Abstract
In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the elementary ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context.
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Notes
As is clear, the two points are mutually connected. In KrV: B872/A 846 and ff., Kant distinguished between “physica rationalis” and “physica generalis” (the actual mathematical physics), in order to depict the possibility of a metaphysical science of physics which would be able to represent the transcendental organon for the critique of the physical concepts. The matter is that physicists do not simply attain empirical concepts: on the contrary, they start from some implicit metaphysical presumptions (see loc. cit., footnote). Physica rationalis is thus needed to clarify the metaphysical heritage of physics, and at the same time it will become very useful to philosophy, insofar as it will provide meaningful empirical examples in the development of the critique of the intellect. This project will be recalled in MAN, which in turn seems to add a very important element to the KrV’s approach. Indeed, in respect of the old arrangement, a particular section of physica rationalis, pertaining to a more strict application of the transcendental move to the actual mathematical physics, is ex novo derived: the very matter is that upon this new part the weight of mathematics result to be strengthened, so that on the classical determination of the nature of the transcendental method mathematical physics seems to play a more decisive role than before [27, pp. 470–471, 17, pp. 136 and ff.].
I am using the term “substance”, but I am perfectly aware of the fact that atoms and particles of QM are not substances as the things and the bodies of our daily experience are [7, pp. 424–479, 9, pp. 131–184, 19, pp. 3–22, 81–11, 36, p. 58]. Afterwards, within Rovelli’s QM, the “relational” or “structural” character of the identity of the objects is fully revealed [14, 29].
As far as I know, Heisenberg worked at the idea of a universal length at least since 1938, as proved by the publication of a memory about the question: Über die in der Theorie der Elementarteilchen auftretende universelle Länge [23, pp. 301–314]. However, he picks the minimum of nuclear radii as spatial constant, in considering Planck length to be not coherent with the physical implications of the theory of elementary particles [23, pp. 306 and ff.]. So the very point is that we are still talking of matter and not of space.
I will limit my exposition to LPQ, in considering the failure of the experiments concerning the supersymmetric particles and the difficulties thus arisen for the string theory [33, pp. 186–192].
On the contrary, monads were in the past conceived as unextended simple substances, for instance in Kant [17, pp. 25 and ff.].
This is still possible in QM, since time is not fully determined as an operator [5, p. 62].
The principle according to which the meaning of a physical concept exclusively depends on its empirical observability [22, p. 262].
This sort of metrological a priori, divergent from the pure logical meaning of Neo-Kantianism, is clearly recognized by Cassirer [6, pp. 409 and ff.].
We must notice that this functional definition was already clear in Kant [KrV: B42/A26-B43/A27, B48-49/A32]. By this point of view, the very problem of Transcendental Aesthetics is the representation of motion according to its dependence on the thing which is actually moving [11, B 57/A40, B58/A41]. The situation seems in any case to be partially changed in [27, pp. 476 and ff.].
The statement is extrapolated from a letter Husserl sent to Cassirer on April 3, 1925 [10, pp. 84–86]. I only add that this constant application into which transcendental method consists, is interpreted by Cassirer in a quite orthodox version of a metaphysical meta-science of physics, whereas in Husserl it will lead to the idea of phenomenology and of the analysis of the genetic laws of objectivity, starting from the eidetic science of Lebenswelt [26, pp. 163 and ff.].
I am convinced that Rovelli’s refutation of the classic Copenhagen dichotomy between classical and quantum world is not decisive at all [14, pp. 12, 22]. I do clearly not discuss the physical foundation of this argument, which is related to the basic superposition principle [32, pp. 194 and ff., 34, pp. 113–114, 142); I only will try to show that from the imaginative point of view, and thus in considering space and time as intellectual functions, we might still need this division as pure methodological construction of experience.
