Download Kantian Causality and Quantum Quarks (II)

Kantian Causality and Quantum Quarks:
(II) Quantum Causality and its Parallels in
Kant’s Quark-Like Noumenal World
1. Bohm’s Quantum Causality as an Alternative to Copenhagen Indeterminacy
Part I of this two-part series introduced an apparent conflict between Kant’s defense
of the synthetic apriority of the principle of causality and the indeterminacy typically thought
to be required as an explanation of the results of experiments in quantum mechanics. After
briefly reviewing the history of quantum mechanics as it led to the development of the socalled “Standard Model”, I argued that a perspectival interpretation of Kant’s Analogies of
Experience reveals, despite the prevalence of claims to the contrary, a deep compatibility
between his transcendental idealism and the quantum indeterminacy required by the
Copenhagen interpretation. Each of two pillars of the latter, Bohr’s inseparability hypothesis
and Heisenberg’s uncertainty principle, is grounded in an empirical version of the very
phenomena-noumena distinction that forms the transcendental basis of Kant’s Critical system.
Moreover, since Kant regarded his theory of the three analogies (and transcendental idealism
in general) as unveiling the necessary conditions for the possibility of experience—i.e., of the
“phenomenal world”—and since the latter refers only to the level of the empirical world that
is open, at least in principle, to observation by the human senses, Kant’s theory does not
require these principles to apply with equal validity to levels of empirical (physical) reality
that are either too large (as in astrophysics) or too small (as in quantum physics) for human
beings to observe.
In defending the compatibility of Kant and quantum mechanics, Part I hinted at
several possible ways of viewing this relationship as more than just one of neutral
Kantian Causality and Quantum Quarks (II) - 2
compatibility, but as a deeper consistency of worldviews, hinting that Kant’s philosophy may
have served as a necessary precursor for quantum theory. Here in Part II we shall explore
these hints in further detail, arguing first, that a special kind of causality might apply at the
quantum level after all, and second, that Kant’s appeal to a noumenal realm includes some
strikingly “quark-like” elements—elements having characteristics that also arise in a causal
interpretation of quantum events.
In searching for a plausible explanation of quantum events, some physicists have
demonstrated that it is possible to avoid appealing to indeterminacy at the quantum level.1
Quantum causality has been conceived in various ways, including the counter-intuitive
hypothesis that future events might somehow “cause” present quantum events to happen.
Here I shall focus on an alternative to reverse causation that has been largely ignored, due to
the dominance of the Copenhagen interpretation (see Cushing 1996): among the four options
listed in Part I of this series (near the end of §2), Bohmian mechanics is the approach to
interpreting quantum theory that portrays the quantum world most explicitly as operating
according to a special (“nonlocal”) type of causality.2 Heisenberg’s uncertainty principle
1Salmon
1998 gives an exhaustive treatment of various contemporary approaches to
understanding the nature of causality, but shows no awareness of Kant’s significance to this
debate, offering only a few passing references.
2A
well-known example of nonlocal causation relating to non-linear mathematics (“chaos
theory”) can serve as a (non-quantum) illustration of cause and effect existing at great
distances from each other, in the absence of any observable contact: the flutter of a butterfly’s
wings in Hong Kong can influence the weather in New York. This so-called “butterfly effect”
describes how minimal causes sometimes produce extreme and unforeseeable results (see
Wieland-Burston 1992). In such situations, the way each part of a system behaves is
determined not so much by the behavior of other parts within the system, as by the way each
Kantian Causality and Quantum Quarks (II) - 3
challenges physicists to give up the idea of causal determination and/or the idea that particles
exist at a particular location. Whereas the Copenhagen interpretation abandons both, David
Bohm demonstrates that a deterministic explanation of quantum events is possible by
postulating a nonlocal, “sub-quantum-mechanical” force that acts on the wave function (see
Bohm 1980, 77f).
The key question that competing quantum theories attempt to answer is: What do the
results of experiments in quantum mechanics actually describe? Schrödinger’s equation,
defining the wave function in a quantum mechanical experiment, does not describe the way
reality itself appears to function; in our ordinary experience we would not expect a cat
(Schrödinger’s famous illustration) to be both alive and dead at the same time. Soon after
Bohm first proposed his theory of quantum causality, Louis de Broglie informed him that this
approach was very similar to the “pilot-wave theory” he had proposed some 25 years earlier
(Bohm 1987, 36), based on “an equation of particle motion equivalent to the guiding equation
for a scalar wave function” (Goldstein 2006); but de Broglie had abandoned his proposal soon
after giving a poor response to Wolfgang Pauli’s objection at the 1927 Solvay Congress—a
crucial turning point, when the Copenhagen interpretation began its dominance of twentieth
century quantum theory (cf. Cushing 1996, 7).
After being personally encouraged by Einstein to join the search for “hidden
variables” (Bohm 1987, 35), Bohm posited the latter as a factor that explains how “the initial
position of a particle…uniquely determines its future behavior” (Cushing 1996, 5), through
the operation of a quantum wave. The theory revises “Schrödinger's equation in terms of
part relates to the whole. As we shall see, such non-linear effects, like Bohm’s nonlocal
quantum causality, have more affinity to Kant’s First Analogy than to his Second Analogy:
the notion of a deep, underlying “causality of the whole” is implicit in the claim that a
permanent substance must underlie all phenomenal alterations.
Kantian Causality and Quantum Quarks (II) - 4
variables that seem interpretable in classical terms” (Goldstein 2006, §6), but at the cost of
increased complexity: Bohm introduces an additional force term, called the quantum
potential, that he admits is “rather strange and arbitrary” (§5, Bohm 1980, 80)—though he
elsewhere adds that the Copenhagen interpretation’s “‘collapse’ of the wave function” is no
less “arbitrary and unexplained” (Bohm 1987, 36). The revised equation ties the velocity of a
particle to its initial position, rather than being an independent factor, as Einstein (with his
more classical notion of causality) had assumed.
The double-slit experiment provides a helpful illustration of why quantum mechanics
is so mysterious. If one determines which slit a given particle passes through, one thereby
destroys the distribution pattern of the wave; but if one preserves and observes the
distribution pattern of the wave, one can know nothing about the position of the particle(s).
Bohm explains why this occurs and solves the problem, at least in theory, by recognizing that
observing (i.e., putting oneself in a position to measure) the position of a particle “must
involve interaction with another system that must also be included in the…mechanical
analysis.” (Goldstein 2006, §6) Appealing to the quantum potential enables the overall
experimental set up to be interpreted holistically, incorporating the observer’s role into the
mathematical framework in a way that preserves the plausibility of a causal explanation, by
conceiving the whole as determining the relations between the parts, rather than (as in
classical mechanics) the parts as determining the relations making up the whole (Bohm 1987,
38).
