The profound truths are often embodied in simplicity

What is it about?

The motivation for this work originated from the author's doubt about the completeness of the FRW standard cosmological metric 20 years ago. At that time, driven by a strong research interest in dark energy problem, the author happened to examine its foundation of observational theory closely and discovered that the FRW standard cosmological metric missed an important physics: that is, there must be a factor b(t) in front of dt in the cosmological metric. This factor represents the gradual decrease of expansion kinetic energy with the expansion of the universe, which should be transformed into an increase in gravitational potential energy, leading to an acceleration of the rate of the local cosmic clock. Consequently, the author transformed from an explorer of dark energy models into a sceptic. By extrapolating upward, considering the later acceleration effect of the rate of the local cosmic clock, the impact on the dark energy issue is logically at least alleviated, and may even be eliminated. Digging deeper downward, based on logical support, the author then questioned the principle of general covariance, followed by Einstein’s strong equivalence principle, and finally the essence of inertial forces, that is, the formal logic of Newton's second law. After several years of exploration, the author indeed derived a new equation for particle dynamics and the true nature of inertial forces.

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Photo by Simon Berger on Unsplash

Photo by Simon Berger on Unsplash

Why is it important?

Incorporating the author’s previously published work, this article systematically develops the theoretical framework of particle dynamics in a translational reference frame. The main contributions are as follows: 1. A symmetric new equation is proposed, which directly holds in any translational reference frame without relying on an inertial reference frame. Newton’s First and Second Laws can be replaced by a single symmetric new equation. 2. It is revealed that the nature of inertial forces is the real force acting on the reference object. Given this definitive explanation, the concept of inertial forces is suggested to be abandoned. And it guides us to the only correct way to construct a more general principle for dynamical relativity. 3. From a naturalistic perspective, by further precisely distinguishing the basic concepts of spacetime, a dialectical unity of absolute spacetime background and relative spacetime scales(basic units) is constructed, only based on the existence of absolute background of spacetime, the symmetric new equation is naturally derived. 4. The principle of work and energy, impulse theorem, and the modified expression for Lagrangian quantity are developed in translational reference frames. The center-of-mass motion theorem and the fixed-axis rotation theorem are rigorously derived for the system of particles in translational reference frames. 5. Using planetary perturbation equations as an example, the correctness and superiority of the new particle dynamics equation are demonstrated. The original planetary perturbation equations can be derived by resorting to a rigorous application of Newton's second law in the center-of-mass frame of reference, followed by a coordinate transformation to the heliocentric system. In contrast, we can directly apply the symmetric new equation in the heliocentric reference frame to obtain the result in one step. Furthermore, this approach can naturally incorporate non-gravitational interactions between planets and gravitational influences from outside the planetary system in the same single step, leading to a more complete and corrected new planetary perturbation equation.

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