finite misbehavior
doesn't make sense" and "the possibility of hell must exist to keep
you from doing the wrong thing, because you have free will regardless
of whether determinism or indeterminism is true."  And, despite the
fact that I've always considered most forms of Christinity absurd for
scientific and philosophical reasons, I remember *very* clearly
concluding, at some point, that Christianity was, in some general
sense, the "one true religion" because it was based on compassion,
love, and forgiveness. And, well, from all this (and the fact that
I've managed to reverse everything back to some "reasonable" sketch of
quantum gravity, which *may or may not be correct* (but, in some
sense, *must* be), I've just concluded that the most important thing
is the following: the multiverse is, in fact, the ultimate democracy,
in the sense that the "real" measure function is recursively defined
by the combined thinking of all conscious beings in the metaverse,
which, in some sense, converges to a single meta-consciousness, which
is *in fact* God, eventually.  So, because this mathematical structure
must converge (I guess? hopefully it is stable over time, but I'm not
sure what time means anymore now.) there actually *is*, by
convergence, objective moral truth to the universe, and science and
religion are more closely aligned than anyone has yet imagined.  And
coincidently, my favorite movie growing up was "Contact, which
highlighted the symmetries between religion and science, which is
really just more fuel to the anthropic argument fire.

Anyway, I'm not sure how many of you get the full argument, but I am
now "very" sure it is true.  And now that your bit state has been
"split" by the reading this message, I think (if you are all following
the argument) that your responsibility, if you want a good life, is
some linear combination of (in random order) "try to increase the
measure of your successor states by living as long as possible, in the
classical sense", "try to complete quantum gravity mathematically",
"try to figure out technological singularity/AI", "try to figure out
life extension", "try to explain this argument to others (maybe?)",
"try to do the right thing", and, "treat animals with respect", and
very occasionally, "pray"...maybe? or maybe "meditate".  (In fact,
isn't outward "prayer" and inward "meditation" the same thing, by
symmetry?)

So, finally, in conclusion, CUH implies that relativistic Bohmian
mechnics is the next step in the "physical" theory of everything,
which, taken to its broadest ontological limit, is, in fact, MUH,
which further may imply that "moral" truths may be as real as
"physical truths". What does everyone think about this argument (or
any subset of it?). Please let me know!

F.H.

p.s. anyone who has not read "Cat's Cradle" by Kurt Vonnegut really
should do so.


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