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New Paper from Ole Ulfbeck and Aage Bohr



[Comments by Peter Mutnick on the paper by Ulfbeck and Bohr]
After listening to a lecture by Ravi Gomatam at UC Berkeley on the role of philosophy in inspiring new theories in physics, I was inspired to look at a paper by Aage Bohr and Ole Ulfbeck that was mentioned in the lecture. I had noticed it before, but I had not paid close attention. I was pleased to find that Aage Bohr is just as wild and wise as his father and just as much fun to read, i.e., he seems to have a good head. The paper that Gomatam had mentioned was the second one, that came out in 2001: "Genuine Fortuitousness. Where Did That Click Come From?" in Foundations of Physics, Vol. 31, No. 5, pp. 757-774. The earlier one, mentioned below, had come out in 1995.

The latter paper seems to have made some corrections to the Ansatz that had been established earlier. In the earlier paper, Bohr and Ulfbeck define the quantum as follows: "As physical variables, the symmetry elements acquire an existence of their own, and the variables of a group together *constitute* an object that will be referred to as a quantum (=quantal object). A full specification of the quantum in general involves the extension of spacetime invariance to include variables associated with gauge transformations."

In the latter paper it is made clear that the symmetry variables are essentially the matrix variables of Heisenberg derived from relativistic invariance by methods of symmetry evolved by Wigner. Also it is made clear that these matrix variables constitute a wholeness by virtue of their group definition. According to the new interpretation of Bohr and Ulfbeck, the matrix variables characterizing the system under observation do not at any point get reduced or actualized, nor is the source subject to transforming events. Rather, the variables in their wholeness manifest themselves upon the spacetime continuum, which is the arena for all observations. This manifestation is affected by the construction and character of the counter, which will focus on one or another of the matrix variables. I would suggest here that the focus is always in principle on the momentum-energy-momentum variable, as mem or I AM THAT I AM, and always in practice on the variable of the spacetime continuum. According to John Bell, measurements in quantum theory are always ultimately position measurements, while in principle the momentum variables of the S-Matrix contain all the information that can ever be extracted.

In any case, the point is that in the new paper it is made clear that the discontinuity or actualization is NOT in the source or the system under observation - it is in the counter, and not just in the counter per se, but in the phenomenal character of the counter as it exists in relation to the spacetime continuum. The quantum is then a feature of the counter, while the system is a feature of the source. Hence the term "quantum system" encompasses both the counter and the source; it does not pass from the source to the counter. The wholeness of the character of the source in relation to the spacetime continuum can be recognized as the quantum implicate order of Bohm.

As I have mentioned in an earlier paper, the spacetime continuum is inherently a phenomenal reality, while energy and momentum are mental and physical, or psycho-physical, and hence noumenal. However, we have the admonition from Niels Bohr, in his discussions with Carl von Weizsacker concerning circular and parallel complementarity, that complementarity must always be between elements on the same level. The only way that the spacetime continuum and the energy-momentum variables can be on the same level is if they are implicate, prior to unfoldment. As such they exist at the top of the seventh or meta-physical (classical) world, in the quantum implicate order, which is the true Mind of the classical Observer. The spacetime continuum is in the sixth or causal world, while the character of the counter in relation to the spacetime continuum is in the fifth or phenomenal world. The quantum system or the counter and the source are in the second or emotional world, between the mental world and the physical world.

So, the essence of the approach of Bohr and Ulfbeck is that the counter and source, which together constitute the quantum system, spontaneously exhibit respective characters in relation to the spacetime continuum. The character of the source, as expressed in the group of the matrix variables, then manifests on the spacetime continuum, and one or the other of its manifestations is observed by the character of the counter. It is the character of the counter, not the character of the source, to undergo transformation, which is more or less due to an event, although an event that is not governed by any known law, even a probabilistic law. The probabilistic law, according to Bohr and Ulfbeck, arises only when we consider the highly complex character of the counter in terms of limited parameters.

I would suggest here that a better way to think of this is to realize that the physical reality determined by the fortuitous click in the counter is not in every sense physical. In some respects it is merely a phenomenal reality and not yet established as either a genuine position measurement of Bohm/Bell or a noumenal reality, which is what the physical reality must ultimately be. It is precisely in order to complete the physical reality coming into being that the probabilistic law and the selection process must intervene. And yet what Bohr and Ulfbeck have discovered is a level of reality prior to such ontological determination.

