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There was a great controversy in the last half century about the physical meaning of the potentials and the quantum potential in particular, with several open questions that persist. In this short article, before solving them, we will try to raise new questions that might have an unexpected impact on the future. In particular, we want to indicate the value of feedback beyond the omnipresent paradigm of control. Calculus is an heuristic device, an interface between mathematics and the physical world, but it is not the only one. There are other ways of exploring this world, although the one we are dealing with here is not incompatible with calculus.

Potentials emerged in physics and calculus as an auxiliary concept but over time they have become essential. It has been said that quantum potentials are completely different from the classical ones relying on phenomena such as the Aharonov-Bohm effect but it is clear that this effect can be derived from classical equations and in fact a strictly analogous example has been found even on the surface of water.

In principle, it is assumed that the potential energy is derived simply from the position and is the passive, reciprocal factor of the active element that originates the kinetic energy and the appreciable movement that is the force —one and the other would be the static and the dynamic case. In Newton the idea of potential is strictly the inverse of the force, then its sum should be by definition equal to zero; but the Lagrangian introduced a century later tells us that the kinetic energy is greater than the potential energy and therefore has a positive value. This should have already raised suspicions, but since the point was to facilitate derivatives and calculations, nobody protested.

If the potential energy is the static case and the kinetic energy the dynamic one, Are they both equivalent? Weber’s force law, applicable both to electrodynamics and to celestial mechanics, allows a different view of the subject: all the invariable forces, as in the case introduced by Newton, are reduced to the static case, and only the forces dependent on the speeds and relative accelerations allow to speak properly of a dynamic case. Weber’s law is the first instance of purely relational force in dynamics but, as we all know, his argument, although perfectly valid, was not followed.

Is the kinetic energy the same than the potential energy for our self-perception? It seems clear that this is not the case: our body deforms with gravity when this one is only potential, but it doesn’t deform when gravity manifests itself directly as motion, as in the case of free fall. And yet the deformation is the first indication of the acting presence of a force! Our body’s interpretation of these things seems quite at odds with the calculus view and its conveniences, though it isn’t incompatible with it either.

Probably the static/dynamic distinction is more important than what the framework of dynamics shows —since dynamics, by its very definition, has already decided what its priority is. That is, the values associated with the positions are already bound to the forces and no other consideration. This is perfectly legitimate from its own point of view and there is no problem with it; but it doesn’t exhaust the case either.

Before the term «potential energy» came in —a term that apparently Rankine first introduced- it was not uncommon to call it tension, as in the celebrated Helmholtz paper of 1847 that so much harmed Weber’s theory; and still today stresses of diverse types and systems are counted as potential energy. This is not something that makes it independent of the priorities of dynamics to our view, but at least it does not relegate it to the purely passive role that we use to grant it.

An additional point is that thinking in terms of forces compels us to think exclusively in terms of controllable quantities. We can measure other values, but if they are not within the framework of what we can control and follow in a deterministic evolution, they are labelled as accidental. This is patent in something as universal and classical as the constitutive law of materials; but we can see it also, for example, in non-local quantum correlations.

Weber’s force law, earlier and more general than Maxwell’s formulation, can be equally extended to hydrodynamics, thermodynamics, and many other situations. It is also the most elementary example of intrinsic feedback in a fundamental physical law, since the length of interaction influences itself through the force of interaction. We have already pointed out elsewhere that the very Newtonian case for the ellipse hides a self-interaction or feedback right from the start, to the point that the closed ellipse can not subsist without it —there is really no local conservation of forces. Therefore, the most general fundamental laws, such as gravity and electromagnetism, to the extent that they require principles of action, do not seem possible without feedback. In other words, the principle of stationary action seems to hide a feedback principle.

In recent times we have witnessed the development of new experimental specialties such as continuous quantum measurement or quantum feedback that allow the manipulation/modulation of individual quantum states, and that will shed new light on the indefinite and controversial transition zone between the classical and the quantum domain. In all this vast field we just begin to explore the possibilities and bifurcations: quantum engineers even talk about self-feedback, for cases in which a resonator interacts not with a controllable system but with an environment with many bodies.

