Time to Welcome Newton Back

The tragedy of modern physics is replacing Newton's Theory of Gravitation NG from 1687 with Einstein's Theory of Gravitation EG as expressed in Einstein's General Theory of Relativity from 1915. This did not happen over night, but only got momentum after Einstein's death in 1955 into a full victory for Einstein as the established doctrine today embraced by all properly educated physicists.  

Before Einstein NG was viewed to be the jewel of mathematical science all times capturing virtually all of celestial mechanics through one single concise expression in the form of the inverse square law. After Einstein this jewel has lost its shine because EG is viewed to be more precise with NG only a rough first approximation. EG is viewed as a triumph of modern physics widely surpassing NG as outdated classical physics.  

But there are caveats in this success story:

• EG differs from NG to any measurable degree only in very extreme cases, if any.
• NG is computable and serves as a very powerful work horse.
• EG is not computable and so is useless in practice. 

The takeover of EG was prepared by a perceived mystery of NG articulated already from its start by in particular Leibniz as Newton's adversary, namely the apparent presence of instant action at distance in the inverse square law, which could not be explained and so was unthinkable: The gravitational attraction from the Sun is felt without time delay on Earth in its path around the Sun. With even a small delay, the Earth would spin out of orbit together with all the other planets, and this is not what is observed. 

In recent posts I have argued that it is possible to view the inverse square law from a different perspective where instant action-at-distance/fast-global-action is replaced by fast-local-action and slow-global-action, both of which are thinkable. 

Here are details in mathematical form expressing the interplay between gravitational potential $\phi$ as primordial, mass density $\rho$ and $u$ material velocity all depending on a Euclidean space coordinate $x$ and time coordinate $t$ with the dot on top representing differentiation with respect to time:

• $\rho = \Delta\phi$                    (inverse square law in differential form)
• $\Delta\dot\phi =-\nabla\cdot (\rho u)$    (conservation of mass)
• $\rho\dot u=-\vert \rho\vert\nabla\phi$            (Newton's 2nd Law)  

Here $\rho$ is created from $\Delta\phi$ by fast-local-action, changes of $\phi$ in time are created  from changes of $\rho u$ in space by slow-global-action (see previous post) and changes of $u$ from gravitational force $-\nabla\phi$ by fast-local-action. We see 3 concise simple equations in 3 variables $\phi$, $\rho$ and $u$ describing all of celestial mechanics. Amazing! How can you ever imagine to throw away this mathematical model? Compare this post: Unthinkable that the inverse square law is incorrect.

We see the Equivalence Principle EP expressed in Newton's 2nd Law with inertial mass $\rho$ on the left being the same as gravitational mass $\rho$ on the right, which makes Newton's 2nd Law take the form $\dot u=-\nabla\phi$ expressing that all objects independent of mass move the same way subject to gravitation, as experimentally observed and theoretically motivated already by Galileo. We can invoke Leibniz' Principle of Sufficient Reason to understand that inertial mass must be equal to gravitational since a reason for inequality is missing, more precisely a Universe without EP would be only chaos.

Altogether, fast-global-action (unthinkable) is replaced by fast-local-action+ slow-global-action (both thinkable). The main reason to abandon NG for EG can thus be seen to be without solid physical ground, and so Newton can be welcomed back after having been put into the wardrobe since Einstein took over in the 1950-60s.  

If NG in fact does not require fast-global-action, then EG is not needed and modern physics is not what it used to be. What will then a new modern physics with Newton instead of Einstein look like? Definitely simpler than EG and so more understandable than EG and in particular more computable than EG. Nothing but a revolution. A 2nd Scientific Revolution 350 years after the 1st initiated by the Calculus of Newton and Leibniz!