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Breakthrough in the Copenhagen Interpretation of Quantum Theory


"In the first place, we must recognize that a measurement can mean nothing else than the unambiguous comparison of some property of the object under investigation with a corresponding property of another system, serving as a measuring instrument, and for which this property is directly determinable according to its definition in everyday language or in the terminology of classical physics. While within the scope of classical physics such a comparison can be obtained without interfering essentially with the behavior of the object, this is not so in the field of quantum theory, where the interaction between the object and the measuring instruments will have an essential influence on the phenomenon itself. Above all, we must realize that this interaction cannot be sharply separated from an undisturbed behavior of the object, since the necessity of basing the description of the properties and manipulation of the measuring instruments on purely classical ideas implies the neglect of all quantum effects in that description, and in particular the renunciation of a control of the reaction of the object on the instruments more accurate than is compatible with the [uncertainty] relation."

- Niels Bohr, "The Causality Problem in Atomic Physics," in New Theories in Physics, 1939, page 19.

"In particular it should not be forgotten that the concept of causality underlies the very interpretation of each result of experiment, and that even in the co÷rdination of experience one can never, in the nature of things, have to do with well-defined breaks in the causal chain. The renunciation of the ideal of causality in atomic physics which has been forced upon us is founded logically only on our not being any longer in a position to speak of the autonomous behavior of a physical object, due to the unavoidable interaction between the object and the measuring instruments which in principle cannot be taken into account if these instruments according to their purpose shall allow the unambiguous use of the concepts necessary for the description of experience. In the last resort an artificial word like "complementarity" which does not belong to our daily concepts serves only briefly to remind us of the epistemological situation here encountered, which at least in physics is of an entirely novel character."

"Not only is the well known dilemma between the corpuscular and undulatory character of light and matter avoidable only by means of the viewpoint of complementarity, but the peculiar stability properties of atomic structures which are in obvious contrast with the properties of any mechanical model, but which are so intrinsically connected with the existence of the quantum of action, form the very condition for the existence of the objects and measuring instruments, with the behavior of which classical physics is concerned."

"On closer consideration, the present formulation of quantum mechanics in spite of its great fruitfulness would yet seem to be no more than a first step in the necessary generalization of the classical mode of description, justified only by the possibility of disregarding in its domain of application the atomic structure of the measuring instruments themselves in the interpretation of the results of experiment. For a correlation of still deeper lying laws of nature involving not only the mutual interaction of the so-called elementary constituents of matter but also the stability of their existence, this last assumption can no longer be maintained, as we must be prepared for a more comprehensive generalization of the complementary mode of description which will demand a still more radical renunciation of the usual claims of so-called visualization."

- Niels Bohr, "Causality and Complementarity," address delivered before the Second International Congress for the Unity of Science, June, 1936, in Philosophy of Science, Vol. 4, No. 3, page 293-4.


Concerning the first quote, people have heard this type of argument so many times from Bohr that they think they know what it means, but it is not at all obvious or trivial. It involves profoundly metaphysical truths that have never really been explicated.

First of all we must inquire as the to the metaphysical structure of classical physics. The laws of classical physics are associated with the attribute of extension in Cartesian philosophy. The presumption is that in the classical world, which turns out to be the physical sub-world of the seventh or meta-physical world in the ontological system of worlds, the attributes of extension and thought are well separated and independent. The properties of matter are explained in terms of extension, while the properties of spirit are explained in terms of thought.

Devoid of a reality principle based on atomism, that would be the end of story, and only the classical world, as defined above, would really exist. However, when we accept the notion of an extensive continuum, which is an unfoldment of the extension attribute, then the ever smaller regions connoted by "continuum" point toward not only a phenomenal reality independent of the classical world, but toward a noumenal reality underlying that. Continuity is an aspect of our phenomenal experience. It does seem to be possible to divide up ever more finely both our perceptions and the things they represent.