The paradoxical “measurement problem”, whereby experiments produce
“measurements [that] typically fail to have outcomes of the sort the theory was created to
explain” (Goldstein 2006, §7), occurs because the wave function (as defined by Schrödinger’s
equation) collapses to an apparently random eigenstate once a particle is observed. Many
theorists respond to the measurement problem by appealing to decoherence (i.e., suppression
of the interference that arises when an experimental system interacts with its environment),
Kantian Causality and Quantum Quarks (II) - 5
thus focusing solely on probabilistic explanations. But no measurement problem arises in
Bohmian mechanics, because it incorporates the collapsed wave function (i.e., the observed
particle together with the apparatus doing the observing) into the overall mathematical
analysis of the results. While the system containing the wave function must be open in order
to be observed, and therefore to allow the wave function to collapse, the larger system that
connects the former subsystem to the observer can be regarded as closed (Goldstein 2006,
§8): “The configuration Q of this larger system naturally splits into X, the configuration of the
subsystem, and Y, the configuration of the environment of the subsystem.” What Bohmian
mechanics calls “the guiding equation” then determines precisely how X is influenced by Y.
The problem for Bohmian mechanics is that it remains unclear “what should be meant by the
wave function of a subsystem” (§8).
Bohmian mechanics requires the quantum theorist to give up the assumption that
context is largely irrelevant. In other words, by postulating that the appearance of randomness
in quantum experiments is sourced in hidden variables associated with the initial position of
particles, Bohm is in effect insisting that the context of an experiment determines the
outcome. The results are essentially the same as with the Copenhagen interpretation; some
might say that (aside from the use of different mathematical formulas) the main difference
between the two is psychological, “amount[ing] to little more than the rather unremarkable
observation that results of experiments should depend upon how they are performed”
(Goldstein 2006, §12).
The plausibility of Bohm’s hypothesis of nonlocal (i.e., wave-based) causality gained
significant support from what is now called “Bell’s theorem”: Bell 1964 proved that the
statistical predictions generated by quantum mechanics are incompatible with the existence of
Kantian Causality and Quantum Quarks (II) - 6
hidden variables that would restore a sense of local causation to quantum events.3 This cast
serious doubt on Einstein’s conviction that ordinary, local causation exists at the quantum
level, but is merely hard to detect due to some hidden variables. Hughes joins those who
regard the usual alternative, the Copenhagen interpretation of quantum events as wholly
undetermined probabilities, as “contra Kant” (1989, 237). However, we saw in Part I that
such a dismissal (typically supported solely by unargued assumptions) is premature, because
Kant never claimed that causality must apply to levels of reality that are by definition
unobservable. As we saw, quantum mechanics can still be rendered thoroughly Kantian, even
though local (Second Analogy) causation is irrelevant at the quantum level. Bohm’s oftenneglected theory of the “causality of the whole” has an advantage over the Copenhagen
interpretation in this respect: while both interpretations view the quantum level as not
conforming to local causation, Bohm’s approach resonates with Kant’s First Analogy in ways
3See
Cushing 1996, 6. Smith 1991, 253-257, gives a detailed mathematical explanation of
Bell’s theorem. Forrest 1988, 91f, clarifies that the argument is “that the appeal to hidden
variables will not restore locality”; it is not “a positive argument against hidden variables.”
However, the results of the famous Aspect experiment (Aspect et al. 1982) require the
quantum theorist to give up either the assumption of local causation (through hidden
variables) or the assumption of the reality of quantum events (or both). Gröblacher 2007 and
Aspect 2007 discuss the apparently non-realist implications of recent extensions of the Aspect
experiment. The present study shows how to avoid a radically non-realist interpretation of
quantum mechanical experiments, by adopting a Kantian interpretation: affirm empirical
realism by rooting the whole experiment in the philosophical context of transcendental
idealism. On the connection between the nonlocal causality required by Bell’s theorem and
the analysis of non-linear systems (as in the “butterfly effect” [cf. note 2, above]), see
Vervoort 2000.
Kantian Causality and Quantum Quarks (II) - 7
that the Copenhagen approach does not.
Bell himself was an explicit proponent of Bohmian mechanics and saw his theorem as
disproving not all “hidden variable” interpretations of quantum events, but only those (like
Einstein’s) postulating local (hidden) causes that would reduce causality at the quantum level
to a super-complex version of classical causality. Bell’s Theorem (especially as confirmed by
the influential experiment of Aspect et al. 1982) consigns Einstein’s position to the realm of
wishful thinking, but preserves the possibility that at the quantum level nonlocal causes
remain in effect. In the wake of Bell and Aspect, quantum theorists now generally agree that
quantum theory requires either nonlocality (i.e., somehow messages at the quantum level
break the basic rules of relativity theory, apparently travelling faster than the speed of light) or
nonreality (i.e., quantum particles simply do not exist before they are observed), or both
({reference deleted for blind review}). How this result can be understood, especially in light
of the almost universal belief that the events we experience at the phenomenal level are both
local (causally determined) and real (independent of our experience of them), is the mystery
that gives rise to the many interpretations of quantum events. Bohm’s demonstration that
quantum causality is possible does not imply that Kant’s Second Analogy is applicable at the
quantum level after all, because quantum causality is nonlocal. Rather, as I shall argue in §2,
by redefining “causality” in terms of an underlying “wholeness”, Bohm implicitly relies on
the principle Kant expresses in the FirstAnalogy (Kant 1781/1787, 224): “In all change of
appearances substance is permanent; its quantum in nature is neither increased nor
diminished.”
2. The First Analogy as the Kantian Grounding for Quantum Causality
What are the implications of Bohm’s interpretation of quantum mechanics with
respect to the defense of Kant’s philosophical system presented in Part I of this series? If
Kant’s philosophy provides a genuinely transcendental grounding for empirical (scientific)
Kantian Causality and Quantum Quarks (II) - 8
knowledge, then it must ground all possible empirical science. Even though (at least until
recently) Bohm’s causal quantum theory appeared to have lost the interpretive battle to the
Copenhagen school, as far as acceptance by the scientific community is concerned, it is
equally plausible as a consistent explanation of the results of quantum experiments. We
therefore turn in this section to an assessment of whether Kant’s philosophy also consistent
with this interpretation. If it is, then this will confirm the conclusion of Part I in this series,
that the experimental results of quantum mechanics cannot be cited as a rationale for treating
Kant’s philosophy as outdated or as falsified by the facts of science. Quite to the contrary, if it
turns out that both the Copenhagen and the Bohmian interpretations are consistent with
Kant’s account of the philosophical foundations for empirical science, then an acceptance of
Kant’s position would provide an explanation for the (otherwise inexplicable and surprising)
fact that the results of quantum experiments can be explained in terms of two such radically
different theoretical frameworks. This approach might then provide a clue for resolving the
even more troublesome conflict between quantum theory and relativity theory.