I very much enjoyed the paper by Bohr and Ulfbeck, and I intend to look into these ideas further. I believe, for instance, that the considerations below, introduced by Bohm, will have a role in defining the symmetry variables properly in a fully quantal way from the outset. As Bohm has pointed out, even our most basic definition of motion is inadequate to the quantum reality and to the reality of our actual experience. Here then is what I have said previously and what Bohm has said:


[Peter Mutnick]
Below is the passage from Bohm that I think is quintessential and foundational to all future physics. It has become the foundation of my approach in all my recent postings. I mention in passing that Aage Bohr has an approach that may be related to this approach. It is even simpler, and strikes me as an oversimplification, but time and close analysis will tell. Aage Bohr claims to be able to derive all of quantum physics from relativistic symmetries, such as translation, reflection, and perhaps rotation. He claims that the state vector and Hilbert space formalism is just a convenient way of handling these underlying symmetries, which are the real source of all the quantum phenomena, such as uncertainty and complementarity. The citation for this paper is: "Primary Manifestation of Symmetry", Reviews of Modern Physics, Vol. 67, No. 1, January 1995, pp. 1-35. Here is Bohm's quintessential idea, which I believe is more likely to be fruitful:


[David Bohm, "Wholeness and the Implicate Order", 1980, Ark edition 1983, pp 201-4]
All of this suggests that quite generally (and not merely for the special case of listening to music), there is a basic similarity between the order of our immediate experience of movement and the implicate order as expressed in terms of our thought. We have in this way been brought to the possibility of a coherent mode of understanding the immediate experience of motion in terms of our thought (in effect thus resolving the Zeno's paradox concerning motion).

To see how this comes about, consider how motion is usually thought of, in terms of series of points along a line. Let us suppose that at a certain time t_1, a particle is at a position x_1, while at a later time t_2, it is at another position x_2. We then say that this particle is moving and that its velocity is

v = x_2 - x_1 / t_2 - t_1 .

Of course, this way of thinking does not in any way reflect or convey the immediate sense of motion that we may have at any given moment, for example, with a sequence of musical notes reverberating in consciousness (or in the visual perception of a speeding car). Rather, it is only an abstract symbolization of movement, having a relation to the actuality of motion, similar to that between a musical score and the actual experience of the music itself.

If, as is commonly done, we take the above abstract symbolization as a faithful representation of the actuality of movement we become entangled in a series of confused and basically insoluble problems. These all have to do with the image in which we represent time, as if it were a series of points along a line that are somehow present together, either to our conceptual gaze or perhaps that of God. Our actual experience is, however, that when a given moment, say t_2, is present and actual, an earlier moment, such as t_1 is past. That is to say, it is *gone*, non-existent, never to return. So, if we say that the velocity of a particular *now* (at t_2) is (x_2 - x_1) / (t_2 - t_1) we are trying to relate *what is* (i.e., x_2 and t_2) to *what is not* (i.e., x_1 and t_1). We can of course do this *abstractly and symbolically* (as is, indeed, the common practice in science and mathematics), but the further fact, not comprehended in this abstract symbolism, is that the velocity *now* is active *now* (e.g., it determines how a particle will act from now on, in itself, and in relation to other particles). How are we to understand the *present activity* of a position (x_1) now non-existent and gone for ever?

It is commonly thought that this problem is resolved by the differential calculus. What is done here is to let the time interval, delta t = t_2 - t_1 become vanishingly small, along with delta x = x_2 - x_1. The velocity *now* is defined as the limit of the ratio delta x / delta t as delta t approaches zero. It is then implied that the problem described above no longer arises, because x_2 and x_1 are in effect taken at the same time. They may thus be present together and related in an activity that depends on both.

A little reflection shows, however, that this procedure is still as abstract and symbolic as was the original one in which the time interval was taken as finite. Thus one has no immediate experience of a time interval of zero length, nor can one see in terms of reflective thought what this could mean.

Even as an abstract formalism, this approach is not fully consistent in a logical sense, nor does it have a universal range of applicability. Indeed, it applies only within the area of *continuous* movements and then only as a technical algorithm that happens to be correct for this sort of movement. As we have seen, however, according to the quantum theory, movement is *not* fundamentally continuous. So even as an algorithm its current field of application is limited to theories expressed in terms of classical concepts (i.e., in the explicate order) in which it provides a good approximation for the purpose of calculating the movements of material objects.

When we think of movement in terms of the implicate order, however, these problems do not arise. In this order, movement is comprehended in terms of a series of inter-penetrating and intermingling elements in different degrees of enfoldment *all present together*. The activity of this movement then presents no difficulty, because it is an outcome of this whole enfolded order, and it is determined by relationships of co-present elements, rather than by the relationships of elements that exist to others that no longer exist.