The phenomenal reality is presumed to be tied to a certain level of coarse graining with respect to the underlying atomic reality. If we divide things up too much they no longer resemble the phenomenal objects of our actual experience. That indicates a fundamental distinction between the phenomenal level and the noumenal level of metaphysical reality. From a classical point of view, we really don't know where the divisibility of nature ends, and so we must assume that it passes into unknowability - hence the Kantian notion of an unknowable noumenon at the base of the physical world.

The principles of atomism and bottom-up local causation then dictate that there are levels of scale supervening in ascending order upon the unknowable noumenon in nature. These levels can be enumerated as: microcosmic, sub-atomic, atomic and molecular, lab scale, and macrocosmic. However, and this is the decisive point, these levels of things in nature are all abstract superimpositions upon whatever might be the real things in nature. We might label our superimposed levels as physical, astral, causal, mental, and etheric sub-worlds, but although these sub-worlds are reflected in the phenomenal world, they must in truth be regarded as mutually configured by the observer and the observed, and they must therefore exist in the oroboric abyss between the physical world of the observed and the meta-physical world of the observer. The five sub-worlds together comprise the reconstituted physical world within the oroboric abyss and it becomes the standard for the causal structure described by physics.

The other presumption of measurement theory, whether classical or quantum, is that within the ontological system of worlds there is an internal sub-system of worlds that raptures the lower worlds of mental, emotional, and physical, which constitute the realm of the observed (von Neumann's I), up into the etheric world, which constitutes the realm of the measuring instrument (von Neumann's II). The mental and physical subject/object polarities become the prototype for the comparable systems of Bohr's "measuring instrument" and "object under investigation", all within the context of the intermediate realm of von Neumann's measuring instrument. The "measuring instrument" represents in this scheme the ultimate observer itself in relation to the observed, but in a more immediate sense it is just the higher part of the intermediate world that interfaces with the next highest world, which is the phenomenal world of consensus reality. All of this corresponds directly to Bohr's statement that "...a measurement can mean nothing else than the unambiguous comparison of some property of the object under investigation with a corresponding property of another system, serving as a measuring instrument, and for which this property is directly determinable according to its definition in everyday language or in the terminology of classical physics."

Bohr then goes on to say, "While within the scope of classical physics such a comparison can be obtained without interfering essentially with the behavior of the object, this is not so in the field of quantum theory, where the interaction between the object and the measuring instruments will have an essential influence on the phenomenon itself." So, the presumption in classical physics is that both of the comparable systems obey the *same* classical law and are separable in such a way that the functioning of one does not impinge upon the other, except in a strictly controllable way determined by the classical law which they both obey. In the quantum case, as we shall see, the comparable systems obey different (quantum) laws and their coming together is a merging that defines, at that particular level, the ongoing quantum process.

In quantum theory, the premises enumerated above for classical theory are somewhat different. For one thing, the quantum reality in nature is not a superimposition upon the underlying noumenal reality in the physical world, but rather it is the lower octave of it. The etheric sub-world as a thing (in a higher octave) becomes the etheric sub-world as an idea (in a lower octave), and the mental, emotional, and physical sub-worlds then assume under it the roles of III, II, and I in von Neumann's quantum measurement theory, which is based on physical reductionism through the principle of the psycho-physical parallelism.

For another thing, the oroboric abyss connecting the physical world to the meta-physical world provides in quantum theory the occasion for another form of II connecting a I and a III. Quantum theory is less abstract and more profoundly metaphysical in its conception of noumenal reality. And so, some new postulates about the character of this oroboric II become necessary, since it is not just an abstract extrapolation of classical world reality. However, quantum theory also depends, in a different way, upon the notion that the noumenal reality can only be described in classical terms.

