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Quantum Kinematics

If David Bohm is right in "Wholeness and the Implicate Order", pp. 200-5, that the formula for velocity, v = x_2 - x_1 / t_2 - t_1, as t_2 - t_1 -> 0, in its usual interpretation is inadequate, the question arises as to whether there is another interpretation in which it is adequate. If not, we need a new formula for velocity.

I maintain that the formula is OK, except perhaps for going to the limit, but it needs to be reinterpreted as holomovement. The problem Bohm saw is that event 1 has vanished by the time event 2 has come into being, and so one is making a categorical error in comparing something that exists to something that does not exist. It is like building a house on quicksand (or landfill).

So, my conclusion is that event 1 is phenomenal (depth, breadth, and height) and event 2 refers to the noumenal (length, breadth, and thickness). The noumenal event (event 2) has unfolded further than the phenomenal event (event 1). The noumenal spatial and temporal elements are the ones measured by rods and clocks, which are presumably noumenally existing things. The phenomenal spatial and temporal elements, which are inherently extension and duration, have to do with the subjective experience of either the sentient beings conducting experiments or the primordial subjects which are the actual entities of nature. In the latter case, one would have to understand the concrescences of those actual entities as fulfilling the function of the rods and clocks. This is not difficult to do.

So, the only remaining problem is how to enfold the noumenal spatial and temporal elements back into the phenomenal level, where they can become a type of extension and duration that can be compared with the phenomenal extension and duration in the formula for velocity. Four of the Aristotelian categories, action, affection, time, and place, accomplish that function. The noumenal spatial and temporal elements conjoined constitute affection in the unobstructed universe. The mental action acting on that emotional affection enfolds the conjoined noumenal spatial and temporal elements back into the meta-physical time and place, as the event 2 of extension and duration.

This same set of Aristotelian categories in a different context also enfolds the quantum dynamics of matter, having to do with state vector substance and potential actual event, back into the phenomenal level, there to function as forward and backward light cones, respectively, in the locally flat Minkowski spacetimes tangential to the spacetime continuum. It should be noted that state and substance are an additional two of the ten Aristotelian categories.

The spacetime of the spacetime continuum, which exists in the sixth or causal world, is obtained by enfolding the duration of event 2 into the extension of event 2, i.e., by spatializing time. The point and instant, defined as unlimited temporal extension without spatial extension and unlimited spatial extension without temporal extension, respectively, are the physically noumenal elements that become, when enfolded in conjunction with the emotionally noumenal spatial and temporal elements, the continuum of the spacetime continuum.

Moreover, in relation to the point and instant, the final four of the Aristotelian categories come into play: quality, quantity, position and relation, leading further to configuration space, motion, and momentum. This conception of motion is precisely the one we have defined by the formula for velocity. In relation to this meta-physical conception of motion, there is also the conception of noumenal matter, energy, space, and time, which is consistent with primary mental matter differentiated into physical mind and body. The conceptions of the physicalists are limited to physical mind and body, which is only a very small subset of what really exists. Such a limited conception must forever remain ignorant of the real group structure of quantum kinematics as well as the metaphysical framework of Descartes and Husserl or Bohr, Pauli, and Heisenberg.

However, it is true that according to the principle of the psycho-physical parallelism, as defined by von Neumann, it should be possible to express all of our metaphysical structures in terms of elements of the physical world. This is a momentous task, but one that would be very rewarding, like threading the eye of the needle of light determination. This is the real key to the physics of immortality. Still, without the prior knowledge of the metaphysical structure, it is highly unlikely that one could guess the reduced form of its corresponding physical structure.

On the other hand, once we have the spacetime continuum on the meta-physical/phenomenal level, we can understand how the spacetime continuum is connected to the energy continuum on the noumenal level by the zero-point energy as an intermediary, and how the energy continuum divides into the subject/object polarity of the quantum and the vacuum, so that the quantum provides the basis states to probe the vacuum: -> , where x represents the vacuum and the noumenon of Kant. A quantum is a subject, although a quantum system represents the objective structure of the subject, gained by prehending all other subjects. The quantum system will have the normal Hilbert space kinematics of . In this conception of the quantum and the vacuum, momentum is the fully physical noumenal element.

