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I don't understand how it follows that, just because a finite, causal universe cannot be fully and consistently described, it cannot also be causally determined.
I agree that it means that we can't predict its causally determined outcomes accurately, but how does that deliver choice about future states to components and systems within the universe?
As I'm sure you know, before Gödel threw his 'monkey wrench' into the 'mix' of western science, Georg Cantor had already 'beaten him to the punch.'
Haven't done the research but the idea it seems is closely tied with what is called the Continuum Hypothesis.
Math can describe the rules of our universe. But it does not explain everything. Western Sciences idea of a TOE would be to describe the 3 dimensions of a box using math. What that box is, where that box came from, what lies outside the box fundementally can not be described by math. Therefore a TOE that strictly uses math will be a flawed TOE. Math is what WE say about the universe, not how it fundementally is. To think otherwise is an anthrophomorphic flaw.
I would be very interested in hearing this too.
Originally posted by visible_villain
reply to post by Incompleteness
Haven't done the research but the idea it seems is closely tied with what is called the Continuum Hypothesis.
Well, I don't know how much math you know ... I've you have the elementary calculus we could probably talk about 'whats wrong with math'
It get's somewhat technical, but the 'issues' are actually pretty simple - it's definately not 'rocket science' ...
Originally posted by Incompleteness
Since our TOE's will always produce at least a few inconsistent situations it means the universe can never be pinned down in a finite system of rules (i.e. a TOE) as soon as we do it new problems will arise that challenges our main theories ad infinitum. And as soon as the TOE is expanded it allows more possibilities.
Originally posted by Astyanax
However, reality at a macroscopic level does indeed exist, and functions in a fairly predictable way.
Originally posted by tobiascore
Space and time are quantized. Thinking you can build a TOE off the current physical model is incorrect. The universe is not mechanical. Look towards digital physics, not Newtons idea of a clockwork universe. It just doesn't work with quantum mechanical systems.
Originally posted by Astyanax
Wonderful, mind-stretching topic, by the way. Ian MacLean, come back!
Originally posted by Ian McLean
Originally posted by tobiascore
Space and time are quantized. Thinking you can build a TOE off the current physical model is incorrect. The universe is not mechanical. Look towards digital physics, not Newtons idea of a clockwork universe. It just doesn't work with quantum mechanical systems.
Doesn't that imply that space and time are not quantized, then? Perhaps, in the 'real universe', at some level the underlying dynamics are not quantized, but the resulting effect of determinable measurability is. A TOE addressing such would, in its theoretical construction, account for multiple (or perhaps innumerable) possible quantum dynamics, with no definitiveness of which interpretation is actually 'true'. So it is possible for a model to construct with dynamics beyond the resolution of Planck-level. Provability within that extent, however, is something else entirely....
Originally posted by tobiascore
Simple, at the planck level, "reality" is just information. If you model it as data, then a whole new world opens up. Like neils bohr said:
"It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature". - Niels Bohr
Fundamentally, we MUST be looking for newer and newer ways of describing our universe. Digital is the BEST way to model it at this point.
Heisenberg's principle states that the product of uncertainties of position and momentum should be no less than the limit set by Planck's constant, ℏ/2. This is usually taken to imply that phase space structures associated with sub-Planck scales («ℏ) do not exist, or at least that they do not matter. Here I show that this common assumption is false: non-local quantum superpositions (or 'Schrödinger's cat' states) that are confined to a phase space volume characterized by the classical action A, much larger than planck, develop spotty structure on the sub-Planck scale, a = ℏ²/A. Structure saturates on this scale particularly quickly in quantum versions of classically chaotic systems—such as gases that are modelled by chaotic scattering of molecules—because their exponential sensitivity to perturbations causes them to be driven into non-local 'cat' states. Most importantly, these sub-Planck scales are physically significant: a determines the sensitivity of a quantum system or environment to perturbations. Therefore, this scale controls the effectiveness of decoherence and the selection of preferred pointer states by the environment. It will also be relevant in setting limits on the sensitivity of quantum meters.
www.nature.com...