Quantum physics (especially Bohmian mechanics) and relativity physics, I shall argue,
rely on the First and Third Analogies just as Newtonian physics relies on the Second
Analogy.4 Thus Bohm claims “the world cannot be analyzed correctly into distinct parts;
4Bohm
1980, 134, expresses this parallel as follows: “Though quantum theory is very
different from relativity, yet in some deep sense they have in common the implication of
undivided wholeness.” In both theories, “there can be no ultimate division between the
observing instrument and the observed object.” Relativity theorists might object to such a
statement as an over-generalization. But Bohm elsewhere acknowledges the crucial
differences: relativity theory is causal, local, and continuous, whereas quantum experiments
produce noncausal, nonlocal, and discontinuous results (176). Another way of expressing the
“deep” similarity Bohm points out would be to say both theories view the world as a
Kantian Causality and Quantum Quarks (II) - 9
instead, it must be regarded as an indivisible unit in which separate parts appear as valid
approximations” (Bohm 1951, 161). The “world” Bohm refers to here is what he later
describes as “the implicate order”, the underlying wholeness that is governed by a hidden
(“implicit”) law he calls “holonomy” (Bohm 1980, 181). This law enfolds within it all that we
eventually experience in the “unfolded” (161) form of the “explicate order”, “but its laws are
no longer mechanical” (185), as are the discrete, analyzable objects of our ordinary
experience. The implicate order is the source of the background wholeness that gives the
explicate order of our material universe its causal appearance at the level of ordinary
experience and its indeterminate appearance at the quantum level. What is generally regarded
as randomness in the latter context is better described as “a certain kind of order which is of
an indefinitely high degree” (117). Because of its high degree of abstraction from our ordinary
experience, Bohm admits that such causality of the implicate order would “not be
deterministic in time” (154). Such comments indicate that Bohm’s distinction between the
implicate and explicate orders corresponds closely to Kant’s distinction between substance
thoroughly interrelated whole, while Newtonian physics requires the world to be discrete and
analyzable (125; cf. Hiley and Peat, 1987, 11); Kant’s First and Third Analogies share
precisely this difference in contrast to the Second. Relativity theory must incorporate these
features for the same reason the Third Analogy comes after the Second; just as the Third
Analogy functions as the synthesis between the first two, relativity theory appeals to
wholeness yet incorporates local causality. Only by seeing the three types of physics as part of
one self-consistent system, as becomes possible by correlating them with Kant’s Analogies of
Experience, can we understand how it happens that each approach to modern physics (i.e.,
relativity theory and quantum theory) “contains classical [Newtonian] theory as a limiting
case” (Bohm 1980, 82; cf. Cushing 1996, 26).
Kantian Causality and Quantum Quarks (II) - 10
(or the hidden “substratum” of all cause-and-effect relationships)5 and the spatio-temporal
“accidents” (empirical changes) we actually experience (see Part I, §4).
The concept of causality in classical physics is virtually devoid of mystery. This thing
here somehow contacts that thing there and thereby alters it in some way. The causal link is
itself, at least in theory, empirical: if we look closely enough we can see it before our very
eyes. This is causality as understood in terms of Kant’s Second Analogy. But the Second
Analogy does not stand alone. When quantum physics hypothesizes a mysterious, underlying
substratum of the physical world, it fulfills the function of Kant’s First Analogy in a
systematic account of our understanding of nature. It is no accident that Kant refers to
substance as a permanent, underlying “quantum in nature”; he seems to have been thinking
that if we view the physical world at its deepest level, far below the level of ordinary
perception, then all changes will appear as mere “accidents”. This is precisely what quantum
theory has confirmed. The Third Analogy (“All substances, in so far as they can be perceived
to coexist in space, are in thoroughgoing reciprocity” [Kant 1781/1787, 256]) likewise
suggests that Kant is now thinking of just the kind of macroscopic “view” of the entire
universe of causally-interrelated phenomena that became the focus of Einstein’s two theories
5Modern
physicists typically describe this substratum in terms of “fields”, the unobservable
context that enables all particles to interrelate. That Kant regarded this substratum as
consisting of an unobservable material called “ether” (see Part I, note 17), whereas modern
physicists believe it consists primarily of energy, should not eclipse their similarity: both
positions regard such a substratum as operating below the level of possible human
observation. Interestingly, Bohm 1980, 191-192, compares the old notion of ether to his own
theory of the implicate order. The main difference is that the ether was assumed to be threedimensional, while Bohm treats the background wholeness as “multi-dimensional”.
Kantian Causality and Quantum Quarks (II) - 11
of relativity.6 “Substance” in the First and Third Analogies functions for empirical science in
much the same way as the thing in itself functions for transcendental philosophy: as the
background “wholeness” that provides the necessary context for understanding how
knowledge itself arises. Kant emphasizes a crucial difference between these two (cf. Kant
1781/1787, 44, A371): he defends idealism from the transcendental perspective (so that the
thing in itself is absolutely unknowable), precisely because this is the only way of defending
realism from the empirical perspective (so that the physical nature of substance, at all three
levels of human experience, becomes a task for empirical science to discover). In light of this
parallel between the two main perspectives Kant adopts, we can regard Bohm’s quantum
(nonlocal) “causality” via the “implicate order” as an empirical, yet quasi-transcendent (i.e.,
observation-defying),7 hypothetical link between empirically observable phenomena that
appear (at the quantum level) to be otherwise unrelated.
Obviously, Kant himself did not have the opportunity to consider and assess how the
methods of quantum mechanics would be understood as fitting into his philosophical system.
One of his purposes in the first Critique was to explain what must be true about our way of
thinking if we are to view the empirical world (i.e., our experience of physical nature) as a
deterministic system. The key assumption that made this possible for Kant was that the world
6Of
course, the First and Third Analogies were not irrelevant to Newtonian science. Kant
obviously saw parallels between the three analogies and Newton’s three laws of motion, as
Friedman 1992 demonstrates. My point here is only about the relative importance of the three
analogies to quantum physics, Newtonian physics, and relativity physics, respectively.
7Bohm
1980, 146, says “the formation of an image [“of a particular atom”] is just what is not
relevant in a ‘quantum’ context.” This is what I mean by “quasi-transcendent”; quantum
theory must appeal to the (observable) results of empirical experiments, but the observed
results are not what the theory is primarily about.
Kantian Causality and Quantum Quarks (II) - 12
in itself (i.e., the “noumenal” world) must not be bound by whatever a priori principles make
this deterministic model possible; this is the whole point of calling scientific knowledge
phenomenal. If science attempts to extend its reach beyond the phenomenal, to the world as it
is apart from our observation, then on Kant’s terms we should expect it to behave in
mysterious ways, because in that case the a priori principles (of which local causality is the
most important) will no longer be applicable. (Bohm 1987, 33, explicitly states that his initial
motivation in searching for a new interpretation of quantum mechanics was that Bohr’s
approach “could not go beyond the phenomena”.) The results of quantum mechanics are
therefore fully compatible with Kant’s epistemology, regardless of which interpretation one
adopts. Bohm’s nonlocal “causality” does not contradict the Kantian principle that local
causality must apply to all empirical (observable) objects any more (or less!) than does Kant’s
own noumenal “causality”—a point we shall explore in more detail below.8
Kant portrays reason itself as organized in the same, thoroughly interconnected way
that modern physicists (of virtually all interpretive persuasions) infer for the physical world,
based on the results of their experiments. Thus Kant says (1783, 263) “pure reason is a sphere
so separate and self-contained that we cannot touch a part without affecting all the rest.”
