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Peter CollinsPeter Collins is from Ireland. He retired recently from lecturing in Economics at the Dublin Institute of Technology. Over the past 50 years he has become increasingly convinced that a truly seismic shift in understanding with respect to Mathematics and its related sciences is now urgently required in our culture. In this context, these present articles convey a brief summary of some of his recent findings with respect to the utterly unexpected nature of the number system.


Part III - Quantum Paradox

Peter Collins

Problems of interpretation with respect to quantum behaviour arise from attempting to apply linear reason that is consistent with the middle levels of the psychological spectrum to lower levels of physical reality (where it is inappropriate). Solving this problem requires that a complementary relationship be maintained as between the understanding of “higher” psychological and corresponding behaviour of “lower” physical stages.


We saw in a previous article how Einstein's special theory of relativity arose out of an unsolved problem regarding the speed of light.

Another unresolved problem relating to electromagnetic radiation, known as the black body problem, eventually gave rise to a second major revolution i.e. quantum physics.

According to the understanding of radiation at the time, energy was emitted in continuous waves. Because it was considered that there was no limit on the types of waves that could be envisaged, the overall radiation emitted for example within an oven would be infinite (which clearly was untenable).

Eventually through an inspired suggestion by Planck the problem was satisfactorily resolved by considering that radiation is emitted in discrete packets or quanta (directly related to the frequency of the radiation in question). Since the frequency was inversely related to wavelength, this therefore placed strict limits on the number of waves that could be considered.

Because of the conventional approach viewing energy as a wave, Planck was initially reluctant to fully accept the physical implications of his finding, interpreting it more in mathematical terms (the exact physical implications of which were yet to be understood).

However Einstein in his 1905 article used the particle notion of light in providing a compelling explanation for what became known as the photoelectric effect. By viewing light as a stream of discrete quanta he was able to successfully explain its observed impact on electrons.

So Einstein was initially one of the great pioneers of quantum physics (for which he was awarded the Nobel Prize in 1922). However he gradually became deeply disillusioned regarding its philosophical implications, which conflicted strongly with his deterministic view of reality. Thus he always tended to view quantum mechanics as an incomplete theory and incompatible with his belief in precise cause and effect relationships with respect to physical phenomena.

However though Einstein gradually dissented from quantum mechanics, others sought to systematise the new theory more fully. Among these were Erwin Schrödinger who formulated the key quantum wave equation; and Niels Bohr and Werner Heisenberg were particularly adept in understanding its philosophical implications.

At a practical level quantum mechanics - despite its strange findings that conflict with common sense - has proven remarkably successful and is responsible for many of the great technical developments of the late 20th century.

However though very successful in its own field, it is incompatible with relativity theory.

Thus, in this sense at least Einstein has been right in regarding it as an incomplete theory.

In what follows I will discuss some key issues with respect to quantum mechanics, once again with a view to providing an integral interpretation. Indeed a key finding that will quickly emerge is that the very reason why so many of its findings appear so strange is precisely because of the lack of an appropriate integral scientific framework.

So, we will look in this article at 1) The I-it relationship and 2) Wave-particle duality. 3) The Uncertainty principle 4) Schrödinger's cat 5) Feynman's view of electron behaviour and 6) The EPR paradox.

The I-it Relationship

It may be helpful with respect to what follows to highlight the general problem that underlines qualitative interpretation of quantum mechanical relationships.

Appropriate scientific understanding of physical relationships requires that the method of psychological interpretation used be complementary with the observed physical phenomena in question.

Conventional macro interpretation of the world corresponds, as we have seen, with the cognitive understanding that typifies the middle band of the spectrum. In this sense the qualitative problem of interpretation does not occur, as the middle is - by definition - complementary with itself. [1]

However when we go lower on the physical spectrum to probe the sub-atomic behaviour of matter, a qualitative problem immediately arises with respect to conventional scientific interpretation, for here we are using a middle band of understanding to interpret a lower level of nature.

So for appropriate qualitative interpretation, we require that a complementary “higher” band of (psychological) understanding be used to interpret the corresponding “lower” band of (physical) nature.

The simplest version of this higher band (corresponding to the h1 stage) is - what I have referred to as - the integral 1 approach which is mainly suited for correct dynamic interpretation of the relationship as between internal and external aspects of understanding. So this is central therefore in appreciating the nature of the I-it problem in quantum mechanics.

It is now accepted that measurement with respect to certain sub-atomic characteristics cannot be carried out in a merely objective manner. For example as Heisenberg's uncertainty principle demonstrates, we can attempt to measure the position of a particle such as an electron or its momentum, but not both simultaneously. Therefore what is objectively measured intimately depends on the subjective choice of what to measure (and has no strict meaning outside this context).

The full implications of this finding are immense as it undermines the very notion of independently existing objects (a key assumption of conventional science).

Therefore in strict terms, physical reality does not exist in any meaningful sense but rather a dynamic interactive reality that is both physical and psychological.

Indeed, this is readily admitted by some key practitioners in the area. For example John Wheeler in speaking about this process,

“To describe what has happened one has to cross out the old word “observer” and put in its place the new word “participator”. In some strange sense the universe is a participatory universe.”