The improvement in the mechanical manipulation leads here to a greater sensitivity in the modulation, and the best modulation allows to specify more precisely the mechanical details and the circumstances of the environment. We get a classic feedback circuit, sensor → calculation → action. And this way, without much noise, the vast realm of microphysics is entering a new territory.

All this not only involves a gradual shift in man/machine interfaces, it will finish provoking a deep change in the man/nature interfaces too, that in the long run can make not only a change but also a turning point.

The idea we have today of this broad change is exclusively technological, relative to the order of manipulations, but the aspect of tuning, of awareness that entails, is still being ignored. However, the very nature of things —the very human nature- allow us to predict that all this will end up affecting both the scope of our perception just as much as that of our action, to both our «efferent» and «afferent» impulses.

Let’s imagine that we are doing biofeedback through output signals of a function of our own body, such as pulse or breath. A rather innocent question is whether there are better signals than others for the sake of self-regulation; that is, whether or not the type of representation or interface of the signal is indifferent. Let us think, for example, of representation in terms of movement and force — kinetics- and representation in terms of position or potential. Since we have just spoken of afferent and efferent impulses, of input and output, it is simply reasonable to think that, for our self-perception, both correspond to the kinetic and potential aspect.

It is clear that with biological signals it is quite easy to check the effectiveness of one or another type of signals/interfaces. Now let’s take a leap and think about how our mind or intention could manipulate/modulate/tune physical systems out of the body —exosystems- through certain mechanisms and interfaces. Are there also different degrees of efficiency here, depending on the intended objective?

Finally, within this context of the mind/machine interface, we could naturally ask ourselves what are the minimum mechanisms and interfaces allowing communication in both directions. And the answer, as ambiguous as we want, is that the very limit depends on how we understand and perceive the Physical Continuum. We have already talked about this in relation to the interface conditions of electromagnetism.

Our idea of self-interaction, at a fundamental physical level, is also important, as in the framework of the law of retarded potentials the principle of action is directly translated into feedback. Retarded potentials fit naturally in continuum mechanics.

What really matters, in any case, is that we can access a perception of nature other than mere motion and extension. Physics is interesting precisely because things are not reducible to motion and extension, but the utilitarian views compel us to forget it.

It is necessary to go beyond motion to capture the transformations in the intensive and apparently immobile. Capturing change in the motionless, and what is motionless in motion itself: this would have to be the value of biofeedback as endoscopy in physical reality. David Finkelstein coined the word «endophysics», which Otto Rossler described to a great extent; but it is useless to deal with the theory of Relativity and quantum mechanics as «participatory frames» when they are explicit ruptures with the notions of the one and only Continuum. If there is no rupture, there is no need for participation, and it is only in the continuum that one can speak of exterior, interior, and what goes beyond these more or less superficial distinctions.

We have already commented in other writings that the constitutive law, strain-stress relations or the theory of deformations and tensions, veils with its metrics the most universal aspects of the physical continuum, of which the known fields are just extracts.

The connection between biological feedback and exosystem feedback is just a matter of interface; and the same would apply to quantum exosystems —if in such a case it were possible to speak of external systems at all. Obviously, there is quite a difference between bound and unbound states. But in all cases this «insider view», which is really only a certain recovery of the physical continuum, must throw a totally new light —the light of what is free of utilitarian aims. Our mathematical descriptions, however accurate in language they may be, are already severely limited by their inherent predictive purposes.

Thus, beyond manipulation and «modulation», it is possible to speak of knowledge by tuning, without ulterior purpose, which takes advantage of the means that modulation and manipulation have made possible. These means, more or less opportune, would be basically accidental.

It seems that the most peculiar aspects of the quantum potential are reducible to those of the field of its wave, and therefore, are due to the notions sustained the continuum and nothing else. Surely a more or less direct and subjective sensitivity to phenomena such as potential wells and the tunnel effect can be developed, which also do not seem to have anything of intrinsic quantum nature and can be explained with a more or less thorough classical description. Here, however, description and interpretation are at the service of something quite different. Bistable and metastable systems, which can be found at both the biological, classical and quantum level, can have decisive features that are independent of coordinates and scale.