To understand this different mode of dependence, consider the following quote from John von Neumann on p. 351 of "Mathematical Foundations of Quantum Mechanics":

We therefore have two fundamentally different types of interventions which can occur in a system S or in an ensemble [S_1,...,S_N]. First, the arbitrary changes by measurements which are given by the formula

(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]

(phi_1, phi_2,... a complete orthonormal set, cf. supra). Second, the automatic changes which occur with passage of time. These are given by

(2.) U -> U_t = e^-iHt/hbar U e^iHt/hbar

(H is the energy operator, t the time; H is independent of t). If H depends on t, then we may divide the time interval under consideration into small time intervals in each of which H does not change -- or changes only slightly -- and apply 2. to these individual intervals. Superposition gives the final result. [end quote]

U is the Density Matrix in the emotional world. It first of all operates upon the Eigenvector in the physical world, and this result forms the bra vector that multiplies as an inner product by the ket vector that is again the Eigenvector in the physical world. These bra and ket vectors that comprise the statistical weight are in the mental sub-world of the physical world. This statistical weight then multiplies by a Projection Operator, representing the same Eigenvector (back to back). This Projection Operator is in the meta-physical world, since all projection operators project onto the classical world. A physically weighted sum of these meta-physical projection operators then constitutes U'. U' is therefore a Density Operator spanning the fifth, sixth, and seventh worlds, rather than a Density Matrix in the second or emotional world.

So, it would be more correct to rewrite von Neumann's interventions as follows:

(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]

(2.) U' -> U'_t = e^-iHt/hbar U' e^iHt/hbar

(3.) U'_t -> U = some presently unknown function of U'_t

where U is the Density Matrix looking downward in the emotional world and U' is the Density Operator looking upward and spanning the fifth, sixth, and seventh worlds.

However, we must now take into account Bohr's admonition that: "Above all, we must realize that this interaction cannot be sharply separated from an undisturbed behavior of the object." If that is so, then (2.) cannot be right, either. Rather, we must have:

(2.) U' -> U'_t = e^-iHt U' U_[U_h-i-j-k X U'] e^iHt

where U_h-i-j-k is an expression that represents the quantum description of all the measuring instruments, both for preparation and observation. It is the hatha-iccha-jnana-kriya operator that represents the etiological description of the noumenon and is in formal symmetry with the density operator as the phenomenal description of the quantum system transformed by an initial von Neumann reduction serving as a preparation. U_[U_h-i-j-k X U'] is the synthesis of U' and U_h-i-j-k, and it is what goes on to become a new density matrix, U, in the second application of the von Neumann reduction or his intervention #1, which constitutes the observation. We see why, from these considerations, the earlier well-known premises of quantum theory, enunciated many times by Bohr and reiterated in 1939, *must* lead to the later unknown and universally ignored conclusion of Bohr (in 1936) that an entirely new quantum theory was both necessary and inevitable. The foundations of that new theory are presented here for the very first time in history.

Of course, the above version of intervention #2 is only meant to indicate some of the elements of the new theory, and although it does show the formal relationships of the those elements, it does not show the mathematical connections between them. The following symbolic formula, employing Vedic mantras directly from the Mind of the Creator, is formally correct and begins to indicate some of the cause and effect connections:


where OM is the internal TIME-ENERGY of absolute CONSCIOUSNESS aware only of ITSELF, as signified by JAYA GURU; OMKARA constitutes the first Hamiltonian, H(1); and JAYA JAYA SAD-GURU is an unfoldment of the Density Operator representation from absolute CONSCIOUSNESS aware only of ITSELF. This Density Operator representation has a dual function - on the one hand it represents the physically weighted sum of meta-physical projection operators, but on the other hand it represents the phenomenal description of the noumenon as it is reconstructed within the phenomenal experience of the observer.

The idea here is that the Copenhagen Interpretation DOES NOT assume that the first intervention of von Neumann is sharp - rather it assumes with Bohm that there will be a residue of quantal entanglement, which is indicated by the terms BRAHMA VISHNU SADA-SIVA HARA HARA HARA HARA MAHA-DEVA. Although this residue is not raised into the phenomenal realm along with the sum of projection operators, it IS transformed by the measurement process from matter, indicated by BRAHMA, into energy, indicated by VISHNU, and into elements which are beyond even energy. This could be the basis for the next generation of weapons, namely for a particle bomb, which would be infinitely more powerful than an atomic bomb or a nuclear bomb - in short it could easily vaporize an entire planet. However, its peaceful use would be to power starships into hyperspace, defined as the realm of pure ideational energy beyond space and time.

