Mass and interactions


• An isolated object may not have inertial mass since the principle of inertia assumes that the object is affected by the notion of motion ; then there is no motion concept if there is nothing to refer to (according to Mach's ideas), and if there is some thing, the concerned object is unable to use it as a reference without interacting with it.

For a massive particle, the proper time between the start and the arrival is different from zero ds.  This may suggest that the massive particle does “interact” during its course, altough if we do not detect those interactions, more or less like a photon propagating within a wave-guide (or through a transparent material), or like an elementary particule leaving a trace in a bubble chamber. It would then be probably a very large amount of infenitesimal interactions (with that is wrongly called “vacuum”), and the mass would be a translation for the mean interaction energy.

One thus rediscovers the ideas used by renormalized theories : the “bare” particles are massless and the mass, connected to a spontaneous break of symetry, proceeds (in connexion with renormalization) from dressing of particles by interactions. Inversely, for virtual (undetected) particles taking part in Feynman's diagrams, one must integrate over all motion possibilities including outside the “mass shell” [1].

This elsewere introduces some divergences since there exists an equivalence between the energy-momentum description and the space-time description, within which large energies are connected to small distances. Consequently infinities do appear when one integrates over large energies, since small “distances” do not exist as such : for lack of knowing how to rectify that (what could replace the integration in question ?), the renormalization used at present consists to “potter” such diagrams combinations as the divergences thus introduced will compensate one another [2].

• However, contrarily to what is generally considered by renormalized theories, such interactions might they be limited to “isolated” virtual interactions ?

masse1
masse2
masse3

Indeed, in the framework of the preceding investigation, diagrams not connected to a significant part of the Univers (such as the first among the three ones shown above) may seem to give no inertial effect : when a particule split into a pair of virtual particles, if this pair has no interaction with something else, it has no reference able to give rise to an inertia phenomenon.

One would then have to consider a multitude of small (“virtual” ?) interactions with the rest of the Univers (as within the two other preceding diagrams, where the propagator ended by  x  indicates an “external” unspecified interaction). By “virtual”, it is here meaned “not dectected” an not directly detectable, in so far as any device allowing to detect them would modify their mode of interaction.

Thus, in a manner, there would exist no strictly isolated system (in the way that what usual quantum theories call “vacuum” is always present and active). It seems to me that the radiation of an accelerated electron shows the connexion between inertia and interaction (electro-magneto-weak-hard ; I think that there is only one) in the same way as the behaviour of the Lorentz strength in a change of the speed shows the connexion between electricity and magnetism. Mass and inertia are one of the properties of interactions (and are only that).

• This is not independent  from the interpretation that Feynman had put forward in order to attempt to eliminate within some calculations the divergences caused by electrons self-interaction [3]. These self-interaction diagrams, with loops like in the first of the following diagrams, Lifchitz et Pitayevski draw them aside by considering “that such a loop corresponds simply to the mean value of the current in the vacuum... thus must inevitably be null after renormalization” [4].

It seems to me that there is a more fundamental reason : to do that the electron of the loop should retrogress in time, therefore to behave like a positon ; without saying it clearly, this does not exactly refer to a self-interaction : this diagram thus includes at least a creation of pair from nothing (“energy of the vacuum”) and/or annihilation of pair giving nothing (“disappearance of energy in the vacuum”), as this can be described by the second of the following diagrams (incorporated, after renormalization, in the effect describes by the second of the preceding diagrams)..

boucle1 
boucle2 

In addition, if an electron would interact with itself, it “would know that” (through relativistic instantaneousness, from which Feynman is not far, altough he does not mention it in that way, when he considers a “distant” interaction), then I think that the electron “as a transmitter” cannot even interact with him “as a receiver” (there can be intersection between its last cone and its future cone only if it undergoes at least another interaction between the two).

But in any case, no matter what it would be, that could not take part in its inertia (only the interactions with the other electrons may contribute to that), therefore not only this may not constitute the mass origin (self-interaction energy), but this may not so much as to contribute to that.

• It should be noted that one can go further in the preceding kind of questioning : can an electron emit a virtual photon then to absorb it, without neither one nor the other would interact meanwhile? If one considers also such diagrams as un-physical ones, that widely modifies the perturbative development and its renormalization. Would it be that some divergences come from loops representing badly (physically) the interactions with an imaginary “vacuum”, which is only the whole of what one “does not see” as taking part in the interaction ?

• From another point of view, it may be asked whether “elementary” (unobserved) interactions, allowed to correspond to the dressing of a propagator, are not associated to a kind of “vibration” (in a dimension not visible at our scale) as those considered in the string theories [5].

corde1 
corde2 

For the research of such an interpretation, the notion of hidden “dimensions” would have to be basically revised since, in the arguments considered here, the notion of dimension does not pre-exist but would be infered from interactions.

• One may finally consider that there would be a connexion between such interactions and the large mass of “dark matter” which seems to miss so as to interpret the motion of stars and galaxies [6].

• The interpretation must however be careful, because one may also think that as they modify the number of elementary interactions, thus as they modify the notion of time, diagrams such as the second beside intervene in the inertia described by the first one.

masse4 
  masse5

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References :

1. this may be possibly described by the interaction with the Higgs boson ; see as example (the phenomenon is quoted in many articles) : “Qui attrapera le Higgs”, La Recherche n° 364, may 2003.

2. see as example : “Les séries divergentes”, J.P. Ramis, Pour la Science n° 350, december 2006.

3. see as example (while observing that the “distant” interaction is not really what its name seems to indicate if the notion of “distance” does nos exist at the scale of an elementary interaction) :  “vous voulez rire”, Pour la Science - les génies de la science, n° 19 (“Feynman, génie magicien”), may 2004.

4. “Théorie quantique relativiste (2)”, E. Lifchitz et L. Pitayevski, Physique théorique tome IV, éd. Mir, 1973.

5. see as example :
            “Le monde des cordes est-il le nôtre ?”, P. Ramond, Pour la Science n° 300, october 2002 ;
            “Le paysage de la théorie des cordes”, R. Bousso et J. Polchinski, Pour la Science n° 326, december 2004 ;
    while however observing the existence of difficulties connected to the theories of this kind (unobserved variations with time for some physical constants) :
  “L'Univers avant le Big Bang”, G. Veneziano, Pour la Science n° 320, june 2004 ;
  “Les constantes... le sont”, C. Pichon, Pour la Science n° 320, june 2004.

6. see as example (the phenomenon is quoted in many articles) : “La face cachée des galaxies”, G. Lagache et B. Guiderdoni, Pour la Science n° 296, june 2002.




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