Mixing Time into Space: Not Physics!

Modern physics is based on Einstein's Special and General Theory of Relativity SR and GR based on concept of spacetime where time is mixed into space as expressed in particular by the Lorentz Transformation LT as the essence of SR. This makes modern physics counter-intuitive with surprising strange effects of time dilation, space contraction and relativistic mass.

Let us take a fresh look at the idea of mixing time into space and ask if it can be possible from physical point of view. Consider a physical world composed of physical bodies with the following characteristics:

1. A physical body has extension in space coming with positive mass. 
2. Extension in space is manifested as existence of the body as the collection of its parts at the same time, that is simultaneous spatial existence/configuration. 
3. It is not meaningful to consider spatial existence of an extended body without simultaneity.  
4. Change of spatial configuration of a body can be seen as a body clock measuring progression of object time in terms of spatial change.
5. Two objects can interact by spatial contact, which synchronises object clocks to read the same.
6. Spatial contact between the parts of a body establishes simultaneity over the body.
7. A physical world does not carry a coordinate system to monitor its changing state. Object configurations change by simultaneous contact, which is represented by changing object configurations without need of representation in human made coordinate systems.
8. A human made spatial coordinate system can be a 3d Euclidean coordinate system fixed to the Earth, Sun or distant galaxy. 
9. Simultaneity of contact respects causality between two objects in the sense that agreement of order in time is possible.  

Notice that SR breaks 2-3. Spatial existence in SR has no extension in space and does not include simultaneity, which means that causality as order in time cannot be secured. Physics without causality cannot work.

So far this is a mechanical world without gravitation, governed by contact. Gravitation can be added by introducing a gravitational potential which depends on simultaneous spatial existence of all the physical bodies of the world asking for complete object time synchronisation (OS). 

Is (OS) possible? How can two far away bodies synchronise time without contact? Is it possible that  the gravitational potential as a massless field carries a master clock and gives birth to object/mass configurations along with object clocks synchronized to the master clock? This connects to the need of "absolute time" in Newtonian mechanics. It represents a non-standard form of causality where the gravitational potential is primary and mass distribution secondary, or possibly have equal roles in a perfect harmony in the sense of Leibniz. 

The gravitational potential of the Universe would thus as extended field carry a simultaneity of presence like that of an extended material body, a simultaneity instantly transmitted to material bodies as gravitational force synchronising all object clocks.

We thus arrive at a material world connected by simultaneity carried by changing spatial configurations connected to a master gravitational potential. 

In any case there will be no mixing of space into time upsetting simultaneity. This is fundamentally the view of Leibniz.  

Summary: In world without gravitation simultaneity is established by spatial  contact, and serves no role without contact. In a world with gravitation, a master gravitational potential can establish global simultaneity, to be used in electromagnetics. 

Mixing Space and Time is Not Physics

According to Leibniz space is coexistence as something sharing the same time, while time is a measure of change of coexistence. The atoms making up the arm of a clock coexist and the change of the position of the arm expresses passage of time. The shadow of a sundial expresses coexistence, while the slow change of the shadow represents a measure of rate of time geared by the Sun.

The 2019 SI Standard defines rate of time in seconds by a standard caesium clock, while spatial distance in meters is defined in terms of travel time of light setting the speed of light to be exactly c=299792458 meter per second. Here time and space are clearly separated and cannot be mixed together into some form of space-time, which has come to serve as a mantra modern physics introduced by Einstein and followed up by the mathematician Minkowski.

To make it possible to speak of space-time Einstein introduced the new concept of event as physics which can be described by a single space coordinate $x$ at some specific time $t$ as a space-time coordinate $(x,t)$. This eliminates all physics of spatially extended bodies consisting of coexisting atoms, which cannot be described by a single spatial coordinate, that is essentially all of physics. What remains is an idealised flash taking place at $\bar x$ at time $t=0$ and then following the trajectory $x=\bar x+ct$. Einstein was then led to the Lorentz transformation supposedly connecting space-time coordinates of one and the same event in different coordinate systems, which led him to the Special Theory of Relativity SR.

An analysis of SR shows that it is based on the false premise that a flash of light sent out in one coordinate system can be identified with a flash sent out in a different coordinate system. 

The result is that SR does not describe the physics of extended bodies consisting of coexisting spatial parts but only space-time events and then in an incorrect way. The net result is that it is not mandatory to replace Newton with Einstein, as the main feature of modern physics, as discussed in recent posts.   

Local Coexistence: Leibniz vs Einstein

Local coexistence.