What Kant calls reason’s “architectonic unity” behaves not unlike nonlocal causality in
Bohm’s depiction of quantum events. Of course, as noted above, the causality defended in the
8The
paradoxical ring of terms such as nonlocal causality, suggesting a mysterious “uncaused
causality”, is typical of pronouncements made by quantum physicists, {text and reference
deleted}. As we shall see in §4, below, the strange character of this type of cause is
reminiscent of the “noumenal causality” Kant sometimes defends. This is because quantum
causality attempts to describe the connection between the empirically observable
(measurable) results of quantum experiments and the unobservable sub-quantum “world”
(i.e., the “substance”) underlying these measurements.
Kantian Causality and Quantum Quarks (II) - 13
Second Analogy is local causality, but nonlocal causality has a transcendental basis in the
First Analogy. As we shall see below, the parallels between Bohm’s position and Kant’s go
even deeper than this.
Because on Kant’s view the principle of causality resides in the mind (i.e., in human
reason), even when physical limitations bar our successful discovery of the cause, we
inevitably find ourselves assuming some type of cause in order to carry on the task of
scientific explanation. Not surprisingly, those who think Kant’s Second Analogy defends
“causality as a property of nature” (Reichenbach 1944, 2), rather than as a transcendental
principle that necessarily governs human understanding, typically regard the discoveries of
quantum mechanics as disproving Kant’s synthetic a priori principles. Properly understood,
Kant’s Copernican revolution requires the rejection of precisely such overly objectified, nonperspectival conceptions of causality. As we have seen, Kant’s position is that we see causal
necessity in the phenomenal world because we put it there, that we do not see it if we trace
the phenomenal world back to its basic nature as a single, permanent “substance” that
underlies all the “accidents” of this world, but that even the latter relationship is reminiscent
of another kind of (transcendent) causality that Kant elsewhere discusses at great length.
The fanciful illustration provided by chaos theory, that of the Hong Kong butterfly
whose fluttering wings influence the weather in New York (see note 2, above), we can help
explain nonlocal causality in a way that reveals how little it corresponds to our ordinary
notion of phenomenal causality. Nonlocal causation is not based on some hidden chain of
unseen (but direct) causal connections, stretching (in this illustration) all the way from Hong
Kong to New York. Rather, the butterfly’s fluttering wings (which do have a classically
causal influence on the immediately surrounding pockets of air—an influence that dissipates
long before reaching New York!) may have a quantum-causal influence on the whole. This
whole (cf. the Kantian substance that undergirds all accidents), as it were, adjusts to the
fluttering of the butterfly’s wings; as a result, any other part of that same whole, whether it be
Kantian Causality and Quantum Quarks (II) - 14
in Kowloon, New York, or even on Mars, instantaneously readjusts to fit the new situation.
(Even if the butterfly were right there in Central Park, Newtonian science would regard it as
being in a separate, closed system of causal relations, irrelevant to the larger system
governing the weather.) As we have seen, this quantum causality does not contradict Kant’s
three analogies, provided they are taken together as three manifestations of one basic
principle—the principle Kant describes as “a necessary connection of perceptions” (Kant
1781/1787, 218). It merely changes the way we understand how the analogies inform our
scientific study of nature. Once this is understood, the suggestion that quantum physics is
actually more Kantian than the old physics becomes reasonable to maintain. For classical
physics was too dependent on an inflated view of the exclusive importance of local (Second
Analogy) causality. Physicists now know that, just as Kant argued, local (phenomenal)
causality is but one aspect of nature’s interconnected wholeness that goes far beyond the
conventional understanding of ordinary causal influence.
3. Kantian Quarks and the Need for a Transcendent (Noumenal) Grounding
By the tantalizing phrase, “Kantian quarks”, I intend to call attention to Kant’s
affirmation of what might be called several “bare facts” about our world—or, more precisely,
about the transcendental underpinnings of our perspectives on the world(s) we construct out
of immediate human experience. These bare facts seem to arise out of nowhere, like quantum
leaps: Kant claims their source (if any) lies so deeply concealed in human nature that, like the
quarks of contemporary quantum mechanics (see Part I of this series, §2), they can never be
directly observed in nature. The aspects of Kant’s System that could be described in this way
include in one sense, all the synthetic a priori principles defended in the Analytic of
Principles, especially the three analogies that have been the focus of our attention throughout
this study. In a statement not unlike Feynman’s confession of ignorance (quoted at the outset
of Part I, §2), Kant says (1781/1787, 756) “no concept given a priori…can, strictly speaking,
Kantian Causality and Quantum Quarks (II) - 15
be defined.” Kant is referring here specifically to the transcendental conditions for the
possibility of empirical knowledge: space, time, and the twelve categories are sui generis.
Like quarks, they have no component parts, as far as we know; they just are. His claim may
seem surprising, until we recall that he applies “a priori” only to what is rooted in reason
rather than in objects of knowledge; the empirical characteristics required for a definition can
be specified only for knowable objects. The “transcendental object” that lies at the base of
Kant’s Critical System is a “something in general = x” that is as elusive as the quark:
ultimately, it is grounded in reason itself. We should not be surprised, therefore, to find that,
just as scientists cannot observe a quark freely wandering around in nature, so also Kant
emphasizes that even the Critical philosopher cannot fathom reason’s depths in at least three
key instances.
Each of these fundamental building-blocks of the Critical System (highlighting, here,
one that functions most potently in each Critique) is directly related to one of Kant’s three
metaphysical ideas of reason. Functioning like a triplet of “Kantian quarks”, these aspects of
reason’s powers are:
1. The first Critique’s unity of apperception, with the transcendental conditions (space, time,
and the categories) flowing from it (cf. the idea of an immortal soul).
2. The second Critique’s moral law, with phenomenally undetermined choice flowing from
it (cf. the idea of freedom in the world).
3. The third Critique’s productive imagination, with beauty, sublimity, and natural
purposiveness flowing from it (cf. the idea of God).
Given Kant’s emphasis on causality in the Second Analogy, we might expect him to argue
that these basic, perspective-defining aspects of our ways of relating to the world are caused
by something. Like a Copenhagen interpreter explaining the experimental data relating to
quarks, however, he normally refuses to do so. Instead, he depicts them as concealed behind a
veil of darkness that human reason is unlikely ever to penetrate. However, Kant sometimes
Kantian Causality and Quantum Quarks (II) - 16
dares to describe the relationship between the two sides of this veil in terms of the
paradoxical notion of a “noumenal causality” that, in a manner strikingly similar to the way
Bohm describes quantum causality as operating, is nonlocal. In other words, Kant postulates
the existence of a hidden, qualitatively different level of reality that in some non-empirical
(i.e., noumenal) sense enables these fundamental “quarks” of transcendental philosophy
(particularly as expressed in terms of the metaphysical ideas of God, freedom, and
immortality) to be “causally” connected to what we experience at the empirical level, even
though we cannot locate any empirical (local) evidence of such a cause.