We see, then, that through thinking in terms of the implicate order, we come to a notion of movement that is logically coherent and that properly represents our immediate experience of movement. Thus the sharp break between abstract logical thought and concrete immediate experience, that has pervaded our culture for so long, need no longer be maintained. Rather, the possibility is created for an unbroken flowing movement from immediate experience to logical thought and back, and thus for an ending t this kind of fragmentation.

Moreover we are now able to understand in a new and more consistent way our proposed notion concerning the general nature of reality, that *what is* is movement. Actually, what tends to make it difficult for us to work in terms of this notion is that we usually think of movement in the traditional way as an active relationship of what is to what is not. Our traditional notion concerning the general nature of reality would then amount to saying that *what is* is an active relationship of what is to what is not. To say this is, at the very least, confused. In terms of the implicate order, however, movement is a relationship of certain phases of *what is* to other phases of *what is*, that are in different stages of enfoldment. This notion implies that the essence of reality as a whole is the above relationship among the various phases in different stages of enfoldment (rather than, for example, a relationship between various particles and fields that are all explicate and manifest).

Of course, actual movement involves more than the mere immediate intuitive sense of unbroken flow, which is our mode of directly experiencing the implicate order. The presence of such a sense of flow generally implies further that, in the next moment, the state of affairs will actually change - i.e., it will be different. How are we to understand this fact of experience in terms of the implicate order?

A valuable clue is provided by reflecting on and giving careful attention to what happens when, in our thinking, we say that one set of ideas *implies* an entirely different set. Of course, the word 'imply' has the same root as the word 'implicate' and thus also involves the notion of enfoldment. Indeed, by saying that something is *implicit* we generally mean more than merely to say that this thing is an inference following from something else through the rules of logic. Rather, we usually mean that from many different ideas and notions (of some of which we are explicitly conscious) a new notion emerges that somehow brings all these together in a concrete and undivided whole.

We see, then, that each moment of consciousness has a certain *explicit* content, which is a foreground, and an *implicit* content, which is a corresponding background. We now propose that not only is immediate experience best understood in terms of the implicate order, but that thought also is basically to be comprehended in this order. Here we mean not just the *content* of thought for which we have already begun to use the implicate order. Rather, we also mean that the actual *structure*, *function* and *activity* of thought is in the implicate order. The distinction between implicit and explicit in thought is thus being taken here to be essentially equivalent to the distinction between implicate and explicate in matter in general.


[Further comments by Peter Mutnick on the paper by Ulfbeck and Bohr]
Having met with some resistance from Henry Stapp and Jerry Finkelstein at LBNL to the new paper from Ole Ulfbeck and Aage Bohr at NBI, I would like to add some more, to try to paint a coherent picture of the presented interpretation, which I believe to be very consistent, if not identical, with the Copenhagen Interpretation of Niels Bohr. The point, it seems to me, is that the macroscopic state vector describes an evolution of the counter as it appears in the context of the spacetime continuum. It is not unlike Heisenberg's considerations of the tracks in the cloud chamber. Even the unitary development of the system must be regarded like that, as tracks or trajectories in the extended device designated here as the counter. We in fact know nothing at all about the noumenal system, other than the symmetry of its algebra which defines it. Everything else is in the first place a property of the counter and precisely the counter as it appears in the context of the spacetime continuum. This is what the elder Bohr meant when he said that the quantum formalism is an algorithm.

So, what we have in the first place is a unitary development, which I believe Ulfbeck and Bohr designate as the "onset", and then the "click" in the phenomenal appearance of the counter. The state vector formalism describes this phenomenal reality, not the noumenal reality, which is unknowable except for the symmetry of its algebra which defines it for us. However, the apparent counter is ontologically a measuring device in the sense of von Neumann, a II in his system of hypostases for quantum measurement theory. This issue, however, does not arise until we begin to answer the question, posed in the title of the paper as a Zen Koan, "Where did that click come from?"

The "where" here does NOT, as I understand it, refer to a location in the spacetime continuum, but rather in the first place to a location in the *ontological* measuring device and secondarily to the location as a noumenon in the metaphysical context of ontological reality. In the first instance, the probabilistic law applies, and in the second instance, the intentional selection process is mandated. In other words, the noumenal microscopic reality is constructed from the phenomenal data and the law is always about that construction of reality, both in the ontological measuring device and in the noumenon itself. To wit, the predictions of quantum theory DO NOT apply to the "click" - they apply to the ontological construction of the measuring device which operates independently of the phenomenal reality of the observer. The point of Ulfbeck and Bohr is just that the phenomenal reality of the observer precedes any such ontological considerations, which are the immediate basis for material science. Material science is a construction of material reality based ultimately on the phenomenal reality of the observer, which is characterized primarily by the fact that it is the context of the spacetime continuum.