The realisation that one participates in creating the universe is a direct product however of the spiritually illuminated understanding that characterises the h1 (psychic/subtle) level. And it is the refined bi-directional understanding as between (internal) observer and (external) observed that is the basis of integral 1 understanding. This in turn provides the appropriate qualitative means for the interpretation of such quantum mechanical relationships.

Indeed this participatory relationship as between observer and observed e.g. in measuring the position of an electron can - through use of such h1 understanding - be given a more compelling explanation.

Once again the external aspect of any object such as an electron has no meaning in experience independent of the - relatively - internal mental perception of electron.

So the actual experience of any object necessarily involves the dynamic interaction of both external and internal aspects of understanding.

As we have seen, unambiguous appreciation - with respect to either aspect - requires that the degree of interaction as between opposite aspects (internal and external) be so severely limited that they can be considered for practical purposes as independent.

In this way the (internal) mental interpretation will appear to directly correspond with the (external) observed reality. This assumption, that characterises the conventional scientific approach, works well as an approximation at the readily visible macro level of reality. Here objects assume a sufficiently rigid identity that they can for practical purposes be considered as independent of the observer. Likewise the interpretative model of conventional science is fully in keeping with this assumption where again dynamic interaction as between opposite polarities (though implicitly necessary) is not formally recognised.

However when we go to the “lower” sub-atomic level of reality, dynamic interactivity as between “object” particles greatly increases where they now exhibit phenomenal manifestations only in a - relatively - independent sense.

Because of the increased interactivity as energy, the interdependence of opposite aspects is so significant that it cannot be ignored, acting now to continually change the phenomenal characteristics that arise.

Likewise at the “higher” spiritual level of reality, dynamic interactivity in terms of the psychological experience of “objects” greatly increases. Again we can identify dual characteristics of these “objects” (in a relatively independent sense). However the degree of interdependence is now so considerable, through spiritual energy as intuition. that it continually changes the phenomena that we observe.

So the secret to appropriate interpretation is to match the “lower” level of physical with the corresponding “higher” level of spiritual reality (with which it is complementary). [2]

However there is a significant additional element to interpretation which conventional science has great difficulty in accepting. Once again conventional scientific observation (and corresponding interpretation) is based on the assumption of independent reference frames for both (external) objects observed and (internal) mental constructs used in interpretation. This approach is consistent therefore with a merely dualistic understanding of scientific phenomena.

However once we accept the interdependence of opposite reference frames, then a vital new nondual ingredient is necessarily involved. This is easy to appreciate at the “higher” level as spiritual emptiness (which then interacts with phenomena as intuitive insight). So from this perspective, phenomena keep changing in experience through being - literally transformed - in a new spiritual light.

The clear implication of this is that a corresponding nondual element must also be admitted at the “lower” level of sub-atomic physical processes for correct interpretation to take place. Here the physical phenomena keep changing through the interaction with energy. However this energy itself is inherently of an empty nondual nature.

Thus we cannot properly interpret the dynamic interaction of phenomena without incorporating both dual and nondual modes of understanding.

This helps to demonstrate clearly that reality strictly has no meaning independent of the interpretations we use in experiencing such reality.

Thus at the conventional macro level of science, the world appears in dualistic terms to be composed of independent object phenomena (that in turn conform to a linear rational mode of cognitive interpretation).

However, now at the integral 1 level, science combines both dual and nondual aspects.

Object phenomena now have a merely relative (provisional) dual existence through being related to a fundamental nondual empty ground (as the potential for all existence).

This (external) view of reality is matched in turn by corresponding (internal) interpretation. Here psychological experience of phenomena continually changes through being related to an absolute nondual spiritual ground of reality. So now rather than just rational linear interpretation, we have a new refined form of reason that continually interacts with spiritual intuition (both of which are explicitly incorporated in understanding).

Contemporary physics - while attempting to properly accommodate the implications of quantum mechanics - still shows extreme reluctance to consider radical new frameworks of interpretation (that can properly accommodate its findings). Even with later developments in particle physics such as string theory, the attempt is still being made to fit its findings to the accepted scientific paradigm (which is quite inadequate for the purpose).

So “object” phenomena have physical and psychological aspects that are interdependent. And because all holons have - by definition - both internal and external aspects that dynamically interact, this is true at all levels of reality (and not just human experience).

There are other important consequences for science arising from this realisation.

Physics is accustomed to dealing with objects as impersonal matter (which in turn corresponds with the accepted rational mode of interpretation).

However all object phenomena have both personal and impersonal characteristics (which dynamically interact in experience). On reflection, one can perhaps appreciate the huge split in consciousness that is brought about through adopting a scientific approach that is not properly integral!

For example a scientist observing a natural phenomenon such as a rainbow will understand it in a merely impersonal manner (corresponding to accepted rational interpretation).

However the same phenomenon has also an important personal meaning that would perhaps be better communicated by an artist or poet.

Thus the task for science - while preserving its distinct cognitive stance - is to find a means of adequately incorporating both personal and impersonal aspects of phenomena in its interpretations.