A basic idea of modern physics is that the conceptions of space and time of classical physics formed by Leibniz/Newton have to be replaced by a concept of curved space-time of Einstein's theory of relativity. Einstein struggled through his entire scientific life to give meaning to this new concept, but today very few modern physicists claim to have a proper understanding of what Einstein wanted to tell humanity, while it is commonly agreed that Einstein was right and so that Leibniz/Newton was wrong.   

But the physics of Leibniz/Newton is the classical physics of the scientific revolution reaching full power with Maxwell's equations at the end of the 19th century thus capturing all of macroscopic mechanics and electromagnetics in differential equations in terms of functions $f(x,t)$ of classical Euclidean space coordinates $x$ and time $t$. It was a formidable success, which met the young patent clerk Einstein preparing for a scientific career at the turn to the 20th century with the demanding question: How to impress the World?

At the patent office Einstein tested his abilities on some main open problems of classical physics including black body radiation, photo-electricity and the (non-)existence of an ether as medium for the propagation of electromagnetic waves. Einstein's efforts resulted in 5 articles on these topics in 1905 named Annus Mirabilis. 

In one of the papers Einstein picked up an observation by Lorentz that wave equations take the same mathematical form under a simple linear transformation of coordinates mixing space and time, named Lorentz transformation. Lorentz cautioned that coordinates transformed from physical coordinates were absolutely not to be viewed as physical coordinates. But here young Einstein found a thread to follow, by opposing Lorentz and claiming that all coordinates subject to Lorentz transformation have a physical meaning. So was Einstein's special theory of relativity formed as the physics of Lorentz transformations, which showed a very new form of physics with space contraction and time dilation unheard of by Leibniz/Newton and classical physics. But this did not impress the physics community at all, which made Einstein double down by extending his special theory to a General Theory of Relativity GR during 10 years of hard struggle to make sense of his curved space-time. Again the physics community was not impressed and GR was not hailed as a trade mark of modern physics until Einstein had passed away and no longer could be asked to clarify his ideas, and so the physics community was free to exploit Einstein's $E=mc^2$ and nuclear power to attract funding to Big Physics, which succeeded very well until lack of results resulted in a backlash as the crisis of modern physics of today...

The mantra of modern physics is that the classical concepts of space and time by Leibniz/Newton have to be replaced by Einstein's space-time coming to expression in the Lorentz transformation mixing space and time into strange new physics. The mantra was based on a perception that Newton's physics required absolute space and time, which was hard to rationalise. 

But Leibniz viewed both space and time to be relational (and so relative) and thus not absolute in Newton's sense: 

• space is order of coexistence
• time is order of succession/change    

which can pull the rug under the necessity to give up classical concepts. It is natural to qualify Leibniz view to 

• space is measure of local coexistence
• time is measure of change of local coexistence.    

The central concept is local coexistence or simultaneity as something appearing with nearby space coordinates at the same time, like an extended body existing at a specified time. The novelty as compared with Newton's absolute space as global space is the aspect of locality. 

This aspect is expressed in explicit time stepping of the heat equation $\dot T(x,t) = \Delta T(x,t)=0$ with $T(x,t)$ temperature depending on a (1d for simplicity) Euclidean space coordinate $x$ and a time coordinate $t$, which takes the form

• $T(x, t+dt) = T(x,t)+0.5(T(x+dx,t)-2T(x,t) + T(x-dx,t))$

where $dx$ is a small space step and $dt=0.5dx^2$ a time step. We see that $T(x,t+dt)$ at new time $t+dt$ is updated from $T(y,t)$ at previous time $t$ and $y=x$ and nearby $y=x\pm dx$ expressing local coexistence (with effectively finite speed of propagation). This connects to the previous post on Newton's law of gravitation and Universe Model.

The Lorentz transformation connects space-time events without extension in space and so has no room for local coexistence/simultaneity. But without local coexistence/simultaneity the World falls apart and so must a physical theory based on the Lorentz transformation. 

Locality of space and time comes to expression by the clock of the local village church telling the villagers when to quit work and go home to eat, or a local Sunset. Global coordination is not needed to make physics without human intervention to go around. Explicit time stepping under local coexistence/simultaneity is enough. 

It is important to make a distinction between man-made physics and natural physics without human intervention. Man-made physics like the GPS system uses global time shared by satellites realised by man-made synchronisation, while natural physics only requires local time as local coexistence. 

Sum up: With a Leibnizian concept of space as local coexistence and time as change of local coexistence there is no compelling reason to replace classical concepts (which make sense) by Einstein's concept of curved space-time (which does not make sense). Leibniz thus offers a theory of relativity without the confusing aspects Einstein's theories.