Coexistence vs Special Theory of Relativity

Two cars sharing time before collision

This is a continuation of the previous post on the special theory of relativity based on the concept of event which is something which can recorded by a space coordinate $x$ and time coordinate $t$ into a space-time coordinate $(x,t)$. This is also the basic element of Minkowski space-time physics closely connected to theory of relativity, where the distinction between space and time of such fundamental importance in classical physics, is given up and space coordinates are mixed into time coordinates as in the Lorentz transformation of special relativity.

An event is thus something without extension in space which takes place (exists) at a specific point in space $x$ and time $t$. But is existence without extension in space possible? Of course not, but a modern physicist would probably say that an event recorded by $(x,t)$ is an idealisation of the position $x$ in space at time $t$ of a physical phenomenon of such small dimension in space that one space coordinate $x$ is enough to describe its position in space.

But in both mathematics and physics it can be misleading to stretch an idealisation into a singularity such as that connected with the concept of a physical phenomenon without extension in space, that is introducing the concept of particle as the basic element of modern particle physics.  Singularities are tricky because they hide their true nature and thus can be misunderstood.

Real physical phenomena like a physical body has extension in space and as such represents coexistence in the sense that the different parts of the body all exist a the same common instant of time and thus can be viewed to share the same time coordinate. The Lorentz transformation has no role for bodies with extension in space because it mixes space into time an upsets coexistence with shared time.

As an illustration consider two objects moving with constant velocity with respect to each other and connect to each body a Euclidean space coordinate system attached to the body with the body at the origin. This gives us two inertial systems $(x,t)$ and $(x^\prime ,t^\prime )$ and we now ask if it is possible that they can be connected by the Lorentz transformation supposed to connect space-time coordinates of inertial systems without common time.

Assume now that the bodies approach each other and collide. In special relativity a collision is viewed as an event without extension in space and as such can be recorded in different inertial systems connected by the Lorentz transformation without common time. But a collision is not an event without extension in space, because it is the end of a process where the two bodies approach each other and thus form a two-body system with extension in space with necessarily coexistence of the two bodies with necessarily shared common time prior to collision.

Collision without shared time is impossible. You cannot decide to meet a good friend at a cafe without sharing time. When meeting you share time. Without shared time there can be no meeting.

We conclude that the theory of special relativity concerned with events without extension in space  misses the physics of real phenomena, which all have extension in space. Even the physics of collision between two particles (even without extension in space), which in special relativity is viewed as an event without extension in space,  in fact is a phenomenon with extension in space because the particles prior to collision approach each other and thus form a system with extension in space, coexistence and shared time.

In order for two particles about to collide they must coexist and corresponding inertial systems then cannot be connected by Lorentz transformation without common shared time.  In order words, special relativity is not a theory about real physics, and as such of no interest from scientific point of view. Special relativity is a fantasy identical to a Lorentz transformation without physical meaning.