In any case, it is essentially the residue that is described by "the phenomenal description of the noumenon as it is reconstructed within the phenomenal experience of the observer". This constitutes the other function of the Density Operator, which is hence not entirely defined by the weighted sum of projection operators - rather there is a correction term that performs the secondary function. The phenomenal description is in the sixth or causal world and it actualizes as THOUGHT (dianoia) within the fourth or etheric world. This is the Platonic conception of intellectual matter, which is copied from its ideal in the causal world. After some descending processes of manifestation, this intellectual matter takes the form of SADASIVA/MAHAKALA, which is the transubstantiation of the pure elements of the residue from the second or emotional world into the fourth or etheric world through the actualization of the phenomenal description.

Finally, the second Hamiltonian, H(2), is the love energy of God, known as HARE. RAMA and KRISHNA transform the interaction of the Density Operator with the quantal aspect of the measuring device, represented by the Hatha-Iccha-Jnana-Kriya Operator, back into a Density Matrix that will undergo the second application of the first intervention, known as the observation. KRISHNA descends through the same spheres as the residue had ascended through in its spiritualizing transformation during the first application of the first intervention, known as the preparation. This has everything to do with the basis state problem, since we DID NOT assume that the initial set of basis states was anything but an approximation. The final set of basis states employed in the second application of the first intervention will evidently involve the residue in an essential way.

The third intervention, as the fourth stage of the measurement process, must now be regarded not as the transformation of the Density Operator back into a Density Matrix, which is now regarded as the culmination of the second intervention that leads to a reiteration of the first intervention, but as what Henry Stapp calls the Heisenberg reduction, which reduces the physically weighted sum of meta-physical projection operators, stemming from the second application of von Neumann's intervention #1, to a single projection operator representing the actually observed result. However, the essential point here is that this does not occur spuriously through the intervention of consciousness itself, but rather through the aspect of the measuring instrument that embodies the Kantian form of consciousness.

There are certain Buddhist mantras, pertaining to the popular cult of Avalokiteshvara, the bodhisattva of compassion, that represent this hypostatizing of cosmic consciousness: OM TARA, TU TARA, TURE SVAHA; OM MANI PADME HUM; and GATE, GATE, PARA GATE, PARA SAM GATE, BODHI SVAHA. The first of these encompasses MATTER as corresponding to the physically weighted sum of meta-physical projection operators, and the third of these encompasses MIND as corresponding to the single meta-physical projection operator actually selected. So, the mantras together signify the transformation of MATTER into MIND, similar to Einstein's transformation of matter into energy. Metaphysically, MATTER is at the top of the etheric world, just beneath the phenomenal world, in the horizontal scheme of worlds, while MIND is directly above the phenomenal world. MIND constitutes the so-called *akasha*, where the akashic records of all experiments and experiences are stored.

The above mantras for the third intervention constitute the aspect of the measuring instrument defined in experiential terms. To understand this overall perspective, we must consider the notion of a *Densite de Presence*, as an *a priori* quantum description of the actual observer, representing the "unity of personality" mentioned by Bohr in the quote directly below this paragraph. The noumenal quantum reality, representing what Bohr calls the "indestructible individuality" of "material particles", then becomes the *etre pour-soi* and the measuring instrument becomes the *etre en-soi*. These comprise the I, II, and III that constitute the oroboric connection between the system actually observed (as a physical I) and the actual observer (as a meta-physical III). The II thus defined, which is the *en-soi*, then has two inner or occult polarities, corresponding to its existence as a transcendental quantum object and its definition in terms of experience necessary for its function as a measuring instrument. The one is employed in the second stage of the measurement process and the other is employed in the fourth and final stage of the measurement process, which is referred to as the "closure of the experiment" by Bohr.