And inevitably there is likewise a collective social aspect to phenomena, which is demonstrated very well by the behaviour of sub-atomic particles.

Indeed there is considerable irony in the fact that from a valid integral perspective, quantum physics should perhaps be best understood as a social science with the distinction as between animate and non-animate matter ultimately untenable.

Wave-Particle Duality

The linear nature of science is highlighted by the attempt to understand objects in unambiguous terms. So for example, Newton suggested that light was composed of particles (corpuscles).

However other physicists such as Huygens believed however that it was composed of waves. Debate therefore raged as to which view was correct until Thomas Young in the early 19th century devised an ingenious experiment to experimentally show that light indeed has a wave pattern. So the wave theory of light thereby became the accepted orthodoxy.

However, early developments with quantum mechanics a century later restored the equal validity of the particle view.

Einstein for example boldly re-affirmed the particle nature of light in his path breaking paper in 1905 on the photoelectric effect.

Gradually, in what Niels Bohr termed wave-particle duality, it became accepted that light has indeed both wave and particle aspects with the detection of one aspect in any experimental context thereby ruling out its complementary partner. Thus we can reveal either the particle or wave aspect of light through experiment (but not both simultaneously). So, these two aspects are only independent of each other in a relative sense with the wave also containing particle and the particle containing wave aspects respectively.

Though initial work with respect to wave and particle aspects was largely confined to the nature of light, De Broglie - using Einstein's famous energy equation - was able to extend this complementarity to other sub-atomic particles such as the electron.

It has since been shown that even object phenomena at the everyday macro level of reality also have both wave and particle aspects. However because the wavelength is typically extremely small for such objects, as a working approximation it can be ignored altogether. Thus, though objects therefore in conventional terms appear to have a distinct unambiguous location in space (with a seeming independent existence) this breaks down badly at the sub-atomic level.

A slight modification of Young's original double-slit experiment can be used to demonstrate the utterly mysterious nature of quantum reality. If we keep one slit closed and pass light through the open slit at a screen (behind both slits), the particle aspect of light will be confirmed with photons lining up in an expected straight line behind the slit.

Then when we keep the two slits open and pass the light through both, light will appear as waves behind the screen thus confirming the complementary aspect.

One might expect then that if we pass the light through one slit (keeping the other closed) and then closing the first slit and opening the second now pass light through this slit, that the particle view would be demonstrated with two straight lines made up of photons behind the slits. However remarkably when this is done, wave particle interference takes place in a manner, which can only suggest that the individual photons (through reference to an alternative wave aspect) are able to maintain a mysterious communication as between each other ensuring therefore that the wave behaviour is maintained. So even though we may try to control each photon emitted (as if independent of others), it will act so as to preserve an overall holistic pattern that is determined by its wave nature.

Once again however this “lower” level behaviour of matter is fully complementary with the corresponding “higher” level of qualitative understanding that unfolds at h2.

In this case instead of looking at the horizontal (external-internal) polarities, we now need to look at the vertical (individual-collective) polarities, which determine the nature of interaction in any context as between wholes and parts.

Psychological understanding of phenomena necessarily entails the use of both concepts and perceptions. For example to form an individual object perception of “a cat”, one must use the collective concept of “cat” (to which all individual perceptions relate). So there is a general holistic quality of “cat” which is required (and given by the corresponding concept) that thereby enables an individual perception of a specific cat to be meaningful. And this relationship as between concepts and perceptions necessarily applies to all phenomena.

However with linear interpretation, which again defines the conventional scientific approach, a somewhat reduced relationship as between perceptions and concepts is employed.

This issue is of the first importance not only for physics but also for mathematics (where unfortunately I can see little recognition of its fundamental importance).

The key point here is that the concept is always qualitatively distinct from its related perceptions and yet must necessarily interact with such perceptions.

However this qualitative distinction of concept from corresponding perceptions is in effect completely lost in conventional scientific interpretation through a basic form of reductionism. In other word concepts are here treated as the general categories of the perceptions to which they relate in merely quantitative terms.

We can see this readily for example in mathematical proof.

We obtain the proof for the general proposition (through conceptual means) and then assume that this applies for all individual perceptions (to which the concept relates).

So the Pythagorean Theorem for example - which has been proven to be true in general theoretical terms - is thereby assumed to apply without distinction to all individual right-angled triangles (within its class). Thereby the qualitative distinction as between the theoretical collective proof and its practical application in individual cases is lost. So in a manner similar to the I-it problem, by assuming that concept and perceptions can be viewed independently of each other, a direct correspondence as between both is thereby obtained.

Now I do not question for a moment the great value of making this assumption as a working approximation at the middle level of understanding.

The problem is that it is only an approximation, which breaks down considerably at the “higher” h2 level (which is then mirrored in complementary physical fashion at the corresponding “lower” sub-atomic level of reality).

So when we view the relationship as between concepts and perceptions from the appropriate H2 level, we can then see that it equates exactly with the kind of behaviour that becomes manifest at the quantum level of reality.

