Let us imagine a biofeedback machine where the three principles of mechanics are expressed in an alternative but quantitatively equivalent form, as in Weber’s force law (1846): instead of inertia, there is a zero sum of forces; instead of a constant force, the intensity of force depends on the environment; instead of simultaneity of action and reaction, there is a «retarded potential» and thus an internal, proper time of the system. The first remarkable difference between these principles and the more familiar ones is that they allow, to a certain extent, the interpolation of consciousness within its framework. The second is that it applies equally to point and extended bodies or events, rendering unnecessary crucial artifices supporting special relativity, general relativity, or quantum mechanics and making them incompatible with each other. The third is that it makes possible a conception of time different from those of physics and psychology.

(Let us recall, if necessary, that as a framework the very principles of mechanics are indemonstrable within the system they frame and are a matter of choice —something Poincaré already made evident when discussing precisely Hertz’s and Weber’s systems). The three principles of mechanics involve, through the quantities that express them, a schematic concept of space, time and causality. Now, what kind of relation exists between the principles of mechanics and time? And here, before speaking of the subjective aspect of time —temporality— one should start considering the time of mechanics itself. Most physicists would now favor a criterion which we may call «operational» and which states that physical time is nothing but the measure of motion; and this criterion is used to argue that without assuming the constancy of forces or the equality of background and coordinate systems, physics would not be possible. This is typical of Newton’s system, which, as later relativity theory would do, conflates absolute and relational concepts; however when we stick to a purely relational idea of dynamics as in Weber’s law, we can consistently dispense with both universal constants and global synchronization in addition to inertia.

If one can establish unequivocal temporal sequences with Newton’s three principles, the same can be done with the three relational principles that Weber does not enunciate but Andre K. T. Assis makes explicit —even if the later is still far from drawing the consequences of these principles. Of course, the principles of mechanics alone, whatever the choice, don’t suffice to account for the inexhaustible complexity of natural flows with a possible temporal interpretation. They are a general frame that often will require a strong statistical component, replacing simple ideal bodies for assemblies —something already contemplated in the distinction between material particle and material point of Hertz’s mechanics. As far as I know, Vladimir V. Aristov is the most prominent proponent of a relational statistical approach to time.

Aristov has done much to enrich the hitherto extremely schematic conventional description of time in physics. This one deals with time intervals —when it does not think of instants as points on a numerical axis— but lacks a concept of time as a state. Of course the big question remains of how time irreversibility arises, something that is not even considered in the so-called fundamental equations. Aristov proposes a model with three reference points instead of two, as well as a number of statistical and axiomatic contributions that also cover biological issues and are needed to make the quantitative treatment of time less simplistic.

However necessary such precisions may be, it is very likely that the most intangible component of time, namely its subjective aspect, does not depend on complexity either. In previous posts we have suggested that the «proper time» or retardation associated with Weber’s mechanics might lie halfway between the purely external limit of global synchronization and the undifferentiated homogeneous medium —and that the subjective sense of the passage of time requires both a constant and a variable relation between a physical proper time and the unit density of background homogeneity, even if for particles the homogeneous background may be considered as a statistical average. These would be three different aspects or planes of time, similar, to some extent, to C. S. Peirce’s categories of thirdness, secondness and firstness in the moments of semiotics or drift of signs in the mind, which also entails a temporal process, though certainly irreversible in contrast to the three laws of mechanics, which in addition can also be put in correspondence with these categories.

Relational mechanics can take various forms which need not be equivalent. If one asks various physicists engaged in this approach what its essential feature is compared to more promoted approaches such as field theories, the most common answer is that it dispenses with space-time as an independent category. Others might say that, at least in Weber’s mechanics, the use of homogeneous quantities should allow for a better understanding of the abundant unexplained numbers in physics. But if we dwell here on the latter as the model par excellence of relational physics, it is above all because it frees us from the idea of inertia, as well as from the global synchronization and universal constants that serve as its safeguard; and with it from many other artifices, such as the cumbersome, scholastic arbitrations with the various reference systems.

But the importance of getting rid of inertia goes far beyond questions of convenience or simplicity. What is at stake is the foundation of our idea of Nature, hijacked by a certain idea of physics, as well as the idea of the living and nonliving, and even of the general drift of our logic and our mind. It took two thousand years to mature the concept of inertia, but less than a century to sit quietly on it — because it was only wanted as a starting point. One can always argue that Weber’s mechanics deviates from relativity at high speeds and energies, just as one can argue that a theory like relativity always has plenty of artifices to rearrange the data in its favor; but at this point we will not enter into such controversies. Of course, there is no room for black holes and many other paradoxes and pathologies without which the fantastic genre is orphaned, but so much the better. In fact, a black hole is not a consequence of relativity, but of the absolute character of a gravitational force regardless of the conditions of the system, which can only be a fiction. On the other hand, there are many other things to keep track of that are still awaiting detection. But first and foremost it is a matter of principle, and since principles already affect the final interpretation, they also affect everything else.

