The source for the tension between Newton’s view of the universe and of Einstein’s stems from each person’s respective choice of axioms. Newton choose to take the most concrete axioms for his mechanics: absolute nature of space and time. These intuitive assumptions mark and define the whole of Newtonian mechanics since all the other definitions and derivations are rooted in this foundation. Einstein decided to take a slightly divergent set of axioms, a set which wouldn’t seem to be all that distinct from Newton’s. Einstein believed that relativity and the consistency in the speed of light to be central assumptions of his work. The principle of relativity claims that observations can only be stated relative to an observer; it maintains that at all times true measurements do not exist in vacuo. The principle of relativity of motion states that a system at constant velocity is identical to a system at rest relative to an observer. To provide an illustration, it would be as if you woke up in a crate and could not see outside. According to relativity, there is no possible experiment which would tell you if you were moving or not (assuming you can’t feel any movement if you were). Since all of these ‘inertial reference frames’ behave the same according to the principle of relativity, then they actually are the same. This precludes the possibility of a privileged reference frame which could be considered ‘still’. In fact, the entire concept of absolute space gets thrown out of the window since absolute space assumes the existence of a special reference frame to which all motion can be measured from. For Einstein any observer has an equally true yet possibly distinct perspective.
Now you might be wondering about acceleration, since after all even Newton knew that all masses in the universe attract one another leading to a force which potentiates an acceleration. Well, you’re right, acceleration is important. By applying the principle of relativity more broadly to include accelerated frames of reference Einstein completely shifted the discussion away from Newton’s absolutes and turned physics into a much different discipline. While limited to inertial reference frames we still maintained the existence of straight lines and a simple lattice upon which to measure motion and distance against. By considering a thought problem similar to the crate above, but this time for accelerated motion, Einstein realized that being accelerated by a force and being accelerated by gravity is one in the same. Through the unification of these two otherwise distinct cases, Einstein realized that space should not be thought of as that rigid lattice but instead as a flexible surface of potential. One example of how important this connection was to understanding physics goes back to an old unknown about mass. If gravitational attraction is quite different from a mechanical force such as a push, why should the gravitation and inertial masses be the same. There is no reason why a mechanical force should be equitable to a gravitation force unless they are one in the same—a extraneous thought for Newtonian mechanics.
With these philosophical underpinning established, let’s take a few minutes to explore the definitions of some of the central concepts such as mass, space, time, and distance. Newton describes space in terms of either an absolute or relative reference frame. Both consist “without regard to anything external and remains always similar” (Scholium) meaning that space is simply a ridged reference frame. If you imagine space as structured as a grid-like scaffolding then you are getting pretty close to what Newton was thinking.
Every day we take for granted the even march of time—or if we don’t then we are cursing either its speed or lack thereof—but how should time be defined? Newton saw time as a perfectly even beat which “from its own nature flows equally and without regard to anything external” (Scholium). This is absolute time: where a clock can be placed anywhere and will tick off the same beat regardless of where you are or how you are moving relative to it. But here, for Einstein the relative motion part is key. By imagining himself riding on a light beam he realized that the tick of the clock is intimately tied to your motion relative to the clock. This is relative time where motion effects time.
Similarly Newton envisioned space as absolute where there exists, somewhere, a privileged point of reference from which all other motion could be judged and measured. This meant that an object could be truly at rest relative to the space that it occupies. Einstein once again objected and redefined space in terms of who is doing the measuring. No longer could an object be at rest, but rather had to be at rest relative to something.
Once space and time are redefined in this manner, so to do a plethora of composite entities such as motion, distance, simultaneity, and a plethora of others. But then does that mean that Einstein’s work was completely independent of Newton’s?
Well, in my opinion, yes and no. As we have seen their definitions and central axioms were quite different; and therefore, you might be quick to segregate the two completely. But it doesn’t change the fact that both Newton and Einstein were attempting to understand and model the world around them—a world they share. Newton may not have framed any hypothesis as to how gravity works, but he did sense that “cause and effect” would “distinguish rest and motion, absolute and relative, one from the other” (Scholium I). A central premise—a premise required to logically understand the world—is that cause will lead to effect and the two should always be separable and consistent.
This dependence on the consistency of cause and effect was shared by Albert Einstein and is reflected in his mechanics. Although simultaneity was rebuked in favor for relativity in Einstein’s work, the logical consistency of the theory was maintained. As a case in point for the strength of Einstein’s allegiance to causality in physics consider one of the most famous debates in physics: the paper titled Can quantum-mechanical description of reality be considered complete?. In Einstein’s now-famous style he proposes a thought experiment consisting of two quantum particles which have become quantumly entangled. The two particles are then separated and the momentum of one particle is measured to as high a precision as possible. Since the two particles are entangled, and therefore share the same quantum wave function, the position of the other particle can only be measured to an accuracy within the limit of Heisenberg’s Uncertainty Principle. Now since we would say that the one measurement caused a change in the measurement of the other, these two events are causally linked, yet the experiment can be setup such that no signal can travel from one particle to the other before until after the measurements. Where does this leave causality, you may ask. Well, this was exactly the issue Einstein struggled with. By removing the cause-effect relationship from the experiment, one of his fundamental principles was directly attacked, and the attack was so acute that Einstein never fully excepted quantum mechanics as inherently defective or amiss of some important understanding.
The fundamental tension between Newton’s mechanics and Einstein’s results from their divergent focus rather than on any idiomatic difference. Newton focused on phenomenon of daily life where as Einstein focused on the phenomenon available to his contemporary physics. Both toyed with gravity in ways undreamt of before them and rested their work on steadfast metaphysical assumptions about how the world works.