# Simultaneity

Let us introduce the concept of space using the notion of reflexive action (or reflex action) between two things. Intuitively, a thing x acts on another thing y if the presence of x disturbs the history of y. Events in the real world seem to happen in such a way that it takes some time for the action of x to propagate up to y. This fact can be used to construct a relational theory of space à la Leibniz, that is, by taking space as a set of equitemporal things. It is necessary then to define the relation of simultaneity between states of things.

Let x and y be two things with histories h(xτ) and h(yτ), respectively, and let us suppose that the action of x on y starts at τx0. The history of y will be modified starting from τy0. The proper times are still not related but we can introduce the reflex action to define the notion of simultaneity. The action of y on x, started at τy0, will modify x from τx1 on. The relation “the action of x on y is reflected to x” is the reflex action. Historically, Galileo introduced the reflection of a light pulse on a mirror to measure the speed of light. With this relation we will define the concept of simultaneity of events that happen on different basic things.

Besides we have a second important fact: observation and experiment suggest that gravitation, whose source is energy, is a universal interaction, carried by the gravitational field.

Let us now state the above hypothesis axiomatically.

Axiom 1 (Universal interaction): Any pair of basic things interact. This extremely strong axiom states not only that there exist no completely isolated things but that all things are interconnected.

This universal interconnection of things should not be confused with “universal interconnection” claimed by several mystical schools. The present interconnection is possible only through physical agents, with no mystical content. It is possible to model two noninteracting things in Minkowski space assuming they are accelerated during an infinite proper time. It is easy to see that an infinite energy is necessary to keep a constant acceleration, so the model does not represent real things, with limited energy supply.

Now consider the time interval (τx1 − τx0). Special Relativity suggests that it is nonzero, since any action propagates with a finite speed. We then state

Axiom 2 (Finite speed axiom): Given two different and separated basic things x and y, such as in the above figure, there exists a minimum positive bound for the interval (τx1 − τx0) defined by the reflex action.

Now we can define Simultaneity as τy0 is simultaneous with τx1/2 =Df (1/2)(τx1 + τx0)

The local times on x and y can be synchronized by the simultaneity relation. However, as we know from General Relativity, the simultaneity relation is transitive only in special reference frames called synchronous, thus prompting us to include the following axiom:

Axiom 3 (Synchronizability): Given a set of separated basic things {xi} there is an assignment of proper times τi such that the relation of simultaneity is transitive.

With this axiom, the simultaneity relation is an equivalence relation. Now we can define a first approximation to physical space, which is the ontic space as the equivalence class of states defined by the relation of simultaneity on the set of things is the ontic space EO.

The notion of simultaneity allows the analysis of the notion of clock. A thing y ∈ Θ is a clock for the thing x if there exists an injective function ψ : SL(y) → SL(x), such that τ < τ′ ⇒ ψ(τ) < ψ(τ′). i.e.: the proper time of the clock grows in the same way as the time of things. The name Universal time applies to the proper time of a reference thing that is also a clock. From this we see that “universal time” is frame dependent in agreement with the results of Special Relativity.

# Reza Negarestani’s Ontology as Science of Cruelty and Deleuzean Excavation of the Architectonic. Thought of the Day 40.0

The problem of the principle of reason/ground is architectonic. As such it is the great theme of modern philosophy: how and where to begin? The two classical answers are provided by romanticism and enlightenment thinking. If there is a romantic side to Heidegger, as Deleuze says, then Meillassoux inherits and continues a long-standing tradition of enlightenment. Whereas the first always looks for a foundation or ground, even if it turns out be an abyss, the critical reason of the latter rabidly dismantles all grounds. Alternatively, Deleuze calls for a third answer which he calls modernism or constructivism and which always begins by the milieu (par le milieu). Instead of rising out of first principles like a tree from its roots, his metaphysics proliferates like a rhizome, never straying far from the events at the surface in a groping experimentation with the conditions of real experience. For Deleuze, the milieu is not the solid ground on which we stand, but neither is it an abyss or a void. Rather it is the fluctuating ground in which we must learn to swim. It is the element of the problematic as such, an element that matters and calls for an ethics of life. To think by the milieu means to think both without reference to a fixed ground yet also without separating thought from the forces it requires to exist. Whereas Meillassoux reinstalls the Kantian tribunal of reason and the generality of its judgments, Deleuze always emphasizes his own conditions of enunciation, i.e. the matters of concern that enable him to learn. While the anti-correlationist position is one of right, Deleuze’s own position is always one of fact.