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)

Simultaneity as Non-Physical Convention along with Special Relativity

The book Concepts of Simultaneity: From Antiquity to Einstein and Beyond is presented by:

• Max Jammer's Concepts of Simultaneity presents a comprehensive, accessible account of the historical development of an important and controversial concept—which played a critical role in initiating modern theoretical physics—from the days of Egyptian hieroglyphs through to Einstein's work in 1905, and beyond. 
• Beginning with the use of the concept of simultaneity in ancient Egypt and in the Bible, the study discusses its role in Greek and medieval philosophy as well as its significance in Newtonian physics and in the ideas of Leibniz, Kant, and other classical philosophers. 
• The central theme of Jammer's presentation is a critical analysis of the use of this concept by philosophers of science, like Poincaré, and its significant role in inaugurating modern theoretical physics in Einstein's special theory of relativity. 
• Particular attention is paid to the philosophical problem of whether the notion of distant simultaneity presents a factual reality or only a hypothetical convention. The study concludes with an analysis of simultaneity's importance in general relativity and quantum mechanics.

In earlier post on I have argued that simultaneity in time at distant points in space is a man-made convention, which is useful to humanity in many ways including GPS, but as convention has no role in describing the physics of material bodies without GPS receivers.  Jammer presents much evidence supporting this view without closing the door to simultaneity as some form of factual reality.

Einstein's special relativity came out from an a simple thought experiment showing that agreement on distant simultaneity defined by a certain conventional form of clock synchronization set up by Einstein, cannot be established for different observers moving with speeds comparable to the speed of light with respect to each other. 

Einstein thus started from a certain ad hoc man-made convention and from the impossibility of making the convention work for moving observers Einstein jumped to the conclusion that our concepts of the physics of space and time will have to be fundamentally changed. And the world  jumped along. But is it possible to change physics by man-made convention? Can we change physics by changing our man-made conventions to measure time and space, by changing from yard to meter? I think not. 

Why believe that special relativity is real physics, when special relativity is based on an impossibility to make a certain man-made convention work?

I have stressed that the notion of distant simultaneity is present in the standard form of Newton's law of gravitation as Poisson's equation $\Delta\phi =\rho$, seemingly creating a gravitational potential $\phi (x)$ depending on a Euclidean space coordinate $x$ from instant action at distance by a primordial matter distribution $\rho (y)$ with $y$ different from $x$,  represented as $\phi =\Delta^{-1}\rho$ with the inverse $\Delta^{-1}$ a non-local (integral) operator.

On the other hand, viewing the gravitational potential $\phi$ as primordial and $\rho =\Delta\phi$ as derived by local differentiation, there is no need to explain the physics of instant action at distance, which Newton left open under the criticism of Leibniz and which has resisted all attempts after Newton.

We conventionally view matter $\rho$ as primordial, since we can see matter at distance if it is sending out light, while we cannot see the gravitational potential $\phi$, only feel that it is there. 

But with a different eyes we may be able to see the gravitational potential $\phi$, but not $\rho$, and we would then naturally view $\phi$ to be primordial. With such eyes we might be able to see a gravitational potential of dark matter and dark energy, which we now cannot see, only feel that it is there.