At h2 therefore the holistic concept is clearly understood as qualitatively distinct from the perceptions to which it relates.

So the concept of cat for example is qualitatively distinct from an individual psychological perception of “a cat” and must necessarily remain in continual interaction with such related perceptions in experience.

Again in this dynamic interactive context - which is the very essence of experience - there is a sense in which we can separate concepts and perceptions (in a relatively independent fashion). However there is also a sense in which concepts and perceptions are interdependent. Once again rational understanding applies for appreciation of the relatively independent aspects; however holistic intuition directly applies with respect to awareness of their mutual interpenetration. And it is through establishing the mutual interdependence of both concepts and perceptions in experience that spiritual intuition grows!

So, we do not have absolutely independent concepts and perceptions in psychological terms. Rather in a relatively independent fashion, we have concepts (in relation to perceptions) and from the other standpoint perceptions (in relation to concepts). Then we also have the overlapping of both in the intuitive recognition of their mutual interdependence.

Now using accepted physical language, concepts apply to the wave aspect of psychological understanding whereas - relatively - corresponding perceptions apply to the particle aspect. Then, wave-particle interference in psychological terms refers to the overlapping of both in holistic intuitive awareness.

In terms of common macro experience of reality, we can simplify all these dynamics by assuming that perceptions are absolutely independent (of their related concepts). And this assumption is then consistent with the viewpoint of external objects (to which the perceptions apply) likewise independently existing.

Thus in common understanding, “a cat” is indeed understood as an independent object and as we will see this basic assumption constitutes the very problem in appreciating the paradox of Schrödinger's cat!

However at the “lower” sub-atomic level, objects are only independent (in a limited relative sense). Likewise at the corresponding “higher” level of understanding, perceptions (to which such objects relate) likewise only exist (in a limited relative sense).

Here both the internal (pyschological) and external (physical) aspects of phenomena are now understood as having both wave and particle aspects (which are relatively independent) and an overlapping or interference (reflecting their mutual interdependence).

Once again whereas the relatively independent aspects correspond in interpretation to a refined form of reason, the mutual interference corresponds directly to holistic intuition.

The clear implication therefore at the quantum level of reality is that a direct form of holistic recognition is involved through the interaction of particles (though necessarily of a primitive instinctive kind).

The Uncertainty Principle

Heisenberg formulated his famous Uncertainty Principle in 1927, which has become widely known for the manner in which it undermines the principle of determinism in physics. [3]

We have already briefly referred to this principle in the I-it problem. Basically it arises from the fact that both the position and momentum of a particle (e.g. electron) cannot be determined simultaneously.

Thus, if we attempt to precisely determine its position the wave must be concentrated as a single point (so that the wavelength is infinite).

Now a basic tenet of classical physics is that of determinism in the sense that given sufficient information we should be able to precisely locate the position of any particle in both time and space. So the uncertainty principle undermines such a belief and demonstrates that an absolute basis for local cause-effect relationships in physics is untenable.

It was this finding above all that disturbed Einstein so much that he remained a convinced determinist throughout his life. He could not accept the inevitable conclusion that predictions at a quantum level were merely of a probable nature.

He maintained that quantum mechanics was incomplete thereby obscuring the principle of determinism that he believed still operated at a more fundamental level of reality. Having debated his position at length with Niels Bohr (a keen advocate of the new position) Einstein's views were eventually shown in this important respect to be mistaken.

However though the Uncertainty Principle is now firmly established, I do not consider that its deeper underlying implications for physics have yet been properly grasped.

What is ultimately involved here is the old problem of discrete versus continuous notions, which has the most fundamental implications for both physics and mathematics.

The basic problem is this! Continuous and discrete notions properly correspond to two distinct logical systems. Whereas discrete correspond directly with linear reason, continuous notions correspond directly with intuition (which indirectly can be translated through circular reason in a paradoxical manner).

So, appropriate interpretation of discrete and continuous requires the use of two logical systems, linear and circular respectively. I refer to this as the holistic binary system, which has the capacity to operate as the qualitative counterpart (encoding transformation processes) to the binary system (that encodes information). However conventional science and mathematics is based on the use of just one logical system i.e. the linear, which inevitably leads to a considerable amount of reductionism and confusion.

In an earlier contribution I pointed to the nature of this problem in mathematics where the continuum hypothesis directly relates to the relationship between continuous and discrete notions of number.

Furthermore it has been shown that this problem i.e. continuum hypothesis cannot be resolved within the current axiomatic (i.e. linear) system of Mathematics. However once again the deeper implication for mathematics i.e. that it needs to incorporate circular with linear logic for a more comprehensive understanding, has not been yet grasped.

A somewhat similar problem exists in physics arising from the wave-particle duality of phenomena.

A wave is essentially a continuous holistic notion whereas a particle is of a finite discrete nature. Thus wave-particle duality actually points to the fact that - ultimately - all phenomena can be understood in terms of two complementary systems i.e. linear and circular logic.

Indeed this recognition can greatly facilitate a better appreciation of the true nature of wave-particle duality. Here however we need to use an Integral 2 approach (which is based on the holistic mathematical interpretation corresponding to 4 dimensions).