From Niels Bohr on p. 98 of "Atomic Theory and the Description of Nature", with my explanations in brackets:

"On the whole, the analysis of our sense impressions discloses a remarkable independence of the psychological foundations of the concepts of space and time, on the one hand, and the conceptions of energy and momentum, based upon actions of force, on the other hand. Above all, however, this domain, as already mentioned, is distinguished by reciprocal relationships which depend upon the unity of our consciousness and which exhibit a striking similarity with the physical consequences of the quantum of action. ...In particular, the apparent contrast between the continuous outward flow of associative thinking [the stream of consciousness] and the preservation of the unity of personality [according to Kant rather than James] exhibits a suggestive analogy with the relation between the wave description of the motions of material particles, governed by the superposition principle, and their indestructible individuality. [This analogy is between {the observer in world 7 and the extended observer in worlds 7-5} and {the observed in world 1 and the extended observed in worlds 1-3}!] The unavoidable influence on atomic phenomena caused by observing them here corresponds to the well-known change of the tinge of the psychological experiences which accompanies any direction of the attention to one of their various elements."

The actual analogy Bohr speaks of here is between the Stream of Consciousness and the *Densite de Presence*, on the one hand, and the State Vector Substance and the Substance-Attribute-Intellect Being Aware of the Bliss of the Atman, on the other hand. The latter conglomeration of concepts is SAI BABA, the God of Spinoza. Each individual mode of this universal substance is an *etre pour-soi*. Thus on p. 112 of "Werner Heisenberg (1901-1976)", by Armin Hermann, we find: "The far-reaching transformability of elementary particles led Heisenberg to view the individual particles as various forms of an 'original substance' that - in view of Einstein's principle of equivalency - can be termed either matter or energy."

And, on p. 97 of "Philosophical Problems of Quantum Physics", by Werner Heisenberg, we find: "...Leucippus and Democritus of Abdera effected the transition to materialism. The polarity of being and non-being was made worldly and became a contrast of Full and Empty. Pure Being contracted to a point, but it could repeat itself any number of times; it became indivisible and indestructible and hence it was called 'atom'. The world was reduced to atoms and the empty space between them." Now it is self-evident that what Bohr refers to again and again as the "indestructible individuality" of a quantum system is intended precisely in this way, so that we can assume that the founders themselves were in some degree of accord with the views of Leucippus and Democritus, as described here by Heisenberg.

People complain that the Copenhagen Interpretation does not make sense, but it does make sense if and only if one can recognize and accept its central premise, which is that the measuring instrument constitutes a different hypostasis of matter than the quantum system actually observed. And yet, it is not "an emergent property of matter", because, as David Bohm emphasized in his 1951 textbook, "Quantum Theory", the classical-like reality must precede the quantum reality of matter, since the former is necessary for the very definition of the latter. In other words, quantum theory requires a metaphysical approach to matter, in which there are several hypostases of matter, well differentiated from each other and ultimately emanating not from the lowest level, but from the highest level.

This view is precisely the synthesis of atomism or materialism with the top-down hypostatic levels of Platonism and Neoplatonism, which Heisenberg explicitly and the others implicitly seemed to advocate. This is also the only way to make proper sense of Bohm's later philosophy of the implicate order. This view does not negate the ostensible truth of atomism, but it does cast it in an idealistic perspective. This idealism, however, is not in contradiction to materialism, per se, since all worlds considered are hypostases of matter. This view has always been the essence of spiritual and occult teachings, which have been affirmed by all authentic religions. Heisenberg often spoke of the "central spiritual order" and of the fact that it must ultimately win out over all of our divisive delusions based on ignorance. Of course, what this means in practice could lead to bitter contention and probably has and probably will.


Peter Joseph Mutnick 1949 - 2000