Dear Dr. Aerts,

I greatly enjoyed reading your recent paper "Undecidable classical properties of observers", quant-ph/0507001 v1 [Ref. 1]. Please keep me posted on your efforts to suggest an alternative formulation of the basic structure of quantum probability. I suppose you'll hit infinite-dimensional spaces, and I'm very curious to see how you would introduce Lebesgue measure,

http://www.God-does-not-play-dice.net/Barbara.html#5

If genuine quantum structure exists in the mind [Ref. 2], I believe we
should examine its possible physical nature. I expect another forthcoming paper on this highly important issue [Ref. 3].

May I ask you and your colleagues for any information on people involved in such fundamental research. I believe there is a *huge* physical thing beyond geometry: the so-called "dark" energy,

http://www.God-does-not-play-dice.net/Ishak.html

All the very best,

Dimi Chakalov
--
http://www.God-does-not-play-dice.net
http://www.God-does-not-play-dice.net/download.html
 

References

[Ref. 1] Sven Aerts, Undecidable classical properties of observers,
quant-ph/0507001 v1,
http://arxiv.org/abs/quant-ph/0507001

p. 10: "The structure that we find when an observer attempts to answer the question of his own non-perfectness, is similar to the well-known Liar paradox, or the Gödel sentence "x : x is not provable", whose very proof would seem to imply the truth of the proposition, which states that it is not provable, and so on... Regarded as a logical proposition, the terminology to indicate this logically circular decision problem was called ‘undecidable’ by Gödel [6], hence the title of this paper. As a consequence of theorem 4, we now prove that no observer can observe his own state perfectly.

"Theorem 5. No observer M can be M-knowledgable.

"Proof: An observer is M-knowledgable if he can perfectly observe all actual properties of the state m he is in. Suppose a is a classical
property of M. There is at least one such a, because we postulated the outcome indicator is a classical property. If M is not a-classical
perfect, then he cannot know his own state. Hence we assume M is a-classical perfect. By theorem 3, pa is classical too, and he needs to be able to observe that property classically perfect. We have shown that he cannot, indicating he cannot observe all his actual properties.
...

"One could say that the property of perfectness is potential only. This stance is viable but begs the question how we should observe if we cannot do it perfectly.
...

"... either we have a dichotomic split between the process of observation and other interactions, or we include both under a single heading and face the undecidability. In an upcoming article we will argue the second possibility can serve as an alternative formulation of the basic structure of quantum probability."
 

[Ref. 2] Diederik Aerts, Sven Aerts, Jan Broekaert, Liane Gabora, The Violation of Bell Inequalities in the Macroworld, quant-ph/0007044 v1,
http://arxiv.org/abs/quant-ph/0007044
Foundations of Physics, Vol. 30(10), 2000
[See Sec. 4.2, The Nonlocality of Concepts]
 

[Ref. 3] Diego Meschini, Markku Lehto, Is empty spacetime a physical thing? gr-qc/0506068 v1,
http://arxiv.org/abs/gr-qc/0506068

"We interpret the appearance of quantum-mechanical correlations as an indication that there must be something amiss with the current geometric description -- which leads to the futile problem of the geometric ether -- and as evidence of physical things beyond geometry.[24]
--
Footnote 24: "In fact, the very consideration of quantum-mechanical ideas in the depiction of spacetime involves, from our point of view, the need for non-geometric physical things. In a future article, we will present quantum theory on the basis of measurement results a_i, and metageometric premeasurement and transition things, P(a_i) and P(a_j|a_i), familiar to human experience. We will argue that, when viewed in this manner, the theory gets rid of the philosophical problems that plague it (e.g. the geometric state vector |psi> and its controversial ontology; cf. the geometric points P and their controversial ontology)."