In mathematical terms we can readily identify linear understanding with what can be consciously known as “real”. So from a conventional perspective, reality is what can be known through the scientific paradigm (which is of a linear conscious nature).

Now circular (unconscious) awareness cannot be directly expressed in a “real” linear manner (as it is qualitatively of a different nature).

However it can be indirectly expressed in an “imaginary” rational fashion with a precise holistic mathematical meaning. So the use of both linear and circular logical systems implies that all phenomena now have a complex qualitative identity i.e. as both “real” and “imaginary”.

In dynamic interactive terms real and imaginary aspects of understanding keep switching (like left and right turns on a road depending on direction).

This means therefore that wave and particle aspects can both be given real and imaginary identities.

Thus when we identify through experiment light as photons, the particle aspect is real (and the unmanifest wave aspect thereby imaginary).

However when we identify light as composed of waves through experiment, this aspect is now real (with the particle aspect imaginary).

So in phenomenal terms, where one aspect is taken as reference frame, light can only reveal itself as real (through concealing the alternative aspect as imaginary). Indeed this parallels very well with Jungian psychology where conscious experience with respect to one function necessarily requires that its complementary pole remains unconscious!

However when we allow for the interdependence of both aspects of light, as real and imaginary simultaneously, then they have a merely empty (non-phenomenal) existence. What is real and imaginary simultaneously (in equal magnitudes) leads to what in physics is known as null lines. So light in its own inherent identity is thereby of a nondual nature. And it is this nondual nature that forms the absolute basis for its relative phenomenal expressions (where complementary wave and particle aspects are separated).

As always, physical notions - when appropriately understood - can be given exactly matching complementary psychological interpretations. And this therefore is true of the uncertainty principle.

Indeed the implications of this psychological counterpart of the uncertainty principle are extremely important. One consequence - as we have seen in a previous article - is that it undermines any strict notion of mathematical proof!

We have already identified the wave aspect with conceptual and the particle aspect with complementary perceptual understanding of a phenomenon.

Again we will illustrate this with respect to the phenomenal notion of a cat.

Now this has a conceptual (wave) aspect in the general qualitative notion of a cat i.e. “catness” that potentially applies to the perceptual observation of any particular cat (particle).

If we try to psychologically fix understanding with the mere quantitative perception of a specific, cat we thereby lose sense of the wider qualitative collective notion required for its recognition. This indeed leads to the familiar fallacy of giving the cat an independent existence.

However when we try to identify alternatively with the mere collective qualitative notion (as concept) we thereby lose ability to precisely fix in experience individual perceptions so that observational power is thereby significantly reduced. Carried to extremes, we may fail to notice object phenomena altogether!

This has an obvious application in science. A person who specialises too much in abstract theory (concepts) risks becoming somewhat inept at applying such theory in an applied context (to particular perceptions).

Likewise the empirical researcher who becomes immersed in particular facts (perceptions) thereby can lose the ability to see more general qualitative patterns to such facts (concepts).

So there is an inherent uncertainty principle in any context attached to the relationship between concepts and related perceptions.

Strictly speaking therefore this undermines the notion of mathematical proof in any absolute sense. The general proof is strictly conceptual applying potentially to all cases (in an infinite manner). However actual specific occurrences are of a quantitative perceptual nature and are finite in nature.

So in maintaining that the general proof applies to all specific cases, a fundamental form of reductionism is involved whereby what is qualitative (and potentially infinite in nature) is now interpreted as merely quantitative (applying to all finite cases).

Let us trace out in a little more detail what happens here. The initial conceptual recognition of a proposition applying potentially to all cases is inherently of an intuitive nature. However because such intuition is not formally recognised in conventional mathematical terms, this understanding becomes quickly reduced in rational interpretation as applying to all actual cases. In this way the key qualitative distinction as between concepts and the perceptions to which they relate is quickly lost.

So from an integral viewpoint, it becomes readily apparent that all mathematical proof is necessarily of a merely relative nature (as the psychological complement of the uncertainty principle). [4]

One further psychological application of the uncertainty principle applies to what I refer to as the existential dilemma, which plays a major role in the spiritual journey. At earlier stages one can avoid this through a general programmatic approach dictating behaviour or alternatively through pragmatic individual decisions based on what feels right in any instance.

However when with authentic spiritual development, intuitive illumination of a qualitative nature is applied to decision-making in a practical phenomenal context, increasing existential uncertainty inevitably arises as to the correct decision to take in any context.

This problem is especially highlighted during the most severe phases of the dark night process. As one becomes engulfed in darkness with external reality cut off, moral decision-making becomes the only area where any individual freedom can be exercised. Because of the necessary uncertainty existing one can spend ages wrestling with one's conscience as to the correct decision to take in any relevant context. This leads to an increasingly refined form of discernment through faint intuitive signals dictating the appropriate decision to take. However as darkness deepens, even this faint inner light is removed so that one eventually feels totally alone and abandoned convinced that the way has been finally lost.

However it is here paradoxically that the existential dilemma can be most fully resolved in the exercise of pure (nondual) faith.

