Sunday, 24 June 2018

Kant, Noumena and Quantum Physics

I am truly grateful that my first major work in Philosophy had recently been published in Contemporary Studies in Kantian Philosophy 3 (2018). In this monograph, I present new interpretations of the philosopher Immanuel Kant's First and Third Critiques as well as a new Kantian interpretation of quantum physics, providing a solution to the one-hundred-year-old problem of reconciling determinism and indeterminism in one conceptual framework. The well-known measurement problem in quantum physics is also resolved. I post the introduction below. 


Willem McLoud
Independent scholar, South Africa

1. General Introduction
1.1 Introduction

Kant is one of the great modern philosophers of science. In his Critique of Pure Reason he developed a scientific epistemology that he used to produce a philosophy of science in his Metaphysical Foundations of Natural Science (1786). In this he laid the philosophical foundations for Newtonian science. Through the years his approach has been reworked and adapted in such a manner that it could ground all classical mathematical science, including the theories of relativity (Friedman 2001:31, 47).

In the second part of the First Critique, Kant engaged with the problem of freedom. In the third antinomy (conflict of laws) he showed how the transcendental idea of freedom, that is, absolute spontaneity, can be introduced without contradiction as a different kind of causality (this is sometimes called “freedom” although it is not the same as practical freedom; it is merely a precondition for practical freedom). He conceptualized this as a different kind of effective causality in opposition to deterministic causality.

In the Critique of the Power of Judgment Kant developed this concept of causality further when he formulated another part of his philosophy of science. He now calls the spontaneous causality of the First Critique that is grounded in the transcendental idea of freedom, “causality of freedom” and the “concept of a causality through freedom” (KU 5:195-196). He develops the idea further in the context of non-extended parts and wholes as a “spontaneity of a cause” (KU 5:411), which is conceptualized in analogy with human ends. In this formulation, Kant allowed for the possibility that some products of nature are not produced in accordance with mechanistic (deterministic) laws. In this essay, I show how these concepts can be fruitfully introduced in that domain of physics where determinism has broken down, namely in quantum physics.

The question of non-determinism in quantum physics goes back to the early pioneers; it is central to the Copenhagen interpretation. Bohr understood quantum indeterminism as involving spontaneity. This was formally introduced in the context of Von Neumann’s formulation of quantum mechanics in terms of two conflicting maxims, namely the deterministic evolution of quantum states and the so-called reduction of the wave packet (called the “projection postulate”) that introduces an indeterministic (spontaneous, according to Bohr) aspect into physics.

The question became even more accentuated in the context of Bell’s inequality. Since the Aspect experiment confirmed the violation of Bell's inequality in quantum mechanics, the debate regarding non-determinism has intensified since determinism is assumed in this inequality as Redhead has demonstrated (Redhead 1987:102). The violation of Bell’s inequality is therefore also a violation of determinism. Redhead has furthermore shown that the Bell inequality can be reformulated to show that the violation thereof negates even what might be called “stochastic” determinism, that is, that there are not even stochastic causal links between the particles in the two arms of the Aspect experiment (Redhead 1987:102).

There are various responses to the question of non-determinism in quantum physics. Some merely assert the fact of such non-determinism taken in the more positive sense as absolute spontaneity (Cartwright 1983); others have tried to adhere to a purely deterministic view (for example, Bohm’s theory). In this case, action-at-a-distance may be assumed (which contradicts special relativity) or even the idea of “many worlds”. In this essay, I develop a Kantian solution to this problem in which determinism and non-determinism are reconciled. In this regard, I understand non-determinism in quantum physics in terms of spontaneity (in accordance with the Kantian concept of spontaneous causality). I argue that we have good reasons to subscribe to a Kantian interpretation of quantum physics in which such spontaneity is conceivably part of our understanding of how the world is like.

