Birth of Modern Physics: Relativity of Simultaneity

In 1905 Einstein pulled the carpet under classical physics by showing that common agreement cannot be reached whether two events at different locations in space are simultaneous in the sense of taking place at at the same time, coined as relativity of simultaneity. Einstein did this in a "thought experiment" showing that synchronisation of clocks to show the same time, is impossible if the clocks are widely separated in space because of the time delay in communication even at the speed of light. Einstein argued:

• So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

Einstein claimed this showed Newton's mechanics to be wrong, because it required absolute simultaneity, which could not be established. This was a revolution forming the new modern physics based on Einstein's theories of relativity: 

• Newton is wrong because of relativity of simultaneity!

But stop! If we give up Newton, then we have very little left to cope with for all matters of life, since Einstein's mechanics is so difficult to both understand and use. 

In particular, the GPS system builds on precise synchronisation of satellite clocks orbiting the Earth, which thus is proved to be possible. What more of "absolute simultaneity" can we ask for?  

It is natural to ask the following

• What role does simultaneity serve for the World to go around?
• Is absolute simultaneity necessary for Newton's mechanics to make sense? 

To get perspective recall how Max Jammer concludes his comprehensive treatise Concepts of Simultaneity:

• While the concept of events occurring at different places in space but at the same moment of time (i.e., distant simultaneity) is the subject of heated discussions, the analogous concept of two events occurring at different moments of time but at the same place in space has hardly, if ever, been given serious attention. 

We thus see the following spectrum of possibilities:

1. Two events happen at the same place at the same time.
2. Two events at distant places happen at the same time.
3. Two events at the same place happen at different times.

We understand that 1. is a case of interest: Two bodies collide/meet/interact at a certain place and then necessarily at the same time. To say that the collision happens at different times would make no  sense. 

Jammer declares that 3. has little interest. We agree. Compare with Kilroy was here!

What then about 2? For bodies interacting only by local contact, we are led back to 1. 

As concerns interaction at distance the common view is that simultaneity plays a role, in particular as concerns gravitation, since it is commonly viewed to involve instantaneous action at distance seemingly requiring some form of simultaneity. This is expressed through the connection between mass density $\rho (x,t)$ and gravitational potential $\phi (x,t)$ through Poisson's equation expressing Newton's Law of Gravitation:

• $\Delta\phi (x,t) = \rho (x,t)$                   (classical law of gravitation)

with $x$ a Euclidean space coordinate and $t$ a time coordinate. The common view is that $\rho (x,t)$ is given at a certain time $t$ with $\phi (x,t)$ at the same time $t$ emerging from a global solution process of Poisson's equation (global integration process) corresponding to instantaneous action at distance. 

But it is possible to turn around the perspective and view instead $\rho (x,t)$ to be locally generated from $\phi (x,t)$ at time $t$ by a local differentiation process,

• $\rho (x,t)=\Delta\phi (x,t)$                   (new law of gravitation)

 which again leads back to 1. This is the basic idea of New Newtonian Cosmology.  

We conclude that 2. may very well have no real intrinsic interest, and so Einstein's motivation to dismiss Newton may lack substance. 

In short: Simultaneity/clock synchronisation is important for a system like GPS to work, or more generally to coordinate human acitivities, but does not play a role in physics without human intervention. Newton's theory of gravitation does not necessarily require instant action at distance/absolute simultaneity, since there is an option requiring only local action (with automatic simultaneity).

The obsession with Einstein in modern physics appears as a main factor in the present crisis of modern physics.  

Many physicists including Stephen Hawking tell people that GPS works because satellite clocks are adjusted according to both Einstein's special and general theory so as to run at the same rate and so show absolute simultaneity, which of course is in contradiction to Einstein's starting point that this is impossible. 

In fact, clocks are continuously synchronised to a base clock on Earth and so the use of relativity theory is superficial and so only show-off. The fact that GPS works is not evidence that relativity theory is correct. 

Note that if we accept that all interaction is local (and then instant) so that we do not have to invoke  instant action at distance, then we do not have to worry about simultaneity and absolute time, as long as we only consider physics without human presence. This means that physical time is local in space and proceeds at a rate given by local conditions as a measure of rate of change. Only when introducing human time required for coordination of human activities, does simultaneity and clock synchronisation serve any real purpose.  Of course, with similar local conditions, we may expect time as rate of change to be similar. 

Sum up: Newtonian physics can be viewed to work without synchronised clocks measuring absolute time. Time can be viewed to be local in space as a measure of local change of state. Understanding that there is no compelling reason to replace Newton by Einstein opens to a resolution of the crisis of modern physics.

Think of that!  

PS We may compare functionality of the following two systems: 

• The bus will leave at 12.00.           (modern society)
• The bus will leave when it is full.  (classical physics)