So in complementary fashion, the uncertainty principle with respect to any physical phenomenon is only reconciled through the simultaneous identity of both its wave and particle aspects (which occurs in a nondual empty fashion). And this state of emptiness once again provides the absolute basis for all relative expressions of phenomena (where opposite polarities are necessarily separated to a degree).

One final telling example of the uncertainty principle relates to the very nature of science itself. In truth science has both holistic (wave) and analytic (particle) aspects. Thus the attempt to fix understanding precisely with one aspect leads to a considerable loss with respect to the other neglected aspect.

And because science still formally recognises solely the analytic aspect, this has meant a severe loss with respect to integral appreciation (directly related to its complementary holistic aspect).

Analytic science is at its best at a more local quantitative level in establishing the applicability of - necessarily - limited partial theories. By its very nature however it is inherently unsuited to the task of establishing a TOE.

Holistic science by contrast is best at establishing the universal nature of physical reality in a qualitatively consistent philosophical manner. Though of limited value in quantitative terms - excepting appropriate interpretation of quantitative results - such understanding is better suited for the establishment of a genuine TOE (though not in the manner that conventional physics would recognise).

However when we come to radial science - where both analytical and holistic aspects are coherently combined - the uncertainty principle necessarily applies.

All quantitative findings therefore are of an approximate nature and reflective of the qualitative basis used to interpret such findings (which itself is also necessarily of an approximate nature).

Schrödinger's Cat

The famous hypothetical thought experiment known as Schrödinger's cat further illustrates the mysterious nature of quantum physics.

In the original thought experiment, a cat was placed inside a concealed chamber. Fitted to this was a device triggered to flood the chamber with poisonous gas that could be controlled in such a way that by the laws of probability there was a 50/50 chance of the cat being killed.

Two explanations in quantum physics that are used to explain this experiment are known respectively as the Copenhagen interpretation and the many worlds hypothesis.

The Copenhagen interpretation arose out of the attempt to give a consistent explanation as to what happens when observing a particle under quantum mechanical conditions.

It was now broadly accepted than a particle such as an electron had no precise location in space and time. Rather it was subject to a wave function, which gave the probability of finding the particle (when measured through experiment) at a particular location. Therefore when a measurement took place - according to this interpretation - the probability wave function collapsed to reveal a precise location.

Once again there is a psychological complement to this physical interpretation, which is quite revealing.

As we have seen the corresponding meaning in psychological terms relates to that between the concept (wave) and a related perception (particle).

For example if we consider the concept of number, this clearly has a conceptual waveform, which potentially can apply to any specific number. Therefore when we carry out a psychological measurement in defining a particular number - say for example the number 2 - the conceptual wave form thereby collapses to become identified with this particular number perception (as particle).

All empirical investigation, in the form of phenomenal perceptions (as particles), thereby necessarily entails the collapse of corresponding related conceptual phenomena (as waves).

To give a full integral explanation for the Copenhagen interpretation we must combine both the physical and psychological aspects of understanding (which are complementary).

So from the physical perspective, when we attempt to measure the precise location of a particle such as an electron, the corresponding wave function for the particle thereby collapses to be identified with a single value; however this cannot be divorced from the corresponding psychological aspect (in the same act of observation) whereby the general concept of the electron (as wave form) thereby likewise collapses to be identified as a single perception (as particle).

Now if we apply the Copenhagen interpretation to the cat in our experiment, the measurement takes place when we open the chamber where we find the cat either dead or alive.

Before opening the box the cat would be interpreted as existing in a superposition of two states defined by the 50/50 probability. So therefore we would maintain that the cat is both dead and alive (or alternatively neither dead nor alive) until the box is opened.

And in the full explanation that combines both physical and psychological aspects of understanding, object phenomena would be matched in complementary fashion by corresponding perceptions.

Critics of such quantum mechanical reasoning e.g. Schrödinger and Einstein attempted to maintain such interpretation as nonsensical.

However their problem arose from attempting to use common sense intuitions - that apply as approximations at the linear level of macro reality - to an entirely different context where they are inappropriate.

The Schrödinger cat experiment, according to the Copenhagen interpretation, reveals that two distinct logical systems are involved in interpretation. So we have the actual outcome (according to linear either/or logic) and the potential outcome (based on circular both/and logic).

And the clear implication here is that the potential outcome (interpreted in paradoxical terms) is necessarily nondual, whereas the actual outcome, revealed through observation, is of a dual nature.

The Copenhagen interpretation when interpreted in this manner therefore accords with integral understanding (1 and 2). Making an observation i.e. whether the cat is dead or alive, clearly requires that we separate internal and external poles (in a relatively independent manner). However before we make the observation these poles remain necessarily interdependent. And as repeatedly stated, interdependent poles are nondual in nature (which can only be rationally translated in an indirect manner through paradox).

The problem therefore arising from the paradox of Schrödinger's cat is not with quantum physics (nor the integral interpretation of reality with which it is consistent). The real problem is with the attempt by physicists such as Schrödinger and Einstein to maintain a limited dualistic interpretation of reality in circumstances where this is clearly inappropriate. [5]

An alternative way of trying to interpret the nature of quantum observations is provided by “the many worlds hypothesis”.