In the same manner that Kant's philosophy answered the quest for the mathematical grounding of Newtonian physics, Bohr made use of it in his effort to formulate an adequate response to the new kind of observations found in quantum physics (Pringe 2007). Since that time various authors have developed Kantian approaches, epistemically grounding both quantum mechanics and quantum field theory (Bitbol 2007; Auyang 1995). Various methodological approaches have been developed, some of which focus on Kant’s Third Critique (Pringe 2007). In contrast, I follow an ontological approach, albeit not in a dogmatic (realist) sense but in accordance with Kant’s Critical metaphysics. As such, I am not primarily concerned with Kant’s epistemology insofar as this concerns objective knowledge, but rather with Kant’s idea of absolute spontaneity which he incorporates in his regulative conception of ‘final causality’ in the Third Critique, which in my view describes quantum collapse. (In this essay I am only concerned with Kant’s Critical philosophy, not his pre- or post-Critical philosophy. I also do not engage with his practical philosophy).
A young man in a white shirt and tie and an older man in suit and tie sit at a table, on which there is a tea pot, plates, cups and saucers and beer bottles.
Werner Heisenberg (left) with Bohr at the Copenhagen Conference in 1934
My view is a weak ontological reading—not in any constitutive sense but merely in a regulative or reflective sense—of Kant’s Critical metaphysics which is then applied to quantum physics. I take Kant as presenting us with a positive conception of the noumenal realm as being ontologically distinct from systemic nature—with these realms finding their application in the quantum and classical ‘worlds’ respectively—without a corresponding epistemic commitment in terms of objective knowledge since no sensible intuition of the noumenal realm is possible. As I am primarily concerned with the contradictory principles of determination and absolute spontaneity and not with experience as such, an ontological approach instead of a methodological one (in which the difference between nature and the noumenal realm would be a transcendental one) makes sense.

I argue that the classical and quantum realms belong to different ontological modes of existence (the first consisting of matter but not the second which nonetheless is a genuine feature of reality even though it is not directly cognizable (Auyang 1995:75; Cartwright 1999:232) and that the non-determinism in quantum mechanics involves not merely the logical possibility of spontaneity, but that such a spontaneous causality (in accordance with the Kantian conception in this regard) becomes conceivable in our hypothetical understanding of what the world is like (i.e., our metaphysical view of the world). To put it differently: Kant provides us with a conceptualization of what the world may hypothetically be like if such spontaneity really exists. I argue that in Kant’s metaphysical system this spontaneous causality governs a non-spatio-temporal potentiality (as is conceptualized in the context of Kant’s “final causality” in the Third Critique), similar to Bohm’s quantum potential. This potentiality allows non-extended “wholes-and-parts” in the noumenal/supersensible realm to produce “material parts and aggregated wholes” in nature. I apply this concept to quantum collapse which takes superpositions of states (wholes-and-parts) to reduced states.

In my approach the mere logical possibility of freedom is contrasted with the conceivability thereof – by which I mean the conditions under which freedom can be conceived of as a real possibility. As such, my view is not concerned with the mere conceivability of freedom but rather with its conceivability under certain conditions. These conditions are 1) a problematically assumed, ontologically distinct, supersensible mode of existence which is different in kind from the sensible word (A420/B448) (i.e., it is not the kind of existence associated with matter) through which such transcendental freedom becomes possible (as the ruling principle of this mode of existence) and 2) that this realm has the ability to (absolutely spontaneously) produce outcomes in nature. Both the supersensible realm and this spontaneous causality are understood as ideas of reason which belong to Kant’s regulative or reflective metaphysics (in the First and Third Critiques respectively). I argue that this is the Kantian position (see chapter 2), although he does not formally introduce such “conditions” in the context of his discussion of freedom in the First Critique. The conceivability of freedom also involves the construction of a conception of such spontaneous potentiality in the framework of an ontologically distinct supersensible realm in the Third Critique (see chapter 3).

