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Les grandeurs de la physique apparaissent souvent par groupes de deux (par exemple les paires {champ ?lectrique, champ magn?tique}, {?nergie, quantit? de mouvement}, {charge, courant} etc.) ; on retrouve ces grandeurs dans des lois physiques se manifestant ?galement en bin?mes (les ?quations de Maxwell vont par paires ; ?nergie et quantit? de mouvement se retrouvent dans deux types d'?quations, exprimant des conservations d'une part et des lois de forces d'autre part, etc.). Nous postulerons que ces constats r?v?lent des qualit?s fondamentales de nos repr?sentations possibles du monde, ? comprendre dans une " pens?e de la relation " : nul sens ? une grandeur seule, mais ? une dualit? de grandeurs, ou mieux ? des variations li?es de deux grandeurs ; et les points de vue possibles (spatial / temporel) sur ces variations peuvent eux-m?mes ?tre ?chang?s. Pour le temps et l'espace, le constat est le m?me : nul sens ? une variable d'espace ou de temps seule, mais ? leur dualit? et ? leurs variations associ?es. Sur cette base, nous proposons qu'une loi ?l?mentaire de la physique relie les d?riv?es partielles de deux grandeurs en dualit?, par rapport au temps et ? l'espace respectivement. Du fait de la sym?trie espace - temps rappel?e ? l'instant, l'?change, dans l'?quation de la loi, des variables temporelles et spatiales, ou des deux grandeurs en dualit?, donne une autre loi admissible. Cette approche permet de comprendre, comme deux formes de la m?me loi, des paires de lois de la physique a priori distinctes, et reliant chacune des combinaisons des d?riv?es temporelles et spatiales des grandeurs en dualit? : ainsi les lois qui expriment des conservations d'une part, et celles qui expriment des fonctions de forces d'autre part, reliant des d?riv?es spatiales (dans des divergences dans le premier cas, dans des gradients dans le second), ? des d?riv?es temporelles. Ainsi pouvons-nous interpr?ter la deuxi?me loi de Newton (la d?riv?e temporelle de la quantit? de mouvement est ?gale au gradient de l'?nergie) et la loi de la conservation de l'?nergie (la divergence de la quantit? de mouvement est ?gale ? la d?riv?e temporelle de l'?nergie) comme deux formes de la m?me loi. On peut lire de la m?me fa?on les diverses ?quations de Maxwell. Sous leur forme ?l?mentaire, les lois propos?es sont invariantes par transformation de Lorentz, et les grandeurs en dualit? se transforment par des relations analogues ? celles portant sur les coordonn?es spatio-temporelles (on pourrait inversement parler du temps et de l'espace comme des fonctions des champs de grandeurs en dualit?). L'ensemble de ces r?sultats est rendu possible en comprenant le temps comme reli? aux m?mes degr?s de libert? que les coordonn?es spatiales. Sur la base du cadre conceptuel ainsi trac? sont propos?es diverses pistes de recherche, en particulier celle d'explorer de nouvelles sym?tries dans les lois physiques.

We propose to consider the concepts of time and space together. Both of these involve the same degrees of freedom of worldly elements and always work in tandem. In discussing their fundamental points, we need to use relation-based thinking, where each is defined in contrast to the other, instead of substance-based thinking, where each is defined by its own set of characteristics. We contrast spatial relations with temporal relations, or relative mobility with relative immobility. The boundary between the two is decided arbitrarily (there is a great deal of flexibility in definitions of associated time and space parameters), but such a decision runs into logical and conceptual obstacles similar to those encountered in quantum mechanics. Given this prospect, we need to revise the concepts of both time and space. Time does not flow, it is change in relation, it is movement; space is abstracted from constant relations or constant slices of movement. The relative movements that express these relations (changing or unchanging) always take both a spatial and a temporal aspect, like two sides of the same reality. More generally, we suggest seeing a spatial aspect (the distance separating the two terms of the relation) and a temporal aspect (travel along the path linking them) in every relation. On this basis, we propose a research program to examine a number of fundamental problems of contemporary physics and avenues for rethinking how we express time and space in the behavioral and social sciences, in culture, and even in everyday life.