Husserl undertook penetrating analyses of the three aspects of time, both in music and in relation to transcendental subjectivity —with the self-referential moment of a consciousness not yet driven by intention, a kind of ‘time zero’ from which the moments of the present, past and future would escape. Husserl’s exposition of temporality is among the most profound reflections on the issue, yet the presentation of the self-referential experience of consciousness as a painful short-circuit or trauma is too reminiscent of the contemporary lucubrations of the father of psychoanalysis. Why should self-consciousness be painful? What prevents it from resting in itself? Here one could argue that this inability is due to the mere inertia of habit or conditioning.

Which would bring us again to biofeedback, that, rather than a way of controlling biological functions, is a means of attenuating their conditioning —it is a negative feedback, as is often the case in natural regulatory mechanisms. A signal of a potential, associated with a system state, seems much more suitable for inducing negative feedback than a signal of force, since the type of influence here is involuntary, not efferent or motor. And what does this have to do with a relational mechanics such as Weber’s? Weber’s or Assis’ mechanics substitutes inertia for dynamic equilibrium, which must exist always by definition. On the other hand, the equilibrium between action and reaction takes place through a time interval, coexisting with the adjustment of the force to its medium, be it external or internal.

In fact there is no distinction between both points of view. In Newtonian or any other mechanics with inertia and the global synchronization that enforces it, everything is externally arranged even if it involves a flagrant contradiction, since after all inertia begs us to assume a closed system that at the same time is not closed. This creates the possibility of temporally reversible laws, which must surely be another fiction, and deepens the divide between physical laws and what Peirce called «the law of mind». Which brings us to another question that is never asked but is nonetheless far-reaching: is Weber’s relational mechanics, taken in its most generic sense, reversible or irreversible? The fact that Weber’s force law and its associated potential emerged in the context of electrodynamics might lead one to think that it is exclusive of reversible systems, but this is a prejudice without further justification, and we have already seen that even Maxwell equations belong to two thermodynamically different categories. In the absence of proper studies on the subject, everything suggests that, assuming that this mechanics does not depend on the chimerical condition imposed by the inertia principle, it allows both reversible and irreversible behaviors. However, contrary to the most widespread opinion, we believe that the latter is the general case, and therefore also the most fundamental.

If relational dynamics admits the irreversible, it allows to transfer to the internal, and also to the mental sphere, a rectification over time between the three moments of its equilibrium, something that in classical mechanics can never be made explicit. In contrast to the relational approach, we have seen other anholonomic formulations of mechanics, of the Cartesian type, which do not have inertia either, but instead make all movement dependent on acceleration or imbalance. Opposed in approach, both dynamics can coincide on the common ground of the shift of the potential, which in modern physics has been introduced through the back door in what is known as the «geometric phase». And we have also seen the ergoentropic equilibrium between minimum energy variation and maximum entropy proposed by Mario Pinheiro for an irreversible reformulation of mechanics. We cannot go into the relationship between these three formulations here, although the subject deserves an in-depth study.

Within Peirce’s semiotic scheme, the retroprogressive arises by tracing back from the tertiary to the secondary categories, and from these to the primary one. The third law of action-reaction defines the conditions of interaction, mediation and measurement; the second law, which defines the action or force, can only have for time an inditial, incomplete character; the first law defines or cuts out the contour of the immediate from which we start. But the point that has not been made is that the same laws of mechanics, being a particular case for the internal use of physics, end up dragging down the drift of the world and the mind into which we have plunged ourselves —since, as a general disposition, they have also determined the entire flight of technology. If techno-science went all out in the external control of the world, it is only natural that the external will now drag us along no matter what our will may want.

Biofeedback can be used as a means of testing the internal, subjective side of certain principles of dynamics, while the relational principles of a dynamics such as Weber’s allow us to see that this internal side also admits an external correlate. Looking for a general context for the man/machine interface, approaches such as «endophysics», a physics «from within» that would combine elements of quantum mechanics, relativity and chaos theory, have been proposed in recent decades; but perspectives of this kind remain tied to the dominant conception in physics of the observer, representation and controllable forces. The interface is presented as a «cut» at various levels, but the great and definitive cut that physics has introduced is inertia and the inertial system, and it is here that we must begin. The «endophysical approach» has not been developed further, but the work to find interfaces between the living and machines grows steadily, and today we find that the geometric phase of potentials is routinely used as a tuning factor in robotics and control theory.