Although my concept of “conceivability” belongs within the context of Kant’s Critical metaphysics which takes us beyond the possibility of experience, it nonetheless translates into the Kantian conception of “transcendental” insofar as this concept captures the possibility of and conditions for absolute spontaneity (freedom). It is true that Kant does not formally state this, but one may suggest that this underlies his conception of ‘transcendental freedom’ (i.e., that it is not merely a transcendental idea of reason). Even though these conditions cannot be satisfied in Kant’s way of thinking (since these are beyond sensible reach) and absolute spontaneity can therefore be no more than an idea of reason, the progress of science had made it possible to engage with these conditions in a way that Kant never thought possible.

The Kantian approach may therefore be fruitfully applied to contemporary science. Within this context, I introduce the questions that I engage with in this essay: How is absolute spontaneity possible and how can it be accommodated in physics as part of our overall conception of the world? I use the philosophy of science that Kant developed in the Third Critique, which involves exactly such spontaneity, to engage with the problem.

1.2 Outline

The problems with such an approach are two-fold. The first concerns Kant’s conception of this other kind of non-deterministic causality and the second his conception of the noumenal realm. These are in fact interwoven problems since such a causality can only be conceivably introduced as something that can in principle exist as a genuine feature of reality (albeit not as part of material reality) when the noumenal realm is taken as an ontologically distinct realm “outside” nature, that is, where the deterministic laws of systemic nature do not apply.

Although Kant speaks of noumena as “outside/beyond” nature in both the First and Third Critiques (see A279/B334, KU 5:360) this should not be understood in a physical sense (as implying substance-dualism) but rather as ‘not belonging to’ systemic nature, which refers to the totality of mechanistic causal relations. The noumenal realm does not belong to systemic nature where mechanism rules. (I use the expression “deterministic causality” as a general concept in contradistinction with “spontaneous causality”. “Mechanistic causality” (or: mechanism) is a more narrow idea of reason used in the context of the Kantian concept of systemic nature).

Even though the Kantian “worlds” of material and noumenal objects (noumena) can be clearly differentiated from each other, there is no reason why these cannot at the same time belong to one world of reality (which in part exists beyond our sensible reach). Although Kant calls noumena “objects” (B306), they are obviously not similar to classical objects. They should be regarded as “objects” in an abstract sense and I prefer to call them “entities”. As such, they can co-exist with material objects in one world. (This is similar to real and imaginary numbers belonging to one numerical system; see the discussion in chapter 4). Kant does, in fact, bring these two worlds together in one conceptual structure in the Third Critique. Accordingly, I distinguish between two ontologically distinct “modes of existence” belonging to one world insofar as this refers to the totality of the reality of our existence. One may call my view a “third alternative” insofar as it is not a two-aspect or two-object view, neither a one-world or two-world view but rather a two-aspect and two-object as well as one-world and two-world view.

In the Third Critique, the noumenal realm is taken as the substratum of systemic nature and plays a very important role in the philosophy of science that Kant developed in that Critique. My interpretation allows for a remarkable and rather straightforward correspondence with contemporary theories in physics. As such, the Kantian concept of systemic nature refers to the “classical world” (where the theories of relativity apply; it is exactly this Kantian conception of nature which makes this application possible), his concept of the noumenal realm as the substratum of systemic nature finds confirmation in the pre-measurement “quantum world” (noumena are identified with quantum entities) and his concept of spontaneous potentiality as a causality finds its application in the reduction of the wave packet. (One should be careful not to confuse this Kantian conception of “nature” with our contemporary concept, which includes both the classical and quantum worlds.) As such, his philosophy of science in the Third Critique becomes applicable to the study of the above-mentioned problems in quantum physics. I argue that Kant's metaphysical position as described above can be formulated as a working hypothesis which prescribes the characteristics that the quantum realm should have for it to be taken as conforming to this interpretation.

