Arjen Dijksman
Article published in Fusion n°75, MarchApril
1999, ISSN 0249.7648
The concept « matter » does not seem to be defined with precision, as well in the current language as in the scientific community. In reference books, one may find indeed the following definitions:
In the standard model of contemporary physics, one admits
commonly that all the particles are material, excepted the
photon, because it does not have inertial mass. The neutrino,
other apparently imponderable «particle » that may hardly be
said to constitute the bodies, is however regarded as matter.
These definitions obviously carry the print of definition I of Principia of Newton^{1} : « The quantity of matter is the measure which one draws from its density and its volume ». Newton specifies a little further that he employs indifferently the concepts quantity of matter, mass and body for the same abstraction.
This fuzziness maintained around the most fundamental concept of «the Science of Matter » is detrimental for the advance of knowledge. How can one indeed hope to describe matter with precision, when the bases on which one melts this explanation are ambiguous?
The statu quo results from the indubitable success that have the laws stated by Newton, using the above mentioned definition. This definition is criticizable and has been criticized. One can for example quote Mach^{2}. « [... ] definition I has only the appearance of a definition. The concept of mass is not clearer because one defines it as product of volume by the density, since the density itself represents no other thing than the mass of the unit of volume ».
Neither is the definition of Newton compatible with the Lagrangian use, where one compares the matter element to a point. The volume of a point being null, the quantity of matter of the material point given by the product of volume and the density must be null. It is of course a calculation artifact, making it possible to describe the physical interactions in the classical domain, but it is not satisfactory for the description of the matter. As soon as one is interested in the interactions between particles of the quantum field, the representation of the material point is of no more use.
Also, at the beginning of quantum physics, we realized that it was necessary to introduce the concept of the antimatter, which, in spite of its evocative name, is no less material than matter. We also had to admit that we could not locate the matter in a point. With the passing of years, the scientific community endeavoured «to standardize » the matter by adding supposedly elementary qualities (spin, strangeness, baryonic number, a leptonic number...) to more traditional qualities as were the mass or the electric charge.
In his correspondence with Bezzo, Einstein^{3} wrote: « We are still far from having a rational theory of the light and matter which is in agreement with the facts! I think that only a bold speculation is capable to make us progress, and not an accumulation of experiments ». In spite of the extraordinary experimental advances carried out since their date of writing, these words are still timely. I am of the opinion that the concept matter should be reconsidered.
Let us take a matter element. What makes it that this element is perceived as a material object? For some, formed at the school of Newton and Lagrange, it is its mass. Let us imagine that I hold this matter element between my fingers. Whether it has a mass or not, I would perceive this element as matter if it has a proper extent. In other words, this element is matter if it cannot be superimposed on another matter element. This point of view is not new. In fact, I only join the dominant idea before Newton revolutionized physics. In his « Principles of philosophy », Descartes^{4} wrote: « Neither gravity, nor hardness, nor the color... constitute the nature of the body but the extension alone ». This more intuitive point of view frees me from the cumbersome concept that is the mass.
To model this idea, I suppose that the matter element is comparable to a short segment of a straight line, with constant length. In order to avoid a confusion with the Newtonian matter element, I will name it materion. To give a more concrete idea of this element, one can evoke the image of a needle or a rod whose mass would be null. Interactions between materions only proceed by contact. Let us take two materions initially without rotation and that are colliding: it seems clear that their state of movement after collision depends on the point of contact (figure opposite). If the point of contact is at the center of the materion, this materion moves away from the collided materion, without rotational movement. If the point of contact is not at the center of the materion, it acquires a rotation after the collision, with a rotation speed depending on the ratio of the distances from the center to the point of impact and from the center to the end of the materion. The effect is similar for the collision between two materions initially in rotation: no change of rotation if the point of impact is at the center of the materion, change of speed of rotation in the contrary case.
Within my conceptual framework of matter without inertial mass, the velocity of the colliding materion with respect to the collided materion can take only one value after collision. Indeed, there is no "occult" quality which would enable us to deduce a variation in the velocity. This reflects the experimental behavior of the photon: whatever the initial relative velocity between the photon and the experimental device, final relative speed seems always equal to a constant value (in vacuum). The directions of the translative velocity and of the axes of rotation result from the geometrical analysis of the collision.