Kant’s surprising (but consistently repeated) claim, that three and only three ideas of
reason constitute the complete system of metaphysics, is grounded in a brief and rather
cryptic argument that has gone virtually unrecognized by commentators. In the Introduction to
the Dialectic (Kant 1781/1787, 364), he claims that a special principle guides all applications
of “reason in general”, from the logical perspective: “to find for the conditioned knowledge
obtained through the understanding the unconditioned whereby its unity is brought to
completion.” In the Aesthetic and Analytic Kant demonstrated that human knowledge arises
according to a three-step process: the “conditioned” (e.g., sensible input, in the form of
“appearances”) must come into contact with a “condition” (e.g., the categories), in order to
produce “the unity of the condition with the conditioned” (e.g., empirical judgments). He now
explains that reason’s special task in applying logic to such established knowledge is to
complete the whole process by locating something “unconditioned” that all empirical
knowledge points toward.
Near the beginning of the Dialectic’s Book I (Kant 1781/1787, 390-391), Kant
explains how this process gives rise to three ideas: human reason’s totalizing power forms
universal concepts through either a “relation to the subject” (i.e., the conditioning power
itself), or a “relation to objects” (i.e., the appearances so conditioned), or “the relation to all
things in general.” To reason about a thing necessarily involves forming an idea of that thing
Kantian Causality and Quantum Quarks (II) - 17
in its “totality”, whether or not we can actually apprehend such a totality empirically. The
abstract totality of all “conditions” residing in the conditioning subject gives rise to the idea
of a soul that, if genuinely total, must be conceived as immortal (existing throughout all
time). The abstract totality of everything that is or can be “conditioned” likewise gives us the
idea of a world of causally-conditioned events, and only in contrast to that world does the
idea of freedom from such causal conditions first arise. Finally, the abstract totality of the
“unity” of these two, and so also of “all things”, leads us directly to the idea of God. This
much-neglected passage explains why every human culture that manages to obtain knowledge
also naturally generates the ideas of God, freedom, and immortality.
An aspect of Kant’s argument in the Dialectic that is often not taken very seriously is
that these three ideas of reason properly function as a guide for science in its ultimate task of
unifying our knowledge of nature. Even though God, freedom, and immortality are
completely unknowable from a purely phenomenal standpoint and therefore play no proper
role in the construction of the detailed knowledge of empirical science, they nevertheless have
a legitimate function as regulative ideas that can guide scientists to a more complete
understanding of nature. A careful reading of Bohm’s work reveals that his attempt to ground
quantum causality in a theory of the implicate order leads him to employ each of these
metaphysical ideas. As the philosophical side of Bohm’s theory is somewhat lacking in
systematic neatness, it can only benefit by tracing its parallels to Kant’s more systematic
account of reason’s unity. That such a comparison is legitimate is suggested by Bohm
himself, when he states at the outset of Wholeness and the Implicate Order that the position
he defends in this book, that “thought itself…[is] part of reality as a whole” (Bohm 1980, ix),
has certain resonances with Kant (5-6). In a passage strikingly reminiscent of Kant’s
perspectival language, Bohm says that, once we view wholeness as including consciousness
within it, we will understand why our fragmented theories are all nothing more than “ways of
looking” (7,9)—i.e., perspectives.
Kantian Causality and Quantum Quarks (II) - 18
Bohm describes the “holomovement”,9 the background wholeness that gives rise to
the flowing interrelation of enfolding and unfolding between the implicate order and the
explicate order, in terms that leave little doubt that he is referring here to what Kant describes
as the noumenal world. He says, for example (Bohm 1980, 204): “not only is immediate
experience best understood in terms of the implicate order, but…the actual structure, function
and activity of thought is in the implicate order.” Thus, as physics comes closer and closer to
examining the background wholeness that informs the explicate order, “the whole notion of
space and time as we know it would fade out, into something that is at present unspecifiable”
(190); time and space are “secondary”, being “derived from a higher-dimensional ground”
(211). Kant, of course, says much the same thing in the Transcendental Aesthetic, when he
argues that space and time are not applicable to things in themselves, but are forms of
intuition that the mind imposes onto the phenomenal world. Just as Kant’s unity of
apperception ultimately transcends the empirical world, yet gives rise to the phenomenon of
human consciousness, Bohm says “consciousness…is to be comprehended in terms of the
implicate order” (196). We learn to think and act as if the explicate order (i.e., the
phenomenal world) is primary; yet the fact that “the manifest static and fragmented content of
consciousness is experienced as the very basis of reality” is “an illusion” (206). Both life (and
with it, consciousness) and inanimate matter have their essential grounding in the
holomovement (194-195).
Although Bohm says comparatively little about freedom and God, he does at least hint
that they play just as important a role in the implicate order as does the idea of the soul,
9Bohm’s
essential metaphysical claim is: “what is is movement” (Bohm 1980, 203).
Movement also looms large in Kant’s understanding of nature, including his first published
work, Thoughts on the True Estimation of Living Forces (1747), and his more mature
philosophy of science, as expounded in Metaphysical Foundations of Natural Science (1786).
Kantian Causality and Quantum Quarks (II) - 19
insofar as the latter is implied by the claim that consciousness is grounded in the
holomovement. For example, he says Heisenberg’s uncertainty principle does not necessarily
imply a lack of determinate causation (Bohm 1980, 105), but “should be regarded as basically
an expression of the incomplete degree of self-determination characteristic of all entities that
can be defined in the quantum-mechanical level.” This suggests that, by replacing
indeterminacy with the new principle of quantum causality, Bohm is not imposing local
(phenomenal) causality onto the quantum world, but is claiming that events at that level can
be regarded as fully self-determined only if we consider their relation to the underlying whole.
This is directly parallel to Kant’s portrayal of free choice as an act of self-determination that
influences the phenomenal world through an underlying noumenal causality that is
undetectable through phenomenal observation alone. Likewise, Bohm notes at one point
(197) that Descartes’ appeal to God fulfills essentially the same function as his own theory of
the implicate order.
Bohm leaves little doubt that his focus on wholeness goes beyond the phenomena of
science as such and touches upon the noumena of philosophy when he laments (1980, 20) that
our modern approaches to empirical knowledge in general and to science in particular tend to
forget the classical way of thinking, whereby “awareness of the inner reasons of things was
seen as the essential key to a healthy, happy, harmonious life.” This focus on “the inner
reasons of things” is precisely what Kant attempts to preserve by his emphasis on the
noumenal grounding of the phenomenal world—a grounding that has the twin implications of
rendering the Copenhagen interpretation’s focus on phenomena entirely acceptable to
“followers of Kant”, as d’Espagnat 1987 (154) points out, and of providing a philosophical
justification for the Bohmian view that the wholeness out of which quantum causality
emerges is an “independent reality [that] is—and will remain—veiled to us” (166). What has
made Kant’s position on the noumenal world so difficult for interpreters to grasp is that he
tends to present this “inner reason” as being paradoxical, and thus “quark-like”, whenever it
Kantian Causality and Quantum Quarks (II) - 20
manifests itself in the phenomenal world. Let us therefore conclude this study by examining
this aspect of Kant’s system more closely.