My application of Kant's philosophy of science requires that the Kantian concepts be understood in a specific manner, especially that the noumenal realm refers to an ontological distinct realm outside (henceforth: systemic) nature, problematically assumed. In this regard, my interpretation stands in contrast with current interpretations (in both the two-object and two-aspect views—see chapter 2) which assume that the noumenal realm, especially in the First Critique, does not refer to an ontologically distinct realm outside nature. In my view the First Critique lays the foundations for both parts of Kant's philosophy of science as presented in the Metaphysical Foundations as well as the Third Critique, and it would be very strange indeed if his view of the noumenal realm in the First Critique differs substantially from that in the Third Critique (as is often asserted) where it is presented as the substratum of nature (and human nature) (KU 5:196, 409, 429).

To arrive at an interpretation of Kant’s First Critique as well as that of his philosophy of science in the Third Critique which allows for a sensible application to the problem of spontaneity in quantum physics, I present my view in three parts which also constitutes the three main chapters.

1.  I argue that the most viable interpretation of the noumenal realm in the First Critique (and therefore also in his Critical philosophy in general) is to understand it as a realm outside Kant's conception of systemic nature (governed by mechanism), regulated by the transcendental principle of freedom (as an absolute spontaneous, albeit, effective causality). In this manner this principle of freedom does not merely become logically possible; it becomes conceivable as something that could really exist if the world is conceived in accordance with Kantian philosophy. I present this reading as an alternative in Kantian interpretation in contrast with the two-object and two-aspect views (which include about all streams of Kantian interpretation; I also discuss or mention views that are an exception to this general description (Langton 1998; Hanna 2006). I show that Kant’s two-aspect and two-object views are reconciled in this manner.

2.   I present a new reading of Kant's philosophy of science in the Third Critique that is in agreement with my new reading of the First Critique (with the focus on the noumenal realm and other relevant concepts). I show that the conception of such a realm, now called the supersensible realm, is essential to the concepts that Kant develops in this part of his philosophy of science. I also show that Kant now argues for the conceivability of both such a realm and a different kind of causality, namely of “final” causes, which is named in analogy to the achievement of human ends. I argue that this causality involves a certain potentiality according to which non-extended wholes-and-parts (in the supersensible realm) can produce material parts and aggregated wholes in nature and builds upon the transcendental idea of freedom introduced in the First Critique. This aspect of Kant’s philosophy of science stands apart from that presented in the Metaphysical Foundations of Natural Science which is directed to the study of matter (grounded on the epistemology developed in the Analytic part of the First Critique).

3.   I show that, although Kant himself did not foresee this possibility, his philosophy allows us to engage with the noumenal realm empirically (albeit indirectly). This is possible when we rework it in such a manner that time is combined not with space, but with mathematical space (Kant calls such space-forms that are constructed through reason and applied to noumena, “ideal” space—see below), as is done in quantum mechanics. (This effectively unites Kant’s two “worlds” into one “world”). I argue that the pre-measurement quantum realm adheres to the three basic requirements/conditions that Kant has for the supersensible realm, namely that it is supersensible, that it is beyond space/time and that it is outside nature (where all interactions are governed by mechanistic causality). As such the quantum realm can be conceived of as an ontologically distinct realm. The concept of absolute spontaneous causality can, therefore, be ascribed to that realm without contradiction and I argue that Kant's approach enables us to positively conceive how this is possible.

I take the reduction of the wave packet as adhering to this kind of causality, namely as a physical event that happens in various contexts, also outside measurement, for example during atomic decay which is the paradigmatic indeterminate process. In my Kantian interpretation of quantum physics, I develop a unified conceptual framework in which spontaneous and deterministic causality are reconciled. When these two kinds of effective causality are regarded as heterogeneous laws that govern two ontologically distinct modes of existence, namely the quantum and classical modes, the well-known measurement problem in quantum physics (that involves the above-mentioned conflict in laws) is resolved. New light is also thrown on some interesting features in quantum mechanics, for example, non-separability and non-locality.