To allow us to correctly judge of the relevance of this model, it is necessary to carry out simulations on a significant number of materions. Let us imagine a cloud of motionless materions (without rotations or relative translations). Let us send a materion with significant rotation in this cloud. By observing the evoked rules of collision, one can deduce that the projectile materion will cause shock waves with propagation of the collided materions. The frequency of these shock waves is equal to the rotational frequency of the projectile materion. This is explained by the fact that when the materion is parallel to its translation velocity, it "pierces" through the cloud; when it is perpendicular, its "cross section" is maximum. However the direction of the extent of the materion varies periodically. There is "phase coincidence" between the rotational frequency of the materion and the frequency of the shock waves induced by same rotation. The shock wave being made up of sole materions, its velocity of propagation is of the same order as the velocity of the projectile materion. Here we find a similarity with the of works of Louis de Broglie^{5}, for who "the incidental photons have a frequency of internal oscillation equal to that of the wave". For de Broglie, it was the wave that controlled the internal frequency of the photon; in the model of the materion, it is the materion that controls the frequency of the wave.
In the preceding cloud of materions, let us
imagine a screen with two slits (device of Young, figure below).
The projectile materion, which crosses one of the two slits, will
interfere with the shock waves which passed through the other
slit. If we compare the rotating materion to a photon, it is not
astonishing that a controlled emission of photons (one by one)
gives interference rings in the experiment of Young. In all taken
experimental measurements, one never evacuated the "cloud"
of ambient photons upstream of the two slits. In fact the
collisions upstream of the screen, generate downstream the
interferences of the projectile photon with the photons of the
induced wave. The waveparticle duality for the light rises quite
naturally from the model of the materion.

In accordance with the statistical laws applying to significant sets of particles, a thermal balance establishes in any significant population of materions. Their energy distribution will then be similar to that of the radiation of a black body. Thus, in this model, even in the absence of "material" bodies, there may be a thermal radiation. On Earth, this experiment is not easily realizable, but the intersidereal vacuum provides such a radiation: the cosmological microwave radiation of the universe^{6}, currently explained within the theoretical framework of the BigBang.
If the spinning velocity of the projectile materion is high enough, it may supplant the constant translation speed after a collision. The contact between the projectile materion and the struck materion will not be instantaneous anymore. Both materions will "slide" on each other. While crossing a cloud of materions, the apparent speed of the projectile materion will be lower. Up from a threshold internal spinning velocity, the materion thus acquires an inertia. With l the length of the materion, f the rotational frequency and let c be the constant universal of translational velocity, this will occur when the rotational component at the end of a materion (= l p f) is higher than c. With the experimental data (frequency of appearance of electron = m_{e}c^{2}/h, approximately 10^{20} Hz), this implies that the length of the materion must be h/p m_{e}c. This length is equivalent to l_{e}/p ~ 0,8.10^{12}m, with l_{e} the Compton wavelength of the electron.
We therefore see that it is possible to deduce the property of inertia out of geometrical considerations on the motion of fixed length rodlike particles. This has an undeniable advantage on all the central force models where inertia must absolutely be introduced a priori, to explain the behavior of the ponderable particles.
By taking identical measurements of the position or speed of a materion, one realizes that there is indeterminacy of the result of measurement. There is a certain probability of presence of the particle in each point of a volume whose section is of about size of l. This "statistical presence" should be interpreted as a rapidly spinning rodlike particle. Since the materion has an extent, measurements of its position or its speed may give several values depending on the position, on the segment, of the point of interaction during detection. This point of view reconciles a mechanistic explanation of matter with quantum mechanics.
We saw that, at the instant of an inertial interaction, the point of contact moves along each of both materions. They separate, when the point of contact reaches the end of one of both materions. If a third materion enters in interaction with one of the two other materions, whereas the first interaction is not finished yet, there are cases where these three materions will form a bound system, since they oppose mutually to slide along the extent of each of the materions. The three materions will present quantified complementary rotations which will not exist any more if they are separate. The experimental data on the structure of quarks in baryons are in agreement with this point of view.
Since these aggregates have "hooking points", they will be able to combine, either with other aggregates, or with other materions, provided that there is compatibility of rotational movements. These systems will form atoms and molecules. According to the conceptual framework of the matérion, the rotational motions inside these systems can take only quantified values. This is an undeniable experimental fact on which rest all the quantum theories of matter.
In his correspondence with Michele Besso, Einstein further
wrote^{7} : « A
truly rational theory would allow us to deduce the elementary
particles (electron,etc.) and not be forced to state them a
priori ». The conventional theories do not make it possible
to answer this requirement, since they are restricted to order
the empirical facts, in terms of concepts that are too far away
from our perceptions. To succeed in building a really rational
theory, it is necessary to reconsider the matter while being
freed from the standard concepts. The few ideas which have been
presented above illustrate the fruitfulness of such an approach.
They are asking to be verified.
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