Here, rather than saying that the waveform gives the probability of the possible occurrence of an observation, we maintain that the particle already exists in all possible worlds that can be observed.

Therefore when we observe the location of an electron in the one world corresponding to our measurement, we would maintain that the same particle exists in all other possible worlds (not revealed by our measurement). The implication of this is that a large number of parallel universes exist (besides that of our existence).

So if we are to apply this interpretation to Schrödinger's cat experiment, we would maintain that once the gas is emitted the cat exists in two worlds. In one world (A) the cat is alive; in the other (B) the cat is dead. When we open the chamber to observe the result of our experiment, we get an unambiguous answer gaining access to just one world. So for example if the cat is found to be still alive we thereby gain access to World (A). However according to this hypothesis, the cat also exists as dead in World (B) to which we cannot gain access.

Though this does indeed provide an interesting perspective, I feel that it is based on a qualitative confusion as between potential and actual existence.

In fact - when properly understood in dynamic interactive terms - all existence necessarily involves parallel worlds.

The basic problem with conventional thinking is the reductionist manner in which wholes are treated quantitatively as the sum of parts. In this way the universe is seen as the aggregate of all its constituent parts conveying the impression that we live in one universe.

However once we properly allow for the interaction of both qualitative and quantitative aspects, it appears very different. Here the whole is reflected in each part and the part in turn reflected in each whole (with the qualitative distinction of both maintained).

In this way each person constitutes a unique world (or universe) yet related in a collective manner to all other universes. Indeed putting it more generally, the universe is contained individually in each holon, which in turn is connected to all other holons in a corresponding collective notion of the universe.

In holistic mathematical terms this means that we extend reality i.e. as what is solely real, to “complex” reality (which has both real and imaginary aspects).

So if we consider the individual holon (as center of the universe) as “real”, then the corresponding collective notion of the relationship of all holons is “imaginary”.

However if we switch reference frames so that the collective relationship of all holons is the “real” universe, then each corresponding individual holon corresponds to an “imaginary” universe.

So therefore we now see the universe properly in dynamic interactive terms that relate individual and collective notions (which are real and imaginary with respect to each other).

So the main problem with the many worlds hypothesis is that it attempts to render an inherently dynamic interpretation of the world, where both quantitative and qualitative aspects are in continual interaction, in a somewhat reduced static manner (geared to merely quantitative notions of interpretation).

Electron Behaviour – Feynman's View

According to Feynman, when in particle interactions, a photon hits an electron it alters the charge of the particle in a manner which can be explained in two ways.

1) We can interpret the particle now as a positron (i.e. the positive counterpart to the negatively charged electron). 2) Alternatively we can still look at it as an electron that now moves backwards - rather than forwards - in time.

In this way natural light acts as a time mirror for the electron.

Once again there is a remarkable complement in psychological understanding. Indeed it is essential for answering the key question as how opposite polarities dynamically switch in experience thus enabling the self to interact with its environment.

So for example we are at times aware of external phenomena (in relation to the internal self). Then at other times we are more aware of the internal self (in relation to external phenomena).

Now the key to this understanding is that spiritual light (through intuitive recognition) is always necessary to enable the switch as between opposite reference frames to take place.

This also explains why customary experience often appears so rigid. Obviously when the degree of intuition is limited, dynamic interaction greatly slows down. Then we become aware of a world of somewhat rigid objects on the one hand complemented by a framework of rigid interpretative constructs on the other.

However what is not generally recognised is how such switching with respect to reference frames subtly alters the very nature of space and time (as conventionally understood).

Normally we think of events having a positive direction (that move forward in space and time).

So we understood events as moving forward in space and time with respect to both the external and internal frames.

Unambiguous interpretation is only possible here where both frames are considered as independent. However to the degree that they are interdependent this interpretation breaks down with paradoxical notions of space and time emerging.

In other words, if events move forward with respect to the external frame, then - relatively - they thereby move backwards with respect to the internal; likewise when events now move forward with respect to the internal fame, they move backwards with respect to the external.

So just as physical light acts as a dimensional mirror for a particle such as the electron, spiritual light (though a pure form of intuitive awareness) acts as a time mirror for our very experience (and consequent interpretation) of events.

And as physical light can cause a particle to switch from its matter to its anti-matter status (as with the electron), spiritual light likewise causes psychic matter to switch to psychic anti-matter in experience. As the interaction of matter and anti-matter leads to the generation of energy in physical terms, likewise the interaction of psychic matter and psychic anti-matter leads to the corresponding generation of (intuitive) energy from a spiritual perspective.

An even more remarkable connection can be suggested here.

Conventional science is accustomed to identifying matter in a merely external manner. However as all holons have both interior and exterior aspects, this would suggest that anti-matter simply represents the internal aspect of a holon's existence.

It is important to remember however that all holons have both physical and psychic aspects. Though the physical aspect clearly predominates at the “lower” levels of material activity, the psychological aspect is never entirely absent - necessarily - remaining connected to the entire course of evolution. So with human beings we have the manifestation of thinking nature that is able to deeply reflect on this evolution.