In this manner three interpretations are developed, namely 1) a new interpretation of the First Critique, 2) an interpretation of Kant's philosophy of science in the Third Critique that is consistent with 1), and 3) a new Kantian interpretation of quantum physics. These interpretations are not independent of each other—together they constitute a consistent interpretation of the First and Third Critiques (and the Critique of Practical Reason, although that is not included in the discussion) that is also consistent with contemporary science. In general, my interpretation of Kantian metaphysics is consistent with special and general relativity as well as quantum physics (quantum field theory and quantum mechanics) (see chapter 4, Appendix 3 & 4).

In contrast with reconciling theories such as natural theology and final causes in nature which assume the reconciliation of determinism and indeterminism (either for reasons such as divine premotion or merely through the underdetermination of empirical facts), my interpretation of Kantian metaphysics also explains how that could conceivably be achieved within our world in posing a concrete hypothesis in this regard with application to quantum physics. The great challenge for all such theories is to show how the real possibility of absolute spontaneity could be established—for which any Kantian calls upon practical reason (even though Kant says that his philosophy could provide no such “proof”). What I discover in Kant’s Critical philosophy, is that he provides another strategy in this regard which does not proceed through practical reason (even though practical reason first suggests it—in the same way that the possibility of experience is first suggested by experience itself).

In the First and Third Critiques, Kant provides the necessary (and I think, sufficient) conditions (albeit not the proof) for the real possibility of absolute spontaneity (which I call the “conceivability” thesis) – which I show in this essay to be satisfied in quantum physics (see chapter 4). This means that we have good reason to think (since the conditions are satisfied) that absolute spontaneity is real (for us) (see section 4.7) and that it co-exists with mechanism as the guiding principles of the quantum and classical modes of existence respectively (which are unified through quantum mechanics into one world).

This does not mean that the existence of absolute spontaneity (or the supersensible realm) is asserted in a dogmatic realist sense but merely that the conditions for its real possibility had been satisfied. It also does not constitute an epistemic claim in accordance with Kant’s conception of “objective” knowledge since the corresponding epistemic conditions in this regard are not satisfied. (In contrast with mere indeterminism, spontaneity cannot be demonstrated through direct empirical means since it belongs to the supersensible realm.) It may, however, be taken as a certain kind of epistemic claim (in satisfying the necessary conditions) which belongs to Kant’s philosophy albeit not the objective Kantian kind. In this my approach goes far beyond that which other reconciling theories can do. In general, my approach also has greater explanatory power.

1.3 Methodology

In deciding on a methodology for my interpretation of Kantian philosophy, I considered what may be called the hermeneutical problem. This problem is that the overall interpretation of a text and the particular arguments are interwoven. In all interpretation, the particular arguments are important whereas for all arguments the overall interpretation is important. The reason for this is that our understanding of philosophical works always involves certain assumptions underlying our premises that are not made explicit. There are so many strings of thought in the overall work (the horizon behind the work) that we can think of it as a thing in itself beyond the possibility of ever bringing those ideas in any objective sense into our premises and arguments. Kant explicitly acknowledged this problem when he argued that reason always has certain limits insofar as we as humans are sensibly and conceptually constrained. In Kant’s formulation of the antinomies, he shows that conflicting paradigms (even mechanism and freedom) that cannot be shown to be true in any final sense, may even under certain conditions both be true.

In this context, I believe that a typical Kantian approach should not be to even try to establish final conclusions in this regard. It should rather acknowledge that the above-mentioned problem makes it impossible to arrive at final conclusions when trying to understand the works of philosophers. As such it is better to speak of interpretations: that we develop certain interpretations that are not truth statements. We can never do better than presenting various interpretations. This is especially relevant in the interpretation and understanding of Kant’s philosophy.

In my reading, I observed two strategies in dealing with the hermeneutical problem in the work of historical philosophers and especially Kant. The first strategy is to try and reconstruct the author's arguments and in that manner to arrive at some conclusion that we may attribute to the author. In this case, the project is often implicitly guided by a preconceived paradigmatic commitment to an overall interpretation of the work (say the two-object view) which is never made explicit. Although some seemingly final conclusions are sometimes arrived at, there cannot be any metaphysical commitment to truth because of the implicit assumptions. The other approach is to start with a broad interpretation (a contextualization) and to proceed within this context with particular reconstructed arguments. In this case, the paradigmatic commitments are made explicit from the start. As such there are also no truth claims to be made. We can call this the analytic and continental approaches and in Kantian studies both are well presented in the literature (for the first, see Guyer 1987, Langton 1998, etc.; for the second, see Allison 2004, Allais 2004, etc.).

