Instant Action at Distance and Simultaneity not Needed in New Theory of Gravitation including Dark Energy

                           Einstein won the game. But what was the game about? Simultaneity?

Einstein's theory of relativity grew out from a question of simultaneity in time of events at different locations in space, which Einstein could not answer in a non-ambiguous way and then jumped to the conclusion that a fundamental revision of our concepts of space and time was necessary. Einstein took so on the responsibility in the service of science and humanity to make the revision and thereby open the door to a modern physics of "curved space-time" with all its wondrous new effects of time dilation and space contraction, albeit too small to be detected.

It is clear that simultaneity plays an important role in our society, to set schedules and allow people to meet at the same place and for these purposes we all have clocks synchronized to a reference clock. And to decide which scientist first submitted an article reporting a certain new scientific break-through and to navigate...

But what role does simultaneity play in physics? In what sense do distant physical objects care about simultaneity? Do they all have synchronised clocks? Of course not. What they do is to react to local forces acting locally in time, and no simultaneity with the action of distant objects is involved.

Or is it? What about gravitation, isn't it supposed to act instantly over distance and thus require a form of exact simultaneity? Yes, it so seems because in Newtonian gravitation the Earth is instantly acted upon by a gravitational force from the Sun directed towards the present position of the Sun, and not towards the position where we see the Sun because of the 8 minute time delay of the light from the Sun.

The standard view on gravitation, is thus that the presence of matter instantly generates a gravitational potential/force (Newton) or "curvature of space" (Einstein) at distance. This view comes with the following questions:

1. What is the physics of the instant action at distance? Gravitons?
2. What is the physics of the simultaneity associated with instant action? 

Since no progress towards any form of answer has been made over all the centuries since Newton, it is natural to shift and instead view the gravitational potential $\phi$ as primordial from which matter density $\rho$ is obtained by the differential equation acting locally in space and time:

• $\Delta\phi =\rho$.    (*)      

With this view there is no instant action at distance to explain and no associated simultaneity, since the action of Laplacian $\Delta$ as differential operator is local is space and time. 

It may thus be that the questions 1. and 2. are not the right questions, and then also that Einstein's relativity originating from a question about simultaneity, is not the right answer to the right question.

More precisely, simultaneity does not appear to be a matter of the physics of the world, since atoms are not equipped with a man-made system of synchronised clocks, and so it is not reasonable to make a complete revision of Newtonian mechanics starting from an ad hoc idea of probably little significance.        

The equation (*) further suggests that with $\phi$ primordial there is no reason to insist that $\rho$ as a derived quantity must be non-negative, thus (*) opens to the possible existence of matter density $\rho$ of both signs, that is to both positive and negative matter. 

This idea is explored in the app Dark Energy on App Store with in particular a simulation of a universe resulting from a fluctuation of the gravitational potential with associated positive and negative matter, with the negative matter forcing a positive matter world into accelerating expansion, which may be the missing dark energy you are looking for. Try it!