The real «interface» would be the shift of the potential, but this does not require any «cut», for in this relational mechanics there is no conceptual separation between the internal and the external, the «living» and “nonliving», the inert and the driving forces. And the “shift of the potential» is not unique to quantum mechanics as is still assumed, but necessarily occurs at all scales since the retardation can only exist with respect to the fictitious global synchronizer of Newtonian mechanics.

As Ruyer would have put it, there is the observable and the participable; the former is the object of intentional consciousness, the latter is not, but it is no less important for that. It can even be said that civilization is the exploitation of the surplus of the participable for the benefit of the observable, which always ends up having an owner. The race for the fusion of man and machine is a compulsive escape that tries to compensate for the self-inflicted cut accomplished with mechanics, but it is clear that our use of machines and tools goes back much earlier than the generalization of the three principles —as is clear that the «instrumentation principle» we sometimes talk about is not the late «instrumental reason» of modern thought but a way of externalizing force with or without tools.

Thus, the internal coordination with what we may, not without malice, call «Weber’s mechanism”, goes beyond physics or technology. To what extent have the specific form of the principles of mechanics been able to influence our subjective temporality? It seems an impossible question to answer, because temporality never moves in vacuum, and yet Newton’s principles are conceived as motion in vacuum. The three classical principles are purely external, in no way can they be internalized. Their influence extends first and foremost as heteronomous drift. In Newtonian mechanics, nothing moves without being moved by something else; in relational mechanics a body can thrust itself in perfect consistence, without any contradiction.

Temporality does not move in vacuum, otherwise it would never have taken hold as an internal form of a culture —as when we speak of vertical, linear, or circular conceptions of time. The three classical principles may represent a causal sequence, but they do not delve into the subjective sensation of time. The three principles of relational mechanics can do so, and yet this «mechanics» does not need, or rather excludes, causal representations —the perspective it provides is really acausal, and thus amechanical. But the question of causality would now take us too far; on the crucial arguments about Newton’s bucket experiment, we can explain the curvature of water by both Pinheiro’s ergoentropic equilibrium and potential energy, but hardly by absolute space as the proponent of the experiment did.

In the face of so much misunderstanding, it is worth remembering that our present civilization has had only one natural philosophy, which is none other than Newton’s. All subsequent «revolutions» do not change the essential question, nor will they change it, because what it takes to do so is not speculative physics, but its antipode, fundamental physics, as well as, of course, natural philosophy itself. To contemplate the world without inertia is equivalent to continually renewing it, but consciousness can barely maintain itself for an instant in such a state of suspension. How can this be, if we said that the laws of classical mechanics are not susceptible to internalization? We have already seen that even the three principles of classical mechanics can be understood both on the same level and on different degrees or levels, according to Peirce’s semiotic implications. It can be argued that intentional consciousness is necessarily external, albeit to very different degrees, and that contemplating non-inertiality drives us back in the direction of that other consciousness prior to intentionality which Husserl called transcendental subjectivity. And within this consciousness we can perhaps distinguish between a stable equilibrium and an unstable one, which can also be associated with certain principles and evolution of dynamics.

Breathing, for example, is both a voluntary and involuntary process, just as it is mechanical and amechanical simultaneously. The bilateral nasal cycle is most likely associated with a retarded potential, and following its axis we can access the amechanical aspect of the breathing phenomenon. This in turn is linked to the perception of time, and to the transformation of intention into attention, and of attention into self-awareness. It is not difficult to glimpse in all this the possibility of both a gradual and a direct path.

The life of the spirit not only has no need of technologies, but rather opposes them in general. But here we glimpse a passage beyond the principle of instrumentation which allows us to see science and technology in a different light; and the fact that all this is taking place at the very heart of mechanics has a special significance which we want to endure.


Henri Poincaré, Nicolae Mazilu, Hertz’s Ideas on Mechanics (1897)

V. V. Aristov, Relative Statistical Model of Clocks and Physical Properties of Time (1995)

Nikolay Noskov, The phenomenon of retarded potentials

K. T. Assis, Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force ( 2014)

Alejandro Torassa, On classical mechanics (1996)

Koichiro Matsuno, Information: Resurrection of the Cartesian physics (1996)

Mario J. Pinheiro, A reformulation of mechanics and electrodynamics (2017)