Concepts of Space and Time over Two Millennia

The concepts of three-dimensional space and one-dimensional time are in modern physics viewed as elements of a deeply mysterious concept of combined four-dimensional space-time where space is time-like and time is space-like.

In classical physics 3d space of Euclidean geometry formed by Euclide as the great geometer of Greek mathematics 300 BC, is represented in Euclidean coordinate systems introduced by Descartes in the 17th century. 

Everybody can understand how Euclidean coordinates can be used to represent collections of points in space as spatial configurations in mathematical models of the world. No mystery!

In classical physics going back to Heraclitus, time is viewed as a change of configuration including change of spatial configuration. Leibniz viewed spatial configurations as cases of coexistence as spatial presence at a given time of bodies extended in space. 

The basic mathematical models of classical physics take the form of an initial value problem (IVP) for a quantity $u(x,t)$ depending on a 3d Euclidean space coordinate $x$ and a 1d time coordinate $t$ of the form envisioned by Heraclitus as expressed above:

• $\dot u(x,t) = f(u(x,t),x,t)$  for all $x$ and $t>0$
• $u(x,0)=u_0(x)$ for all $x$, 

where the dot signifies differentiation with respect to $t$, $f(u,x,t)$ is a given function depending on $(u,x,t)$ and $u_0(x)$ is a given initial value, which typically is extended in space. An (IVP) can be solved by time-stepping, starting at $t=0$ and computing $u(x,dt)$ after one small time step $dt>0$ for $t=dt$ by the update formula

• $u(x,dt)=u(x,0)+dt*f(u(x,0),x,0),$ for all $x$,

and so on for $t=2*dt$, $t=3*dt$ et cet. We note that in an (IVP) the space coordinates $x$ are clearly separated from the time coordinate $t$ as expressed by the initial value $u(x,0)=u_0(x)$ and update formula for all $x$ as coexistence. 

We can view $u(x,\bar t)$ for any given time $\bar t$ with $x$ variable as coexistence, while the variation of $u(\bar x,t)$ for any given $\bar x$ with $t$ variable as change. This is something everybody can understand. No mystery!

The central concepts are: 

• coexistence at given time (space),
• change of coexistence (time). 

We note that theses classical concepts of time, which are easy to understand, have essentially been the same over more than two millennia. 

But all this was thrown overboard when Einstein formed his Special Theory of Relativity SR in 1905 where no longer space and time are separate, but are mixed together into space-time without clear separation. This is the effect of the Lorentz transformation underlying SR where $x$ appears as time and $t$ as space formalised in 4d Minkowski coordinates, which has become the trade mark of modern physics.

Two millennia of solid understanding of the basic physics of space and time, was suddenly replaced by a concept of space-time without physics in an unfortunate misunderstanding by an unknown patent clerk in Bern in 1905, as exposed in the previous post. This ended the age of scientific understanding going back to the Greeks with perfection during the Enlightenment into 1905. After now soon 120 years the confusion from 1905 is now so solidly built into physics that escape to understanding is virtually impossible. See  yourself by asking a physicist of today anything about SR to get the response that everything is settled since long and so no discussion is needed nor any understanding of SR...