Calculus is an heuristic device, an interface between mathematics and the physical world, but not the only one. There are other means of exploring this world, although the one we have noted here is not incompatible with Calculus.


Nature is not simply the background on which society has been built, and which we recognize «out there» as forests, skies and oceans; unrecognizable, it crosses us internally also as passions, as perceptions, even as silent consciousness in the midst of the procession of thoughts and words that are the social currency proper. Science, which is the most opposite to instinct that can be imagined, can only be incorporated into Nature as an external object and as an abstracted law of phenomena. This perspective is bound to instrumentality even with the best will of the world.

This being understood, is foolish to think that man can develop science and technology for the mastery and exploitation of external nature without doing the same, measure by measure, with our internal nature; but perhaps the very social illusion depends on the systematic ignorance of something so plausible.

If everything were descending forces in this world, and the same goes for the ascending ones, things would soon come to a halt: it is like imagining a body with only efferent or afferent functions. Thus, even against our will, trends always seek balance. I can assume this is why I am writing here, without being able to explain to myself what I am looking a way out for, even when I don’t feel the need to justify it. Instinct will tell some of us that it is necessary to insist on this direction regardless of utility or purpose. Someone who is drowning or wants to break through the siege does not need them.

To live in the Society of Control is to tempt its external and internal limits up to the threshold of its cessation.

Appendix: The pulse wave, the retarded potentials and the Continuous Proportion

As we know, the profile of the pressure of the pulse wave over time is the sum of the cardiac impulse and a reflex wave created by the peripheral vascular system at the interface between large arteries and the smaller vessels that cause resistance. At any time and in any part of the arterial system there are three factors: the amplitude, the duration of the contractile impulse of the heart, and the amplitude of the reflex wave.

It has been said that the ratio between the time of systole and diastole in humans and other mammals tends on average to the Continuous Proportion; likewise the systolic pressure in the aorta is 0.382 and the diastolic 0.618; this proportion is also found in the electrical activity of the brain. There are good reasons to be skeptical about such numerical associations when they are not connected to mechanical reasons, which use to be the case; but perhaps here, if time and pressure are under the same unexplained common denominator, there is an opportunity to find the desirable connection with dynamics; the systolic time of the profile already involves the reflex wave, and the same goes for the diastole.

On the other hand there is the pulse wave speed, which is a measure of arterial elasticity: both are derived from the Second Law through the Moens-Korteweg equation. This wave velocity varies with pressure, as well as with the elasticity of the vessels, and it increases with their stiffness. The return distance of the reflex wave and the time it takes increases with height, and a lower diastolic pressure, which indicates lower resistance of the whole vascular system, reduces the magnitude of the reflex wave. Treatment of hypertension should focus, it is said, on decreasing the amplitude of the reflex wave, decreasing its velocity, and increasing the distance between the aorta and the return points of this wave.

To a large extent, it seems that we can consider the elasticity of the reflex wave as a Weber-Noskov retarded potential dependent on distance, force and phase velocity, and see if this provides a coupling or resonance condition that, incidentally, would tend to to the values of the extreme and mean ratio. The myocardium is a self-excitable muscle but this entails also the return of the reflex wave, so we have a beautiful example of a circuit of stress-pressure-deformation transformations that are fed back and that should not be far from the most basic problems of physics that we have dealt with in other articles and that also involve a certain feedback.

There is a remarkable similarity here that demands a detailed exploration. Not only can we model it anew, it can also be simulated numerically and even physically with elastic tubes and artificial pumps.

Peter J. Riggs, Reflections on the de Broglie–Bohm Quantum Potential
Nikolay Noskov, The phenomenon of the retarded potentials
Zhang J, Liu Y, Wu R, Jacobs K, Nori F, Quantum feedback: theory, experiments, and applications
V. D. Zvetkov, V. D, Heart, Golden Ratio and Symmetry
Miguel A. Martínez Iradier, Self-energy and Self-interaction
Miguel A. Martínez Iradier, Between stress and pressure