Re: Von Neumann's Mistake

Omega (
Sat, 01 Feb 1997 02:19:33 -0800


> David Wick's survey of the theories and their conceptual development in
> these areas is good ("The Infamous Boundary" (1996)). He seems to struggle
> a bit over the shape of better theories, especially whether it is better
> for the theories to violate active vs. passive locality as long as they
> have a well-defined notion of outcomes, but in the end he says: "The last
> possibility, and clearly the correct one, is that there is some totally new
> way of looking at Nature." Isn't this always true?

Seems like I answered this in advance in my other post. Funny how
metaphysics always keeps coming back from the dead no matter how many
times human culture tries to drive a stake through its heart.

> <In the formal interpretation, these backward in time answers also carry
> negative energy, and so nothing really weird comes from it except for the
> clarity that 50% of all microcausality is happening as a result of advanced
> action.>
> I realize that discrete models of microcausality have been proposed for a
> couple hundred years, and have been repeatedly rejected in favor of
> indiscrete models by the scientific community. However, I believe that a
> discrete model will eventually prevail in explanatory power.

Discrete or not, unless someone can get rid of that second order differential
equation, we seem stuck with this 50% backward in time causality in any case.

> Feynman hinted at such a possibility in "QED": "It's surprising that the
> [QED] theory still hasn't been proved self-consistent one way or the other
> by now.... What is certain is that we do not have a good mathematical way
> to describe the theory of QED.... Another way of describing this
> difficulty is to say that perhaps the idea that two points can be
> infinitely close together is wrong ­ the assumption that we can use
> geometry down to the last notch is false."

I highly suspect that the failure of the geometrical approach is directly
related to this problem of Fourier spaces as the Heisenberg uncertainty
which lies at the heart of quantum physics IS nothing but this business
of Fourier spaces showing up as a general principle in physical reality

Of course, this just begs the question of the priority of, and relation
between, mental spaces and physical spaces. One of the biggest unanswered
questions in the philosophy of science is the uncanny correlation physical
reality and the totally arcane branches of mathematics that sometimes get
discovered centuries before they are shown to have any relationship to
physical reality.

> We'll leave aside the completeness of complex-number realms for now.

But not for too long I hope?

> Katsuhiro Nakamura in "Quantum Chaos" (1993) discusses how quantum chaos
> requires that we "go beyond Schrödinger's or Feynman's framework of quantum
> mechanics." He begins discussing 'broken symmetry in dissipative
> structures' and energy systems without time-reversal symmetry. He improves
> Schrödinger's formalism of quantum mechanics by replacing the time
> derivative in the time-dependent equation with a time difference, because
> he wants to refer to time-chaotic waves rather than time-periodic waves.
> Thus, he discretizes time with a delta-t, a suitable 'time quantum,' and
> uses a discrete version of the time-dependent Schrödinger equation.
> He goes on to say: "Time discretization will necessitate much more complete
> discretization of space-time.... [I]f temporal chaos is brought into
> quantum mechanics, our ideas on time, stationary states, the adiabatic
> ansatz and their relationship with the uncertainty principle should be
> carefully re-examined. These intriguing questions (even within
> nonrelativistic quantum mechanics) would be comparable to Einstein's great
> challenge in 1905 which revolutionized Galilean thought on space and time.
> In nature, external sources of randomness such as noise, impurities and
> random potentials are inevitable elements. These effects have so far been
> regarded as the unique source of spectral width in magnetic resonance,
> fluctuations in conductance, etc., but quantum chaos ­ deterministic
> randomness ­ may be a novel alternative candidate for spectral width and
> fluctuations in various observables."
> I cannot help but think that with a more complete discretization of
> space-time, that one discrete state cannot happen, the universal discrete
> state of *now* cannot de duplicated exactly in the next 'time quantum' for
> obvious reasons. This closes off one propagation avenue in the negative
> energy direction, leaving advanced action with more than 50% of
> microcausality. Thus, we go forward instead of backward, time-reversal
> asymmetry.

Actually I see it as a very really possibility that we will find a dichotomy
in which both continuous (above plank scale that is) and discrete time systems
coexist. In fact by symmetry, it must be this way considering how energy and
time are tied together the way they are; the more one is continuous, the more
the other must be quantized. We fail to notice this symmetry because, we fail
to take seriously the reality of momentum space and the fact that what we see
as quantized energy IS time itself from the perspective of momentum space.

Yes, momentum space has its own arrow of time which is not only backwards to
ours, but quantized by what we call energy to boot (the direction of the
arrow being defined by the default temporal direction that wave packets in
that Fourier space spontaneously spread). This is the overlooked symmetry
that allows time-symmetric dynamic laws to create asymmetric time in the
first place. The symmetry reappears when we realize that momentum space
has its own (backwards to us) arrow of time with its own 2nd law of thermo-
dynamics that must be obeyed.

Likewise, we might expect that a "global" 2nd law also exists such that
violations of probability are allowed within either realm so long as it's
conserved globally. Such a global conservation of the 2nd law is not phy-
sically impossible, but the only good metaphor for describing this sort of
meta-time that I've yet seen is P. K. Dick's idea of "an orthogonal time"
that operates in the meta-reality behind what we currently know. In this
system of meta-time, the 2nd law would be conserved globally so long as
the mass and volume of the cosmos never decreases within meta-time.

Modern cosmology already knows this in its understanding that "bouncing
big-bangs" must always get larger. There is no new physics here, only
a recognition of the time-symmetries that comes from a generalization of
our concept of reality as applying equally to all Fourier spaces. With
this comes an understanding that a generalized math capable of reconcil-
ing all the Fourier spaces within reality is going to require a system
that combines continuous differential equations with fractals and other
forms of discrete math into a seamless whole. There is certainly, in
this, a nobel prize awaiting some young mathematical genius (Eliezer?).

This also leads to the realization of the ultimate extropian dream of
physically relocating to an alternative Fourier space when one's local
"universe" becomes too "entropic". It's just another more advanced form
of uploading. Just like we could well gain a general ability to do up-
loading and other forms of "personal designer life" in the near future,
there is no reason why, in the far future trillions of years from now,
we couldn't build bodies in an alternative Fourier space; after all with
modern QM we already know how to manipulate momentum space. In fact, we
don't even need any fundamentally new science here, just a few eons of
practice developing our quantum engineering skills, which is something
that our existing universe is certainly still good for. In doing this,
we need merely brush up on our ability to utilize the momentum space
analogs of gravity and electromagnetism (which we already know about in
the phenomena of Bose-Einstein condensation and fermion spin-pairing
respectively) to build up the structures we need.

Not withstanding my own writings about the role of Fourier spaces in
human thought, it's clear that our monkey brains aren't really good at
viewing this equally well from all angles. And yet I find it amazing
that we do as well as we do in understanding this stuff.

In the Ecstatic Service of Life -- Omega