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Originally Posted by modest
Clearly the difference (as Anssi has now pointed out) is that you have derived Schrödinger's equation in three-dimensional space with your equation while my banana-analogy has not been so derived. As such, the analogy is ill-made.
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I think the fact that you originally missed this tells something about how confusing this thread has become, and was the reason for my previous post...
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I think my trouble is the leap from 'a consistent (or internally consistent perhaps) explanation of unknown data' to what often seems characterized in this thread: 'a useful explanation for any given universe or any given reality'. If I accepted that DD's fundamental equation is indeed something that any consistent explanation of an unknown reality must follow then it would not immediately follow that any explanation derived from the fundamental equation would be a useful explanation for *any* realty. With the example I've been using:
If Newtonian mechanics in 2 dimensions is a useful and self-consistent explanation for some unknown data (or reality) then it should obey the fundamental equation. If Newtonian mechanics in 3 dimensions is a useful and self-consistent explanation for some unknown data (or reality) then it should obey the fundamental equation. It does not follow that deriving 2 dimensional Newtonian mechanics from the fundamental equation means that it will be a useful explanation for any given reality. It's a converse error.
Now, I may be right and I may be wrong about this.
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Maybe so, I think if you dwell on that possibility, perhaps it is possible to point out that by an amazing guesswork, and if ontological reality was appropriate for it, one might come across definitions that yielded absolutely correct predictions for all our past. I think, if one wants to cover that possibility too, we should perhaps say something like
"if any reality is expressed by first transforming it to "patterns", that are then transformed to a self-coherent model of persistent entities, then the probability of specific future for those self-defined persistent entities can be properly expressed via Schrödinger's equation"
Meaning, that's just one way to do it, and if instead of following the general symmetry requirements during making your world model, you rather made just the proper guesses about the ontological reality, and the ontological reality really was a set of persistent entities, and their behaviour was proper for absolute prediction (no unaccountable feedback from the rest of the universe etc), then perhaps you could land upon a more accurate model of reality.
There are a lot of difficult details involved with that idea, and I think it would be a good idea to look at the epistemological analysis first in terms of what it explains about our current physics models, before going into that issue. (Especially its implications to Bell Experiments are in my opinion quite striking)
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But, regardless, I find it troubling that in bringing up the question I've yet to see it resolved by anybody addressing the issue or explaining the analysis. In fact, I've been away from this thread for a couple days (been too busy) and I return to find I've developed some interesting motives in my absence:
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I can honestly say that I just tried to explain, as best I could, how that result would be within the realm of possibility. As I assumed you had picked up that it was the results of the analysis that implied it, so then it just sounded like you felt its results were non-sense. I.e. I felt like you were uninterested to even look at the proof.
Nevertheless, I must say;
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If two people have absolutely equivalent worldviews (including the definition of a dimension) except that one worldview is 3D while the other is 4D then the worldviews are mutually exclusive and they cannot both be useful to the same reality.
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Unless I'm misinterpreting you in some very strange way, that is unequivocally false. They can certainly both describe the same reality in a manner that yields proper predictions, much the same way as Minkowski Spacetime can be viewed as a description of 4 dimensional persistent objects (static, or perhaps following some multiverse scheme, dynamic?), or 3 dimensional persistent objects governed by very specific dynamics.
The problem in your example is simply that...
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One person will deduce that 6 2D faces are required to bind an element while the other deduces that 24 are required. They can't both be right (if they share the same reality).
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...you have restricted their worldviews more than necessary. They are not both forced to see those 2D faces as 2D faces in their conception of reality, and judging from your posts, I think you should easily understand why "they are not forced", yes? (their perception being their interpretation of the raw data and all that)
And if you follow the epistemological analysis all the way to Schrödinger's Equation, I think you can see more about that issue; that if the same raw data is available to both, what happens is simply that they'd come to conceive the same data in terms of very different looking persistent entities. In the form of defined entities, there just couldn't be things disappearing and re-appearing in manners that would break the self-coherence & symmetry requirements.
I'm sorry if you feel like I'm just repeating the same argument over and over. I don't want you to feel like I've just made things up or otherwise given a coloured picture to you just for keeping you motivated; I just really think this exact issue is resolved by the epistemological analysis. And thus, perhaps it is not necessary to dwell on this "conceptual explanation".
-Anssi
