relativite

Relativity and quantum theory ; wich interpretation for the “vacuum” ?

• The theory of general relativity considers in a certain way that space-time is not pre-existant to its contents : Einstein does not describe a space with a pre-defined metric, in which appears a gravitationnal field (even if it would be associated with another metric) but on the contrary a space which “field” and metric are one only and same thing, direct consequence of the contents [1].

The quantum theories, on the contrary, were considered in a pre-existing flat space. Therefore it has been tried to generalize them in a space described by a curved metric deduced from non quantic general relativity. Elsewhere, a quantic theory of general relativity has been searched for, but in some manner independent of the others quantum theories (relativistic quantum theory of gravitation) [2].

But the “empty” space-time does it exist in the absence of interactions, or is it an absurd notion ? I feel better to consider the first of the two approaches : to deduce the space-time from the properties of quantum interactions [3, 4].

• Thus, in a space (?) which is “empty” except for an isolated material point, this material point is it able to move ? No, since in order to move, it would have to move with respect to something else and there is nothing else. In particular, the principle of inertia in a galilean framework, which says that every isolated material point moves with an uniforme motion, requires to consider that the empty space (the framework) is an active object in interaction with the point (which in this case is not really isolated). Moreovec : might it exist a space (?) “empty” of everything except for an isolated material point ? No, since so that “elsewhere” may exist, it would be necessary that the material point interact.

In a space (?) which is “empty” except for two isolated material points, one of these material points is it able to move with respect to the other ? No, since in order to move, it would have to modify the distance or the direction with respect to the other and there is as reference neither other direction nor distance than those corresponding to the couple of points (which necessarily always remain identical to themselves). It is thus necessary to have at least three material points so as one may consider a motion.

In a space (?) which is “empty” except for three isolated material points, one of these material points is it able to move with respect to system of the two others ? May be, but it is far from evident since for isolated points, the absence of interaction forbids the comparison of distances. It must even be asked if the notion of distance has a signification for two points without interaction between them (the distance variation might it not have as only signification a variation of the way it interacts ?).

• The interaction between two electric charges supposed “isolated material points” must take effect in the direction defined by both two points, but the scale invariance would impose that the interaction does not depend on the “distance” (?)... except if there is something else in the “vacuum” (the 1/r² dependence may contrarily seems as logical in the R³ space if one considers the statistical effect of an “infinity” of virtual interactions within wich those studied are only a few ones).

• In a space (?) which is “empty” except for an isolated material point, does the time flows ? No, since in order to get a difference between a moment and another it would be necessary that happens a phenomenon which distinguiches between them (according to Prigogine, the time is made by the interactions).

• If, in relativistic theory, space and time combine themselves during frameworks changes, whereas they seem for us to have fundamentally different properties, it is (in my opinion) because the fundamental nature of these quantities is not what it seems to us within our scale. All things considered, I think that the space-time structure must be not only a consequence of its contents, but moreover : a consequence of the interactions of its contents. In particular, the motion must be considered as a kind of interaction.

The theory of general relativity, now very well verified [5], seems to me as the best possible at the level where it stands : its only defect is to suppose that a (metrical) space exists beside interactions, but to use these latter as essential basis of the metric definition. In fact, as soon as the fundamentally quantic aspect disapears and that the notion of coordinates emerge from it, then the relativistic invariance is effective (but probably not “before”) : the general relativity goes as far as it is possible when referring upon coordinates (and deducing the metric from them through an intrinsic reasoning) [6].

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References :

1. It is the same for the generalisations attempts ; see as example :
“Einstein et la théorie unitaire : 40 ans de perdus ?”, C. Goldstein and J. Ritter, Pour la Science n° 326, december 2004.

2. This is discussed among others by S. Hawking ; see as example :
“La nature de l'espace et du temps”, S. Hawking and R. Penrose, Princeton University Press 1996 (Gallimard 1997 for the translation), chapter I.

3. A team from Alabama, searchinf for perceptible effects of a possible quantification of space-time, has concluded by negative ; see as example : “Fluidité du temps”, La Recherche n° 363, april 2003, and quoted reference (not verified) : R. Lieu and L. W. Hilman, ApJ Lett., 585, L77, 2003. Nevertheless their approach does not look general in so far as it seems that they supposed a “simple” quantification (starting from “traditional” space-time and simply considering that coordinates are quantified), contrarily to what I suggest : that the whole “macroscopic” space-time structure would be the statistical aspect of quantized events having as “place” and “date” only those that they constitute by themselves.

4. Several theories have considered modifications of the “standard model” the effects of which would be felt in the vicinity of Planck's scale ; some experiments have been propound in order to test their validity, but it is not evident that such effects would be detectable (the relativistic invariance may proceed, after space-time renormalization, from properties valid as well at the underlying level where the true notion of space-time does not necessarily exist in the way that is usual for us) ; see as example :

“La relativité est-elle inviolable ?”, A. Kostelecky, Pour la Science n° 326, december 2004 ;
“La gravitation sous surveillance”, S. Reynaud, Pour la Science n° 326, december 2004.

5. See as example : “La relativité à l'épreuve des pulsars binaires”, G. Esposito-Farèze, Pour la Science n° 326, décembre 2004.

6. See as example : “L'idée de géométrie différentielle intrinsèque de Gauss à Einstein”, R. Chorlay, Bulletin de l'Union des Professeurs de Spéciales n° 208, october 2004.

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