Although this is the truth of the macroscopic state vector in QM, I believe that QFT is best understood as a theory of the microscopic state vector. Each creation operator creates a new state vector, which is the thing-in-itself, as Max Born has explained in "My Life and My Views". Each destruction operator is related to an actual event, that reverses the unfoldment of the state vector. This ontological interpretation of QFT is the implementation of the ideas of William James and Alfred North Whitehead. The full algebra is described in my previous paper, which I include here:


[The New Algebra for Radically Unified Quantum Field Theory]
In conventional quantum theory, the wave function is just a probability for finding a particle, and the particle only has existence at the moment of measurement. So, we say that the existence of the particle is connected with the transformation of the potential (as an extension of the noumenal *potentia*) into an actual event. In genuine Bohm theory, however, this is not the case. The existence of the particle is indeed associated not with the potential|actual event, but with the state vector|substance. The state vector is assumed to have real substance and to be a real substance. Now here is the kicker: this was in fact the firm conviction of none other than Max Born, as he expressed unambiguously in his autobiography, "My Life and My Views".

Now, when we go over to quantum field theory, it now becomes clear that the state|vector substance will have the character of a creation operator and an unfoldment, while the potential|actual event will have the character of a destruction operator and an enfoldment. It should be noted that state and substance are two of the ten Aristotelian categories of logic. The destruction operator now signifies primarily the destruction of the past in the present moment, while the creation operator now signifies the creation of the future in the present moment. The present moment itself will represent the construction of reality or the ideation that must precede all creation. It is represented by the Aristotelian categories (only the first four are actually categories): quality, quantity, position, relation, configuration space, motion, momentum, matter, energy, space, time, primary mental matter, physical mind and physical body. The last three express the categories of quantity, quality and quantum.

Physical mind is Pythagorean, where the things of the sense *are* numbers, while physical body is Platonic, where mathematical entities are intermediate between the ideas and the things of the senses. The latter is dialectical, according to Aristotle in the "Metaphysics", but what he evidently means is that the latter is arrived at through consideration of the overarching metaphysical dialectic. These categories constitute a holomovement of a very special kind, that is essentially an unfoldment, but in which there is some enfoldment and equilibrium between unfoldment and enfoldment.

So, the idea is that the destruction and creation operators of particles are a rather specialized abstraction of the more general dialectical processes. We call Maharishi Mahesh Yogi the destruction operator, in this specialized sense, and we call Brahma|Saraswati/Sananda-Sanaka the creation operator. Sananda is a special kind of Substance, namely Self-Luminous Intelligent Substance, or Consciousness, while Sanaka is the Substance of the world. Hence Sananda (Jesus Christ) said: "Fear not, for he who is in you [Consciousness] is greater than he who is in the world." In Vedantic philosophy, we say that the former is God's *para* energy, while the latter is His *apara* energy.

In any case, we have the general categories of logic as the wave and the specialized creation and destruction operators of particles as the wave within the wave. The latter unfolds into the former and there is in turn a wave within that wave. In the specialized context of creation and destruction of particles, thought plays the role of a reduction operator, while in the more general sense THOUGHT plays the role of the destruction operator. It is in this way that the specialized wave unfolds into a generalized wave, which is in turn the seat of another specialized wave.

There are actually five operators in the new algebra: Destruction, Ideation, Reduction, Affection, and Creation, or DIRAC. In the specialized context, these are symmetric, whereas that symmetry is broken in the generalized sense. The reduction operator in the general sense just looks like: state vector|reduction, while the affection operator unfolds from a higher level and looks like: time, place, action, affection; where these are of course four of the ten Aristotelian categories of logic.

The outermost wave, which interfaces with the really existing particle, is called the Quantum Ground, while the particle is called the Classical Universe Particle, or BOHM POINT. The connection, through the wave within wave concept, of particle creation and destruction to the flow of process time establishes the synthesis of von Neumann's process 2 and his process 1 into one world process. This is in fact the whole import of the quantum formalism. Moreover, we do not bifurcate time into process time and Einstein time - we assume that process time is the true Einstein time, which will require of course the quantization of even special relativity.



Peter Joseph Mutnick 1949 - 2000


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