The T<>D principle in quantum theory

(T<>D) What?

The T<>D principle is at the heart of the ‘theory of everything’ explained in Surimposium. It is extremely simple: Everything emanates from a conflict between individuation and collectivization. Between “I am” and “belong to”. Between the T of soliTary and the D of soliDary. Each state of a thing is a setting between its soliTary and soliDary tendencies, a T<>D setting.

The T<>D principle is found in one form or another in all scientific disciplines. When its theoretical importance is identified, it always reveals itself of great conceptual richness. Let us take the example of the reconstruction of quantum theory operated by Carlo Rovelli (1996):

Quantum by Carlo Rovelli

Rovelli starts from two axioms:
A1: There is a maximum amount of relevant information that can be extracted from a system.
A2: It is always possible to obtain new information from a system.
These axioms may seem contradictory, but no: everything depends on the ‘relevance’ of the information of the 1st axiom. It draws a limit to the information that can be retrieved in a system… for an observer.

For Rovelli, information is observer-dependent. This is also Shannon’s definition. It is impossible to separate the definition from the information from the observer who collects it. There is no such thing as inherently objective information, entirely defined by itself.

Translation

Translated into the T<>D language, this means that the T, the soliTary, individuation, does not exist in isolation. It can only refer to the D, the soliDary, to the whole. What exactly is this “whole”? Is it really ‘all that exists’, or only a significant whole for the relationship with the individual, i.e. the context of that relationship? Or is it an even smaller part, the fraction of the context in which the observer intervenes? The “whole” is in fact a nested whole, an observer housed in a context itself housed in a larger framework. We do not know how many boxes make up the series and even if there is one ultimately large box and one ultimately small.

Rovelli’s axioms indicate a variability in the dependence of individuation on the whole, concretizing the presence of several possible observers. The information may appear in a certain way to all of them, or only one. This is the principle of T<>D adjustment; the information can be positioned anywhere, towards the T or the D, without ever reaching them.

Change of direction

Note that the observer also exists in Rovelli’s second axiom —”it is always possible to obtain new information from a system”— but the direction of the relationship changes:
1st direction: The observer/context is the starting point —”there is a maximum amount of relevant information that can be extracted from a system”. The observer is the one who sucks up the information. For her, the system reaches a maximum of relevant information.
2nd direction: The system is the starting point. It can always produce new information, either through its intrinsic evolution or in front of different extrinsic observers/contexts.

The principle underlying these two axioms is that there is an indissoluble relationship between unitary information and the totality of which it is a part. The formulation of the T<>D principle adds that the Whole is also dependent on units. Obvious for classical bottom-up ontology, but also for top-down teleology: the whole is itself unity, therefore individuation in a larger context. We find the hierarchy of our nested boxes.

What’s the point?

What is the point of reconstructing quantum theory? Let’s give the floor to Rovelli:

« Quantum mechanics will cease to look puzzling only when we will be able to derive the formalism of the theory from a set of simple physical assertions (‘postulates,’ ‘principles’) about the world. Therefore, we should not try to append a reasonable interpretation to the quantum mechanical formalism, but rather to derive the formalism from a set of experimentally motivated postulates. »

Attempts at complete reconstruction from simple axioms have so far failed. Rovelli, with only two axioms, has gone furthest in reduction, but its development forces choices to be made to achieve quantum Hilbert space. Its ontological reconstruction is not reduced to these two axioms.

Beyond information

The reason, in my opinion, is that the axioms are already too differentiated. Yet they are based on one of the most abstract “root concepts”: information. Starting from such a basic foundation seems the right direction. Some theorists (Tegmark) would like to make information the ultimate background of reality. Unfortunately a crippling handicap prevents it from claiming this title. Information is based on relationships between individuations, on a quantification of reality. But not everything can be explained from a discontinuous, discreet reality. The whole, precisely, which we have an imperative need, is a continuity, a fusion.

Additional problem of discretion: how do two radically separate individuations go about exchanging? Discretion introduces a tiny but abysmal gulf between units, similar to mind-body dualism. Each unit is its own universe. How is it interested in its neighbour? How does reality become indiscreet?

Continuity of conflict and discontinuity of information

So we have to go back to a deeper concept than information, something of which information is an emanation. Certainly it is a sufficiently fundamental emanation to generate the real, in the physical world, and the virtual, in the mind. Thanks to information we progress towards a monistic reality, by reconnecting real and virtual to the neural interface, as I showed in Surimposium. But it is now necessary to reunite discreetly and continuously. Information is not enough. It is necessary to investigate the very principle of individuation and especially that of the dimensions in which this knowledge takes place. Dimensions allow our knowledge to take shape, but the original principle has no form yet. It is illusory to make it a mathematical expression. That would be to reduce it to the language that is our only way of grasping it. In this case, it is better to use oral language, which is certainly more blurred but this vagueness better identifies what we want to catch.

This is why the principle I proposed has its mathematical acronym (T<>D), but is best explained with a common word: conflict. The conflict, in everything, between its individualized part and its belonging part. “I am” and “be us” reunited irreconcilably. We already have in this principle the engine of reality, the explanation that it is not a static background. It eternally occupies itself with seeking an impossible conciliation. Eternally in the sense of an infinite sequence and not of a time —which is the emanation of it. If reality never stops on a final conciliation, it meets many provisional ones. Metastable balances that transform pure chaos into series of organizations. These organized levels generate their own conflicts. Another interactive explorer sequence is surimposed on¹Surimposition (superposition + imposition) is the emergence of resultant information over the constituent, intricate but independent. the stability of the previous one.

Which engineer to rescue the welder?

Surimposition? This is the neologism I created to translate the elevation of a notch in the complex dimension. This dimensional variety is the most fundamental. The only one that accepts together the discreet and the continuous. Each level has a discrete/constitutive and continuous/holistic face. It is the only “welded” dimension, devoid of those tiny infinite ditches that characterize the discrete dimensions of our usual frames.

It remains to understand the nature of the weld. But let us remember that any final agreement on this is impossible. This is the nature of the conflict…

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Reconstruction of Quantum Theory, Grinbaum Alexei, The British Journal for the Philosophy of Science 2007-jun 23 vol. 58 iss. 3

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