The hermeneutical problem is especially relevant to my own approach since I am not committed to any of the current paradigms in Kantian interpretation (namely the two-object and two-aspect views). I can therefore neither start with particular arguments (which always depend on some overall interpretation) nor work from within any accepted paradigm. The result is that readers who have different paradigmatic commitments (standing outside my newly introduced paradigm) might read the work in their own terms, understanding the terminology in their own way and not as I do.

The problem is alleviated by the fact that my interpretation accepts the two-aspect view insofar as Kant’s epistemology is concerned (i.e., in the Analytic part of the First Critique), but not insofar as Kant's views regarding freedom and the noumenal realm are concerned (i.e., in the Dialectic part; for which I hold a two-object view). These two-aspect and two-object views can be reconciled in my ontological approach (which involves a regulative/reflective metaphysics) since no constitutive claims are made regarding freedom or the noumenal realm. The acceptance of the two-aspect view allows me to use a continental approach according to which I first provide a contextualization of Kant's overall program (i.e., give my own take on it) before proceeding with arguments regarding the details of Kant's concepts and their relation to each other.

We find the same problem in mathematical texts where mathematical formulations are sometimes thought of as giving precise descriptions of what happen in the same manner that precise formulations of arguments are often conceived of. This is an extensive problem and I am not going to discuss it in any detail. What is of importance, however, for my own approach, is that there are always various ways to understand the physics behind the equations (and even the equations themselves). This is why various interpretations of quantum physics have been developed.

In the chapter where I give my Kantian interpretation of quantum physics—I develop my ideas in a formal manner but have on purpose not included any equations—I have tried to present my understanding of the mathematics and the physics involved without taking the short route through mathematics where presenting equations is regarded as stating “obvious” truths or interpretations. Although mathematical expressions can provide logical (methodological) possibilities, the understanding of how this relates to what the world is like goes beyond that. In not including equations I try to facilitate the reader's engagement with my own paradigm of understanding quantum physics. Even in this case I, again, give a contextualization of my Kantian approach before commencing with the detailed discussion.

I follow the continental approach throughout (in all the main chapters), starting with contextualization before engaging with the details of Kant’s position. I develop an interpretation of Kant’s philosophy in the First Critique, of his philosophy of science in the Third Critique, and eventually produce a new Kantian interpretation of quantum physics in which I use these interpretations. In the final, instance I produce arguments for my position but I do not try to establish any final conclusions. I nevertheless hope that my arguments will be convincing and my interpretations sophisticated enough to accommodate the many strings of Kantian thought into a unified perspective.

1.4 Conclusion

Kant’s philosophy is not easy to engage with. The historical context in which he presented his major work played an important role in the formulation of the traditional two-object view in which Kant is read primarily as an idealist. This has changed over the last fifty years or so with the wide acceptance of the two-aspect view (see Gardner 1999). I believe that this has brought more balance to Kantian interpretation. The problem, however, is that Kant's conception of freedom is still understood for the most part in moral terms.

In this essay I try to change that view and show that freedom (understood as absolute spontaneity) constituted an essential part of Kant’s scientific thought—both in the groundwork that he laid in the First Critique as well as in the Third Critique. Once this is recognized, the way is prepared for the application of these Kantian concepts to contemporary scientific debate. There is no short route—the work presented here involves many detailed discussions of seemingly forgotten concepts. But I hope that in the end, it will be worth the effort for the reader.

To read the rest of the monograph, click on:

Published in Contemporary Studies in Kantian Philosophy 3 (2018)


No comments:

Post a Comment