4. Kant’s Three Metaphysical Quarks as Noumenal Correlates of Empirical Knowledge
Recalling that Kant sees a form of noumenal causality operating in and through each
of the three ideas of reason enables us to discover an interesting correlation between Kant’s
arguments regarding the necessary incompleteness of empirical science (as advanced mainly
in the Transcendental Dialectic) and key differences between the various interpretations of
quantum mechanics. The Copenhagen interpretation assumes the idea of freedom to operate at
the quantum level. Since freedom conflicts with local causality, those affirming this way of
interpreting the results of quantum mechanical experiments tend to view it as contradicting
Kant’s Second Analogy. The various types of Modal and “Many Worlds” interpretations can
be regarded as appealing (implicitly) to the metaphysical idea of immortality, in the sense that
they metaphorically totalize the conditions of this life, depicting the wider universe (the
universe as it is in itself, beyond our limited, phenomenal view of it) as one that consists of
many (indeed, all possible) lives. The Bohmian interpretation, as we have seen, appeals to all
three ideas, but relies most fully (at least implicitly) on the idea of God, insofar as God just is
the wholeness that constitutes the ultimate source of noumenal causality.
These correlations are admittedly programmatic and should be regarded as hypotheses
worthy of further examination rather than as conclusions that have been formally established.
Having briefly highlighted the possibility of correlating Kant’s three ideas of reason with
these approaches to interpreting quantum mechanics, let us now examine in turn each of the
three above-mentioned forms of nonlocal (noumenal) causality that emerge from Kant’s triad
of transcendental ideas: the unity of apperception, the moral law, and the productive
imagination. The first of Kant’s three metaphysical quarks, the idea of the immortal soul,
corresponds to what Kant calls “transcendental apperception”, an absolutely necessary, “pure
Kantian Causality and Quantum Quarks (II) - 21
original unchangeable consciousness”, with “numerical unity” (Kant 1781/1787, A107). All
the basic, transcendental conditions for the possibility of experience (space, time, and the
categories) must be related to this focal point of my self-consciousness in order for me to
recognize any experience as “mine” (e.g., 110,145,151). Paradoxically, we cannot see or
experience the unity of apperception itself, but only its empirical effects. As such, it is the
archetype of all a priori concepts, just as physicists postulate quarks as the building blocks of
all physical objects. As Kant argues toward the end of the Analytic of the first Critique, all
such concepts are completely unintelligible if we try to understand them apart from their
influence on the empirical world:
Although all these principles…are generated in the mind completely a priori, they
would mean nothing, were we not always able to present their meaning in
appearances, that is, in empirical objects. We therefore demand that a bare concept be
made sensible… Otherwise the concept would…be without sense, that is, without
meaning….
That this is also the case with all categories and the principles derived from
them, appears from the following consideration. We cannot define any one of them in
any real fashion…without at once descending to the conditions of sensibility… For if
this condition be removed, all meaning, that is, relation to the object, falls away; and
we cannot through any example make comprehensible to ourselves what sort of a
thing is to be meant by such a concept. (Kant, 1781/1787, 299-300)
Thus the analogies and other principles, as well as our sense of “I” that constitutes their
ground, can be known by their effects; but like quarks, they cannot be directly observed as
objects. When we nevertheless allow reason to direct our thinking beyond the sensible world,
in search of the unconditioned object towards which such concepts point us, our empirical “I”
suggests the idea of a noumenal self, a substantial soul with an immortal existence.
Interestingly, the Standard Model of quarks and leptons bears a structural resemblance
Kantian Causality and Quantum Quarks (II) - 22
to Kant’s table of categories. In both cases, the most general division is twofold: between
quarks and leptons on the one hand and between mathematical and dynamical categories on
the other. Within each division we find another twofold opposition: between positively and
negatively charged particles and between extensive and intensive categories. Each of the
resulting four types of particle/category can manifest itself in three “generations” or
“moments”, making a total of twelve. Is this parallelism just a coincidence? Kant’s
Copernican Perspective suggests it may not be: the main point of the “clue” Kant provides in
his so-called “metaphysical deduction” of the categories (Kant 1781/1787, 91-116) is that
patterns of twelve arise naturally out of the reciprocal analytic and synthetic forms of thinking
that our mind inevitably uses to interpret the world; we should therefore hardly be surprised
when our theories of nature (themselves a result of human conceptualization) conform to such
patterns. While most interpreters of Kant have downplayed, if not openly mocked, his love of
such architectonic distinctions, Kant himself regarded them with utmost sincerity as the key
to the success of the whole Critical enterprise.10
Anyone who does not share Kant’s explicit fondness for architectonic parallels will be
quick to point out that the twelvefold organization of subnuclear particles described by the
Standard Model of quantum mechanics (see Part I, §2) applies only to fermions and that the
picture begins to look significantly messier when the other particles present in the nucleus of
an atom are taken into consideration. The force-mediating particles (photons, the three guage
bosons, and the eight gluons) do not follow such a neat pattern, to say nothing of the even
more anamolous Higgs boson. A thoroughgoing response to this objection from an
architectonic point of view would be far too complex to attempt here. Instead, we can respond
merely by pointing out that the six quarks and six leptons are generally recognized as basic,
while the other particles all arise out of various combinations of interactions between these
10{Text
and references deleted}.
Kantian Causality and Quantum Quarks (II) - 23
twelve. Similarly, Kant makes room in his epistemology for a variety of mental functions,
such as schematism, that mediate between the more basic faculties. Architectonic thinking
does not require all concepts in a system to fit perfectly into the neat, twelvefold pattern that
the mind naturally tends to impose upon objects; the pattern appears primarily in relation to
the most basic, system-grounding distinctions.
As we saw in Part I of this series, regarding the principle of causality as a necessary
feature of the empirical world as we experience it does not compel us (i.e., we human beings,
whose thinking, or “noumenal”, nature is fundamentally free) to interpret our experience
causally at all times. Instead, we are free to impose other formal determining conditions onto
our experience, including what Kant calls the “moral law”. Doing this does not require us to
deny the truth or applicability of a scientific explanation of the same experience; we are
merely giving an alternative interpretation that exists on another “plane” (or as Kant puts it, in
another “realm”, the noumenal). We interpret the same experience in both cases; the results
differ because we have adopted a new set of conditioning principles, based on an alternative
standpoint. This standpoint is grounded in the second Kantian quark, the idea of freedom.
Kant emphasizes that the moral law “is not an empirical fact but the sole fact of pure
reason, which by it proclaims itself as originating law” (Kant 1788, 31). This “fact”, however,
is unlike anything we would normally regard as fact, for we can neither empirically observe
nor logically prove its existence. Yet, Kant assures us, it is “not empty” (1788, 6), but
“provides reality to a supersensible object of the category of causality, i.e., to freedom.” Like
physicists with their quarks, moral agents are impelled to take freedom and the moral law as
givens when we look at the evidence observed in our moral life. The moral law is closely
related to what Kant calls the “good will”. As Kant says in the famous opening sentence of
the First Section of Groundwork of the Metaphysics of Morals (Kant 1785, 393): “Nothing in
the world—indeed nothing even beyond the world—can possibly be conceived which could
be called good without qualification except a good will.” Freedom is the mysterious,
Kantian Causality and Quantum Quarks (II) - 24
unconditioned root of the moral law, so moral beings are just as bound to formulate the idea
of freedom as we are, in our nature as self-conscious (apperceptive) beings, to conceive the
idea of the soul.