A modified law of gravitation is proposed which takes account of the relative speeds of the moving masses. The law simulates a "supplement" of mass with respect to the standard Newtonian law. Its application to several gravitation problems provides a good order of magnitude for the apparent supplement of mass associated with the motion of the Pioneer satellites, that of stars in galaxies or galaxies in galaxy clusters, for the same value of one additional parameter. The law equally simulates a lack of attraction, for the later stages as compared to the early stages, for a system of expanding masses, imitating a repulsive force. The order of magnitude of the corresponding energy fits with what is found in the literature for the "acceleration" of universe expansion. The conceptual framework in which the law is proposed is sketched out: it is based on the assertion of the fundamental link between the space and time concepts, and on a better symmetry of the physical laws with respect to these parameters. The study is preliminary, it simply establishes orders of magnitude for the expected effects, by an approximate approach of the two-body problem. In the near future it seems interesting to perform quantitative computer simulations so as to check whether the proposed law resists to further confrontations with observational data. If it did, it would avoid in the same time the use of dark matter and dark energy. The present work also gives clues to help reconsider the theory of relativity, in continuity with the modified law of gravitation, and its links with gravitation and electromagnetism.

Deux grandes classes de transformations de Lorentz sont d?finies dans la litt?rature : - les
transformations sp?ciales, ou boosts, et - les transformations g?n?rales. Ces derni?res incluent
des rotations spatiales et permettent des compositions de transformations de directions
quelconques non permises par la composition des premi?res. Ces deux types de
transformations reposent sur des hypoth?ses physiques diff?rentes, les secondes n??tant pas
une simple extension des premi?res de une ? trois dimensions d?espace. Selon notre analyse,
les transformations g?n?rales cachent un certain nombre de difficult?s, tenant essentiellement
en la perte de sym?trie entre variables spatiales et temporelles, pr?sente dans les
transformations sp?ciales en se restreignant ? un axe de coordonn?es. Nous proposons de
restaurer cette sym?trie dans le cas g?n?ral en utilisant un param?tre temporel associ? ? un
d?placement dans l?espace et ayant un caract?re vectoriel. Cela permet de soulager les
diverses difficult?s rencontr?es. Cette approche est appuy?e sur une nouvelle compr?hension
de nature fondamentale de la nature du temps et de l?espace : temps et espace ne sont pas des
substances pr?existantes de la nature ? d?couvrir, ce sont des concepts ? construire en
opposition l?un ? l?autre. Cette construction met en ?vidence des qualit?s d?incertitude,
d?incompl?tude etc., d?j? rep?r?es ? propos de la m?canique quantique, et qui sont bien
pr?sentes dans la th?orie de la relativit?. L?approche propos?e fournit un nouvel angle pour
aborder divers probl?mes en physique qui nous paraissent reli?s ? la question du temps. Elle
permet aussi un nouveau regard sur les liens entre le temps de la physique et celui, ou ceux,
de la culture et des sciences humaines ; de ce c?t?, elle permet d??clairer diverses questions,
comme certaines fameuses apories du temps.

The foundations of the time and space concepts must be discussed, not inside a thinking of
substance (each of the two concepts is then defined by a series of characters of its own) but
inside a thinking of relation (each concept is defined in opposition to the other). We can speak
of an opposition between spatial and temporal relations, or between relative immobility and
mobility relations (relations are defined between the material points, or elements, of the
world). We are thus led to the movement concept to which we give a "primary" character.
Space-time duality is not based on a duality of substances, but on the multiplicity of the
elements of the world, and the possible sharing (based on their relative movements) of their
mutual relations, between two (or more) groups. This sharing does not avoid a number of
conceptual and logical difficulties and the need for a (at least provisional) stop, and the facing
of situations containing some uncertainty, incompleteness, recursivity, contradiction? All
such situations are already discussed about quantum mechanics and one finds them in the
thinking of space and time. This approach also makes appear, within a very general abstract
structure, the steps, or conditions, for thinking by relation.