The EPR Experiment

As we know Einstein was greatly skeptical regarding quantum mechanics as a fundamental explanation of reality. In 1935 he devised a thought experiment (with Podolsky and Rosen) which would test the non-locality claims of quantum mechanics.

In the mid 60's John Bell found a way to express the puzzle in terms of an experiment that could in principle be performed on a pair of photons emitted from an atom simultaneously in two directions. Comprehensive tests were indeed carried out in the 1980's and confirmed (though debate still continues) that non-locality does rule in the quantum world. The key experiment involved measuring the polarisation of light. Without going into details, the finding was that measurement in terms of one photon, automatically determined the state of the other (even when separated by a vast distance). This is referred to as non-locality or quantum entanglement. Einstein referred to it more graphically as "spooky action at a distance".

Of course non-locality is the very basis of the dynamic (both/and) logic of the complementarity of opposites. Ultimately all events are connected through the present moment (in a simultaneous state where everything is equally both cause and effect). Indeed synchronicity and paranormal activity are intimately linked to this acausal principle.

There is a considerable irony in the fact that conventional science continues to be deeply skeptical regarding the status of paranormal events. Yet its own findings - in the highly important area of quantum mechanics - tell us that this in fact is exactly the case. Photons therefore can directly communicate with each other!

Though paranormal gifts are not an essential aspect of development at the h1 stage, they often flourish at this time. What underlies all paranormal activity is an intuitive (rather than a rational logic).

Again conventional scientific notions are misleading. We are inclined to think in terms of the self as a person and the external world as impersonal.

However in dynamic terms both "self" and "world" have personal and impersonal aspects that ceaselessly interact. So the correct way to look on nature is as a special friend with whom we can share an intimate dialogue.

Not surprisingly, when nature is treated in this fashion it responds in like manner.

Meaningful synchronous events are commonplace for people who are in spiritual harmony with their environment. When one truly accepts the interdependence of all events - through the spirit - regular coincidences in experience can be expected as an automatic by-product.

When we take on board the implications of quantum mechanics, we are left with a delicious irony. In other words, correctly speaking, physical reality - or more correctly psycho-physical reality - is paranormal. So what we consider as “normal” with respect to physical activity is really just a convenient approximation that does not strictly hold (even at the conventional macro level).

And once again the paranormal behaviour at the “lower” physical level is fully complemented by corresponding intuitive (paranormal) awareness at the corresponding “higher” psychological stage.


We have looked briefly at some of the most puzzling issues of quantum mechanics.

What I have been at pains to demonstrate is that we cannot possibly hope to understand the important philosophical issues raised by quantum behaviour without properly incorporating the integral aspect of science. This in turn requires the coherent mapping of the “higher” cognitive structures of development as a means of interpreting corresponding “lower” levels of physical nature.

Though physicists to varying degrees are indeed aware of the severe problem of interpretation posed by quantum mechanics, they have not yet properly faced their deeper implications. For this requires nothing less than a radical revision of what is currently meant by science!


1. This is the root of the basic reductionism which pervades conventional scientific understanding i.e. the qualitative aspect is not properly distinguished from the quantitative. And this in turn reflects the Middle Band of the Spectrum (which by definition is complementary with itself). At all other Bands a subtle complementary relationship exists as between “higher” and “lower” enabling proper distinction of qualitative and quantitative aspects respectively.

2. So with appropriate quantum mechanical interpretation we must match - at a minimum - the “higher” spiritual understanding of h1 (where reality is understood in terms of complementary opposite poles such as internal and external) with the “lower” physical behaviour of l1 (where sub-atomic particles are likewise understood in terms of the dynamic interaction of complementary opposite poles).

3. Though the “Uncertainty principle” is associated with Heisenberg it seems that Max Born would also have valid claims with respect to its initial formulation.

4. We must distinguish this finding with respect to the strict nature of all mathematical proofs from propositions, which have no absolute proof (even within the accepted reduced linear framework of conventional mathematics). So in an earlier article, when I maintained that the Riemann hypothesis had no proof, this was in the context of what is acceptable from a conventional mathematical perspective.

5. Many physicists had great difficulties in accepting the implications of such an explanation. For example Einstein posed the question:

"Do you really think the moon isn't there if you aren't looking at it?"

This very question reveals the objectivist fallacy in physical terms i.e. of trying to give a phenomenon an independent existence (without need of a general qualitative category). From a corresponding psychological perspective, it reveals the fallacy of trying to give a perception an existence independent of its general concept.

At the conventional linear level, we can indeed ignore this distinction to obtain good approximations in terms of physical understanding. However this clearly breaks down at the quantum level. So the point I am making - which Einstein could never accept - is that it requires a distinctly more refined type of rational understanding, pertaining to a “higher” level of spiritual awareness, to adequately interpret relationships at a corresponding “lower” physical level.

So in appealing to - what appears as - common sense at the conventional macro level of reality, Einstein ignored the crucial point that such “common-sense” is no longer applicable at the quantum level.


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