As regards the question of individuality in QM, it must be pointed out that the experimental situation seeming to reject the possibility of a strict individuation, can be reconsidered in the light of the concept of “absolute becoming”, according to which “an event e ‘becomes’ in an absolute sense (or ‘comes into existence’) at a certain time-place simply means that e occurs or happens at that-time place” [14, p. 24]. Indeed, if it is not possible to reconstruct the whole space of a particle, it is also true that the collapse of the wave function produced by measurement actualizes the particle and gives us the actual meaning of quantum individuality. If we assume it is perfectly localised, we will not able to reckon particle’s velocity, but this will solely mean we will not get any trajectory of the particle. Therefore, assuming the measurement perturbation, we may define individuality as it were more selective as regards its unity, as though the worth of this intensive definition loses its meaning as soon as we try to connect observations: in considering two observations, the concept of identity cannot be sustained anymore in its classical representation (as if the object were not changed by the physical interactions into which it is involved). As is well known, Heisenberg fixed the glitch concerning the problem of individuality recalling Aristotle’s concept of potentiality [21, pp. 147–166]: hence he solved the question of the connection between the statistical considerations to be made as regards the evolution of particles, by recalling the concept of a unitary matter (energy). By the same token, the interpretation of Rovelli’s QM seems to imply a “dispositionalist” or “propensitive” interpretation to justify the fact that “the only reality is given by events that are the outcome of interactions or mutual information between two different systems” [14, pp. 14, 10]: thus, at first glance, the locality of Rovelli’s QM seems to be compatible with the meaning of individuality we upheld. However, I must add that a whole definition of individuality is not here accomplished, for I did not take into account one of the most important questions concerning quantum field theory: the problem of the identical particles, viz. of those particles which are in principle undistinguishable, for they have the same physical properties but they do not satisfy some basic assumptions of Aristotle’s ontology and especially Leibniz’s principle of indiscernibles. Finally, in settling the problem of individuality in quantum physics, it must be considered the basic distinction between the oneness of a particle and the oneness of a quantum, which do accomplish different requests, e.g. the circumstance that particles can still be considered at some extent, as said, in their concrete localizability, while the unity of quanta is not basically defined by localization [36, pp. 89–90]. Hence I would solely like to specify that my arguments do concern the attempt of giving a transcendental definition of the particle individuality as logical and general a priori pattern, the strict minimum necessary to address the main question we asked upon the nature of space and time.
I think that the peculiar combination of ideas remounting both to the concept of prōtē hylē and to the concept of the existence of atoms allow a quite plain solution of the epistemological problems related to possibly upholding monism in Rovelli’s QM (which summarized in one statement may be put as follows: “The problem with priority monism is that it concentrates exclusively on the dependence of the part from the whole, neglecting completely the converse type of dependence”, [14, pp. 25–26]), for he refuses to consider LQG as UFT [31, pp. 9 and ff.].
It is also clear that the analysis of the structures of knowledge does not mean to underestimate the influence that the structures themselves have within the ontological determination of reality [6, IV].
Physically speaking, the refutation of the concept of substance completely agrees with the new ontological context of QM, according to which the primary matter and the very form of being must be conceived as a sort of “omnipresence” [9, p. 217].
I should here remark that this argument does not imply a defence of subjectivism: observer, indeed, does not directly influence the definition of objectivity, which in this case would be meaningless as such, but he has to realize that every judgment upon scientific experience presupposes the work of some basic functions of coordination, which do not depend on any specific axiomatic system. Accordingly, the crucial problem becomes the grounding of the theoretical validity of those functions.
It could be perhaps desirable to specify the terms of the question by highlighting the difference between space and place, recalling Aristotle’s definition of space as “extension of magnitude” [2, 209b5 and ff.]. In its general meaning, space is the general opening of dimensionality, originated by the run and the different history of the quanta of space; here we still find ourselves in a world of pure potentiality, within which nothing has its position yet. Place is on the contrary the single spot as a result of the interaction among quanta, so that we may say that between space and place runs the same relation valid between potency and act.
Zinkernagel applies this argumentation to a field into which LQG has proved its fruitfulness, viz. the Big Bang theory. He points out that if the model foresees that it is impossible to speak of the very early stage of the Universe in respect of time, it is also true that the concept of a chronological coordination must be premised, otherwise the same attempt to individuate the very beginning of the Universe would not make sense. Indeed, no time would mean also the impossibility of arguing the concept of beginning [39, pp. 13–15]. I also mean that such an interpretation can be endorsed in considering that the definition of the quanta of space does not allow us to consider physical reality as if it were actually built by ultimate substances and thus empirically filled: the quanta appear rather to be the consequent manifestation of “a quantum superposition of states whose geometry has discrete features, not a collection of elementary discrete objects” [32, p. 110].
As far as I can see, this relationship seems to be more clear in the string theory, above all for the intrinsic tendency of the theory to give a unified account of natural forces [5, pp. 71 and ff].
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Laino, L. Is Knowledge of Physical Reality Still Kantian? Some Remarks About the Transcendental Character of Loop Quantum Gravity. Found Phys 48, 783–802 (2018). https://doi.org/10.1007/s10701-018-0182-z
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DOI: https://doi.org/10.1007/s10701-018-0182-z