Two parts of applications are proposed:

• first to physics; several topics may be discussed within the present approach: the
  identification that we can do between time and movement is not without practical
  consequences. It leads us to use three coordinates to construct the time parameter, not in
  supplement to spatial coordinates, but as three of them, and that one must add to those of the
  spatial points: they correspond to the coordinates of a particular point, measured in the same
  spatial frame, the movement of which we use to define time. This has many implications for
  the functioning of the formalism (writing general conservation laws in physics, Lorentz
  transformations, Maxwell's equations; modification of the equations of gravity ...).
• second, application to culture in the large; the time paradoxes may be discussed and we
  propose a solution. The difficulties that arise (existence of a multiplicity of times, meaning of
  the past / present / future categories) are clarified by two statements: - the multiplicity of
  relations generates a multiplicity of times and ? a single time parameter must necessarily be
  chosen in order to communicate but it is conventional.

We conclude about the question set by the title of the paper: can we think of space and time
?together?? Yes, at least provisionally, by means of the mental image that links them within
the movement. Yes, only for a moment, within an ephemeral acceptation of contradiction,
before a compulsory "stop." Let us remember Aristotle's Physics indeed: "we must stop."
Only this stop allows us to build our knowledge, and after it, we no longer tolerate
contradiction. But what we can highlight now, is the conventional, fragile, never ended nature
of this stop, along an infinite transhumance, which constantly asks us to renovate our way to
speak of the world. More generally, we propose to see, in any relation, a spatial aspect (the
gap between the two terms of the relation) and a temporal aspect (the travel along the path
that connects them).

There does not exist, as beside the world, something invisible that would flow everywhere and that one would try to approach thanks to instruments called clocks. There does not exist, as existing before the world, an invisible frame that one would find everywhere and that one would try to landmark thanks to instruments called rulers. Rulers and clocks do not exist independently of the world, they are only choices among the phenomena. Time and space do not exist the one without the other, they are the two faces of the same substance. This primary substance, we will call it movement, is associated to any finite amount of matter, to any finite amount of tangible reality. Space is associated to the cardinal aspect, the total amplitude, the stop, the completion, the fraction of the movement; time is associated to the ordinal aspect, to the unfolding, the process of the movement. By saying that, we cannot avoid a shift in the meaning and in the bearing of the words space, time and movement. The practical distinction between space and time does not refer to a pre-established cut within the reality, but is made possible thanks to the multiplicity of the material points of the world. These considerations make it possible to read again the theory of relativity, and to re-write the Lorentz equations by giving to t a temporarily vectorial character. They make it possible to solve a great number of problems and paradoxes that arise in natural philosophy and in contemporary physics.

This paper aka "Thinking the Movement as Primary, Deriving Space and Time from It: A New Paradigm in Natural Philosophy and Physics"

Time does not exist: there is no mysterious substance that would flow everywhere but that one would never see. Time does not flow. Time does not exist alone, time is relation. But space that matters is also relation. It is thus necessary to think time as a non separable way to think space, as relativity theory already implicitly invites us to say. Some consequences of this approach are outlined on a general standpoint and on the point of view of the equations. The difficulty in seizing this point of view puts the mind in front of an epistemological circle, the (provisional) stop of which requires a renouncement of thought: thought is not founded on itself; we cannot avoid sometime to show something of the reality external to thought, and to allot to it some qualities that we are not ?sure? of (cf. the postulate of the constancy of light speed). One retrieves the concepts of uncompleteness, uncertainty, undecidable propositions, withdrawal of foundations etc. which are a general characteristic of the contemporary scientific and philosophical thought. Pascal already said in his ?Pens?es?: ?whatever the end at which we were aiming in order to stop and rest, it escapes, slips from our grasp and flees for an eternal run ". But does one think time better today?