Moreover, here we clearly display spacetime and energy-momentum as independent variables, which they must be in quantum theory, according to Bohm in his 1951 textbook called "Quantum Theory". Here, however, we clearly understand that the relation between the sets of conjugate variables has to do with one being phenomenal (the spacetime continuum) and the other being noumenal (the energy continuum and especially the momentum variable). This is contrary to Bohr's own understanding that complementary elements must be on the *same* level, but it is the basis for a genuine and thoroughgoing ontological treatment. Nor is *this* conception of momentum compatible with Bohm's 1952 theory, although the earlier definition of motion *is*.

In the unified field, organism and environment are what is unified. The field arises as the abiding relationship of the environment to the separated individuality of the organism. It moreover gets introjected by the organism to serve as a Bohm-like guidance field which instructs the organism in its internal construction of monadic reality. As a consequence of this function, the unified field obeys a nonlinear equation, similar to the sine-Gordon equation of Skyrmie. The components of the Fourier transform of such a field cannot necessarily be identified with energy and momentum. So, the question of how to get the momentum space version of the unified field is not obvious.

It turns out that the unified field is defined on the spacetime continuum, but another field, the life field, is defined on the energy continuum and on the momentum variable, by the principle of the psycho-physical parallelism, since energy-momentum is indeed psycho-physical, ontologically speaking. There is yet another field, the ghost field, which is more or less the same as the unified field, except that the ghost field is defined on a lattice, perhaps the world crystal of Kleinert, and its function is to extract the particle spectrum from the unified field. The life field has a German incarnation as the *lebensfeld*, in the *lebenswelt* of Husserl, which is more or less the Kingdom of God. The ghost field has a German incarnation as the *gespensterfeld*, and of course the unified field is the *urfeld*.

It is moreover the essence of this ontological approach to kinematics that motion or noumenal momentum is what is quantized, while spacetime is a continuum and energy is a continuum. This is of course distinct from the situation in nuclear physics, where energy is what is quantized. MASS, according to the ontological view, is attained by the interaction of the inherent Measuring Apparatus, as the embodiment of the subjective aim, with the Subject-Superject of the System. In the ontological approach, motion, or momentum, is the great enigma, and it has a known aspect, which is described in the formula for motion, and an unknown aspect, which is noumenal momentum as an independent variable.

By a careful analysis of all these metaphysical structures we can solve the basis state problem for a quantum reality independent of human observers. As Henry Stapp has shown, the basis state problem is an absolute no-go theorem for Everett theory *and* Bohm theory in all of their present forms. My solution involves the following line of reasoning. The zero-point energy is the mediator between the universal spacetime continuum and the energy continuum. However, the spacetime continuum has a subjective or phenomenal character, as we have already demonstrated. So, we may conclude that it is also relative to organism and environment, on the phenomenal level. In that sense, it will be the body-world schema of the organism that mediates between the spacetime continuum and the Hilbert space of the state vector substance. The body-world schemas are the desired basis states.

It should also be pointed out that the essence of process theory involves the phenomenal temporal element, which is inherently a duration in several senses, one having to do with event 1, as we have already described, and the other having to do with the whole formalized process of becoming that culminates in the Kantian activity of gaining knowledge. Accompanying this formalized process, having to do with enduring objects, is the primary Whiteheadian process of the standing apart of the present subject from its phenomenal nexus of past and future.

In the attempt to escape impermanence and contingency, such a present subject hurtles itself across the oroboric abyss separating the meta-physical from the physical and incarnates as an actual entity, first physical, then mental, then dipolar that becomes physical by the principle of the psycho-physical parallelism. Such a dipolar subject is then joined by its superjective process to the objects that have arisen as essential structural elements of the prehensions of its subjective process and also been made physical by the principle of the psycho-physical parallelism. The objects are harmonized by the superjective process into a unified system of objects, and when the superject is also fully reduced to the physical, by the principle of the psycho-physical parallelism, then all elements of the process transcend the physical and become a completed concrescence in the emotional world.

The phenomenal and noumenal spatial and temporal elements are not ultimately independent, since the noumenal elements are unfolded from the phenomenal elements, especially the phenomenal temporal element of duration as an element of the formalized Kantian process of gaining knowledge. This Kantian process is the mechanism of the unfolding.

Peter Joseph Mutnick 1949 - 2000