Kant’s willingness to allow phenomenal causality to coexist with a radically different
kind of causality, the “causality” of freedom (a cause of events in the empirical world that is,
as such, entirely indeterminate from the empirical perspective) suggests that he would have
no problem accepting Bohm’s quantum causality as fully compatible with the ordinary
causality we perceive, in conformity to the Second Analogy. However, this argument does not
justify us in drawing any firm conclusions about how such apparently indeterminate
“causality” operates, from a phenomenal (scientific) perspective. When Kant defends such
claims about human freedom (as, for example, in Section 3 of Kant 1785), he is careful to
emphasize that we remain ignorant of the details of how the mechanism of noumenal
causality works. This might seem to invalidate the metaphorical relationship I am proposing,
between noumenal causality and quantum causality, since the latter obviously does seek to
draw scientifically valid conclusions. However, this objection is overcome once we realize
that quantum theory requires us to adopt rules of thinking that are diametrically opposed (at
certain points) to the rules of conventional logic. As we saw in §2 of Part I, quantum theorists
are often the first to admit that we cannot understand how quantum events actually take place;
all we can affirm is that they happen. This is virtually identical to Kant’s position on
noumenal causality: we can (and do) know that freedom is a fact of practical reason without
understanding the mechanism of how our choices actually interact with phenomenal reality.
Although they could be regarded as two applications of one and the same conception, I have
here presented these two approaches to causality more cautiously, as having a metaphorical
relationship.
Just as the first two Kantian “quarks” correspond mainly to the first and second
Critiques, respectively, the third corresponds mainly to the third Critique, where Kant
Kantian Causality and Quantum Quarks (II) - 25
examines the transcendental underpinnings of our experiences of beauty, sublimity, and
natural purposiveness. The mental power that makes such experiences possible, according to
Kant, is imagination. In the first Critique Kant distinguishes between reproductive
imagination (memory) and the transcendental function of productive imagination (Kant
1781/1787, A118). The latter, he claims, is the power that generates the “schematism” of the
categories, whereby these pure concepts are made amenable to intuitions, enabling the
principles to be applied so that empirical knowledge can arise. Although he has no trouble
detecting its effects, Kant calls imagination itself (Kant 1781/1787, 180-1) “an art concealed
in the depths of the human soul, whose real modes of activity nature is hardly likely ever to
allow us to discover, and to have open to our gaze.” When imagination comes into its own
arena in the third Critique, the situation hardly improves. For, although Kant offers us
plentiful insights into the nature of beauty, sublimity, and natural purposiveness, he frequently
appeals to paradoxical (quark-like) notions, such as “subjective universality” and
“purposiveness without a purpose” (1790, 213-216,236). Without straying into a detailed
discussion of these obscure corners of the Critical edifice, we may merely take note of Kant’s
claim that, when we allow reason to follow this power of productive imagination to its
unconditioned source, the idea of God, as the synthesis of the immortal soul and its freedom
from the world, inevitably arises.11
Identifying these Kantian quarks highlights how Kant’s overall method of thinking is
actually closer to modern physics than to classical physics. Far from proving Kant’s System
11Buchdahl
1965, 204, is one of the few interpreters who recognizes that ultimately Kant’s
“archetype” for the regulative unity of science is “located in the image of a God.” Indeed, he
even claims the purpose of the first Critique’s limitation of knowledge to phenomena “is to
make possible the creative development of ‘nature’ in these systematic constructions, and
ultimately, the archetypes of religious experience.”
Kantian Causality and Quantum Quarks (II) - 26
to be mistaken, the revolutionary nature of quantum physics exhibits parallels to it, even
though we cannot expect Kant himself to have foreseen the specific way modern physics has
developed. The world of classical science would regard it as a gross blunder to postulate
unknown and unknowable realities that are somehow fundamentally altered by the very act of
observing them. But now, with the advent of quantum mechanics, such a viewpoint has come
to seem plausible. As we have seen, this just is the Kantian perspective on science, when the
latter is understood in its full systematic context. To view the human mind as “quark-like” is
a direct implication of Kant’s transcendental idealism. Passing from what is unknowable
because of being infinitely close to us to what is unknowable because of being infinitely far
away, we could also compare Kant’s conception of reason’s ideas to a kind of intellectual
“black hole”: an unobservable reference point, detectable only because of how it affects other
concepts, drawing everything to itself, yet excluding everything but itself from its inner core
(cf. note 4, above).
Like all metaphors, such comparisons have only limited application. Whereas
quantum theorists believe quarks join with other particles to constitute the substratum of
empirical reality (underlying and unifying the diversity of the whole material world as we
observe it), these three Kantian “quarks” underlie and unify the diversity of all human
experience in a way that transcends the physical. Many physicists refer to quantum quarks as
physical objects that exist in nature; Kantian quarks, by contrast, are metaphysical ideas of
reason that constitute the noumenal substratum of our rationality. If scientists eventually
decide quarks are made out of some still smaller sub-subatomic particles, then this metaphor
would apply instead to those newly postulated entities. For the comparison being made in this
concluding section is not between these three building-blocks of Kant’s System and quarks as
such, but between the way Kant viewed the former and the way contemporary quantum
theorists view the latter.
In conclusion, let us draw together the key perspectival distinctions that have helped
Kantian Causality and Quantum Quarks (II) - 27
us demonstrate the compatibility between Kant’s philosophical revolution and the scientific
revolution of quantum mechanics. That the nature and function of light has cropped up on
several occasions is more than just an interesting coincidence. For light, more than any other
natural phenomenon, makes perspectives possible. A perspective is a way of seeing
something; as insight into reason’s mode of operation, it is directly analogous to the sight that
is possible only when we are in the presence of light. Light manifests itself on three levels,
corresponding to three perspectives, or “worlds”, depicted in Figure 1 of Part I. Although
observation seems unlimited in the ordinary world, we noted in Part I (§4) that the physical
properties of light define upper and lower limits of observation. Einstein demonstrated how
otherwise definite space-time relations become relative at velocities approaching the speed of
light. Thus light functions for physics (especially astrophysics) as the transcendental perspective functions for Kant’s System. Planck’s constant, by contrast, determines the smallest
possible quantum of energy; beyond it, we can only infer the presence of hypothetical objects
such as quarks. The submicroscopic world it demarcates is, as quantum mechanics
demonstrates, highly irregular. Yet neither of these quasi-transcendent perspectives on light
denies the reality of the ordinary, empirical light that makes our phenomenal world visible.
Newton was right to assume everything that appears in this light comes under predictable,
causal laws, yet Einstein was also right to view the whole realm where these laws apply as
itself relative to a higher perspective that describes the general physics of the natural world
more accurately; likewise, quantum mechanics accurately describes the deep structure of the
world’s unobservable substratum in a starkly contrasting way, because it adopts yet another
perspective on what this world is. Table 2 shows the correspondences between these three
perspectives on light, the three “worlds” shown in Figure 1 of Part I, Kant’s three analogies,
and the three Kantian quarks (with their corresponding metaphysical ideas) outlined here in
the last half of Part II.
Kantian Causality and Quantum Quarks (II) - 28
Table 2: Perspectival Distinctions in Kant’s Foundation for Modern Science
scientific “world”
(focal perspective)
the microscopic,
quantum world
(hypothetical)
the observable,
ordinary world
(empirical)
the macroscopic,
astral world
(transcendental)
Kant’s Analogy
Kantian “quark”
(corresponding idea)
character of light
(physical limit)
unity of apperception
unpredictable
First Analogy:
permanent substance (immortality of the soul) (Planck’s constant)
Second Analogy:
cause and effect
the moral law
absolutely predictable
(freedom in the world) (apparently none)
Third Analogy:
productive imagination relatively predictable
reciprocity/coexistence
(God)
(speed of light)
Two implications follow from the perspectival correspondence between the Kantian
noumenal realm and the hypothetical realm of quarks. Most obviously, interpreters can no
longer merely dismiss Kant’s philosophy as irrelevant to the cutting edge of modern physics.
Second, a new question is raised, regarding the philosophical status of quantum mechanics:
Does this metaphorical connection imply that quantum theory (i.e., the theoretical
assumptions and interpretive superstructure that support the experimental science of quantum
mechanics) is a form of metaphysics, rather than itself being an independent branch of
physics? Kant was adamant in denying the legitimacy of an approach to physics such as that
of Leibniz, whereby self-sufficient monads interact in a transcendent realm not open to our
direct observation. Would Kant have no more patience with quantum theory than he had with
Leibniz? I believe the answer is no; the difference is that Leibniz believed his admittedly
metaphysical principles could provide insight into the physical world through pure thought.
Quantum theory faces us with a very different situation: physicists whose attempts to observe
the empirical world at the deepest possible physical levels have led them to the very boundary
of that world have drawn inferences regarding what lies beyond that boundary of observation.
The contribution that Kant’s position can make to the debate is not to question the validity of
Kantian Causality and Quantum Quarks (II) - 29
quantum mechanical experiments, but to explain humbly why science has encountered this
metaphysical boundary and what to do about it. For Kant, speculative metaphysics is the
realm of “dialectical illusion”, where reason naturally leads us simultaneously to affirm
opposing truth-claims. Is it any wonder, therefore, that quantum mechanics in all of its
interpretations openly embraces paradoxical claims when it seeks to explain the behavior of
particles that lie behind the metaphysically necessary but empirically determined quantum
boundary of possible observation?
Can one be a Kantian and adhere to the tenets of quantum theory? This pair of essays
has been a sustained explanation of how this question can be answered affirmatively: a
perspectival interpretation of Kant’s philosophy shows not only how the further advances of
science need not conflict with Kant’s transcendental principles, but also how the post-Kantian
sciences of the very small and of the very large naturally emerged on the basis of this very
philosophical grounding. Those who regard these approaches as clashing have tended to
conclude that we must reject Kant’s claim that causality is a necessary and universal principle
for all empirical knowledge. I have argued that quantum theory questions this principle only
as it applies to a realm beyond what Kant would have regarded as strictly “phenomenal”, and
that Kant himself viewed the noumenal realm as being quark-like in relation to the
phenomenal. No essential conflict remains between these two approaches, once we recognize
that both affirm the applicability of causality to the realm of observable appearances, and both
affirm that it can at best have a dialectical and metaphorical relationship to the unobservable
realm that lies beyond our grasp.12
12{Text
deleted for blind review}.
Kantian Causality and Quantum Quarks (II) - 30
References
Aspect, Alain, et al. (1982), “Experimental Realization of Einstein-Podolsky-Rosen-Bohm
Gedankenexperiment: A New Violation of Bell’s Inequalities”, Physics Review
Letters 49, 91.
Aspect, Alain (2007), “To be or not to be local”, Nature 446 (April): 866.
Bell, J.S. (1964), “On the Einstein-Podolsky-Rosen paradox”, Physics 1: 195-200.
Bohm, David (1951), Quantum Theory. Englewood Cliffs: Prentice-Hall.
——— (1980), Wholeness and the Implicate Order. London: Ark.
——— (1987), “Hidden variables and the implicate order”, in Hiley and Peat (1987), 33-45.
Buchdahl, Gerd (1965), “Causality, Causal Laws and Scientific Theory in the Philosophy of
Kant”, British Journal for the Philosophy of Science 16: 187-208.
Cushing, James (1996), “The causal quantum theory program”, in J.T. Cushing, A. Fine & S.
Goldstein (eds.), Bohmian Mechanics and Quantum Theory. Dordrecht: Kluwer, 1-19.
Daumer, M., et al. (1997), “Naive Realism About Operators” , Erkenntnis 45: 379-397.
d’Espagnat, Bernard (1987), “Meaning and being in contemporary physics”, in Hiley and Peat
(1987), 151-168.
Forrest, Peter (1988), Quantum Mechanics. Oxford: Blackwell.
Friedman, Michael (1992), Kant and the Exact Sciences. Cambridge: Harvard.
Goldstein, Sheldon (2006), “Bohmian Mechanics”, Stanford Encyclopedia of Philosophy,
http://plato.stanford.edu/entries/qm-bohm/.
Gröblacher, Simon, et. al. (2007), “An experimental test of non-local realism”, Nature 446
(April): 871.
Hiley, B.J., and F. David Peat, eds. (1987), Quantum Implications. London: Routledge.
Holmes, Eugene C. (1955), “The Kantian Views on Space and Time Reevaluated”,
Philosophy and Phenomenological Research 16.2: 240-244.
Kantian Causality and Quantum Quarks (II) - 31
Hughes, R.I.G. (1989), The Structure and Interpretation of Quantum Mechanics. Cambridge,:
Harvard.
Kant, Immanuel ([1781/1787] 1929), Critique of Pure Reason, tr. Norman Kemp Smith.
London: Macmillan. References cite the second “B” edition, unless prefaced by “A”.
——— ([1783] 1950), Prolegomena to Any Future Metaphysics, tr. L.W. Beck. New York:
Bobbs-Merrill.
——— ([1785] 1949), Foundations of the Metaphysics of Morals, tr. L.W. Beck. Chicago:
UCP.
——— ([1788] 1950), Critique of Practical Reason, tr. L.W. Beck. Indianapolis: BobbsMerrill.
——— ([1790] 1952), Critique of Judgement, tr. James Meredith. Oxford: OUP.
Reichenbach, Hans (1944), Philosophic Foundations of Quantum Mechanics. Berkeley: UCP.
Salmon, Wesley (1998), Causality and Explanation. New York: OUP.
Smith, Henrik (1991), Introduction to Quantum Mechanics. Singapore: World Scientific.
Vervoort, L. (2000), “Bell’s theorem and non-linear systems”, Europhysics Letters 50.2 (15
April): 142-147.
Wieland-Burston, Joanne (1992), Chaos and Order in the World of the Psyche. New York:
Routledge.